Secret language of cells KAUST paper
https://actu.epfl.ch/news/a-secret-language-of-cells-new-cell-computations-u/
A secret language of cells? New cell computations uncovered
2022-07-25
None
<div><div><div><p> Throughout evolution, individual cells have been making successful decisions on their own, even while forming parts of vast networks, such as neurons and glia in the human brain. Now scientists from the EPFL Blue Brain Project and King Abdullah University of Science and Technology (KAUST) have published a new theory describing a secret language that cells may use for internal dialog about the external world.</p><p> Using a computational model, they hypothesize that metabolic pathways, which are primarily a means of extracting energy and building block molecules from glucose and other substrates to feed the brain, might also be capable of coding details about neuromodulators that stimulate increases in energy consumption. If true, this would open the door to a nearly infinite number of possibilities for information processing in nervous systems as component cells could compute in previously unexplored ways. Such a mechanism would also help explain the remarkable energy efficiency of brains.</p></div><p><p>The aim of the Blue Brain Project is to establish simulation neuroscience as a complementary approach to understanding the brain, alongside experimental, theoretical and clinical neuroscience, by building the world’s first biologically detailed digital reconstructions and simulations of the mouse brain. In a study recently <a href="https://doi.org/10.1016/j.jtbi.2022.111090">published in the Journal of Theoretical Biology</a>, the collaboration with KAUST demonstrated how two of these pillars – theory and simulation - can work in tandem using a model of astrocytic energy metabolism. The authors confirmed the plausibility that this type of pathway might be capable of coding information about stimuli in addition to its known functions in cellular energy and carbon budgets. Considering how many metabolic pathways are active simultaneously, these mechanisms could significantly increase the computational capabilities of neurons by giving them an expanded tool set for adaptation and decision-making.</p><p>The flux of matter through these pathways involves handing-off metabolite-products from one enzyme-catalyzed reaction to the next in the chain. The results in this study suggest that these pathways can also quantitatively capture and transmit various characteristics about stimuli, including intensity and duration features of waves of neuromodulators arriving at the cell surface. The mechanism involves considering the entire chain of events from neuromodulator receptor activation to energy metabolite production as an excitable unit or metabolic state machine (<a href="https://doi.org/10.1016/j.jtbi.2019.110123">Coggan et al., 2020</a>).</p><p>“From this,” explains Lead Author, Blue Brain’s <a href="https://www.epfl.ch/research/domains/bluebrain/blue-brain/people/our-people/simulation-neuroscience-division/jay-s-coggan/">Jay S. Coggan</a>, “we could show how a metabolic pathway can translate external stimuli into production profiles of energy-carrying molecules such as lactate with a precision beyond simple signal transduction or amplification. Such metabolic pathways, and possibly other kinds of coupled enzymatic reactions, might be well-positioned to code an additional level of salient information about a cell’s environmental demands. This hypothesis has implications for the computational power and energy efficiency of the brain,” he concludes.</p><p><strong>Single cells could still have some undiscovered tricks</strong></p><p>“The teams’ simulations of neuromodulator-stimulated glucose metabolism in an astrocyte suggest that metabolic pathways could be capable of more information processing than we previously realized,” explains KAUST’s Prof. Pierre Magistretti. “These systems exhibit concentration-dependent responses with state changes similar to the more familiar action potentials that can capture and transmit signal properties from ligand-receptor binding through controllable metabolite fluxes. Despite everything that is already known about how single-cells think or respond to their environment, they likely still have some undiscovered tricks.”</p><p>--------------------------</p><p><strong>Citation</strong></p><p>Coggan, J. S., Keller, D., Markram, H., Schürmann, F., &amp; Magistretti, P. J. (2022). <strong>Representing stimulus information in an energy metabolism pathway</strong>. <em>Journal of Theoretical Biology</em>, 540, 111090. <a href="https://doi.org/10.1016/j.jtbi.2022.111090">https://doi.org/10.1016/j.jtbi.2022.111090</a></p></p><div><p><strong>Funding</strong></p><p>This study was supported by a CRG grant from King Abdullah University of Science and Technology "KAUST-EPFL Alliance for Integrative Modeling of Brain Energy Metabolism" [OSR-2017-CRG6-3438] (PJM); the Blue Brain Project, a research center of the École Polytechnique Fédérale de Lausanne, from the Swiss government's ETH Board of the Swiss Federal Institutes of Technology (HM); and NCCR Synapsy (PJM).</p></div><hr /></div>||||I|||| * Homepage of the site
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 A secret language of cells? New cell computations uncovered

 © 2022 EPFL

 Throughout evolution, individual cells have been making successful decisions on their own, even while forming parts of vast networks, such as neurons and glia in the human brain. Now scientists from the EPFL Blue Brain Project and King Abdullah University of Science and Technology (KAUST) have published a new theory describing a secret language that cells may use for internal dialog about the external world.

 Using a computational model, they hypothesize that metabolic pathways, which are primarily a means of extracting energy and building block molecules from glucose and other substrates to feed the brain, might also be capable of coding details about neuromodulators that stimulate increases in energy consumption. If true, this would open the door to a nearly infinite number of possibilities for information processing in nervous systems as component cells could compute in previously unexplored ways. Such a mechanism would also help explain the remarkable energy efficiency of brains.

 The aim of the Blue Brain Project is to establish simulation neuroscience as a complementary approach to understanding the brain, alongside experimental, theoretical and clinical neuroscience, by building the world’s first biologically detailed digital reconstructions and simulations of the mouse brain. In a study recently published in the Journal of Theoretical Biology, the collaboration with KAUST demonstrated how two of these pillars – theory and simulation - can work in tandem using a model of astrocytic energy metabolism. The authors confirmed the plausibility that this type of pathway might be capable of coding information about stimuli in addition to its known functions in cellular energy and carbon budgets. Considering how many metabolic pathways are active simultaneously, these mechanisms could significantly increase the computational capabilities of neurons by giving them an expanded tool set for adaptation and decision-making.

 The flux of matter through these pathways involves handing-off metabolite-products from one enzyme-catalyzed reaction to the next in the chain. The results in this study suggest that these pathways can also quantitatively capture and transmit various characteristics about stimuli, including intensity and duration features of waves of neuromodulators arriving at the cell surface. The mechanism involves considering the entire chain of events from neuromodulator receptor activation to energy metabolite production as an excitable unit or metabolic state machine (Coggan et al., 2020).

 “From this,” explains Lead Author, Blue Brain’s Jay S. Coggan, “we could show how a metabolic pathway can translate external stimuli into production profiles of energy-carrying molecules such as lactate with a precision beyond simple signal transduction or amplification. Such metabolic pathways, and possibly other kinds of coupled enzymatic reactions, might be well-positioned to code an additional level of salient information about a cell’s environmental demands. This hypothesis has implications for the computational power and energy efficiency of the brain,” he concludes.

 Single cells could still have some undiscovered tricks

 “The teams’ simulations of neuromodulator-stimulated glucose metabolism in an astrocyte suggest that metabolic pathways could be capable of more information processing than we previously realized,” explains KAUST’s Prof. Pierre Magistretti. “These systems exhibit concentration-dependent responses with state changes similar to the more familiar action potentials that can capture and transmit signal properties from ligand-receptor binding through controllable metabolite fluxes. Despite everything that is already known about how single-cells think or respond to their environment, they likely still have some undiscovered tricks.”

 --------------------------

 Citation

 Coggan, J. S., Keller, D., Markram, H., Schürmann, F., & Magistretti, P. J. (2022). Representing stimulus information in an energy metabolism pathway. Journal of Theoretical Biology, 540, 111090. https://doi.org/10.1016/j.jtbi.2022.111090

 Funding

 This study was supported by a CRG grant from King Abdullah University of Science and Technology "KAUST-EPFL Alliance for Integrative Modeling of Brain Energy Metabolism" [OSR-2017-CRG6-3438] (PJM); the Blue Brain Project, a research center of the École Polytechnique Fédérale de Lausanne, from the Swiss government's ETH Board of the Swiss Federal Institutes of Technology (HM); and NCCR Synapsy (PJM).

 Source: Blue Brain Project

 25.07.22

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Throughout evolution, individual cells have been making successful decisions on their own, even while forming parts of vast networks, such as neurons and glia in the human brain. Now scientists from the EPFL Blue Brain Project and King Abdullah University of Science and Technology (KAUST) have published a new theory describing a secret language that cells may use for internal dialog about the external world.  Using a computational model, they hypothesize that metabolic pathways, which are primarily a means of extracting energy and building block molecules from glucose and other substrates to feed the brain, might also be capable of coding details about neuromodulators that stimulate increases in energy consumption. If true, this would open the door to a nearly infinite number of possibilities for information processing in nervous systems as component cells could compute in previously unexplored ways. Such a mechanism would also help explain the remarkable energy efficiency of brains.   The aim of the Blue Brain Project is to establish simulation neuroscience as a complementary approach to understanding the brain, alongside experimental, theoretical and clinical neuroscience, by building the world’s first biologically detailed digital reconstructions and simulations of the mouse brain. In a study recently published in the Journal of Theoretical Biology, the collaboration with KAUST demonstrated how two of these pillars – theory and simulation - can work in tandem using a model of astrocytic energy metabolism. The authors confirmed the plausibility that this type of pathway might be capable of coding information about stimuli in addition to its known functions in cellular energy and carbon budgets. Considering how many metabolic pathways are active simultaneously, these mechanisms could significantly increase the computational capabilities of neurons by giving them an expanded tool set for adaptation and decision-making. The flux of matter through these pathways involves handing-off metabolite-products from one enzyme-catalyzed reaction to the next in the chain. The results in this study suggest that these pathways can also quantitatively capture and transmit various characteristics about stimuli, including intensity and duration features of waves of neuromodulators arriving at the cell surface. The mechanism involves considering the entire chain of events from neuromodulator receptor activation to energy metabolite production as an excitable unit or metabolic state machine (Coggan et al., 2020). “From this,” explains Lead Author, Blue Brain’s Jay S. Coggan, “we could show how a metabolic pathway can translate external stimuli into production profiles of energy-carrying molecules such as lactate with a precision beyond simple signal transduction or amplification. Such metabolic pathways, and possibly other kinds of coupled enzymatic reactions, might be well-positioned to code an additional level of salient information about a cell’s environmental demands. This hypothesis has implications for the computational power and energy efficiency of the brain,” he concludes.  Single cells could still have some undiscovered tricks  “The teams’ simulations of neuromodulator-stimulated glucose metabolism in an astrocyte suggest that metabolic pathways could be capable of more information processing than we previously realized,” explains KAUST’s Prof. Pierre Magistretti. “These systems exhibit concentration-dependent responses with state changes similar to the more familiar action potentials that can capture and transmit signal properties from ligand-receptor binding through controllable metabolite fluxes. Despite everything that is already known about how single-cells think or respond to their environment, they likely still have some undiscovered tricks.” --------------------------  Citation  Coggan, J. S., Keller, D., Markram, H., Schürmann, F., &amp; Magistretti, P. J. (2022). Representing stimulus information in an energy metabolism pathway. Journal of Theoretical Biology, 540, 111090. https://doi.org/10.1016/j.jtbi.2022.111090     Funding  This study was supported by a CRG grant from King Abdullah University of Science and Technology "KAUST-EPFL Alliance for Integrative Modeling of Brain Energy Metabolism" [OSR-2017-CRG6-3438] (PJM); the Blue Brain Project, a research center of the École Polytechnique Fédérale de Lausanne, from the Swiss government's ETH Board of the Swiss Federal Institutes of Technology (HM); and NCCR Synapsy (PJM).
A secret language of cells? New cell computations uncovered
https://actu.epfl.ch/news/a-secret-language-of-cells-new-cell-computations-u/
https://phys.org/news/2022-07-secret-language-cells-cell-uncovered.html
Secret language of cells? New cell computations uncovered
2022-07-25
King Abdullah University; Technology
<div><div>
	
<div>
 <figure>
 
 <figcaption>
 Graphic illustrates information processing in an energy metabolism pathway. Credit: EPFL Blue Brain Project
 </figcaption> </figure>
 </div>
<p>Throughout evolution, individual cells have been making successful decisions on their own, even while forming parts of vast networks, such as neurons and glia in the human brain. Now scientists from King Abdullah University of Science and Technology (KAUST) and the EPFL Blue Brain Project (École Polytechnique Fédérale de Lausanne in Switzerland) have published a new theory describing a secret language that cells may use for internal dialogue about the external world.
	 
	 </p>
	 
	 	 
<p>Using a <a href="https://phys.org/tags/computational+model/">computational model</a>, they hypothesize that metabolic pathways, which are primarily a means of extracting energy and building block molecules from glucose and other substrates to feed the brain, might also be capable of coding details about neuromodulators that stimulate increases in <a href="https://phys.org/tags/energy+consumption/">energy consumption</a>. Neuromodulators are chemical messengers that regulate the exchange of information in the brain.
</p><p>If true, this implies a nearly infinite number of possibilities for information processing in nervous systems and component cell computations. Such a mechanism would also help explain the remarkable energy efficiency of brains.
</p><p>The aim of the Blue Brain Project is to establish simulation neuroscience as a complementary approach to understanding the brain, alongside experimental, theoretical and clinical neuroscience, by building the world's first biologically detailed digital reconstructions and simulations of the mouse brain.
</p><p>In a study recently published in the <i>Journal of Theoretical Biology</i>, KAUST-Blue Brain Project collaborators demonstrated how two of these pillars—theory and simulation—can work in tandem using a model of astrocytic energy metabolism. Astrocytes are star-like glial cells in the central nervous system. The model centers on how they cooperate with neurons to fuel the brain and participate in computations.
</p><p>The authors confirmed the plausibility that an energy metabolic pathway might be capable of coding information and transmitting detailed characteristics about stimuli, such as intensity and duration features, in addition to its known functions in cellular energy and carbon-based molecule budgets. Examples of stimuli include waves of neuromodulators arriving at the cell surface.
</p><p>Considering how many metabolic pathways are active simultaneously, these mechanisms could significantly increase the computational capabilities of neurons by giving them an expanded toolset for adaptation and decision-making. Scientists have long been impressed by the energy efficiency of the brain compared to human-made computers. Assigning new computational roles to <a href="https://phys.org/tags/single+cells/">single cells</a> that then pass that information to neuronal networks could help explain this observation.
</p><p>Co-author Pierre Magistretti, Distinguished Professor of Bioscience at KAUST and director of the KAUST Smart Health Initiative, said tht "the teams' simulations of neuromodulator-stimulated glucose metabolism in an astrocyte suggest that metabolic pathways could be capable of more information processing than we previously realized. Despite everything that is already known about how single cells think or respond to their environment, they likely still have some undiscovered tricks."
</p><p>The flux of matter through these pathways involves handing-off metabolite-products from one enzyme-catalyzed reaction to the next across the entire chain of events, from neuromodulator receptor activation to energy metabolite production as an excitable unit, or metabolic state machine.
</p><p>Blue Brain's Jay S. Coggan, lead author of the study, says that their "model shows how a <a href="https://phys.org/tags/metabolic+pathway/">metabolic pathway</a> can translate external stimuli into production profiles of energy-carrying molecules such as lactate with a precision beyond simple signal transduction or amplification. Such <a href="https://phys.org/tags/metabolic+pathways/">metabolic pathways</a>, and possibly other kinds of coupled <a href="https://phys.org/tags/enzymatic+reactions/">enzymatic reactions</a>, might be well-positioned to code an additional level of information about a cell's environmental demands. This hypothesis has implications for the computational power and energy efficiency of the brain."
	 	
	</p><div>
	<p><strong>More information:</strong>
	Jay S. Coggan et al, Representing stimulus information in an energy metabolism pathway, <i>Journal of Theoretical Biology</i> (2022). <a href="https://dx.doi.org/10.1016/j.jtbi.2022.111090">DOI: 10.1016/j.jtbi.2022.111090</a>
	</p>
	</div>
 	
	
 	 
	<div>
	 <p><strong>Citation</strong>:
	Secret language of cells? New cell computations uncovered (2022, July 25)
	retrieved 6 February 2023
	from https://phys.org/news/2022-07-secret-language-cells-cell-uncovered.html
	 </p>
	 <p>
	 This document is subject to copyright. Apart from any fair dealing for the purpose of private study or research, no
	 part may be reproduced without the written permission. The content is provided for information purposes only.
	 </p>
	</div>
 
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 July 25, 2022

 Secret language of cells? New cell computations uncovered

 by King Abdullah University of Science and Technology

 Graphic illustrates information processing in an energy metabolism pathway. Credit: EPFL Blue Brain Project

 Throughout evolution, individual cells have been making successful decisions on their own, even while forming parts of vast networks, such as neurons and glia in the human brain. Now scientists from King Abdullah University of Science and Technology (KAUST) and the EPFL Blue Brain Project (École Polytechnique Fédérale de Lausanne in Switzerland) have published a new theory describing a secret language that cells may use for internal dialogue about the external world.

 Using a computational model, they hypothesize that metabolic pathways, which are primarily a means of extracting energy and building block molecules from glucose and other substrates to feed the brain, might also be capable of coding details about neuromodulators that stimulate increases in energy consumption. Neuromodulators are chemical messengers that regulate the exchange of information in the brain.

 If true, this implies a nearly infinite number of possibilities for information processing in nervous systems and component cell computations. Such a mechanism would also help explain the remarkable energy efficiency of brains.

 The aim of the Blue Brain Project is to establish simulation neuroscience as a complementary approach to understanding the brain, alongside experimental, theoretical and clinical neuroscience, by building the world's first biologically detailed digital reconstructions and simulations of the mouse brain.

 In a study recently published in the Journal of Theoretical Biology, KAUST-Blue Brain Project collaborators demonstrated how two of these pillars—theory and simulation—can work in tandem using a model of astrocytic energy metabolism. Astrocytes are star-like glial cells in the central nervous system. The model centers on how they cooperate with neurons to fuel the brain and participate in computations.

 The authors confirmed the plausibility that an energy metabolic pathway might be capable of coding information and transmitting detailed characteristics about stimuli, such as intensity and duration features, in addition to its known functions in cellular energy and carbon-based molecule budgets. Examples of stimuli include waves of neuromodulators arriving at the cell surface.

 Considering how many metabolic pathways are active simultaneously, these mechanisms could significantly increase the computational capabilities of neurons by giving them an expanded toolset for adaptation and decision-making. Scientists have long been impressed by the energy efficiency of the brain compared to human-made computers. Assigning new computational roles to single cells that then pass that information to neuronal networks could help explain this observation.

 Co-author Pierre Magistretti, Distinguished Professor of Bioscience at KAUST and director of the KAUST Smart Health Initiative, said tht "the teams' simulations of neuromodulator-stimulated glucose metabolism in an astrocyte suggest that metabolic pathways could be capable of more information processing than we previously realized. Despite everything that is already known about how single cells think or respond to their environment, they likely still have some undiscovered tricks."

 The flux of matter through these pathways involves handing-off metabolite-products from one enzyme-catalyzed reaction to the next across the entire chain of events, from neuromodulator receptor activation to energy metabolite production as an excitable unit, or metabolic state machine.

 Blue Brain's Jay S. Coggan, lead author of the study, says that their "model shows how a metabolic pathway can translate external stimuli into production profiles of energy-carrying molecules such as lactate with a precision beyond simple signal transduction or amplification. Such metabolic pathways, and possibly other kinds of coupled enzymatic reactions, might be well-positioned to code an additional level of information about a cell's environmental demands. This hypothesis has implications for the computational power and energy efficiency of the brain."

 More information: Jay S. Coggan et al, Representing stimulus information in an energy metabolism pathway, Journal of Theoretical Biology (2022). DOI: 10.1016/j.jtbi.2022.111090

 Journal information: Journal of Theoretical Biology

 Provided by King Abdullah University of Science and Technology

 Citation: Secret language of cells? New cell computations uncovered (2022, July 25) retrieved 6 February 2023 from https://phys.org/news/2022-07-secret-language-cells-cell-uncovered.html
 This document is subject to copyright. Apart from any fair dealing for the purpose of private study or research, no part may be reproduced without the written permission. The content is provided for information purposes only.

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Graphic illustrates information processing in an energy metabolism pathway. Credit: EPFL Blue Brain Project
  
 
Throughout evolution, individual cells have been making successful decisions on their own, even while forming parts of vast networks, such as neurons and glia in the human brain. Now scientists from King Abdullah University of Science and Technology (KAUST) and the EPFL Blue Brain Project (École Polytechnique Fédérale de Lausanne in Switzerland) have published a new theory describing a secret language that cells may use for internal dialogue about the external world.
	 
	 
	 
	 	 
Using a computational model, they hypothesize that metabolic pathways, which are primarily a means of extracting energy and building block molecules from glucose and other substrates to feed the brain, might also be capable of coding details about neuromodulators that stimulate increases in energy consumption. Neuromodulators are chemical messengers that regulate the exchange of information in the brain.
 If true, this implies a nearly infinite number of possibilities for information processing in nervous systems and component cell computations. Such a mechanism would also help explain the remarkable energy efficiency of brains.
 The aim of the Blue Brain Project is to establish simulation neuroscience as a complementary approach to understanding the brain, alongside experimental, theoretical and clinical neuroscience, by building the world's first biologically detailed digital reconstructions and simulations of the mouse brain.
 In a study recently published in the Journal of Theoretical Biology, KAUST-Blue Brain Project collaborators demonstrated how two of these pillars—theory and simulation—can work in tandem using a model of astrocytic energy metabolism. Astrocytes are star-like glial cells in the central nervous system. The model centers on how they cooperate with neurons to fuel the brain and participate in computations.
 The authors confirmed the plausibility that an energy metabolic pathway might be capable of coding information and transmitting detailed characteristics about stimuli, such as intensity and duration features, in addition to its known functions in cellular energy and carbon-based molecule budgets. Examples of stimuli include waves of neuromodulators arriving at the cell surface.
 Considering how many metabolic pathways are active simultaneously, these mechanisms could significantly increase the computational capabilities of neurons by giving them an expanded toolset for adaptation and decision-making. Scientists have long been impressed by the energy efficiency of the brain compared to human-made computers. Assigning new computational roles to single cells that then pass that information to neuronal networks could help explain this observation.
 Co-author Pierre Magistretti, Distinguished Professor of Bioscience at KAUST and director of the KAUST Smart Health Initiative, said tht "the teams' simulations of neuromodulator-stimulated glucose metabolism in an astrocyte suggest that metabolic pathways could be capable of more information processing than we previously realized. Despite everything that is already known about how single cells think or respond to their environment, they likely still have some undiscovered tricks."
 The flux of matter through these pathways involves handing-off metabolite-products from one enzyme-catalyzed reaction to the next across the entire chain of events, from neuromodulator receptor activation to energy metabolite production as an excitable unit, or metabolic state machine.
 Blue Brain's Jay S. Coggan, lead author of the study, says that their "model shows how a metabolic pathway can translate external stimuli into production profiles of energy-carrying molecules such as lactate with a precision beyond simple signal transduction or amplification. Such metabolic pathways, and possibly other kinds of coupled enzymatic reactions, might be well-positioned to code an additional level of information about a cell's environmental demands. This hypothesis has implications for the computational power and energy efficiency of the brain."
	 	
	 
	 More information:
	Jay S. Coggan et al, Representing stimulus information in an energy metabolism pathway, Journal of Theoretical Biology (2022). DOI: 10.1016/j.jtbi.2022.111090
	
	
 	
	
 	 
	
	  Citation:
	Secret language of cells? New cell computations uncovered (2022, July 25)
	retrieved 6 February 2023
	from https://phys.org/news/2022-07-secret-language-cells-cell-uncovered.html
	 
	 
	 This document is subject to copyright. Apart from any fair dealing for the purpose of private study or research, no
	 part may be reproduced without the written permission. The content is provided for information purposes only.
Secret language of cells? New cell computations uncovered
https://phys.org/news/2022-07-secret-language-cells-cell-uncovered.html
https://www.amazon.com/Secret-Language-Cells-Biological-Conversations/dp/1948836041
The Secret Language of Cells: What Biological Conversations Tell Us About the Brain-Body Connection, the Future of Medicine, and Life Itself: Lieff, Jon: 9781948836043: Amazon.com: Books
2020-09-22
Jon Lieff
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 The Secret Language of Cells: What Biological Conversations Tell Us About the Brain-Body Connection, the Future of Medicine, and Life Itself Hardcover – September 22, 2020

 by Jon Lieff (Author)
 4.5 4.5 out of 5 stars 147 ratings
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 Your cells are talking about you.

 Right now, both your inner and outer worlds are abuzz with chatter among living cells of every possible kind—from those in your body and brain to those in the environment around you. From electrical alerts to chemical codes, the greatest secret of modern biology, hiding in plain sight, is that all of life's activity boils down to one thing: conversation.

 While cells are commonly considered the building block of living things, it is actually the communication between cells that brings us to life, controlling our bodies and brains, determining whether we are healthy or sick, and directly influencing how we think, feel, and behave.

 In The Secret Language of Cells , doctor and neuroscientist Jon Lieff lets us listen in on these conversations, and reveals their significance for everything from mental health to cancer. He explains the surprising science of how very different cells—bacteria and brain cells, blood cells and viruses—all speak the same language. This overarching principle has been long overlooked because scientific journals use impenetrable jargon that makes it hard to be understood across disciplines, much less by the general public.

 Lieff presents a fascinating and accessible look into cellular communication science—a groundbreaking and comprehensive exploration of this biological phenomenon. In these pages, discover the intriguing lives of cells as they ask questions, get answers, give feedback, gather information, call for each other, and make complex decisions. During infections, immune T-cells tell brain cells that we should "feel sick" and lie down. Cancer cells warn their community about immune and microbe attacks. Gut cells talk with microbes to determine which are friends and which are enemies, and microbes talk with each other and with much more complicated human cells in ways that determine which medicines work and which will fail.

 With applications for immunity, chronic pain, weight loss, depression, cancer treatment, and virtually every aspect of health and biology, cellular communication is revolutionizing our understanding not just of disease, but of life itself. The Secret Language of Cells is required reading for anyone interested in following the conversation.
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 1. Print length
 368 pages
 2. Language
 English
 3. Publisher
 BenBella Books
 4. Publication date
 September 22, 2020
 5. Dimensions
 6.25 x 1.2 x 9.31 inches
 6. ISBN-10
 1948836041
 7. ISBN-13
 978-1948836043
 8. See all details
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 Editorial Reviews

 Review


 The Secret Language of Cells takes us on an exciting journey into a world where we can visualize elaborate conversations among immune cells, brain cells, gut cells, bacteria, and even viruses. Dr. Lieff gives a wealth of examples for his thesis that this cellular signaling is the basis of life. It is a must read for anyone seeking to understand modern biology and advanced medical science. It is equally important for those of us who wonder, as I do, how this ubiquitous information transfer in the form of cellular conversations might be related to the emergence of intelligence and consciousness.
 Ray Kurzweil,
 Inventor, author and futurist.

 As a storyteller, my imagination is sparked by the insights Dr. Lieff brings to our innermost world and the mysteries at the edge of our understanding. The Secret Language of Cells reveals how the micro world reflects the macro, alive with heroes and villains, shapeshifters and tricksters, vigilant guards and gullible bystanders, helpers that commit suicide for the common good and warriors that seize the day or collapse from exhaustion. Lieff's fascinating exploration inspires awe for the astonishing dialogues and clarion calls at the heart of the intelligence within.
 Antonia Felix, Ed.D., MFA, New York Times bestselling author

 Review

 "Using the common theme of 'cellular conversations,' this book covers an astonishing breadth of biological topics. By removing most of the 'impenetrable jargon' from his descriptions, geriatric psychiatry specialist Lieff succeeds in making the complex interactions between cells accessible for most readers."

 — Choice Reviews

 “ The Secret Language of Cells takes us on an exciting journey into a world where we can visualize elaborate conversations among immune cells, brain cells, gut cells, bacteria, and even viruses. Dr. Lieff gives a wealth of examples for his thesis that this cellular signaling is the basis of life. It is a must-read for anyone seeking to understand modern biology and advanced medical science.”

 — Ray Kurzweil, inventor, author, and futurist

 “ The Secret Language of Cells explains the complex ways that cells in the body communicate and presents a new paradigm for understanding health and disease. It also suggests new possibilities for treatment and for promoting healing. I’m pleased that my former Harvard colleague, Jon Lieff, has written this important book.”

 — Andrew Weill, MD, director of the Andrew Weil Center for Integrative Medicine, professor at University of Arizona College of Medicine, and author

 “Through a brilliant synthesis of cellular biology, microbiology, immunology, and neuroscience, The Secret Language of Cells offers a lucid explanation of the marvelous intricacies of cellular life. The result is a masterful exploration of the profound implications of cellular intelligence for understanding pathophysiology, human health, and even our origins."

 —William B. Miller, Jr., MD, physician, biologist, author of The Microcosm Within: Evolution and Extinction in the Hologenome , and internationally recognized expert on Cognition-Based Evolution

 “Jon Lieff’s description of cellular communication is insightful, provocative, illuminating, and engaging and provides deep and novel observations into the remarkable symphony of how life happens. Mimicking the cellular world he describes, Dr. Lieff is the great communicator and muse of living things. An inspiring and informative read.”

 — Ted Kaptchuk, professor of medicine at Harvard Medical School

 “This journey into the dynamic realm of cellular conversations is a tour-de-force—fascinating, vital, and especially timely for understanding emerging viruses. As we learn about intelligence in smaller and smaller animals, it’s not surprising that the tiniest creatures—microbes and even viruses—exhibit elaborate communication and complex decision making. Read The Secret Language of Cells !”

 — Marc Bekoff, PhD, professor emeritus of ecology and evolutionary biology at the University of Colorado, Boulder and author of Canine Confidential: Why Dogs Do What They Do

 “ The Secret Language of Cells reveals how the micro world reflects the macro, alive with heroes and villains, shapeshifters and tricksters, vigilant guards and gullible bystanders, helpers that commit suicide for the common good and warriors that seize the day or collapse from exhaustion. Lieff’s fascinating exploration inspires awe for the astonishing dialogues and clarion calls at the heart of the intelligence within.”

 — Antonia Felix, EdD, MFA, New York Times bestselling author

 “Calling all physicians, microbiologists, medical students, and fellow science enthusiasts—you’re going to love The Secret Language of Cells !This book reveals fascinating ongoing conversations between cells, bacteria, and viral particles that provide the basis for understanding growth, development, healthy biology, and pathology. Perhaps more importantly, they provide the blueprint for novel interventions, treatments, and cures for ailments ranging from chronic inflammatory diseases, to cancers and even viral infections. The COVID-19 pandemic has focused the world’s lens on the world of microbes like never before. Read this book and join the conversation.”

 — Jill Grimes, MD, family physician, speaker, author, and educator

 “ The Secret Language of Cells is ideal for the education of medical and science students, as well as for practicing physicians. Dr. Lieff’s remarkable synthesis of the scientific literature provides a current view of the intricate communication systems determining our physiology. He clearly explains how conversations among cells are the bridge between immunology, neuroscience, microbiology, and cancer research.”

 — Sharon Redd, MD, senior associate in anesthesia at Boston Children's Hospital and

 assistant professor in anesthesia at Harvard Medical School

 “In The Secret Language of Cells , Dr. Lieff, brilliantly and effectively, communicates the complexities of modern biology to clinicians, and even laypeople, in understandable terms. In the process, he elucidates how communications between diverse varieties of cells determine our physical, mental, and emotional health, as well as the potential social implications.”

 — Sanford Finkel MD, founder of AAGP, cofounder of IPA and APA Council on Aging, and clinical professor of Psychiatry at University of Chicago Medical School

 “Dr. Jon Lieff’s The Secret Language of Cells is a tour-de-force . . . I highly recommend this fascinating book to science readers and anyone wanting to better understand the role and importance of cellular functions and communications in health and disease.”

 — George T. Grossberg, MD, director of Geriatric Psychiatry for the Department of Psychiatry & Behavioral Neuroscience at Saint Louis University School of Medicine

 “Dr. Lieff has synthesized an extensive literature on the biological communications that underlie life into a highly accessible book. His integrative summary will appeal to a broad audience, from high school biology students to professionals with specific areas of expertise.”

 — Barnett Meyers, MD, professor emeritus at Weill Cornell Medical College of Cornell University

 “ The Secret Language of Cells makes it possible for a healthy dialogue between biology and philosophy, a step closer to making a bridge between life-science and various monistic and non-dual philosophies.”

 —Dr. Sthaneshwar Timalsina, professor for the Department of Religious Studies at San Diego State University





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 Product details

 * Publisher ‏ : ‎ BenBella Books (September 22, 2020)
 * Language ‏ : ‎ English
 * Hardcover ‏ : ‎ 368 pages
 * ISBN-10 ‏ : ‎ 1948836041
 * ISBN-13 ‏ : ‎ 978-1948836043
 * Item Weight ‏ : ‎ 1.25 pounds
 * Dimensions ‏ : ‎ 6.25 x 1.2 x 9.31 inches
 * Best Sellers Rank: #1,185,290 in Books ( See Top 100 in Books )
 + #263 in Cell Biology (Books)
 * Customer Reviews:
 4.5 4.5 out of 5 stars 147 ratings
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  5 Stars
  A model of clarity and innovation
  I discovered Dr Jon Lieff's blog about five years ago and was astounded at the breadth and depth of his interests. I was trying to make sense of the immune system and cancer in my partner's treatment for ovarian cancer. Jon's blog was prolific, well written and beautiful illustrated. And extremely useful.I looked forward to his book and expected something similar. My first reading gave a surprise. Jon has concentrated on producing a book that anyone can read. It is clear and uses straightforward language. It is very well organised. He gives a quite different synthesis to other writers in the general field, although I suspect he owns the field himself. There are so many interesting areas that get a distinctly new approach. See below his section on COV-19. I got more from these few paragraphs than from whole articles:"THE NOVEL CORONAVIRUS—VERY CAPABLE WITH FIFTEEN GENES The novel coronavirus (technically called SARS-CoV-2), the virus that causes the illness COVID-19, has great capabilities, with fifteen genes that produce at least twenty-nine proteins. One very large protein is actually sixteen different ones that are cut and released by other proteins. Several of these proteins produce a bubble filled with fluid where the virus builds a factory to produce more viruses. Inside the bubble, two proteins produce new RNA, and another brings material to build the RNA; a medicine for SARS can attack this step. Three other proteins unwind the RNA to make it useful, correct errors, and cut up leftover RNA to keep the host cell from reacting to it. Other proteins alter the human cell’s environment to help the virus survive in the cell and escape. Still others block immune signals to other cells, influence the flow of molecules in and out of the cell nucleus, and turn human genes on and off. Others poke holes in the cell’s membrane, making escape easier, and disable a protein on the surface of human cells trying to grab the escaping virus. One stimulates inflammation and another induces human cells to commit suicide. Four of SARS-CoV-2’s proteins build the structure that has been seen so frequently in the media. All four help with assembly and release from the host cell. One protects the RNA deep inside. Another produces the famous spikes that make it appear as a crown, also known as a corona. These spikes attach to the human cell receptor ACE2 molecule in the airways and other places. This molecule is also an important enzyme blocked by a class of blood pressure medications (ACE inhibitors), likely causing an association of increased risk of COVID-19 symptoms in those who have high blood pressure. Attaching to this receptor allows the virus to enter into cells and creates a strong attachment that causes the symptoms to linger. Of all the proteins, this one might be the one that causes the COVID-19 virus to be so dangerous to humans, since it attaches so firmly to human cells.Lieff, Jon. The Secret Language of Cells (pp. 202-204). BenBella Books, Inc.. Kindle Edition.The main text does not have any references which some may regret. But the extensive list by chapter given at the end of the book more than makes up for this.This review is based on my first fly-through of the text. Below is another snippet from the latter part of the book that give a good idea of where it ends up."WHAT CONCLUSIONS CAN BE DRAWN from this tour of cellular conversations? Although cells are considered the most basic characteristic that defines life, it is actually the conversations among cells, and also the conversations that take place inside them, that determine biological activity and produce the essence of life. The science of cell communication allows new ways to understand health and disease. It also has implications for understanding evolution as well as consciousness. While elaborate signals among neurons have been observed for years, why hasn’t signaling among all other cells been obvious before now? It has been hidden from general view because of impenetrable jargon in scientific journals. Arcane terminologies of signals, receptors, genes, and cell subtypes aren’t generally known, even across various research areas. Professional articles and books on molecular signaling are complex and don’t provide this overarching synthesis. They are hard to understand, even for clinicians and scientists who don’t actively work in a particular field. Also, most of this information has been discovered in the past several years, and biology dogmas die hard. The synthesis of scientific data in this book makes it easy to see why communication among cells has wide-ranging significance. Descriptions of cellular conversations help demystify the latest research on immunity, digestion, cancer, neuroscience, pain, and other topics. This overview—not available anywhere else in one place—is particularly important for those who are ill and trying to follow advanced treatments."Lieff, Jon. The Secret Language of Cells (p. 289). BenBella Books, Inc.. Kindle Edition.I just hope that Jon is sketching the outline for his next book!
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  Dr. Peter R. Best
  5.0 out of 5 stars A model of clarity and innovation
  Reviewed in the United States on October 7, 2020
  Verified Purchase
  I discovered Dr Jon Lieff's blog about five years ago and was astounded at the breadth and depth of his interests. I was trying to make sense of the immune system and cancer in my partner's treatment for ovarian cancer. Jon's blog was prolific, well written and beautiful illustrated. And extremely useful.

  I looked forward to his book and expected something similar. My first reading gave a surprise. Jon has concentrated on producing a book that anyone can read. It is clear and uses straightforward language. It is very well organised. He gives a quite different synthesis to other writers in the general field, although I suspect he owns the field himself. There are so many interesting areas that get a distinctly new approach. See below his section on COV-19. I got more from these few paragraphs than from whole articles:

  "THE NOVEL CORONAVIRUS—VERY CAPABLE WITH FIFTEEN GENES The novel coronavirus (technically called SARS-CoV-2), the virus that causes the illness COVID-19, has great capabilities, with fifteen genes that produce at least twenty-nine proteins. One very large protein is actually sixteen different ones that are cut and released by other proteins. Several of these proteins produce a bubble filled with fluid where the virus builds a factory to produce more viruses. Inside the bubble, two proteins produce new RNA, and another brings material to build the RNA; a medicine for SARS can attack this step. Three other proteins unwind the RNA to make it useful, correct errors, and cut up leftover RNA to keep the host cell from reacting to it. Other proteins alter the human cell’s environment to help the virus survive in the cell and escape. Still others block immune signals to other cells, influence the flow of molecules in and out of the cell nucleus, and turn human genes on and off. Others poke holes in the cell’s membrane, making escape easier, and disable a protein on the surface of human cells trying to grab the escaping virus. One stimulates inflammation and another induces human cells to commit suicide. Four of SARS-CoV-2’s proteins build the structure that has been seen so frequently in the media. All four help with assembly and release from the host cell. One protects the RNA deep inside. Another produces the famous spikes that make it appear as a crown, also known as a corona. These spikes attach to the human cell receptor ACE2 molecule in the airways and other places. This molecule is also an important enzyme blocked by a class of blood pressure medications (ACE inhibitors), likely causing an association of increased risk of COVID-19 symptoms in those who have high blood pressure. Attaching to this receptor allows the virus to enter into cells and creates a strong attachment that causes the symptoms to linger. Of all the proteins, this one might be the one that causes the COVID-19 virus to be so dangerous to humans, since it attaches so firmly to human cells.

  Lieff, Jon. The Secret Language of Cells (pp. 202-204). BenBella Books, Inc.. Kindle Edition.

  The main text does not have any references which some may regret. But the extensive list by chapter given at the end of the book more than makes up for this.

  This review is based on my first fly-through of the text. Below is another snippet from the latter part of the book that give a good idea of where it ends up.

  "WHAT CONCLUSIONS CAN BE DRAWN from this tour of cellular conversations? Although cells are considered the most basic characteristic that defines life, it is actually the conversations among cells, and also the conversations that take place inside them, that determine biological activity and produce the essence of life. The science of cell communication allows new ways to understand health and disease. It also has implications for understanding evolution as well as consciousness. While elaborate signals among neurons have been observed for years, why hasn’t signaling among all other cells been obvious before now? It has been hidden from general view because of impenetrable jargon in scientific journals. Arcane terminologies of signals, receptors, genes, and cell subtypes aren’t generally known, even across various research areas. Professional articles and books on molecular signaling are complex and don’t provide this overarching synthesis. They are hard to understand, even for clinicians and scientists who don’t actively work in a particular field. Also, most of this information has been discovered in the past several years, and biology dogmas die hard. The synthesis of scientific data in this book makes it easy to see why communication among cells has wide-ranging significance. Descriptions of cellular conversations help demystify the latest research on immunity, digestion, cancer, neuroscience, pain, and other topics. This overview—not available anywhere else in one place—is particularly important for those who are ill and trying to follow advanced treatments."

  Lieff, Jon. The Secret Language of Cells (p. 289). BenBella Books, Inc.. Kindle Edition.

  I just hope that Jon is sketching the outline for his next book!
  Read more
  Dr. Peter R. Best
  5.0 out of 5 stars A model of clarity and innovation
  Reviewed in the United States on October 7, 2020
  I discovered Dr Jon Lieff's blog about five years ago and was astounded at the breadth and depth of his interests. I was trying to make sense of the immune system and cancer in my partner's treatment for ovarian cancer. Jon's blog was prolific, well written and beautiful illustrated. And extremely useful.

  I looked forward to his book and expected something similar. My first reading gave a surprise. Jon has concentrated on producing a book that anyone can read. It is clear and uses straightforward language. It is very well organised. He gives a quite different synthesis to other writers in the general field, although I suspect he owns the field himself. There are so many interesting areas that get a distinctly new approach. See below his section on COV-19. I got more from these few paragraphs than from whole articles:

  "THE NOVEL CORONAVIRUS—VERY CAPABLE WITH FIFTEEN GENES The novel coronavirus (technically called SARS-CoV-2), the virus that causes the illness COVID-19, has great capabilities, with fifteen genes that produce at least twenty-nine proteins. One very large protein is actually sixteen different ones that are cut and released by other proteins. Several of these proteins produce a bubble filled with fluid where the virus builds a factory to produce more viruses. Inside the bubble, two proteins produce new RNA, and another brings material to build the RNA; a medicine for SARS can attack this step. Three other proteins unwind the RNA to make it useful, correct errors, and cut up leftover RNA to keep the host cell from reacting to it. Other proteins alter the human cell’s environment to help the virus survive in the cell and escape. Still others block immune signals to other cells, influence the flow of molecules in and out of the cell nucleus, and turn human genes on and off. Others poke holes in the cell’s membrane, making escape easier, and disable a protein on the surface of human cells trying to grab the escaping virus. One stimulates inflammation and another induces human cells to commit suicide. Four of SARS-CoV-2’s proteins build the structure that has been seen so frequently in the media. All four help with assembly and release from the host cell. One protects the RNA deep inside. Another produces the famous spikes that make it appear as a crown, also known as a corona. These spikes attach to the human cell receptor ACE2 molecule in the airways and other places. This molecule is also an important enzyme blocked by a class of blood pressure medications (ACE inhibitors), likely causing an association of increased risk of COVID-19 symptoms in those who have high blood pressure. Attaching to this receptor allows the virus to enter into cells and creates a strong attachment that causes the symptoms to linger. Of all the proteins, this one might be the one that causes the COVID-19 virus to be so dangerous to humans, since it attaches so firmly to human cells.

  Lieff, Jon. The Secret Language of Cells (pp. 202-204). BenBella Books, Inc.. Kindle Edition.

  The main text does not have any references which some may regret. But the extensive list by chapter given at the end of the book more than makes up for this.

  This review is based on my first fly-through of the text. Below is another snippet from the latter part of the book that give a good idea of where it ends up.

  "WHAT CONCLUSIONS CAN BE DRAWN from this tour of cellular conversations? Although cells are considered the most basic characteristic that defines life, it is actually the conversations among cells, and also the conversations that take place inside them, that determine biological activity and produce the essence of life. The science of cell communication allows new ways to understand health and disease. It also has implications for understanding evolution as well as consciousness. While elaborate signals among neurons have been observed for years, why hasn’t signaling among all other cells been obvious before now? It has been hidden from general view because of impenetrable jargon in scientific journals. Arcane terminologies of signals, receptors, genes, and cell subtypes aren’t generally known, even across various research areas. Professional articles and books on molecular signaling are complex and don’t provide this overarching synthesis. They are hard to understand, even for clinicians and scientists who don’t actively work in a particular field. Also, most of this information has been discovered in the past several years, and biology dogmas die hard. The synthesis of scientific data in this book makes it easy to see why communication among cells has wide-ranging significance. Descriptions of cellular conversations help demystify the latest research on immunity, digestion, cancer, neuroscience, pain, and other topics. This overview—not available anywhere else in one place—is particularly important for those who are ill and trying to follow advanced treatments."

  Lieff, Jon. The Secret Language of Cells (p. 289). BenBella Books, Inc.. Kindle Edition.

  I just hope that Jon is sketching the outline for his next book!
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  Amazon Customer
  5.0 out of 5 stars Highly recommend, even to the non scientist!
  Reviewed in the United States on July 12, 2022
  Verified Purchase
  This is a fantastic read for anyone interested in really understanding how our bodies work. The author explains the very complex functions of our body in a way that’s understandable to the average reader. I am not a scientist and personally found the examples that Dr Lieff uses extremely relatable and interesting, he really brings our cells to life. Thank you for writing this book and explaining what’s really happening inside our complicated bodies.
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  James
  5.0 out of 5 stars Lots of information.
  Reviewed in the United States on June 19, 2023
  Verified Purchase
  I really like the section on the brain. However great book from a cell anatomy standpoint.
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  William R. Walsh
  4.0 out of 5 stars Worthwhile read
  Reviewed in the United States on April 15, 2021
  Verified Purchase
  Fascinating look at the cellular level of life. I’m not a biologist but was able to understand most of what’s explained and was amazed at how much has been learned since I was in high school biology class.
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  Lisa C. Tener
  5.0 out of 5 stars "Your Cells Are Talking About You"
  Reviewed in the United States on September 24, 2020
  Verified Purchase
  This is the claim on the book jacket and the rest of the journey of The Secret Language of Cells is about learning what those cells are saying and how they say it. I imagine this is the closest I'll ever get to overhearing their conversations. In The Secret Language of Cells, Dr. Jon Lieff does the near impossible and takes research findings about cellular communication from esoteric fields of science and puts these findings in plain English, opening a world of discovery for the lay reader interested in pioneering science. This is a book you'll find yourself thinking about throughout the day. Fascinating! Dr. Lieff's unifying theory of the Mind and the essence of life are likely to open up new areas of understanding and research. This book is truly groundbreaking.
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  11 people found this helpful
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  Grace O'Malley
  5.0 out of 5 stars Complex info explained beautifully
  Reviewed in the United States on April 21, 2021
  Verified Purchase
  This book deserves pride of place in the library of anyone with any interest in how the human body works at the cellular level. I think the genius of the book is that the author describes very complex processes in terms that can be easily visualized. If you can picture cars on a freeway, phone conversations, rescuers swarming against an enemy, you can follow the author’s explanations. Nothing is dumbed down...it’s just all explained in terms of familiar objects and operations. The illustrations and especially the photos taken through electron microscopes look like sculpture. A timeless book!
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  3 people found this helpful
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  extremelyAwake
  5.0 out of 5 stars Fascinating
  Reviewed in the United States on August 21, 2023
  Verified Purchase
  This will help you understand the genes and other parts of the cell that are being used to treat cancer
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  Steve G
  3.0 out of 5 stars Interesting but too much is introduced
  Reviewed in the United States on September 22, 2020
  I was somewhat disappointed by this book. Although the writing is conversational and in plain English, I felt that too much is introduced and not enough detail is given to really get a good sense of how communication between cells takes place. On the other hand, the photomicrographs are outstanding. To be upfront, I do have a biology background, but I have read many popular science biology books that have held my attention throughout. A good recent example is Deadliest Enemy by Osterholm and Olshaker.
  Disclosure: I received an advance reader copy via Netgalley for review purposes.
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  6 people found this helpful
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  Danilo
  1.0 out of 5 stars Noiosissimo !
  Reviewed in Italy on March 16, 2021
  Verified Purchase
  Avevo grandi aspettative di questo libro, come medico. Ma è orribilmente noioso. In più, il titolo non corrisponde a ciò che scrive. Il linguaggio segreto delle cellule: ma qual'è il segreto ? I segnali che si mandano le cellule ? Lo sapevamo già. Quali segnali ? Chimici, elettrici, elettromagnetici, fotonici. Bè ? Il segreto qual'è ? E' che non lo sa nemmeno lui. Non compratelo. Non serve. Nessuna applicazione pratica. Non mi è piaciuto.
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 The Secret Language of Cells: What Biological Conversations Tell Us About the Brain-Body Connection, the Future of Medicine, and Life Itself Hardcover – September 22, 2020
 by Jon Lieff (Author)
 4.5 4.5 out of 5 stars 147 ratings
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 Your cells are talking about you.
 Right now, both your inner and outer worlds are abuzz with chatter among living cells of every possible kind—from those in your body and brain to those in the environment around you. From electrical alerts to chemical codes, the greatest secret of modern biology, hiding in plain sight, is that all of life's activity boils down to one thing: conversation.
 While cells are commonly considered the building block of living things, it is actually the communication between cells that brings us to life, controlling our bodies and brains, determining whether we are healthy or sick, and directly influencing how we think, feel, and behave.
 In The Secret Language of Cells , doctor and neuroscientist Jon Lieff lets us listen in on these conversations, and reveals their significance for everything from mental health to cancer. He explains the surprising science of how very different cells—bacteria and brain cells, blood cells and viruses—all speak the same language. This overarching principle has been long overlooked because scientific journals use impenetrable jargon that makes it hard to be understood across disciplines, much less by the general public.
 Lieff presents a fascinating and accessible look into cellular communication science—a groundbreaking and comprehensive exploration of this biological phenomenon. In these pages, discover the intriguing lives of cells as they ask questions, get answers, give feedback, gather information, call for each other, and make complex decisions. During infections, immune T-cells tell brain cells that we should "feel sick" and lie down. Cancer cells warn their community about immune and microbe attacks. Gut cells talk with microbes to determine which are friends and which are enemies, and microbes talk with each other and with much more complicated human cells in ways that determine which medicines work and which will fail.
 With applications for immunity, chronic pain, weight loss, depression, cancer treatment, and virtually every aspect of health and biology, cellular communication is revolutionizing our understanding not just of disease, but of life itself. The Secret Language of Cells is required reading for anyone interested in following the conversation.
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 1. Print length
 368 pages
 2. Language
 English
 3. Publisher
 BenBella Books
 4. Publication date
 September 22, 2020
 5. Dimensions
 6.25 x 1.2 x 9.31 inches
 6. ISBN-10
 1948836041
 7. ISBN-13
 978-1948836043
 8. See all details
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 Editorial Reviews
 Review
 The Secret Language of Cells takes us on an exciting journey into a world where we can visualize elaborate conversations among immune cells, brain cells, gut cells, bacteria, and even viruses. Dr. Lieff gives a wealth of examples for his thesis that this cellular signaling is the basis of life. It is a must read for anyone seeking to understand modern biology and advanced medical science. It is equally important for those of us who wonder, as I do, how this ubiquitous information transfer in the form of cellular conversations might be related to the emergence of intelligence and consciousness.
 Ray Kurzweil,
 Inventor, author and futurist.
 As a storyteller, my imagination is sparked by the insights Dr. Lieff brings to our innermost world and the mysteries at the edge of our understanding. The Secret Language of Cells reveals how the micro world reflects the macro, alive with heroes and villains, shapeshifters and tricksters, vigilant guards and gullible bystanders, helpers that commit suicide for the common good and warriors that seize the day or collapse from exhaustion. Lieff's fascinating exploration inspires awe for the astonishing dialogues and clarion calls at the heart of the intelligence within.
 Antonia Felix, Ed.D., MFA, New York Times bestselling author
 Review
 "Using the common theme of 'cellular conversations,' this book covers an astonishing breadth of biological topics. By removing most of the 'impenetrable jargon' from his descriptions, geriatric psychiatry specialist Lieff succeeds in making the complex interactions between cells accessible for most readers."
 — Choice Reviews
 “ The Secret Language of Cells takes us on an exciting journey into a world where we can visualize elaborate conversations among immune cells, brain cells, gut cells, bacteria, and even viruses. Dr. Lieff gives a wealth of examples for his thesis that this cellular signaling is the basis of life. It is a must-read for anyone seeking to understand modern biology and advanced medical science.”
 — Ray Kurzweil, inventor, author, and futurist
 “ The Secret Language of Cells explains the complex ways that cells in the body communicate and presents a new paradigm for understanding health and disease. It also suggests new possibilities for treatment and for promoting healing. I’m pleased that my former Harvard colleague, Jon Lieff, has written this important book.”
 — Andrew Weill, MD, director of the Andrew Weil Center for Integrative Medicine, professor at University of Arizona College of Medicine, and author
 “Through a brilliant synthesis of cellular biology, microbiology, immunology, and neuroscience, The Secret Language of Cells offers a lucid explanation of the marvelous intricacies of cellular life. The result is a masterful exploration of the profound implications of cellular intelligence for understanding pathophysiology, human health, and even our origins."
 —William B. Miller, Jr., MD, physician, biologist, author of The Microcosm Within: Evolution and Extinction in the Hologenome , and internationally recognized expert on Cognition-Based Evolution
 “Jon Lieff’s description of cellular communication is insightful, provocative, illuminating, and engaging and provides deep and novel observations into the remarkable symphony of how life happens. Mimicking the cellular world he describes, Dr. Lieff is the great communicator and muse of living things. An inspiring and informative read.”
 — Ted Kaptchuk, professor of medicine at Harvard Medical School
 “This journey into the dynamic realm of cellular conversations is a tour-de-force—fascinating, vital, and especially timely for understanding emerging viruses. As we learn about intelligence in smaller and smaller animals, it’s not surprising that the tiniest creatures—microbes and even viruses—exhibit elaborate communication and complex decision making. Read The Secret Language of Cells !”
 — Marc Bekoff, PhD, professor emeritus of ecology and evolutionary biology at the University of Colorado, Boulder and author of Canine Confidential: Why Dogs Do What They Do
 “ The Secret Language of Cells reveals how the micro world reflects the macro, alive with heroes and villains, shapeshifters and tricksters, vigilant guards and gullible bystanders, helpers that commit suicide for the common good and warriors that seize the day or collapse from exhaustion. Lieff’s fascinating exploration inspires awe for the astonishing dialogues and clarion calls at the heart of the intelligence within.”
 — Antonia Felix, EdD, MFA, New York Times bestselling author
 “Calling all physicians, microbiologists, medical students, and fellow science enthusiasts—you’re going to love The Secret Language of Cells !This book reveals fascinating ongoing conversations between cells, bacteria, and viral particles that provide the basis for understanding growth, development, healthy biology, and pathology. Perhaps more importantly, they provide the blueprint for novel interventions, treatments, and cures for ailments ranging from chronic inflammatory diseases, to cancers and even viral infections. The COVID-19 pandemic has focused the world’s lens on the world of microbes like never before. Read this book and join the conversation.”
 — Jill Grimes, MD, family physician, speaker, author, and educator
 “ The Secret Language of Cells is ideal for the education of medical and science students, as well as for practicing physicians. Dr. Lieff’s remarkable synthesis of the scientific literature provides a current view of the intricate communication systems determining our physiology. He clearly explains how conversations among cells are the bridge between immunology, neuroscience, microbiology, and cancer research.”
 — Sharon Redd, MD, senior associate in anesthesia at Boston Children's Hospital and
 assistant professor in anesthesia at Harvard Medical School
 “In The Secret Language of Cells , Dr. Lieff, brilliantly and effectively, communicates the complexities of modern biology to clinicians, and even laypeople, in understandable terms. In the process, he elucidates how communications between diverse varieties of cells determine our physical, mental, and emotional health, as well as the potential social implications.”
 — Sanford Finkel MD, founder of AAGP, cofounder of IPA and APA Council on Aging, and clinical professor of Psychiatry at University of Chicago Medical School
 “Dr. Jon Lieff’s The Secret Language of Cells is a tour-de-force . . . I highly recommend this fascinating book to science readers and anyone wanting to better understand the role and importance of cellular functions and communications in health and disease.”
 — George T. Grossberg, MD, director of Geriatric Psychiatry for the Department of Psychiatry & Behavioral Neuroscience at Saint Louis University School of Medicine
 “Dr. Lieff has synthesized an extensive literature on the biological communications that underlie life into a highly accessible book. His integrative summary will appeal to a broad audience, from high school biology students to professionals with specific areas of expertise.”
 — Barnett Meyers, MD, professor emeritus at Weill Cornell Medical College of Cornell University
 “ The Secret Language of Cells makes it possible for a healthy dialogue between biology and philosophy, a step closer to making a bridge between life-science and various monistic and non-dual philosophies.”
 —Dr. Sthaneshwar Timalsina, professor for the Department of Religious Studies at San Diego State University
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 Product details
 * Publisher ‏ : ‎ BenBella Books (September 22, 2020)
 * Language ‏ : ‎ English
 * Hardcover ‏ : ‎ 368 pages
 * ISBN-10 ‏ : ‎ 1948836041
 * ISBN-13 ‏ : ‎ 978-1948836043
 * Item Weight ‏ : ‎ 1.25 pounds
 * Dimensions ‏ : ‎ 6.25 x 1.2 x 9.31 inches
 * Best Sellers Rank: #1,185,290 in Books ( See Top 100 in Books )
 + #263 in Cell Biology (Books)
 * Customer Reviews:
 4.5 4.5 out of 5 stars 147 ratings
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  5 Stars
  A model of clarity and innovation
  I discovered Dr Jon Lieff's blog about five years ago and was astounded at the breadth and depth of his interests. I was trying to make sense of the immune system and cancer in my partner's treatment for ovarian cancer. Jon's blog was prolific, well written and beautiful illustrated. And extremely useful.I looked forward to his book and expected something similar. My first reading gave a surprise. Jon has concentrated on producing a book that anyone can read. It is clear and uses straightforward language. It is very well organised. He gives a quite different synthesis to other writers in the general field, although I suspect he owns the field himself. There are so many interesting areas that get a distinctly new approach. See below his section on COV-19. I got more from these few paragraphs than from whole articles:"THE NOVEL CORONAVIRUS—VERY CAPABLE WITH FIFTEEN GENES The novel coronavirus (technically called SARS-CoV-2), the virus that causes the illness COVID-19, has great capabilities, with fifteen genes that produce at least twenty-nine proteins. One very large protein is actually sixteen different ones that are cut and released by other proteins. Several of these proteins produce a bubble filled with fluid where the virus builds a factory to produce more viruses. Inside the bubble, two proteins produce new RNA, and another brings material to build the RNA; a medicine for SARS can attack this step. Three other proteins unwind the RNA to make it useful, correct errors, and cut up leftover RNA to keep the host cell from reacting to it. Other proteins alter the human cell’s environment to help the virus survive in the cell and escape. Still others block immune signals to other cells, influence the flow of molecules in and out of the cell nucleus, and turn human genes on and off. Others poke holes in the cell’s membrane, making escape easier, and disable a protein on the surface of human cells trying to grab the escaping virus. One stimulates inflammation and another induces human cells to commit suicide. Four of SARS-CoV-2’s proteins build the structure that has been seen so frequently in the media. All four help with assembly and release from the host cell. One protects the RNA deep inside. Another produces the famous spikes that make it appear as a crown, also known as a corona. These spikes attach to the human cell receptor ACE2 molecule in the airways and other places. This molecule is also an important enzyme blocked by a class of blood pressure medications (ACE inhibitors), likely causing an association of increased risk of COVID-19 symptoms in those who have high blood pressure. Attaching to this receptor allows the virus to enter into cells and creates a strong attachment that causes the symptoms to linger. Of all the proteins, this one might be the one that causes the COVID-19 virus to be so dangerous to humans, since it attaches so firmly to human cells.Lieff, Jon. The Secret Language of Cells (pp. 202-204). BenBella Books, Inc.. Kindle Edition.The main text does not have any references which some may regret. But the extensive list by chapter given at the end of the book more than makes up for this.This review is based on my first fly-through of the text. Below is another snippet from the latter part of the book that give a good idea of where it ends up."WHAT CONCLUSIONS CAN BE DRAWN from this tour of cellular conversations? Although cells are considered the most basic characteristic that defines life, it is actually the conversations among cells, and also the conversations that take place inside them, that determine biological activity and produce the essence of life. The science of cell communication allows new ways to understand health and disease. It also has implications for understanding evolution as well as consciousness. While elaborate signals among neurons have been observed for years, why hasn’t signaling among all other cells been obvious before now? It has been hidden from general view because of impenetrable jargon in scientific journals. Arcane terminologies of signals, receptors, genes, and cell subtypes aren’t generally known, even across various research areas. Professional articles and books on molecular signaling are complex and don’t provide this overarching synthesis. They are hard to understand, even for clinicians and scientists who don’t actively work in a particular field. Also, most of this information has been discovered in the past several years, and biology dogmas die hard. The synthesis of scientific data in this book makes it easy to see why communication among cells has wide-ranging significance. Descriptions of cellular conversations help demystify the latest research on immunity, digestion, cancer, neuroscience, pain, and other topics. This overview—not available anywhere else in one place—is particularly important for those who are ill and trying to follow advanced treatments."Lieff, Jon. The Secret Language of Cells (p. 289). BenBella Books, Inc.. Kindle Edition.I just hope that Jon is sketching the outline for his next book!
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  Dr. Peter R. Best
  5.0 out of 5 stars A model of clarity and innovation
  Reviewed in the United States on October 7, 2020
  Verified Purchase
  I discovered Dr Jon Lieff's blog about five years ago and was astounded at the breadth and depth of his interests. I was trying to make sense of the immune system and cancer in my partner's treatment for ovarian cancer. Jon's blog was prolific, well written and beautiful illustrated. And extremely useful.
  I looked forward to his book and expected something similar. My first reading gave a surprise. Jon has concentrated on producing a book that anyone can read. It is clear and uses straightforward language. It is very well organised. He gives a quite different synthesis to other writers in the general field, although I suspect he owns the field himself. There are so many interesting areas that get a distinctly new approach. See below his section on COV-19. I got more from these few paragraphs than from whole articles:
  "THE NOVEL CORONAVIRUS—VERY CAPABLE WITH FIFTEEN GENES The novel coronavirus (technically called SARS-CoV-2), the virus that causes the illness COVID-19, has great capabilities, with fifteen genes that produce at least twenty-nine proteins. One very large protein is actually sixteen different ones that are cut and released by other proteins. Several of these proteins produce a bubble filled with fluid where the virus builds a factory to produce more viruses. Inside the bubble, two proteins produce new RNA, and another brings material to build the RNA; a medicine for SARS can attack this step. Three other proteins unwind the RNA to make it useful, correct errors, and cut up leftover RNA to keep the host cell from reacting to it. Other proteins alter the human cell’s environment to help the virus survive in the cell and escape. Still others block immune signals to other cells, influence the flow of molecules in and out of the cell nucleus, and turn human genes on and off. Others poke holes in the cell’s membrane, making escape easier, and disable a protein on the surface of human cells trying to grab the escaping virus. One stimulates inflammation and another induces human cells to commit suicide. Four of SARS-CoV-2’s proteins build the structure that has been seen so frequently in the media. All four help with assembly and release from the host cell. One protects the RNA deep inside. Another produces the famous spikes that make it appear as a crown, also known as a corona. These spikes attach to the human cell receptor ACE2 molecule in the airways and other places. This molecule is also an important enzyme blocked by a class of blood pressure medications (ACE inhibitors), likely causing an association of increased risk of COVID-19 symptoms in those who have high blood pressure. Attaching to this receptor allows the virus to enter into cells and creates a strong attachment that causes the symptoms to linger. Of all the proteins, this one might be the one that causes the COVID-19 virus to be so dangerous to humans, since it attaches so firmly to human cells.
  Lieff, Jon. The Secret Language of Cells (pp. 202-204). BenBella Books, Inc.. Kindle Edition.
  The main text does not have any references which some may regret. But the extensive list by chapter given at the end of the book more than makes up for this.
  This review is based on my first fly-through of the text. Below is another snippet from the latter part of the book that give a good idea of where it ends up.
  "WHAT CONCLUSIONS CAN BE DRAWN from this tour of cellular conversations? Although cells are considered the most basic characteristic that defines life, it is actually the conversations among cells, and also the conversations that take place inside them, that determine biological activity and produce the essence of life. The science of cell communication allows new ways to understand health and disease. It also has implications for understanding evolution as well as consciousness. While elaborate signals among neurons have been observed for years, why hasn’t signaling among all other cells been obvious before now? It has been hidden from general view because of impenetrable jargon in scientific journals. Arcane terminologies of signals, receptors, genes, and cell subtypes aren’t generally known, even across various research areas. Professional articles and books on molecular signaling are complex and don’t provide this overarching synthesis. They are hard to understand, even for clinicians and scientists who don’t actively work in a particular field. Also, most of this information has been discovered in the past several years, and biology dogmas die hard. The synthesis of scientific data in this book makes it easy to see why communication among cells has wide-ranging significance. Descriptions of cellular conversations help demystify the latest research on immunity, digestion, cancer, neuroscience, pain, and other topics. This overview—not available anywhere else in one place—is particularly important for those who are ill and trying to follow advanced treatments."
  Lieff, Jon. The Secret Language of Cells (p. 289). BenBella Books, Inc.. Kindle Edition.
  I just hope that Jon is sketching the outline for his next book!
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  Dr. Peter R. Best
  5.0 out of 5 stars A model of clarity and innovation
  Reviewed in the United States on October 7, 2020
  I discovered Dr Jon Lieff's blog about five years ago and was astounded at the breadth and depth of his interests. I was trying to make sense of the immune system and cancer in my partner's treatment for ovarian cancer. Jon's blog was prolific, well written and beautiful illustrated. And extremely useful.
  I looked forward to his book and expected something similar. My first reading gave a surprise. Jon has concentrated on producing a book that anyone can read. It is clear and uses straightforward language. It is very well organised. He gives a quite different synthesis to other writers in the general field, although I suspect he owns the field himself. There are so many interesting areas that get a distinctly new approach. See below his section on COV-19. I got more from these few paragraphs than from whole articles:
  "THE NOVEL CORONAVIRUS—VERY CAPABLE WITH FIFTEEN GENES The novel coronavirus (technically called SARS-CoV-2), the virus that causes the illness COVID-19, has great capabilities, with fifteen genes that produce at least twenty-nine proteins. One very large protein is actually sixteen different ones that are cut and released by other proteins. Several of these proteins produce a bubble filled with fluid where the virus builds a factory to produce more viruses. Inside the bubble, two proteins produce new RNA, and another brings material to build the RNA; a medicine for SARS can attack this step. Three other proteins unwind the RNA to make it useful, correct errors, and cut up leftover RNA to keep the host cell from reacting to it. Other proteins alter the human cell’s environment to help the virus survive in the cell and escape. Still others block immune signals to other cells, influence the flow of molecules in and out of the cell nucleus, and turn human genes on and off. Others poke holes in the cell’s membrane, making escape easier, and disable a protein on the surface of human cells trying to grab the escaping virus. One stimulates inflammation and another induces human cells to commit suicide. Four of SARS-CoV-2’s proteins build the structure that has been seen so frequently in the media. All four help with assembly and release from the host cell. One protects the RNA deep inside. Another produces the famous spikes that make it appear as a crown, also known as a corona. These spikes attach to the human cell receptor ACE2 molecule in the airways and other places. This molecule is also an important enzyme blocked by a class of blood pressure medications (ACE inhibitors), likely causing an association of increased risk of COVID-19 symptoms in those who have high blood pressure. Attaching to this receptor allows the virus to enter into cells and creates a strong attachment that causes the symptoms to linger. Of all the proteins, this one might be the one that causes the COVID-19 virus to be so dangerous to humans, since it attaches so firmly to human cells.
  Lieff, Jon. The Secret Language of Cells (pp. 202-204). BenBella Books, Inc.. Kindle Edition.
  The main text does not have any references which some may regret. But the extensive list by chapter given at the end of the book more than makes up for this.
  This review is based on my first fly-through of the text. Below is another snippet from the latter part of the book that give a good idea of where it ends up.
  "WHAT CONCLUSIONS CAN BE DRAWN from this tour of cellular conversations? Although cells are considered the most basic characteristic that defines life, it is actually the conversations among cells, and also the conversations that take place inside them, that determine biological activity and produce the essence of life. The science of cell communication allows new ways to understand health and disease. It also has implications for understanding evolution as well as consciousness. While elaborate signals among neurons have been observed for years, why hasn’t signaling among all other cells been obvious before now? It has been hidden from general view because of impenetrable jargon in scientific journals. Arcane terminologies of signals, receptors, genes, and cell subtypes aren’t generally known, even across various research areas. Professional articles and books on molecular signaling are complex and don’t provide this overarching synthesis. They are hard to understand, even for clinicians and scientists who don’t actively work in a particular field. Also, most of this information has been discovered in the past several years, and biology dogmas die hard. The synthesis of scientific data in this book makes it easy to see why communication among cells has wide-ranging significance. Descriptions of cellular conversations help demystify the latest research on immunity, digestion, cancer, neuroscience, pain, and other topics. This overview—not available anywhere else in one place—is particularly important for those who are ill and trying to follow advanced treatments."
  Lieff, Jon. The Secret Language of Cells (p. 289). BenBella Books, Inc.. Kindle Edition.
  I just hope that Jon is sketching the outline for his next book!
  Images in this review
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  5.0 out of 5 stars Highly recommend, even to the non scientist!
  Reviewed in the United States on July 12, 2022
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  This is a fantastic read for anyone interested in really understanding how our bodies work. The author explains the very complex functions of our body in a way that’s understandable to the average reader. I am not a scientist and personally found the examples that Dr Lieff uses extremely relatable and interesting, he really brings our cells to life. Thank you for writing this book and explaining what’s really happening inside our complicated bodies.
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  James
  5.0 out of 5 stars Lots of information.
  Reviewed in the United States on June 19, 2023
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  I really like the section on the brain. However great book from a cell anatomy standpoint.
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  William R. Walsh
  4.0 out of 5 stars Worthwhile read
  Reviewed in the United States on April 15, 2021
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  Fascinating look at the cellular level of life. I’m not a biologist but was able to understand most of what’s explained and was amazed at how much has been learned since I was in high school biology class.
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  Lisa C. Tener
  5.0 out of 5 stars "Your Cells Are Talking About You"
  Reviewed in the United States on September 24, 2020
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  This is the claim on the book jacket and the rest of the journey of The Secret Language of Cells is about learning what those cells are saying and how they say it. I imagine this is the closest I'll ever get to overhearing their conversations. In The Secret Language of Cells, Dr. Jon Lieff does the near impossible and takes research findings about cellular communication from esoteric fields of science and puts these findings in plain English, opening a world of discovery for the lay reader interested in pioneering science. This is a book you'll find yourself thinking about throughout the day. Fascinating! Dr. Lieff's unifying theory of the Mind and the essence of life are likely to open up new areas of understanding and research. This book is truly groundbreaking.
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  11 people found this helpful
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  Grace O'Malley
  5.0 out of 5 stars Complex info explained beautifully
  Reviewed in the United States on April 21, 2021
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  This book deserves pride of place in the library of anyone with any interest in how the human body works at the cellular level. I think the genius of the book is that the author describes very complex processes in terms that can be easily visualized. If you can picture cars on a freeway, phone conversations, rescuers swarming against an enemy, you can follow the author’s explanations. Nothing is dumbed down...it’s just all explained in terms of familiar objects and operations. The illustrations and especially the photos taken through electron microscopes look like sculpture. A timeless book!
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  extremelyAwake
  5.0 out of 5 stars Fascinating
  Reviewed in the United States on August 21, 2023
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  This will help you understand the genes and other parts of the cell that are being used to treat cancer
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  Steve G
  3.0 out of 5 stars Interesting but too much is introduced
  Reviewed in the United States on September 22, 2020
  I was somewhat disappointed by this book. Although the writing is conversational and in plain English, I felt that too much is introduced and not enough detail is given to really get a good sense of how communication between cells takes place. On the other hand, the photomicrographs are outstanding. To be upfront, I do have a biology background, but I have read many popular science biology books that have held my attention throughout. A good recent example is Deadliest Enemy by Osterholm and Olshaker.
  Disclosure: I received an advance reader copy via Netgalley for review purposes.
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  Danilo
  1.0 out of 5 stars Noiosissimo !
  Reviewed in Italy on March 16, 2021
  Verified Purchase
  Avevo grandi aspettative di questo libro, come medico. Ma è orribilmente noioso. In più, il titolo non corrisponde a ciò che scrive. Il linguaggio segreto delle cellule: ma qual'è il segreto ? I segnali che si mandano le cellule ? Lo sapevamo già. Quali segnali ? Chimici, elettrici, elettromagnetici, fotonici. Bè ? Il segreto qual'è ? E' che non lo sa nemmeno lui. Non compratelo. Non serve. Nessuna applicazione pratica. Non mi è piaciuto.
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The Secret Language of Cells: What Biological Conversations Tell Us About the Brain-Body Connection, the Future of Medicine, and Life Itself: Lieff, Jon: 9781948836043: Amazon.com: Books
https://www.amazon.com/Secret-Language-Cells-Biological-Conversations/dp/1948836041#:~:text=The%20Secret%20Language%20of%20Cells%20reveals%20how%20the%20micro%20world,day%20or%20collapse%20from%20exhaustion.
https://www.pnas.org/doi/10.1073/pnas.1207814109
Energetic costs of cellular computation
2012-10-30
Pankaj Mehta; David J Schwab; Mehta; Pankaj; Schwab; David J
<div><article><header><div><div><p>Edited by Herbert Levine, University of California, San Diego, La Jolla, CA, and approved September 10, 2012 (received for review May 9, 2012)</p></div><div><p></p><p> () </p></div></div></header><div><section><h2>Abstract</h2><p>Cells often perform computations in order to respond to environmental cues. A simple example is the classic problem, first considered by Berg and Purcell, of determining the concentration of a chemical ligand in the surrounding media. On general theoretical grounds, it is expected that such computations require cells to consume energy. In particular, Landauer’s principle states that energy must be consumed in order to erase the memory of past observations. Here, we explicitly calculate the energetic cost of steady-state computation of ligand concentration for a simple two-component cellular network that implements a noisy version of the Berg–Purcell strategy. We show that learning about external concentrations necessitates the breaking of detailed balance and consumption of energy, with greater learning requiring more energy. Our calculations suggest that the energetic costs of cellular computation may be an important constraint on networks designed to function in resource poor environments, such as the spore germination networks of bacteria.</p></section>
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</div><div><p>The relationship between information and thermodynamics remains an active area of research despite decades of study (<a href="#B1">1</a>–<a href="#B4">4</a>). An important implication of the recent experimental confirmation of Landauer’s principle, relating the erasure of information to thermodynamic irreversibility, is that any irreversible computing device must necessarily consume energy (<a href="#B2">2</a>, <a href="#B3">3</a>). The generality of Landauer’s argument suggests that it is true regardless of how the computation is implemented. A particularly interesting class of examples relevant to systems biology and biophysics is that of intracellular biochemical networks that compute information about the external environment. These biochemical networks are ubiquitous in biology, ranging from the quorum-sensing and chemotaxis networks in single-cell organisms to networks that detect hormones and other signaling factors in higher organisms.</p><p>A fundamental issue is the relationship between the information processing capabilities of these biochemical networks and their energetic costs (<a href="#B5">5</a>–<a href="#B8">8</a>). It is known that energetic costs place important constraints on the design of physical computing devices as well as on neural computing architectures in the brain and retina (<a href="#B9">9</a>–<a href="#B11">11</a>), suggesting that these constraints may also influence the design of cellular computing networks.</p><div><p>The best studied example of a cellular computation is the estimation of the steady-state concentration of a chemical ligand in the surrounding environment (<a href="#B12">12</a>–<a href="#B14">14</a>). This problem was first considered in the seminal paper by Berg and Purcell who showed that the information a cell can acquire about its environment is fundamentally limited by stochastic fluctuations in the occupancy of the membrane-bound receptor proteins that detect the ligand (<a href="#B12">12</a>). In particular, they considered the case of a cellular receptor that binds ligands with a concentration-dependent rate and unbinds particles at a uniform rate (see <a href="#F1">Fig. 1</a>). They argued that cells could estimate the ambient chemical concentration by calculating the average time a receptor is bound during a chosen measurement time <i>T</i>≫1. Recently, however, it was shown that the optimal strategy for a cell is instead to calculate the average duration of the unbound intervals during <i>T</i> or, equivalently, the total time that the receptor was unbound during <i>T</i>. This later computation implements maximum likelihood estimation (MLE) (<a href="#B14">14</a>). In these previous studies, the biochemical network downstream of the receptors that implements the desired computations was largely ignored because the authors were primarily interested in calculating fundamental limits on how precisely cells can compute external concentrations. However, calculating energetic costs requires us to explicitly model the downstream biochemical networks that implement these computations (<a href="#B15">15</a>).</p><div><header><p>Fig. 1.</p></header><figure><figcaption>A cellular network for the computation of an external ligand concentration. External ligands are detected by a receptor that can exist in two conformations: A high-activity on state and a low-activity off state. Receptors switch between states at rate <i>k</i><sub>off</sub> and <i>k</i><sub>on</sub>. Receptors in state <i>s</i> = {on,off} can post-translationally activate (i.e., phosphorylate) a downstream protein at a rate . The protein is deactivated (i.e., dephosphorylated) at a constant rate <i>k</i><sub>1</sub>.</figcaption></figure></div></div><div><p>Here, we consider a simple two-component biochemical network that encodes information about ligand concentration in the steady-state concentration of the activated form of a downstream protein (as shown in <a href="#F1">Fig. 1</a>). Such two-component networks are a common signal transduction motif found in bacteria and are often used to sense external signals through receptor-catalyzed phosphorylation of a downstream response regulator (<a href="#B16">16</a>). The membrane-bound receptors can be in an either an active “on” state or an inactive “off” state. For simplicity, as in previous works (<a href="#B12">12</a>–<a href="#B14">14</a>), we assume that the binding affinity of the on state is extremely high such that all ligand-bound receptors are always in the on state and all unbound receptors are in the off state. Receptors can switch between the off state and on state at a concentration-dependent rate and from the on state to the off state at a concentration-independent rate . Receptors additionally convert a downstream signaling protein from an inactive form <i>X</i> to an active form <i>X</i><sup>∗</sup>, by, for example, phosphorylation, at a state-dependent rate , where <i>s</i> = on,off. The proteins are deactivated at a state-independent rate <i>k</i><sub>1</sub>. The dependence of on the receptor state is what propagates information about ligand concentration downstream. The biochemical network described above contains all the basic elements of a computing device (see <a href="#T1">Table 1</a>).</p><div><header><p>Table 1.</p></header><figure><figcaption>Summary of the biological realization of basic computational elements</figcaption><div><table><thead><tr><th>Computational element</th><th>Biological realization</th></tr></thead><tbody><tr><td>Memory</td><td>Number of activated (phosphorylated) proteins</td></tr><tr><td>Writing to memory</td><td>Concentration dependent activation (phosphorylation) of proteins</td></tr><tr><td>Erasure of memory</td><td>Deactivation (dephosphorylation) of proteins</td></tr><tr><td>Energy dissipation</td><td>Entropy production due to a lack of detailed balance in chemical kinetic of activation/deactivation</td></tr></tbody></table></div></figure></div></div><p>Importantly, the deactivation rate of the off state is small yet must be nonzero for thermodynamic consistency (<a href="#B17">17</a>). We also note that for the case where proteins are activated through phosphorylaltion, includes nonspecific phosphorylation arising from other kinases as well as contributions from the reverse reactions of the phosphotases. The inactivation rate sets the scale for the effective measurement time because it is the rate at which information encoded in downstream proteins is lost due to inactivation. In order to compute external concentrations accurately, the measurement time must be much longer than the typical switching times between receptor states, . We show below that this simple network in fact implements a noisy version of the original Berg–Purcell calculation. Our explicit construction allows us to study the relationship between information and power consumption in this network.</p><p>The paper is organized as follows. In the first section, we compute the steady-state behavior of the system, first within the linear-noise approximation and then through an exact solution of the corresponding master equation. In the next two sections, we quantify the efficacy of chemosensation through the variance in estimated concentration (using the linear-noise approximation) and calculate the power consumption required to maintain the network in steady state (using the exact solution). Finally, we show there exists a tradeoff between these two quantities and discuss implications for the design of cellular sensing systems. We begin each section with a general discussion that summarizes the major ideas, results, and interpretations followed by a more technical and mathematical discussion.</p><section><h2>Characterization of the Network’s Steady-State Properties</h2><div><p>In this section, we derive the steady-state properties of the cellular network considered above. The network translates the external ligand concentration into an internal concentration of activated proteins. This mapping between external ligand concentration and downstream protein number is probabilistic due to the stochasticity inherent in biochemical networks. For this reason, we can characterize the output of the network by a probability distribution of activated proteins, <i>p</i>(<i>n</i>). The shape of the distribution <i>p</i>(<i>n</i>) depends explicitly on the kinetic parameters (<i>k</i><sub>1</sub>, , ) (see <a href="#F2">Fig. 2</a>). In the following sections, we focus on the fast-switching regime where receptors switch between the on and off states quickly as compared to the deactivation rate, and as we will see, <i>p</i>(<i>n</i>) is unimodal (see <a href="#F2">Fig 2</a><i>B</i>).</p><div><header><p>Fig. 2.</p></header><figure><figcaption><i>Top</i> Slow switching regime, , with a bimodal distribution of activated proteins. Probability of having <i>n</i> activated proteins at steady-state (black solid line), probability of having <i>n</i> activated proteins when receptor is in the on state (blue dash-dot line), probability of having <i>n</i> activated proteins when receptor is in the off state (red dashed line). <i>Middle</i> Fast switching regime, , where the distribution of activated proteins is unimodal. Total probability (black solid line), probability when receptor is in the on state (blue dash-dot line), probability when receptor is in the off state (red dashed line). <i>Bottom</i> The uncertainty in ligand concentration, as a function of <i>k</i><sub>1</sub> with mean number of active proteins (dashed red line) and . This can be compared to the Berg–Purcell result (solid black line). Parameters: , .</figcaption></figure></div></div><p>In this regime, two important characteristics of the distribution <i>p</i>(<i>n</i>) are the mean, protein number, , and variance . The mean protein number is the cell’s best estimate of the external ligand concentration. On the other hand, the variance characterizes the cell’s uncertainty about external ligand concentrations due to stochasticity in the underlying biochemical network. Though it is possible to decrease the variance by increasing the mean protein number, it will be always be nonzero due to fluctuations in the state of the receptors (<a href="#B12">12</a>).</p><div><p>We begin by first deriving the steady-state mean and variance of the number of activated proteins, <i>n</i>, within the linear-noise approximation. Afterwards, we will study the full probability distribution. The deterministic dynamics of the biochemical network in <a href="#F1">Fig. 1</a> is captured by simple rate-equations for the time dependence of the receptor state probabilities and the mean number of activated proteins. We can augment these equations to account for stochastic fluctuations within the linear-noise approximation by adding appropriate Langevin noise terms. In the remainder of this paper, we assume for simplicity that proteins are abundant and ignore saturation effects. The dynamics of the circuit is therefore described by a pair of Langevin equations for the probabilities <i>p</i><sub>on</sub> and <i>p</i><sub>off</sub> (i.e. 1 - <i>p</i><sub>on</sub>) for the receptor to be in the on or off states, respectively, together with the number of activated proteins <i>n</i>,</p><div><div><p></p></div><p>[1]</p></div><div><div><p></p></div><p>[2]</p></div><p>The variance of the Langevin terms is given by the Poisson noise in each of the reactions:</p><div><div><p></p></div><p>[3]</p></div><p>where δ(<i>t</i> - <i>t</i><sup>′</sup>) denotes the Dirac-delta function and the overbar denotes the mean steady-state value of the respective quantity (<a href="#B18">18</a>, <a href="#B19">19</a>).</p></div><div><p>At steady-state, we can calculate the mean probability and number of proteins by setting the time derivative in <a href="#FD2">Eq. <b>2</b></a> equal to zero while ignoring noise terms, yielding</p><div><div><p></p></div><p>[4]</p></div><p>and</p><div><div><p></p></div><p>[5]</p></div><p>where we have defined the dimensionless parameters with <i>j</i> = {2,4} and <i>s</i> = {on,off}. For the biologically realistic case , the mean number of proteins is simply proportional to the kinase activity in the on state times the probability of being in the on state, , as expected. One can further calculate the variance in protein numbers (<a href="http://www.pnas.org/lookup/doi/10.1073/pnas.1207814109#supplementary-materials"><i>SI Text</i></a>)</p><div><div><p></p></div><p>[6]</p></div><p>The first term on the right-hand side of the equation results from Poisson noise in the synthesis and degradation of activated protein, whereas the second term is due to stochastic fluctuations in the state of the receptors.</p></div><div><p>In addition to the mean and variance, we will need the full steady-state probability distribution for <i>n</i> to calculate the power consumption of the network. The steady-state distribution can be calculated from the master equation for the probability, <i>p</i><sub><i>s</i></sub>(<i>n</i>), of there being <i>n</i> active proteins with the receptor in a state <i>s</i>:</p><div><div><p></p></div><p>[7]</p></div><p>where (on) when <i>s</i> = on (off). This equation is similar to those found in (<a href="#B20">20</a>, <a href="#B21">21</a>) and the steady-state distribution can be solved via a generating function approach (see <a href="http://www.pnas.org/lookup/doi/10.1073/pnas.1207814109#supplementary-materials"><i>SI Text</i></a>).</p></div><p>Depending on the parameters, the steady-state distributions can have two qualitatively distinct behaviors as shown in <a href="#F2">Fig. 2</a>. In the “slow switching” regime with and , receptors switch at rates much slower than the protein deactivation rate <i>k</i><sub>1</sub>. The result is a bimodal distribution of activated proteins that can be intuitively understood to arise from the superposition of the probability distributions of activated proteins when the receptor is the on and off states. Similar behavior has been found in the steady-state expression of a self-regulation of a gene (<a href="#B22">22</a>). As approaches , the distributions in the two states merge and the overall probability distribution becomes unimodal. On the other hand, in the “fast switching” regime, characterized by , the distribution of activated proteins is always unimodal. In this limit, the measurement time, , is much longer than the average time a receptor remains in the on or off state, and the biochemical network “time-averages” out the stochastic fluctuations in receptor states. In what follows, we restrict our considerations to this latter regime.</p></section><section><h2>Quantification of Learning</h2><p>The biochemical circuit in <a href="#F1">Fig. 1</a> “computes” the external concentration of a chemical ligand. As emphasized by Berg and Purcell in their seminal paper (<a href="#B12">12</a>), the chief obstacle in determining external concentration is the stochastic fluctuations in the state of the ligand-binding receptors. Berg and Purcell argued that a reasonable measure of how much cells learn is the uncertainty cells have about external concentration as measured by the variance of the estimated concentration, (δ<i>c</i>)<sup>2</sup>. (δ<i>c</i>)<sup>2</sup> measures the uncertainty about the external ligand concentration based on the probability distribution of downstream activated proteins. Using standard arguments, we show below that this uncertainty is directly related to the variance, (δ<i>n</i>)<sup>2</sup>, of the corresponding protein probability distribution. This framework allows us to use the results of the last section to quantify how much cells learn about external ligand concentrations as a function of kinetic parameters. The results are plotted in <a href="#F2">Fig. 2</a><i>C</i>.</p><div><p>To compute uncertainty, Berg and Purcell assumed that the cell computes the average receptor occupancy by time-averaging over a measurement time <i>T</i>. They showed (<a href="#B12">12</a>) that</p><div><div><p></p></div><p>[8]</p></div><p>where , is independent of <i>c</i>, and <i>N</i><sub><i>b</i></sub> is the number of binding events during the time <i>T</i>. It was later shown that cells could compute concentration more accurately by implementing MLE with (<a href="#B14">14</a>, <a href="#B23">23</a>)</p><div><div><p></p></div><p>[9]</p></div><p>The factor of two decrease in uncertainty derives from the fact that MLE ignores noise due to unbinding of ligands from the cell. We note that this "forgetting" of ligand unbinding, in turn, requires the receptors themselves to be out of equilibrium, further contributing to the system’s energy consumption. We do not, however, consider the additional energetic costs of nonequilibrium receptors here.</p></div><div><p>To quantify learning in our biochemical circuit, we follow Berg and Purcell and estimate the fluctuations in (δ<i>c</i>)<sup>2</sup> as</p><div><div><p></p></div><p>[10]</p></div><p>with . Substituting and and computing the derivative using <a href="#FD5">Eq. <b>5</b></a> gives</p><div><div><p></p></div><p>[11]</p></div><p>Substituting <a href="#FD5">Eqs. <b>5</b></a> and <a href="#FD6"><b>6</b></a> into <a href="#FD10">Eq. <b>10</b></a> yields</p><div><div><p></p></div><p>[12]</p></div><p>Similar to the linear-noise calculation, the first term on the right-hand side arises from the Poisson fluctuations in activated protein number, while the second term results from the stochastic fluctuations in the state of receptors. <a href="#F2">Fig. 2</a> shows the uncertainty, (δ<i>c</i>)<sup>2</sup>/<i>c</i><sup>2</sup>, as a function of the degradation rate of activated protein, <i>k</i><sub>1</sub>, when and and .</p></div><div><p>By identifying the degradation rate with the inverse measurement time, <i>k</i><sub>1</sub> = 2<i>T</i><sup>-1</sup>, we can also compare the results with Berg–Purcell. The factor of two is due to the slight difference in how the variance of the average receptor occupancy is calculated for a biochemical network when compared to the original Berg–Purcell calculation (<a href="#B23">23</a>). As shown in <a href="#F2">Fig. 2</a>, when is increased, the Poisson noise in protein production is suppressed and the performance of the cellular network approaches that due to Berg-Purcell. To make the connection with Berg–Purcell more explicit, it is helpful to rewrite <a href="#FD12">Eq. <b>12</b></a> in terms of the average number of binding events, <i>N</i><sub><i>b</i></sub>, during the averaging time, <i>T</i>:</p><div><div><p></p></div><p>[13]</p></div><p>This form allows us to see the approach to the Berg–Purcell limit. When the measurement time is much longer than the timescale of fluctuations in receptor activity, i.e., (or equivalently ) and the average number of activated proteins is large, , the expression above reduces to (δ<i>c</i>)<sup>2</sup>/<i>c</i><sup>2</sup> ≈ 2/<i>N</i><sub><i>b</i></sub> in agreement with <a href="#FD8">Eq. <b>8</b></a>.</p></div></section><section><h2>Power Consumption and Entropy Production in Steady State</h2><div><p>We now compute the energy consumed by the circuit in <a href="#F1">Fig. 1</a> as a function of the kinetic parameters. To do so, we exploit the fact that dynamics of the circuit can be formulated as a nonequilbrium Markov process (see <a href="#F3">Fig. 3</a>). A nonequilibrium steady-state (NESS) necessarily implies the breaking of detailed balance in the underlying Markovian dynamics and, therefore, possesses a nonzero entropy production rate. The entropy production rate is precisely the amount of power consumed by the biochemical circuit in maintaining the nonequilibrium steady state. Thus, by calculating the entropy production rate as function of kinetic parameters, we can calculate the power consumed by the biochemical network implementing the computation. To calculate entropy production, we utilize the full steady-state probability distribution and standard formulas from the theory on nonequilibrium Markov processes.</p></div><div><p>Consider a general Markov process with states labeled by σ and transition probability from σ to σ<sup>′</sup> given by <i>k</i>(σ,σ<sup>′</sup>). Defining the steady-state probability of being in state σ by <i>P</i><sub>σ</sub>, the entropy production rate, <i>EP</i>, for a NESS is given by (<a href="#B24">24</a>)</p><div><div><p></p></div><p>[14]</p></div><p>For our problem this general formula reduces to</p><div><div><p></p></div><p>[15]</p></div><p>where we again use (see <a href="http://www.pnas.org/lookup/doi/10.1073/pnas.1207814109#supplementary-materials"><i>SI Text</i></a>). In deriving this formula, we assumed that the receptors were in thermal equilibrium and obeyed detailed balance. Using explicit expressions for the steady-state distributions, <i>p</i><sub><i>s</i></sub>(<i>n</i>), we can calculate the energy consumption of the network as a function of kinetic parameters (see <a href="http://www.pnas.org/lookup/doi/10.1073/pnas.1207814109#supplementary-materials"><i>SI Text</i></a>). The physical content of this expression is summarized in <a href="#F3">Fig. 3</a>. The expression states that any nonzero cyclic flux must necessarily produce entropy. Otherwise, one would have a chemical version of a perpetual motion machine. <a href="#F3">Figs. 3</a> and <a href="#F4">4</a> show the power consumption as a function of and <i>k</i><sub>1</sub>. Notice that the power consumption tends to zero as both these parameters go to zero. Note that we cannot, however, set <i>k</i><sub>1</sub> = 0 identically because there then no longer exists a steady-state distribution.</p></div></section><section><h2>Energetics, Information, and Landauer’s Principle</h2><p>We now highlight the fundamental connection between the energy consumed by the network and the information the network acquires about the environment and briefly discuss its relation to Landauer’s principle. First, note that learning information about the environment requires energy consumption by the network. This relationship can be seen in <a href="#F3">Fig. 3</a>, which shows that as Δ<i>k</i><sub>2</sub> → 0, the uncertainty about the concentration tends to infinity. Moreover, we show in the <a href="http://www.pnas.org/lookup/doi/10.1073/pnas.1207814109#supplementary-materials"><i>SI Text</i></a> that the entropy production, <a href="#FD15">Eq. <b>15</b></a>, is zero if and only if Δ<i>k</i><sub>2</sub> = 0. In conjunction with <a href="#FD12">Eq. <b>12</b></a>, which diverges as Δ<i>k</i><sub>2</sub> → 0, these observations imply that learning requires consuming energy. Mathematically, in the limit where Δ<i>k</i><sub>2</sub> = 0, the dynamics of the Markov process in <a href="#F3">Fig. 3</a> become “one-dimensional” instead of a two-legged ladder, and the dynamics obeys detailed balance. Physically, in this limit the number of downstream proteins becomes insensitive to external ligand concentrations because all information about concentration is contained in the relative probabilities of being in the on or off state.</p><p>Second, as shown in <a href="#F4">Fig. 4</a>, the power consumption of the circuit tends to zero as <i>k</i><sub>1</sub> → 0. This result is consistent with, and a manifestation of, Landauer’s principle: Entropy production stems from erasing memory in a computing device. The number of activated proteins serves the function of a memory of ligand concentration, which is erased at the dephosphorylation rate <i>k</i><sub>1</sub>. Thus, as the erasure rate of the memory tends to zero, the device consumes less energy per unit time, as expected. Yet despite the fact that the power consumption tends to zero as <i>k</i><sub>1</sub> decreases, the total energy consumed per measurement, namely the power times the measurement time, , still increases (see <a href="#F4">Fig. 4</a>). Thus, learning more requires consuming more total energy despite the fact that power consumption is decreasing. In effect, one is approaching the reversible computing limit where memory is erased adiabatically. Again note, however, that when erasure is performed infinitely slowly, <i>k</i><sub>1</sub> = 0, the system no longer has an NESS and our formalism does not apply.</p><p>Finally, we note that one of the important open problems in our understanding of chemosensation is a full characterization of the constraints placed on the measurement time <i>T</i>. In principle, cells can always learn more by measuring the environment for longer periods of time. However, in most biological systems, these measurement times are observed to be quite short. There are a number of constraints that can limit this measurement time, including rotational diffusion (<a href="#B12">12</a>) (in the case of swimming bacteria) and the restrictions placed on motility. Here, we highlight another restriction that may be important in resource-starved environments: Sensing external concentration necessarily requires cells to consume energy.</p></section><section><h2>Discussion and Conclusion</h2><p>Cells often perform computations using elaborate biochemical networks that respond to environmental cues. One of the most common simple networks found in bacteria are two-component networks where a receptor phosphorylates a downstream response regulator (<a href="#B16">16</a>). In this work, we have shown that these simple two-component networks can implement a noisy version of the Berg–Purcell strategy to compute the concentration of external ligands. Furthermore, by mapping the dynamics of the biochemical network to nonequilibrium steady-states in Markov processes, we explicitly derived expressions for the power consumed by the network and showed that learning requires energy consumption. Taken together, these calculations suggest that, much like man-made and neural computing (<a href="#B3">3</a>, <a href="#B9">9</a>–<a href="#B11">11</a>), energetic considerations may place important constraints on the design of biochemical networks that implement cellular computations. They also suggest a fundamental tradeoff between the efficiency of cellular computing and the requisite energy consumption.</p><p>Bacterial cells such as <i>Bacillus subtilis</i> can sporulate during times of environmental stress and remain metabolically dormant for many years. Although sporulation is relatively well understood, the reverse process of germination is much more difficult to study. One current model for how a spore knows when to germinate in response to external cues involves integrating the signal and triggering commitment when an accumulation threshold is reached (<a href="#B25">25</a>, <a href="#B26">26</a>). Such a scheme corresponds to the limit of vanishingly small <i>k</i><sub>1</sub> in our model, so that power consumption is minimized at the expense of retaining the entire integrated signal. Our results indicate that this behavior may be due to the extreme energetic constraints imposed on a metabolically dormant spore, rather than an evolutionarily optimized strategy.</p><p>An important insight of this work is that even a simple Berg–Purcell strategy for sensing external concentrations requires the consumption of energy. It is likely that more complicated strategies that increase how much cells learn, such as maximum likelihood, require additional energetic inputs. For example, it was argued in (<a href="#B23">23</a>) that MLE can be implemented by a network similar to the perfect adaptation network where bursts are produced in response to binding events. These bursts break detailed balance and therefore require energy consumption. It will be interesting to investigate further how the tradeoff between learning and energy consumption manifests itself in the design of computational strategies employed by cells.</p><p>In this work, we restricted ourselves to the simple case where cells calculate the steady-state concentration of an external signal. In the future, it will be useful to generalize the analysis performed here to other computations such as responding to temporal ramps (<a href="#B23">23</a>) and spatial gradients (<a href="#B27">27</a>, <a href="#B28">28</a>). It will also be interesting to understand how to generalize the considerations here to arbitrary biochemical networks. An important restriction on our work is that we reduced our considerations to nonequilibrium steady states. It will be interesting to ask how to generalize the work here to biochemical networks with a strong temporal component.</p></section></div><div><section><h2>ACKNOWLEDGMENTS.</h2><p>P.M. and D.J.S. would like to thank the Aspen Center for Physics, where this work was initiated. We are especially grateful to Thierry Mora for clarifying the relationship between the rate <i>k</i><sub>1</sub> and the average integration time <i>T</i>. This work was partially supported by National Institute of Health Grants K25GM086909 (to P.M.). DS was partially supported by Defense Advanced Research Projects Agency grant HR0011-05-1-0057 and National Science Foundation grant PHY-0957573.</p></section><section><h2>Supporting Information</h2><div><div><p>Supporting Information (PDF)</p><p>Supporting Information</p></div><div><ul><li><a href="https://www.pnas.org/doi/suppl/10.1073/pnas.1207814109/suppl_file/pnas.1207814109_si.pdf">Download</a></li><li>87.51 KB</li></ul></div></div></section><section><h2>References</h2><div><div><p>1</p><div><p>R Landauer, Irreversibility and heat generation in the computing process. <em>IBM J Res Dev</em> <b>5</b>, 183–191 (1961).</p></div></div><div><p>2</p><div><p>A Berut, et al., Experimental verification of Landauers principle linking information and thermodynamics. <em>Nature</em> <b>483</b>, 187–189 (2012).</p></div></div><div><p>3</p><div><p>C Bennett, The thermodynamics of computation: A review. <em>Int J Theor Phys</em> <b>21</b>, 905–940 (1982).</p></div></div><div><p>4</p><div><p>L Del Rio, J Berg, R Renner, O Dahlsten, V Vedral, The thermodynamic meaning of negative entropy. <em>Nature</em> <b>474</b>, 61–63 (2011).</p></div></div><div><p>5</p><div><p>H Qian, T Reluga, Nonequilibrium thermodynamics and nonlinear kinetics in a cellular signaling switch. <em>Phys Rev Lett</em> <b>94</b>, 28101 (2005).</p></div></div><div><p>6</p><div><p>H Qian, Thermodynamic and kinetic analysis of sensitivity amplification in biological signal transduction. <em>Biophys Chem</em> <b>105</b>, 585–593 (2003).</p></div></div><div><p>7</p><div><p>G Lan, P Sartori, S Neumann, V Sourjik, Y Tu, The energy-speed-accuracy trade-off in sensory adaptation. <em>Nat Phys</em> <b>8</b>, 422–428 (2012).</p></div></div><div><p>8</p><div><p>Y Tu, The nonequilibrium mechanism for ultrasensitivity in a biological switch: Sensing by Maxwell’s demons. <em>Proc Natl Acad Sci USA</em> <b>105</b>, 11737–11741 (2008).</p></div></div><div><p>9</p><div><p>S Laughlin, Energy as a constraint on the coding and processing of sensory information. <em>Curr Opin Neurobiol</em> <b>11</b>, 475–480 (2001).</p></div></div><div><p>10</p><div><p>S Laughlin, R van Steveninck, J Anderson, The metabolic cost of neural information. <em>Nat Neurosci</em> <b>1</b>, 36–41 (1998).</p></div></div><div><p>11</p><div><p>V Balasubramanian, D Kimber, M II, Metabolically efficient information processing. <em>Neural Comput</em> <b>13</b>, 799–815 (2001).</p></div></div><div><p>12</p><div><p>H Berg, E Purcell, Physics of chemoreception. <em>Biophys J</em> <b>20</b>, 193–219 (1977).</p></div></div><div><p>13</p><div><p>W Bialek, S Setayeshgar, Physical limits to biochemical signaling. <em>Proc Natl Acad Sci USA</em> <b>102</b>, 10040–10045 (2005).</p></div></div><div><p>14</p><div><p>R Endres, N Wingreen, Maximum likelihood and the single receptor. <em>Phys Rev Lett</em> <b>103</b>, 158101 (2009).</p></div></div><div><p>15</p><div><p>M Magnasco, Chemical kinetics is turing universal. <em>Phys Rev Lett</em> <b>78</b>, 1190–1193 (1997).</p></div></div><div><p>16</p><div><p>M Laub, M Goulian, Specificity in two-component signal transduction pathways. <em>Annu Rev Genet</em> <b>41</b>, 121–145 (2007).</p></div></div><div><p>17</p><div><p>D Beard, H Qian <em>Chemical biophysics: Quantitative analysis of cellular systems</em> (Cambridge Univ Press, Cambridge, MA, 2008).</p></div></div><div><p>18</p><div><p>P Detwiler, S Ramanathan, A Sengupta, B Shraiman, Engineering aspects of enzymatic signal transduction: Photoreceptors in the retina. <em>Biophys J</em> <b>79</b>, 2801–2817 (2000).</p></div></div><div><p>19</p><div><p>P Mehta, S Goyal, N Wingreen, A quantitative comparison of sRNA-based and protein-based gene regulation. <em>Mol Syst Biol</em> <b>4</b>, 221 (2008).</p></div></div><div><p>20</p><div><p>S Iyer-Biswas, F Hayot, C Jayaprakash, Stochasticity of gene products from transcriptional pulsing. <em>Phys Rev E</em> <b>79</b>, 031911 (2009).</p></div></div><div><p>21</p><div><p>P Visco, R Allen, M Evans, Statistical physics of a model binary genetic switch with linear feedback. <em>Phys Rev E</em> <b>79</b>, 031923 (2009).</p></div></div><div><p>22</p><div><p>JE Hornos, et al., Self-regulating gene: An exact solution. <em>Phys Rev E</em> <b>72</b>–051907 (2005).</p></div></div><div><p>23</p><div><p>T Mora, N Wingreen, Limits of sensing temporal concentration changes by single cells. <em>Phys Rev Lett</em> <b>104</b>, 248101 (2010).</p></div></div><div><p>24</p><div><p>J Lebowitz, H Spohn, A gallavotti–cohen-type symmetry in the large deviation functional for stochastic dynamics. <em>J Stat Phys</em> <b>95</b>, 333–365 (1999).</p></div></div><div><p>25</p><div><p>X Yi, J Liu, J Faeder, P Setlow, Synergism between different germinant receptors in the germination of Bacillus subtilis spores. <em>J Bacteriol</em> <b>193</b>, 4664–4671 (2011).</p></div></div><div><p>26</p><div><p>K Indest, W Buchholz, J Faeder, P Setlow, Workshop report: Modeling the molecular mechanism of bacterial spore germination and elucidating reasons for germination heterogeneity. <em>J Food Sci</em> <b>74</b>, R73–R78 (2009).</p></div></div><div><p>27</p><div><p>R Endres, N Wingreen, Accuracy of direct gradient sensing by single cells. <em>Proc Natl Acad Sci USA</em> <b>105</b>, 15749–15754 (2008).</p></div></div><div><p>28</p><div><p>B Hu, W Chen, W Rappel, H Levine, Physical limits on cellular sensing of spatial gradients. <em>Phys Rev Lett</em> <b>105</b>, 48104 (2010).</p></div></div></div></section></div><div><div><header><h2>Information &amp; Authors</h2></header><section><h3>Information</h3><section><h4>Published in</h4><div>
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<div><p></p><p> | <br/></p></div></div></section><section><h4>Classifications</h4><div><ol><li><a href="https://www.pnas.org/topic/bio-sci">Biological Sciences</a></li><li><a href="https://www.pnas.org/topic/biophys-bio">Biophysics and Computational Biology</a></li><li><a href="https://www.pnas.org/topic/phys-sci">Physical Sciences</a></li><li><a href="https://www.pnas.org/topic/phys">Physics</a></li></ol></div></section><section><h4>Submission history</h4><p><b>Published online</b>: October 8, 2012</p><p><b>Published in issue</b>: October 30, 2012</p></section><section><h4>Keywords</h4><ol><li><a href="https://www.pnas.org/action/doSearch?AllField=biophysics&amp;stemming=yes&amp;publication=pnas">biophysics</a></li><li><a href="https://www.pnas.org/action/doSearch?AllField=signaling&amp;stemming=yes&amp;publication=pnas">signaling</a></li><li><a href="https://www.pnas.org/action/doSearch?AllField=inference&amp;stemming=yes&amp;publication=pnas">inference</a></li><li><a href="https://www.pnas.org/action/doSearch?AllField=nonequilibrium&amp;stemming=yes&amp;publication=pnas">nonequilibrium</a></li></ol></section><section><h4>Acknowledgments</h4><p>P.M. and D.J.S. would like to thank the Aspen Center for Physics, where this work was initiated. We are especially grateful to Thierry Mora for clarifying the relationship between the rate <i>k</i><sub>1</sub> and the average integration time <i>T</i>. This work was partially supported by National Institute of Health Grants K25GM086909 (to P.M.). DS was partially supported by Defense Advanced Research Projects Agency grant HR0011-05-1-0057 and National Science Foundation grant PHY-0957573.</p></section><section><h4>Notes</h4><p>This article is a PNAS Direct Submission.</p></section></section><section><h3>Authors</h3><section><h4>Affiliations</h4><div><p></p></div><div><p> </p><div><p></p></div></div></section><section><h4>Notes</h4><p>Author contributions: P.M. and D.J.S. designed research, performed research, contributed new reagents/analytic tools, analyzed data, and wrote the paper.</p></section><section><h4>Competing Interests</h4><p>The authors declare no conflict of interest.</p></section></section></div><div><header><h2>Metrics &amp; Citations</h2></header><section><h3>Metrics</h3><section>
 
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 Energetic costs of cellular computation

 Pankaj Mehta [email protected] and David J. Schwab Authors Info & Affiliations
 Edited by Herbert Levine, University of California, San Diego, La Jolla, CA, and approved September 10, 2012 (received for review May 9, 2012)
 October 8, 2012
 109 ( 44 ) 17978 - 17982
 https://doi.org/10.1073/pnas.1207814109
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 * Contents
 Vol. 109 | No. 44
 + Abstract
 + Characterization of the Network’s Steady-State Properties
 + Quantification of Learning
 + Power Consumption and Entropy Production in Steady State
 + Energetics, Information, and Landauer’s Principle
 + Discussion and Conclusion
 + ACKNOWLEDGMENTS.
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 + References
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 Abstract

 Cells often perform computations in order to respond to environmental cues. A simple example is the classic problem, first considered by Berg and Purcell, of determining the concentration of a chemical ligand in the surrounding media. On general theoretical grounds, it is expected that such computations require cells to consume energy. In particular, Landauer’s principle states that energy must be consumed in order to erase the memory of past observations. Here, we explicitly calculate the energetic cost of steady-state computation of ligand concentration for a simple two-component cellular network that implements a noisy version of the Berg–Purcell strategy. We show that learning about external concentrations necessitates the breaking of detailed balance and consumption of energy, with greater learning requiring more energy. Our calculations suggest that the energetic costs of cellular computation may be an important constraint on networks designed to function in resource poor environments, such as the spore germination networks of bacteria.

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 The relationship between information and thermodynamics remains an active area of research despite decades of study (1–4). An important implication of the recent experimental confirmation of Landauer’s principle, relating the erasure of information to thermodynamic irreversibility, is that any irreversible computing device must necessarily consume energy (2, 3). The generality of Landauer’s argument suggests that it is true regardless of how the computation is implemented. A particularly interesting class of examples relevant to systems biology and biophysics is that of intracellular biochemical networks that compute information about the external environment. These biochemical networks are ubiquitous in biology, ranging from the quorum-sensing and chemotaxis networks in single-cell organisms to networks that detect hormones and other signaling factors in higher organisms.
 A fundamental issue is the relationship between the information processing capabilities of these biochemical networks and their energetic costs (5–8). It is known that energetic costs place important constraints on the design of physical computing devices as well as on neural computing architectures in the brain and retina (9–11), suggesting that these constraints may also influence the design of cellular computing networks.
 The best studied example of a cellular computation is the estimation of the steady-state concentration of a chemical ligand in the surrounding environment (12–14). This problem was first considered in the seminal paper by Berg and Purcell who showed that the information a cell can acquire about its environment is fundamentally limited by stochastic fluctuations in the occupancy of the membrane-bound receptor proteins that detect the ligand (12). In particular, they considered the case of a cellular receptor that binds ligands with a concentration-dependent rate and unbinds particles at a uniform rate (see Fig. 1). They argued that cells could estimate the ambient chemical concentration by calculating the average time a receptor is bound during a chosen measurement time T≫1. Recently, however, it was shown that the optimal strategy for a cell is instead to calculate the average duration of the unbound intervals during T or, equivalently, the total time that the receptor was unbound during T. This later computation implements maximum likelihood estimation (MLE) (14). In these previous studies, the biochemical network downstream of the receptors that implements the desired computations was largely ignored because the authors were primarily interested in calculating fundamental limits on how precisely cells can compute external concentrations. However, calculating energetic costs requires us to explicitly model the downstream biochemical networks that implement these computations (15).
 Fig. 1.

 A cellular network for the computation of an external ligand concentration. External ligands are detected by a receptor that can exist in two conformations: A high-activity on state and a low-activity off state. Receptors switch between states at rate koff and kon. Receptors in state s = {on,off} can post-translationally activate (i.e., phosphorylate) a downstream protein at a rate . The protein is deactivated (i.e., dephosphorylated) at a constant rate k1.

 Here, we consider a simple two-component biochemical network that encodes information about ligand concentration in the steady-state concentration of the activated form of a downstream protein (as shown in Fig. 1). Such two-component networks are a common signal transduction motif found in bacteria and are often used to sense external signals through receptor-catalyzed phosphorylation of a downstream response regulator (16). The membrane-bound receptors can be in an either an active “on” state or an inactive “off” state. For simplicity, as in previous works (12–14), we assume that the binding affinity of the on state is extremely high such that all ligand-bound receptors are always in the on state and all unbound receptors are in the off state. Receptors can switch between the off state and on state at a concentration-dependent rate and from the on state to the off state at a concentration-independent rate . Receptors additionally convert a downstream signaling protein from an inactive form X to an active form X∗, by, for example, phosphorylation, at a state-dependent rate , where s = on,off. The proteins are deactivated at a state-independent rate k1. The dependence of on the receptor state is what propagates information about ligand concentration downstream. The biochemical network described above contains all the basic elements of a computing device (see Table 1).
 Table 1.

 Summary of the biological realization of basic computational elements

 Computational element Biological realization  
 Memory Number of activated (phosphorylated) proteins 
 Writing to memory Concentration dependent activation (phosphorylation) of proteins 
 Erasure of memory Deactivation (dephosphorylation) of proteins 
 Energy dissipation Entropy production due to a lack of detailed balance in chemical kinetic of activation/deactivation
 

 Importantly, the deactivation rate of the off state is small yet must be nonzero for thermodynamic consistency (17). We also note that for the case where proteins are activated through phosphorylaltion, includes nonspecific phosphorylation arising from other kinases as well as contributions from the reverse reactions of the phosphotases. The inactivation rate sets the scale for the effective measurement time because it is the rate at which information encoded in downstream proteins is lost due to inactivation. In order to compute external concentrations accurately, the measurement time must be much longer than the typical switching times between receptor states, . We show below that this simple network in fact implements a noisy version of the original Berg–Purcell calculation. Our explicit construction allows us to study the relationship between information and power consumption in this network.
 The paper is organized as follows. In the first section, we compute the steady-state behavior of the system, first within the linear-noise approximation and then through an exact solution of the corresponding master equation. In the next two sections, we quantify the efficacy of chemosensation through the variance in estimated concentration (using the linear-noise approximation) and calculate the power consumption required to maintain the network in steady state (using the exact solution). Finally, we show there exists a tradeoff between these two quantities and discuss implications for the design of cellular sensing systems. We begin each section with a general discussion that summarizes the major ideas, results, and interpretations followed by a more technical and mathematical discussion.

 Characterization of the Network’s Steady-State Properties

 In this section, we derive the steady-state properties of the cellular network considered above. The network translates the external ligand concentration into an internal concentration of activated proteins. This mapping between external ligand concentration and downstream protein number is probabilistic due to the stochasticity inherent in biochemical networks. For this reason, we can characterize the output of the network by a probability distribution of activated proteins, p(n). The shape of the distribution p(n) depends explicitly on the kinetic parameters (k1, , ) (see Fig. 2). In the following sections, we focus on the fast-switching regime where receptors switch between the on and off states quickly as compared to the deactivation rate, and as we will see, p(n) is unimodal (see Fig 2B).
 Fig. 2.

 Top Slow switching regime, , with a bimodal distribution of activated proteins. Probability of having n activated proteins at steady-state (black solid line), probability of having n activated proteins when receptor is in the on state (blue dash-dot line), probability of having n activated proteins when receptor is in the off state (red dashed line). Middle Fast switching regime, , where the distribution of activated proteins is unimodal. Total probability (black solid line), probability when receptor is in the on state (blue dash-dot line), probability when receptor is in the off state (red dashed line). Bottom The uncertainty in ligand concentration, as a function of k1 with mean number of active proteins (dashed red line) and . This can be compared to the Berg–Purcell result (solid black line). Parameters: , .

 In this regime, two important characteristics of the distribution p(n) are the mean, protein number, , and variance . The mean protein number is the cell’s best estimate of the external ligand concentration. On the other hand, the variance characterizes the cell’s uncertainty about external ligand concentrations due to stochasticity in the underlying biochemical network. Though it is possible to decrease the variance by increasing the mean protein number, it will be always be nonzero due to fluctuations in the state of the receptors (12).
 We begin by first deriving the steady-state mean and variance of the number of activated proteins, n, within the linear-noise approximation. Afterwards, we will study the full probability distribution. The deterministic dynamics of the biochemical network in Fig. 1 is captured by simple rate-equations for the time dependence of the receptor state probabilities and the mean number of activated proteins. We can augment these equations to account for stochastic fluctuations within the linear-noise approximation by adding appropriate Langevin noise terms. In the remainder of this paper, we assume for simplicity that proteins are abundant and ignore saturation effects. The dynamics of the circuit is therefore described by a pair of Langevin equations for the probabilities pon and poff (i.e. 1 - pon) for the receptor to be in the on or off states, respectively, together with the number of activated proteins n,
 [1]
 [2]
 The variance of the Langevin terms is given by the Poisson noise in each of the reactions:
 [3]
 where δ(t - t′) denotes the Dirac-delta function and the overbar denotes the mean steady-state value of the respective quantity (18, 19).
 At steady-state, we can calculate the mean probability and number of proteins by setting the time derivative in Eq. 2 equal to zero while ignoring noise terms, yielding
 [4]
 and
 [5]
 where we have defined the dimensionless parameters with j = {2,4} and s = {on,off}. For the biologically realistic case , the mean number of proteins is simply proportional to the kinase activity in the on state times the probability of being in the on state, , as expected. One can further calculate the variance in protein numbers (SI Text)
 [6]
 The first term on the right-hand side of the equation results from Poisson noise in the synthesis and degradation of activated protein, whereas the second term is due to stochastic fluctuations in the state of the receptors.
 In addition to the mean and variance, we will need the full steady-state probability distribution for n to calculate the power consumption of the network. The steady-state distribution can be calculated from the master equation for the probability, ps(n), of there being n active proteins with the receptor in a state s:
 [7]
 where (on) when s = on (off). This equation is similar to those found in (20, 21) and the steady-state distribution can be solved via a generating function approach (see SI Text).
 Depending on the parameters, the steady-state distributions can have two qualitatively distinct behaviors as shown in Fig. 2. In the “slow switching” regime with and , receptors switch at rates much slower than the protein deactivation rate k1. The result is a bimodal distribution of activated proteins that can be intuitively understood to arise from the superposition of the probability distributions of activated proteins when the receptor is the on and off states. Similar behavior has been found in the steady-state expression of a self-regulation of a gene (22). As approaches , the distributions in the two states merge and the overall probability distribution becomes unimodal. On the other hand, in the “fast switching” regime, characterized by , the distribution of activated proteins is always unimodal. In this limit, the measurement time, , is much longer than the average time a receptor remains in the on or off state, and the biochemical network “time-averages” out the stochastic fluctuations in receptor states. In what follows, we restrict our considerations to this latter regime.

 Quantification of Learning

 The biochemical circuit in Fig. 1 “computes” the external concentration of a chemical ligand. As emphasized by Berg and Purcell in their seminal paper (12), the chief obstacle in determining external concentration is the stochastic fluctuations in the state of the ligand-binding receptors. Berg and Purcell argued that a reasonable measure of how much cells learn is the uncertainty cells have about external concentration as measured by the variance of the estimated concentration, (δc)2. (δc)2 measures the uncertainty about the external ligand concentration based on the probability distribution of downstream activated proteins. Using standard arguments, we show below that this uncertainty is directly related to the variance, (δn)2, of the corresponding protein probability distribution. This framework allows us to use the results of the last section to quantify how much cells learn about external ligand concentrations as a function of kinetic parameters. The results are plotted in Fig. 2C.
 To compute uncertainty, Berg and Purcell assumed that the cell computes the average receptor occupancy by time-averaging over a measurement time T. They showed (12) that
 [8]
 where , is independent of c, and Nb is the number of binding events during the time T. It was later shown that cells could compute concentration more accurately by implementing MLE with (14, 23)
 [9]
 The factor of two decrease in uncertainty derives from the fact that MLE ignores noise due to unbinding of ligands from the cell. We note that this "forgetting" of ligand unbinding, in turn, requires the receptors themselves to be out of equilibrium, further contributing to the system’s energy consumption. We do not, however, consider the additional energetic costs of nonequilibrium receptors here.
 To quantify learning in our biochemical circuit, we follow Berg and Purcell and estimate the fluctuations in (δc)2 as
 [10]
 with . Substituting and and computing the derivative using Eq. 5 gives
 [11]
 Substituting Eqs. 5 and 6 into Eq. 10 yields
 [12]
 Similar to the linear-noise calculation, the first term on the right-hand side arises from the Poisson fluctuations in activated protein number, while the second term results from the stochastic fluctuations in the state of receptors. Fig. 2 shows the uncertainty, (δc)2/c2, as a function of the degradation rate of activated protein, k1, when and and .
 By identifying the degradation rate with the inverse measurement time, k1 = 2T-1, we can also compare the results with Berg–Purcell. The factor of two is due to the slight difference in how the variance of the average receptor occupancy is calculated for a biochemical network when compared to the original Berg–Purcell calculation (23). As shown in Fig. 2, when is increased, the Poisson noise in protein production is suppressed and the performance of the cellular network approaches that due to Berg-Purcell. To make the connection with Berg–Purcell more explicit, it is helpful to rewrite Eq. 12 in terms of the average number of binding events, Nb, during the averaging time, T:
 [13]
 This form allows us to see the approach to the Berg–Purcell limit. When the measurement time is much longer than the timescale of fluctuations in receptor activity, i.e., (or equivalently ) and the average number of activated proteins is large, , the expression above reduces to (δc)2/c2 ≈ 2/Nb in agreement with Eq. 8.

 Power Consumption and Entropy Production in Steady State

 We now compute the energy consumed by the circuit in Fig. 1 as a function of the kinetic parameters. To do so, we exploit the fact that dynamics of the circuit can be formulated as a nonequilbrium Markov process (see Fig. 3). A nonequilibrium steady-state (NESS) necessarily implies the breaking of detailed balance in the underlying Markovian dynamics and, therefore, possesses a nonzero entropy production rate. The entropy production rate is precisely the amount of power consumed by the biochemical circuit in maintaining the nonequilibrium steady state. Thus, by calculating the entropy production rate as function of kinetic parameters, we can calculate the power consumed by the biochemical network implementing the computation. To calculate entropy production, we utilize the full steady-state probability distribution and standard formulas from the theory on nonequilibrium Markov processes.
 Fig. 3.

 Upper The probabilistic Markov process underlying the circuit in Fig. 1 takes the form of a two-legged ladder. Any nonzero cyclic flux (depicted in red) results in entropy production and power consumption. Lower Power consumption (solid black line) and uncertainty (dashed purple line) as a function of when , and .

 Consider a general Markov process with states labeled by σ and transition probability from σ to σ′ given by k(σ,σ′). Defining the steady-state probability of being in state σ by Pσ, the entropy production rate, EP, for a NESS is given by (24)
 [14]
 For our problem this general formula reduces to
 [15]
 where we again use (see SI Text). In deriving this formula, we assumed that the receptors were in thermal equilibrium and obeyed detailed balance. Using explicit expressions for the steady-state distributions, ps(n), we can calculate the energy consumption of the network as a function of kinetic parameters (see SI Text). The physical content of this expression is summarized in Fig. 3. The expression states that any nonzero cyclic flux must necessarily produce entropy. Otherwise, one would have a chemical version of a perpetual motion machine. Figs. 3 and 4 show the power consumption as a function of and k1. Notice that the power consumption tends to zero as both these parameters go to zero. Note that we cannot, however, set k1 = 0 identically because there then no longer exists a steady-state distribution.
 Fig. 4.

 Total energy per independent measurement () as a function of k1 when . (Inset) Power consumption as a function of k1 over the same parameter range. Note that although the system’s power consumption decreases with decreasing k1, the energy per measurement increases.

 Energetics, Information, and Landauer’s Principle

 We now highlight the fundamental connection between the energy consumed by the network and the information the network acquires about the environment and briefly discuss its relation to Landauer’s principle. First, note that learning information about the environment requires energy consumption by the network. This relationship can be seen in Fig. 3, which shows that as Δk2 → 0, the uncertainty about the concentration tends to infinity. Moreover, we show in the SI Text that the entropy production, Eq. 15, is zero if and only if Δk2 = 0. In conjunction with Eq. 12, which diverges as Δk2 → 0, these observations imply that learning requires consuming energy. Mathematically, in the limit where Δk2 = 0, the dynamics of the Markov process in Fig. 3 become “one-dimensional” instead of a two-legged ladder, and the dynamics obeys detailed balance. Physically, in this limit the number of downstream proteins becomes insensitive to external ligand concentrations because all information about concentration is contained in the relative probabilities of being in the on or off state.
 Second, as shown in Fig. 4, the power consumption of the circuit tends to zero as k1 → 0. This result is consistent with, and a manifestation of, Landauer’s principle: Entropy production stems from erasing memory in a computing device. The number of activated proteins serves the function of a memory of ligand concentration, which is erased at the dephosphorylation rate k1. Thus, as the erasure rate of the memory tends to zero, the device consumes less energy per unit time, as expected. Yet despite the fact that the power consumption tends to zero as k1 decreases, the total energy consumed per measurement, namely the power times the measurement time, , still increases (see Fig. 4). Thus, learning more requires consuming more total energy despite the fact that power consumption is decreasing. In effect, one is approaching the reversible computing limit where memory is erased adiabatically. Again note, however, that when erasure is performed infinitely slowly, k1 = 0, the system no longer has an NESS and our formalism does not apply.
 Finally, we note that one of the important open problems in our understanding of chemosensation is a full characterization of the constraints placed on the measurement time T. In principle, cells can always learn more by measuring the environment for longer periods of time. However, in most biological systems, these measurement times are observed to be quite short. There are a number of constraints that can limit this measurement time, including rotational diffusion (12) (in the case of swimming bacteria) and the restrictions placed on motility. Here, we highlight another restriction that may be important in resource-starved environments: Sensing external concentration necessarily requires cells to consume energy.

 Discussion and Conclusion

 Cells often perform computations using elaborate biochemical networks that respond to environmental cues. One of the most common simple networks found in bacteria are two-component networks where a receptor phosphorylates a downstream response regulator (16). In this work, we have shown that these simple two-component networks can implement a noisy version of the Berg–Purcell strategy to compute the concentration of external ligands. Furthermore, by mapping the dynamics of the biochemical network to nonequilibrium steady-states in Markov processes, we explicitly derived expressions for the power consumed by the network and showed that learning requires energy consumption. Taken together, these calculations suggest that, much like man-made and neural computing (3, 9–11), energetic considerations may place important constraints on the design of biochemical networks that implement cellular computations. They also suggest a fundamental tradeoff between the efficiency of cellular computing and the requisite energy consumption.
 Bacterial cells such as Bacillus subtilis can sporulate during times of environmental stress and remain metabolically dormant for many years. Although sporulation is relatively well understood, the reverse process of germination is much more difficult to study. One current model for how a spore knows when to germinate in response to external cues involves integrating the signal and triggering commitment when an accumulation threshold is reached (25, 26). Such a scheme corresponds to the limit of vanishingly small k1 in our model, so that power consumption is minimized at the expense of retaining the entire integrated signal. Our results indicate that this behavior may be due to the extreme energetic constraints imposed on a metabolically dormant spore, rather than an evolutionarily optimized strategy.
 An important insight of this work is that even a simple Berg–Purcell strategy for sensing external concentrations requires the consumption of energy. It is likely that more complicated strategies that increase how much cells learn, such as maximum likelihood, require additional energetic inputs. For example, it was argued in (23) that MLE can be implemented by a network similar to the perfect adaptation network where bursts are produced in response to binding events. These bursts break detailed balance and therefore require energy consumption. It will be interesting to investigate further how the tradeoff between learning and energy consumption manifests itself in the design of computational strategies employed by cells.
 In this work, we restricted ourselves to the simple case where cells calculate the steady-state concentration of an external signal. In the future, it will be useful to generalize the analysis performed here to other computations such as responding to temporal ramps (23) and spatial gradients (27, 28). It will also be interesting to understand how to generalize the considerations here to arbitrary biochemical networks. An important restriction on our work is that we reduced our considerations to nonequilibrium steady states. It will be interesting to ask how to generalize the work here to biochemical networks with a strong temporal component.

 ACKNOWLEDGMENTS.

 P.M. and D.J.S. would like to thank the Aspen Center for Physics, where this work was initiated. We are especially grateful to Thierry Mora for clarifying the relationship between the rate k1 and the average integration time T. This work was partially supported by National Institute of Health Grants K25GM086909 (to P.M.). DS was partially supported by Defense Advanced Research Projects Agency grant HR0011-05-1-0057 and National Science Foundation grant PHY-0957573.

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 Information & Authors

 Information

 Published in

 Proceedings of the National Academy of Sciences
 Vol. 109 | No. 44
 October 30, 2012
 PubMed : 23045633

 Classifications

 1. Biological Sciences
 2. Biophysics and Computational Biology
 3. 
 4. Physical Sciences
 5. Physics
 6. 

 Submission history

 Published online: October 8, 2012
 Published in issue: October 30, 2012

 Keywords

 1. biophysics
 2. signaling
 3. inference
 4. nonequilibrium

 Acknowledgments

 P.M. and D.J.S. would like to thank the Aspen Center for Physics, where this work was initiated. We are especially grateful to Thierry Mora for clarifying the relationship between the rate k1 and the average integration time T. This work was partially supported by National Institute of Health Grants K25GM086909 (to P.M.). DS was partially supported by Defense Advanced Research Projects Agency grant HR0011-05-1-0057 and National Science Foundation grant PHY-0957573.

 Notes

 This article is a PNAS Direct Submission.

 Authors

 Affiliations

 Pankaj Mehta 1 [email protected]
 Department of Physics, Boston University, Boston, MA 02215; and
 View all articles by this author
 David J. Schwab
 Department of Molecular Biology and Lewis-Sigler Institute, Princeton University, Princeton, NJ 08854
 View all articles by this author

 Notes

 1
 To whom correspondence should be addressed. E-mail: [email protected] .
 Author contributions: P.M. and D.J.S. designed research, performed research, contributed new reagents/analytic tools, analyzed data, and wrote the paper.

 Competing Interests

 The authors declare no conflict of interest.

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Edited by Herbert Levine, University of California, San Diego, La Jolla, CA, and approved September 10, 2012 (received for review May 9, 2012)      ()       Abstract Cells often perform computations in order to respond to environmental cues. A simple example is the classic problem, first considered by Berg and Purcell, of determining the concentration of a chemical ligand in the surrounding media. On general theoretical grounds, it is expected that such computations require cells to consume energy. In particular, Landauer’s principle states that energy must be consumed in order to erase the memory of past observations. Here, we explicitly calculate the energetic cost of steady-state computation of ligand concentration for a simple two-component cellular network that implements a noisy version of the Berg–Purcell strategy. We show that learning about external concentrations necessitates the breaking of detailed balance and consumption of energy, with greater learning requiring more energy. Our calculations suggest that the energetic costs of cellular computation may be an important constraint on networks designed to function in resource poor environments, such as the spore germination networks of bacteria. 
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  The relationship between information and thermodynamics remains an active area of research despite decades of study (1–4). An important implication of the recent experimental confirmation of Landauer’s principle, relating the erasure of information to thermodynamic irreversibility, is that any irreversible computing device must necessarily consume energy (2, 3). The generality of Landauer’s argument suggests that it is true regardless of how the computation is implemented. A particularly interesting class of examples relevant to systems biology and biophysics is that of intracellular biochemical networks that compute information about the external environment. These biochemical networks are ubiquitous in biology, ranging from the quorum-sensing and chemotaxis networks in single-cell organisms to networks that detect hormones and other signaling factors in higher organisms. A fundamental issue is the relationship between the information processing capabilities of these biochemical networks and their energetic costs (5–8). It is known that energetic costs place important constraints on the design of physical computing devices as well as on neural computing architectures in the brain and retina (9–11), suggesting that these constraints may also influence the design of cellular computing networks.  The best studied example of a cellular computation is the estimation of the steady-state concentration of a chemical ligand in the surrounding environment (12–14). This problem was first considered in the seminal paper by Berg and Purcell who showed that the information a cell can acquire about its environment is fundamentally limited by stochastic fluctuations in the occupancy of the membrane-bound receptor proteins that detect the ligand (12). In particular, they considered the case of a cellular receptor that binds ligands with a concentration-dependent rate and unbinds particles at a uniform rate (see Fig. 1). They argued that cells could estimate the ambient chemical concentration by calculating the average time a receptor is bound during a chosen measurement time T≫1. Recently, however, it was shown that the optimal strategy for a cell is instead to calculate the average duration of the unbound intervals during T or, equivalently, the total time that the receptor was unbound during T. This later computation implements maximum likelihood estimation (MLE) (14). In these previous studies, the biochemical network downstream of the receptors that implements the desired computations was largely ignored because the authors were primarily interested in calculating fundamental limits on how precisely cells can compute external concentrations. However, calculating energetic costs requires us to explicitly model the downstream biochemical networks that implement these computations (15).   Fig. 1.   A cellular network for the computation of an external ligand concentration. External ligands are detected by a receptor that can exist in two conformations: A high-activity on state and a low-activity off state. Receptors switch between states at rate k off and k on. Receptors in state s = {on,off} can post-translationally activate (i.e., phosphorylate) a downstream protein at a rate . The protein is deactivated (i.e., dephosphorylated) at a constant rate k 1.     Here, we consider a simple two-component biochemical network that encodes information about ligand concentration in the steady-state concentration of the activated form of a downstream protein (as shown in Fig. 1). Such two-component networks are a common signal transduction motif found in bacteria and are often used to sense external signals through receptor-catalyzed phosphorylation of a downstream response regulator (16). The membrane-bound receptors can be in an either an active “on” state or an inactive “off” state. For simplicity, as in previous works (12–14), we assume that the binding affinity of the on state is extremely high such that all ligand-bound receptors are always in the on state and all unbound receptors are in the off state. Receptors can switch between the off state and on state at a concentration-dependent rate and from the on state to the off state at a concentration-independent rate . Receptors additionally convert a downstream signaling protein from an inactive form X to an active form X ∗, by, for example, phosphorylation, at a state-dependent rate , where s = on,off. The proteins are deactivated at a state-independent rate k 1. The dependence of on the receptor state is what propagates information about ligand concentration downstream. The biochemical network described above contains all the basic elements of a computing device (see Table 1).   Table 1.   Summary of the biological realization of basic computational elements     Computational element Biological realization     Memory Number of activated (phosphorylated) proteins   Writing to memory Concentration dependent activation (phosphorylation) of proteins   Erasure of memory Deactivation (dephosphorylation) of proteins   Energy dissipation Entropy production due to a lack of detailed balance in chemical kinetic of activation/deactivation        Importantly, the deactivation rate of the off state is small yet must be nonzero for thermodynamic consistency (17). We also note that for the case where proteins are activated through phosphorylaltion, includes nonspecific phosphorylation arising from other kinases as well as contributions from the reverse reactions of the phosphotases. The inactivation rate sets the scale for the effective measurement time because it is the rate at which information encoded in downstream proteins is lost due to inactivation. In order to compute external concentrations accurately, the measurement time must be much longer than the typical switching times between receptor states, . We show below that this simple network in fact implements a noisy version of the original Berg–Purcell calculation. Our explicit construction allows us to study the relationship between information and power consumption in this network. The paper is organized as follows. In the first section, we compute the steady-state behavior of the system, first within the linear-noise approximation and then through an exact solution of the corresponding master equation. In the next two sections, we quantify the efficacy of chemosensation through the variance in estimated concentration (using the linear-noise approximation) and calculate the power consumption required to maintain the network in steady state (using the exact solution). Finally, we show there exists a tradeoff between these two quantities and discuss implications for the design of cellular sensing systems. We begin each section with a general discussion that summarizes the major ideas, results, and interpretations followed by a more technical and mathematical discussion.  Characterization of the Network’s Steady-State Properties  In this section, we derive the steady-state properties of the cellular network considered above. The network translates the external ligand concentration into an internal concentration of activated proteins. This mapping between external ligand concentration and downstream protein number is probabilistic due to the stochasticity inherent in biochemical networks. For this reason, we can characterize the output of the network by a probability distribution of activated proteins, p(n). The shape of the distribution p(n) depends explicitly on the kinetic parameters (k 1, , ) (see Fig. 2). In the following sections, we focus on the fast-switching regime where receptors switch between the on and off states quickly as compared to the deactivation rate, and as we will see, p(n) is unimodal (see Fig 2 B).   Fig. 2.    Top Slow switching regime, , with a bimodal distribution of activated proteins. Probability of having n activated proteins at steady-state (black solid line), probability of having n activated proteins when receptor is in the on state (blue dash-dot line), probability of having n activated proteins when receptor is in the off state (red dashed line). Middle Fast switching regime, , where the distribution of activated proteins is unimodal. Total probability (black solid line), probability when receptor is in the on state (blue dash-dot line), probability when receptor is in the off state (red dashed line). Bottom The uncertainty in ligand concentration, as a function of k 1 with mean number of active proteins (dashed red line) and . This can be compared to the Berg–Purcell result (solid black line). Parameters: , .    In this regime, two important characteristics of the distribution p(n) are the mean, protein number, , and variance . The mean protein number is the cell’s best estimate of the external ligand concentration. On the other hand, the variance characterizes the cell’s uncertainty about external ligand concentrations due to stochasticity in the underlying biochemical network. Though it is possible to decrease the variance by increasing the mean protein number, it will be always be nonzero due to fluctuations in the state of the receptors (12).  We begin by first deriving the steady-state mean and variance of the number of activated proteins, n, within the linear-noise approximation. Afterwards, we will study the full probability distribution. The deterministic dynamics of the biochemical network in Fig. 1 is captured by simple rate-equations for the time dependence of the receptor state probabilities and the mean number of activated proteins. We can augment these equations to account for stochastic fluctuations within the linear-noise approximation by adding appropriate Langevin noise terms. In the remainder of this paper, we assume for simplicity that proteins are abundant and ignore saturation effects. The dynamics of the circuit is therefore described by a pair of Langevin equations for the probabilities p on and p off (i.e. 1 - p on) for the receptor to be in the on or off states, respectively, together with the number of activated proteins n,      [1]       [2]  The variance of the Langevin terms is given by the Poisson noise in each of the reactions:      [3]  where δ(t - t ′) denotes the Dirac-delta function and the overbar denotes the mean steady-state value of the respective quantity (18, 19).   At steady-state, we can calculate the mean probability and number of proteins by setting the time derivative in Eq. 2  equal to zero while ignoring noise terms, yielding      [4]  and      [5]  where we have defined the dimensionless parameters with j = {2,4} and s = {on,off}. For the biologically realistic case , the mean number of proteins is simply proportional to the kinase activity in the on state times the probability of being in the on state, , as expected. One can further calculate the variance in protein numbers ( SI Text )      [6]  The first term on the right-hand side of the equation results from Poisson noise in the synthesis and degradation of activated protein, whereas the second term is due to stochastic fluctuations in the state of the receptors.   In addition to the mean and variance, we will need the full steady-state probability distribution for n to calculate the power consumption of the network. The steady-state distribution can be calculated from the master equation for the probability, p  s (n), of there being n active proteins with the receptor in a state s:      [7]  where (on) when s = on (off). This equation is similar to those found in (20, 21) and the steady-state distribution can be solved via a generating function approach (see  SI Text ).  Depending on the parameters, the steady-state distributions can have two qualitatively distinct behaviors as shown in Fig. 2. In the “slow switching” regime with and , receptors switch at rates much slower than the protein deactivation rate k 1. The result is a bimodal distribution of activated proteins that can be intuitively understood to arise from the superposition of the probability distributions of activated proteins when the receptor is the on and off states. Similar behavior has been found in the steady-state expression of a self-regulation of a gene (22). As approaches , the distributions in the two states merge and the overall probability distribution becomes unimodal. On the other hand, in the “fast switching” regime, characterized by , the distribution of activated proteins is always unimodal. In this limit, the measurement time, , is much longer than the average time a receptor remains in the on or off state, and the biochemical network “time-averages” out the stochastic fluctuations in receptor states. In what follows, we restrict our considerations to this latter regime.   Quantification of Learning The biochemical circuit in Fig. 1 “computes” the external concentration of a chemical ligand. As emphasized by Berg and Purcell in their seminal paper (12), the chief obstacle in determining external concentration is the stochastic fluctuations in the state of the ligand-binding receptors. Berg and Purcell argued that a reasonable measure of how much cells learn is the uncertainty cells have about external concentration as measured by the variance of the estimated concentration, (δc)2. (δc)2 measures the uncertainty about the external ligand concentration based on the probability distribution of downstream activated proteins. Using standard arguments, we show below that this uncertainty is directly related to the variance, (δn)2, of the corresponding protein probability distribution. This framework allows us to use the results of the last section to quantify how much cells learn about external ligand concentrations as a function of kinetic parameters. The results are plotted in Fig. 2 C.  To compute uncertainty, Berg and Purcell assumed that the cell computes the average receptor occupancy by time-averaging over a measurement time T. They showed (12) that      [8]  where , is independent of c, and N  b  is the number of binding events during the time T. It was later shown that cells could compute concentration more accurately by implementing MLE with (14, 23)      [9]  The factor of two decrease in uncertainty derives from the fact that MLE ignores noise due to unbinding of ligands from the cell. We note that this "forgetting" of ligand unbinding, in turn, requires the receptors themselves to be out of equilibrium, further contributing to the system’s energy consumption. We do not, however, consider the additional energetic costs of nonequilibrium receptors here.   To quantify learning in our biochemical circuit, we follow Berg and Purcell and estimate the fluctuations in (δc)2 as      [10]  with . Substituting and and computing the derivative using Eq. 5  gives      [11]  Substituting Eqs. 5  and  6  into Eq. 10  yields      [12]  Similar to the linear-noise calculation, the first term on the right-hand side arises from the Poisson fluctuations in activated protein number, while the second term results from the stochastic fluctuations in the state of receptors. Fig. 2 shows the uncertainty, (δc)2/c 2, as a function of the degradation rate of activated protein, k 1, when and and .   By identifying the degradation rate with the inverse measurement time, k 1 = 2T -1, we can also compare the results with Berg–Purcell. The factor of two is due to the slight difference in how the variance of the average receptor occupancy is calculated for a biochemical network when compared to the original Berg–Purcell calculation (23). As shown in Fig. 2, when is increased, the Poisson noise in protein production is suppressed and the performance of the cellular network approaches that due to Berg-Purcell. To make the connection with Berg–Purcell more explicit, it is helpful to rewrite Eq. 12  in terms of the average number of binding events, N  b , during the averaging time, T:      [13]  This form allows us to see the approach to the Berg–Purcell limit. When the measurement time is much longer than the timescale of fluctuations in receptor activity, i.e., (or equivalently ) and the average number of activated proteins is large, , the expression above reduces to (δc)2/c 2 ≈ 2/N  b  in agreement with Eq. 8 .    Power Consumption and Entropy Production in Steady State  We now compute the energy consumed by the circuit in Fig. 1 as a function of the kinetic parameters. To do so, we exploit the fact that dynamics of the circuit can be formulated as a nonequilbrium Markov process (see Fig. 3). A nonequilibrium steady-state (NESS) necessarily implies the breaking of detailed balance in the underlying Markovian dynamics and, therefore, possesses a nonzero entropy production rate. The entropy production rate is precisely the amount of power consumed by the biochemical circuit in maintaining the nonequilibrium steady state. Thus, by calculating the entropy production rate as function of kinetic parameters, we can calculate the power consumed by the biochemical network implementing the computation. To calculate entropy production, we utilize the full steady-state probability distribution and standard formulas from the theory on nonequilibrium Markov processes.   Consider a general Markov process with states labeled by σ and transition probability from σ to σ′ given by k(σ,σ′). Defining the steady-state probability of being in state σ by P σ, the entropy production rate, EP, for a NESS is given by (24)      [14]  For our problem this general formula reduces to      [15]  where we again use (see  SI Text ). In deriving this formula, we assumed that the receptors were in thermal equilibrium and obeyed detailed balance. Using explicit expressions for the steady-state distributions, p  s (n), we can calculate the energy consumption of the network as a function of kinetic parameters (see  SI Text ). The physical content of this expression is summarized in Fig. 3. The expression states that any nonzero cyclic flux must necessarily produce entropy. Otherwise, one would have a chemical version of a perpetual motion machine. Figs. 3 and 4 show the power consumption as a function of and k 1. Notice that the power consumption tends to zero as both these parameters go to zero. Note that we cannot, however, set k 1 = 0 identically because there then no longer exists a steady-state distribution.    Energetics, Information, and Landauer’s Principle We now highlight the fundamental connection between the energy consumed by the network and the information the network acquires about the environment and briefly discuss its relation to Landauer’s principle. First, note that learning information about the environment requires energy consumption by the network. This relationship can be seen in Fig. 3, which shows that as Δk 2 → 0, the uncertainty about the concentration tends to infinity. Moreover, we show in the  SI Text  that the entropy production, Eq. 15 , is zero if and only if Δk 2 = 0. In conjunction with Eq. 12 , which diverges as Δk 2 → 0, these observations imply that learning requires consuming energy. Mathematically, in the limit where Δk 2 = 0, the dynamics of the Markov process in Fig. 3 become “one-dimensional” instead of a two-legged ladder, and the dynamics obeys detailed balance. Physically, in this limit the number of downstream proteins becomes insensitive to external ligand concentrations because all information about concentration is contained in the relative probabilities of being in the on or off state. Second, as shown in Fig. 4, the power consumption of the circuit tends to zero as k 1 → 0. This result is consistent with, and a manifestation of, Landauer’s principle: Entropy production stems from erasing memory in a computing device. The number of activated proteins serves the function of a memory of ligand concentration, which is erased at the dephosphorylation rate k 1. Thus, as the erasure rate of the memory tends to zero, the device consumes less energy per unit time, as expected. Yet despite the fact that the power consumption tends to zero as k 1 decreases, the total energy consumed per measurement, namely the power times the measurement time, , still increases (see Fig. 4). Thus, learning more requires consuming more total energy despite the fact that power consumption is decreasing. In effect, one is approaching the reversible computing limit where memory is erased adiabatically. Again note, however, that when erasure is performed infinitely slowly, k 1 = 0, the system no longer has an NESS and our formalism does not apply. Finally, we note that one of the important open problems in our understanding of chemosensation is a full characterization of the constraints placed on the measurement time T. In principle, cells can always learn more by measuring the environment for longer periods of time. However, in most biological systems, these measurement times are observed to be quite short. There are a number of constraints that can limit this measurement time, including rotational diffusion (12) (in the case of swimming bacteria) and the restrictions placed on motility. Here, we highlight another restriction that may be important in resource-starved environments: Sensing external concentration necessarily requires cells to consume energy.   Discussion and Conclusion Cells often perform computations using elaborate biochemical networks that respond to environmental cues. One of the most common simple networks found in bacteria are two-component networks where a receptor phosphorylates a downstream response regulator (16). In this work, we have shown that these simple two-component networks can implement a noisy version of the Berg–Purcell strategy to compute the concentration of external ligands. Furthermore, by mapping the dynamics of the biochemical network to nonequilibrium steady-states in Markov processes, we explicitly derived expressions for the power consumed by the network and showed that learning requires energy consumption. Taken together, these calculations suggest that, much like man-made and neural computing (3, 9–11), energetic considerations may place important constraints on the design of biochemical networks that implement cellular computations. They also suggest a fundamental tradeoff between the efficiency of cellular computing and the requisite energy consumption. Bacterial cells such as Bacillus subtilis can sporulate during times of environmental stress and remain metabolically dormant for many years. Although sporulation is relatively well understood, the reverse process of germination is much more difficult to study. One current model for how a spore knows when to germinate in response to external cues involves integrating the signal and triggering commitment when an accumulation threshold is reached (25, 26). Such a scheme corresponds to the limit of vanishingly small k 1 in our model, so that power consumption is minimized at the expense of retaining the entire integrated signal. Our results indicate that this behavior may be due to the extreme energetic constraints imposed on a metabolically dormant spore, rather than an evolutionarily optimized strategy. An important insight of this work is that even a simple Berg–Purcell strategy for sensing external concentrations requires the consumption of energy. It is likely that more complicated strategies that increase how much cells learn, such as maximum likelihood, require additional energetic inputs. For example, it was argued in (23) that MLE can be implemented by a network similar to the perfect adaptation network where bursts are produced in response to binding events. These bursts break detailed balance and therefore require energy consumption. It will be interesting to investigate further how the tradeoff between learning and energy consumption manifests itself in the design of computational strategies employed by cells. In this work, we restricted ourselves to the simple case where cells calculate the steady-state concentration of an external signal. In the future, it will be useful to generalize the analysis performed here to other computations such as responding to temporal ramps (23) and spatial gradients (27, 28). It will also be interesting to understand how to generalize the considerations here to arbitrary biochemical networks. An important restriction on our work is that we reduced our considerations to nonequilibrium steady states. It will be interesting to ask how to generalize the work here to biochemical networks with a strong temporal component.     ACKNOWLEDGMENTS. P.M. and D.J.S. would like to thank the Aspen Center for Physics, where this work was initiated. We are especially grateful to Thierry Mora for clarifying the relationship between the rate k 1 and the average integration time T. This work was partially supported by National Institute of Health Grants K25GM086909 (to P.M.). DS was partially supported by Defense Advanced Research Projects Agency grant HR0011-05-1-0057 and National Science Foundation grant PHY-0957573.   Supporting Information   Supporting Information (PDF) Supporting Information     Download  87.51 KB      References   1  R Landauer, Irreversibility and heat generation in the computing process. IBM J Res Dev 5, 183–191 (1961).    2  A Berut, et al., Experimental verification of Landauers principle linking information and thermodynamics. 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    |       Classifications    Biological Sciences   Biophysics and Computational Biology   Physical Sciences   Physics      Submission history  Published online: October 8, 2012  Published in issue: October 30, 2012   Keywords   biophysics   signaling   inference   nonequilibrium     Acknowledgments P.M. and D.J.S. would like to thank the Aspen Center for Physics, where this work was initiated. We are especially grateful to Thierry Mora for clarifying the relationship between the rate k 1 and the average integration time T. This work was partially supported by National Institute of Health Grants K25GM086909 (to P.M.). DS was partially supported by Defense Advanced Research Projects Agency grant HR0011-05-1-0057 and National Science Foundation grant PHY-0957573.   Notes This article is a PNAS Direct Submission.    Authors  Affiliations               Notes Author contributions: P.M. and D.J.S. designed research, performed research, contributed new reagents/analytic tools, analyzed data, and wrote the paper.   Competing Interests The authors declare no conflict of interest.      Metrics &amp; Citations   Metrics 
 
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Energetic costs of cellular computation
https://www.pnas.org/doi/10.1073/pnas.1207814109
https://www.nature.com/articles/s41467-019-13232-z
Pathways to cellular supremacy in biocomputing - Nature Communications
2019-11-20
Grozinger; Lewis; Amos; Martyn; Gorochowski; Thomas E; Carbonell; Pablo; Oyarzún; Diego A; Stoof; Ruud; Fellermann; Harold; Zuliani; Paolo; Tas; Huseyin; Goñi-Moreno; Angel
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 <div><h2>Abstract</h2><p>Synthetic biology uses living cells as the substrate for performing human-defined computations. Many current implementations of cellular computing are based on the “genetic circuit” metaphor, an approximation of the operation of silicon-based computers. Although this conceptual mapping has been relatively successful, we argue that it fundamentally limits the types of computation that may be engineered inside the cell, and fails to exploit the rich and diverse functionality available in natural living systems. We propose the notion of “cellular supremacy” to focus attention on domains in which biocomputing might offer superior performance over traditional computers. We consider potential pathways toward cellular supremacy, and suggest application areas in which it may be found.</p></div>
 
 
 
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 <div><h2>Introduction</h2><div><p>Synthetic biology<sup><a href="/articles/s41467-019-13232-z#ref-CR1">1</a>,<a href="/articles/s41467-019-13232-z#ref-CR2">2</a></sup> is a rapidly growing field of research which applies engineering concepts and principles to the rational engineering of living systems, such as bacteria and yeast. The promise of synthetic biology lies in its potential to provide new substrates for computation<sup><a href="/articles/s41467-019-13232-z#ref-CR3">3</a></sup>, production<sup><a href="/articles/s41467-019-13232-z#ref-CR4">4</a></sup>, pollution control<sup><a href="/articles/s41467-019-13232-z#ref-CR5">5</a></sup> and medical diagnosis<sup><a href="/articles/s41467-019-13232-z#ref-CR6">6</a></sup> (among many areas), and to harness the “wetware”<sup><a href="/articles/s41467-019-13232-z#ref-CR7">7</a></sup> inside the living cell for human-defined purposes. Synthetic biology is set to become a significant component of the multi-billion dollar bio-economy<sup><a href="/articles/s41467-019-13232-z#ref-CR8">8</a></sup>, but, in addition to tangible benefits such as cheaper drug production or more precise bio-sensing, many researchers in the field believe that the very process of re-engineering life will both require and inform a reexamination of our fundamental understanding of cellular processes<sup><a href="/articles/s41467-019-13232-z#ref-CR9">9</a></sup>. This position underpins the current paper.</p><p>Much existing work in synthetic biology is concerned with the construction of “circuits” of biological components (such as genes and proteins) that receive some input (either endogenous, or exogenous), perform some transformation of that input, and produce a result determined by the “rules” encoded in the circuit. This input-transform-output pipeline is entirely consistent with the notion of a computation, as traditionally defined, and it is wholly unsurprising that synthetic biology has, so far, largely adhered to the genetic “logic circuit” model (groundbreaking examples include the genetic toggle switch<sup><a href="/articles/s41467-019-13232-z#ref-CR10">10</a></sup> and the “repressilator”<sup><a href="/articles/s41467-019-13232-z#ref-CR11">11</a></sup>).</p><p>The roots of this biological circuit metaphor date back to the mechanistic view of the cell; the idea that living systems may be viewed as machines, which, in turn, can be traced as far back as Descartes (and beyond). Characterisations of the cell as a “factory”, a “little engine”, and a “chemical machine” dominated early discourse in cell biology, and the post-war development of cybernetics and computer science, combined with the emergence of molecular biology, provided significant support for this conceptual interpretation of living systems<sup><a href="/articles/s41467-019-13232-z#ref-CR12">12</a></sup>.</p><p>The “machine model” of the cell was further cemented by the pioneering work of Jacob and Monod, which established that the <i>lac</i> operon<sup><a href="/articles/s41467-019-13232-z#ref-CR13">13</a></sup> facilitates metabolic switching within <i>E. coli</i> in a manner that may be interpreted as a simple Boolean circuit. In his highly influential popular book, <i>Chance and Necessity</i> (a chapter of which is titled “Microscopic Cybernetics”), Monod made explicit the connection between biological processes and the basis of electronic circuits:</p><p>“The logic of biological regulatory systems abides not by Hegelian laws but, like the workings of computers, by the propositional algebra of George Boole.”<sup><a href="/articles/s41467-019-13232-z#ref-CR14">14</a></sup></p><p>Since the discovery of the <i>lac</i> operon, the machine model has largely dominated molecular biology<sup><a href="/articles/s41467-019-13232-z#ref-CR15">15</a></sup>, and the notion of the genome serving as a “genetic program” is still relatively common<sup><a href="/articles/s41467-019-13232-z#ref-CR16">16</a></sup>. Of course, abstracting biological processes to the level of circuits (Boolean or otherwise) or even programs may be a necessary step in terms of making sense of their operation. Conversely, in the context of engineered biological systems, the availability of a set of well-characterised, modular and tunable components are perhaps necessary for creating controllable and predictable systems<sup><a href="/articles/s41467-019-13232-z#ref-CR17">17</a></sup>. We emphasise here that we do not seek to overturn or abandon an extremely powerful and useful metaphor. However, it may give a misleading impression regarding the reliability and predictability of genetic circuits, compared to their electronic counterparts<sup><a href="/articles/s41467-019-13232-z#ref-CR18">18</a></sup>. Moreover, as we argue in this paper, by restricting ourselves to the computational palette offered by (Boolean) combinatorial logic, we inherently (and seriously) limit the power and scope of synthetic biology.</p><p>It is perhaps instructive at this point to discuss the field of molecular computing<sup><a href="/articles/s41467-019-13232-z#ref-CR19">19</a></sup>, which many see as a conceptual precursor to synthetic biology, if not a direct predecessor. Although the notion of computing with individual atoms and molecules was attributed to Richard Feynman as early as the 1950s<sup><a href="/articles/s41467-019-13232-z#ref-CR20">20</a></sup>, the field was only reified in 1994, when Leonard Adleman published his groundbreaking paper on computing solutions to the Hamiltonian Circuit Problem using molecular operations with strands of DNA<sup><a href="/articles/s41467-019-13232-z#ref-CR21">21</a></sup>. At the time, a commonly-held belief was that the future promise of DNA computation<sup><a href="/articles/s41467-019-13232-z#ref-CR22">22</a></sup> lay in solving instances of hard computational problems that were beyond the capabilities of traditional silicon-based computers<sup><a href="/articles/s41467-019-13232-z#ref-CR23">23</a></sup>. Much early work on producing general DNA-based computational models focussed on molecular emulation of the Boolean circuit model<sup><a href="/articles/s41467-019-13232-z#ref-CR24">24</a>,<a href="/articles/s41467-019-13232-z#ref-CR25">25</a></sup>. Discussion of the field’s overall direction was, for a time, dominated by the quest for the “killer application”, the application of DNA computing that would establish its superiority over existing computational substrates<sup><a href="/articles/s41467-019-13232-z#ref-CR26">26</a>,<a href="/articles/s41467-019-13232-z#ref-CR27">27</a></sup>. In some ways, this may be viewed as a restricted form of the search for so-called “quantum supremacy” in the quantum computing domain<sup><a href="/articles/s41467-019-13232-z#ref-CR28">28</a></sup>.</p><p>As the field of molecular computing evolved, it rapidly became clear that the killer application would not be found by solving large instances of computationally hard problems using any variant of Adleman’s original model. The elegance of the original solution derived from the encoding used to construct all possible paths through a given graph; vertices and edges were represented as strands of DNA that self-assembled into a collection of paths, which was then rapidly filtered in parallel using molecular manipulations to gradually extract valid solutions. Crucially, this reasonable run-time required the entire solution space for a given problem instance to be represented in an initial “test tube” at the start of the computation; the problem was to find the “needle” (valid solution(s)) in a molecular “haystack”. Essentially, the entire space of solutions was tested in polynomial time using molecular operations, but this came at the cost of having to represent the whole solution set in a single volume of liquid<sup><a href="/articles/s41467-019-13232-z#ref-CR22">22</a></sup>. For even small problem instances, the amount of DNA required to represent all possible solutions would be astronomical; Hartmanis calculated that if Adleman’s experiment were scaled up from 7 to 200 vertices, the amount of DNA required would weigh more than the Earth<sup><a href="/articles/s41467-019-13232-z#ref-CR29">29</a></sup>. We note, however, that this inherent time-space tradeoff would appear to hold regardless of whether the underlying substrate is DNA, silicon, or a more exotic material (with the possible exception of substrates for quantum computers<sup><a href="/articles/s41467-019-13232-z#ref-CR30">30</a></sup>).</p><p>Importantly, this assessment emphasised the fact that the killer application would probably not be derived from single-use, finite DNA-based systems (albeit ones that were large and potentially massively-parallel in nature). Subsequent influential work on DNA self-assembly<sup><a href="/articles/s41467-019-13232-z#ref-CR31">31</a></sup> and strand displacement architectures<sup><a href="/articles/s41467-019-13232-z#ref-CR32">32</a></sup> emulated traditional computational models such as cellular automata<sup><a href="/articles/s41467-019-13232-z#ref-CR33">33</a></sup> and artificial neurons<sup><a href="/articles/s41467-019-13232-z#ref-CR34">34</a></sup>, but also took advantage of biochemical processes that provided power beyond mere miniaturisation. That is, rather than simply harnessing the potential for massively-parallel laboratory operations on large (but finite) numbers of molecules, these systems co-opted specific physical and chemical properties of the underlying substrate to generate the potential for autonomous operation and dynamic behaviour. In the context of synthetic biology, we suggest the killer application for engineered living systems will be similarly derived; one that will use features of the living system that are unavailable via traditional silicon-based substrates, for the purposes of applications that exploit autonomy and the ability to perform in uncertain environments.</p></div></div><div><h2>The search for cellular supremacy</h2><div><p>If we accept that a driving motivation for synthetic biology should be the search for a killer application, then this naturally leads to a consideration of the class of problems in which engineered living systems might offer what we call cellular supremacy (deliberately echoing the well-established notion of quantum supremacy<sup><a href="/articles/s41467-019-13232-z#ref-CR28">28</a>,<a href="#ref-CR35">35</a>,<a href="#ref-CR36">36</a>,<a href="/articles/s41467-019-13232-z#ref-CR37">37</a></sup>). That is, we seek a set of problem domains in which cell-based systems will offer capabilities beyond the reach of existing computers, due to cost or technological constraints. Simply put, cellular supremacy will be determined by the set of problems that biocomputers can practically solve that traditional microprocessor-based devices cannot. To identify this set of problems, we naturally focus on the “added value” that living systems offer beyond silicon-based hardware. In the following sections, we discuss a number of features of living systems that we believe give synthetic biology-based solutions a distinct “edge” over traditional computers. Importantly, we focus on aspects of computation and information transformation, rather than simply on the ability of the cell to act as a micro-scale drug precursor “production plant” or miniaturised bio-sensor. While these applications are important and valuable, they are not the main focus of the current discussion, which centres on the general computational capabilities of living systems if we go beyond the limitations of Boolean logic-based systems. In what follows, we use the term “cellular computing”<sup><a href="/articles/s41467-019-13232-z#ref-CR38">38</a>,<a href="/articles/s41467-019-13232-z#ref-CR39">39</a></sup> to emphasise this focus on computation.</p><p>When assessing cellular computing against traditional computing, it may be useful to frame the comparison using a scheme that emerged from an exercise on roadmapping the so-called “unconventional computation” domain. The authors identified a number of criteria or benchmarks against which emerging computational models may be measured, each accompanied by its own motivating question<sup><a href="/articles/s41467-019-13232-z#ref-CR40">40</a></sup>. In what follows, we focus on the quality criterion, which asks the following question: Does the alternative model offer qualitatively different computation to traditional models? The authors define “quality” in terms of precision, richness, stochasticity and repeatability. Quality is concerned with the ability of the system to provide an analysis of inputs that is different to that offered by a traditional computer. If we focus on problems that fall within the remit of traditional silicon-based machines, and use existing metrics, then cellular computing will inevitably fall short on some of the other criteria identified<sup><a href="/articles/s41467-019-13232-z#ref-CR40">40</a></sup>, such as speed and cost. However, we would argue that the real power of cell-based systems derives from the richness of their internal (and collective) architectures, and on their inherent stochasticity.</p><p>This leads us to a consideration of the specific computationally expressive mechanisms that are available to us, and which act both inside and between living cells. In what follows we focus on five (non-exclusive) features of living cells that (we believe) offer the most potential in terms of the search for cellular supremacy; these are reconfigurability (that is, the ability to change internal state/structure in response to signals), noise (the ability to not only tolerate but to harness and exploit biological “messiness”), concurrency (the multitude and richness of inter-cellular processes that facilitate massively-parallel communication and coordination), representation (the ability to use non-binary representations for signals), and evolution (the population-level ability to seek out novel solutions to problems over time). By harnessing these capabilities, we will obtain bio-computing systems that are self-organising, self-repairing, resilient, distributed, and adaptive<sup><a href="/articles/s41467-019-13232-z#ref-CR41">41</a></sup>.</p><p>First, we consider aspects of computational theory that suggest how cellular computers may out-perform traditional machines. We then describe a number of features of biological systems that lend themselves to non-standard computation. Taken together, these two perspectives point towards a number of possible areas for investigation in which the killer application for cellular computing may reside.</p></div></div><div><h2>Information processing beyond digital logic</h2><div><p>The current definition of digital computation is based on the abstract model defined by Turing in the 1930s<sup><a href="/articles/s41467-019-13232-z#ref-CR42">42</a></sup>, and the von Neumann architecture<sup><a href="/articles/s41467-019-13232-z#ref-CR43">43</a></sup> used to implement the types of computations performed by the Turing Machine. Although Turing’s model provides a framework for answering fundamental questions about computation, “…as soon as one leaves the comfort provided by the abundance of mathematical machinery used to describe digital computation, the world seems to be packed with paradoxes.”<sup><a href="/articles/s41467-019-13232-z#ref-CR44">44</a></sup>.</p><p>The important thing to note here is that although genetic circuits may appear to behave digitally, it is only the collective behaviour of a large number of inherently analogue components that give rise to this property. The fact remains that we still currently lack any formal framework within which to argue that a cell computes, according to any understood model of computation (although recent work has started to address this<sup><a href="/articles/s41467-019-13232-z#ref-CR45">45</a></sup>).</p><p>The nature of computation is not of purely theoretical interest. Mathematical models of computation and their properties inform the engineering of their physical manifestations (Fig. <a href="/articles/s41467-019-13232-z#Fig1">1</a>). Many such implementations may be possible, but all inherit the characteristics of their abstract counterparts—both their abilities and their limitations. The fact that the nature of computation within a given model is independent of its implementation allows the application of theoretical computer science to all kinds of physical systems, including cells. However, the cost of this generality is a semantic gap between the model and the physical processes that actually perform the computation. That is, mapping computations from an abstract model to a real system may be more or less difficult, depending on the model chosen. The cellular computing substrate is quite different from that of silicon computers, offering opportunities for implementing some models with a narrower semantic gap. Practical considerations such as these could guide future applications of cellular computing.</p><div><figure><figcaption><b>Fig. 1</b></figcaption><div><div><a href="/articles/s41467-019-13232-z/figures/1"></a></div><p>The cell as a “physical” computer. A model of computation formally defines inputs and outputs, as well as how an algorithm processes inputs into outputs. Though the same theoretical model of computation can be physically implemented in many different ways, the nature of computation remains the same. Electronic implementations receive electronic data for inputs/outputs, while cells are able to sense/deliver a wide range of physical, chemical and biological inputs/outputs. The encoding of information into inputs can be done in different ways. Temperature, for instance, can be encoded as the height of mercury in a tube, the voltage of an electronic thermometer or the state of a DNA thermosensor</p></div><p><a href="/articles/s41467-019-13232-z/figures/1">Full size image</a></p></figure></div><p>Conventional silicon computers are fundamentally implementations of a deterministic, centralised and digital model of computation, and they excel at computational tasks which are easily described by such models. In contrast, cellular computing has been optimised over billions of years of evolution to perform very different computational tasks, and we are unlikely to find cellular supremacy in applications such as discrete mathematics, sending emails or reading documents. However, computer science has developed models in which the nature of computation is quite different to that of the Turing Machine<sup><a href="#ref-CR46">46</a>,<a href="#ref-CR47">47</a>,<a href="#ref-CR48">48</a>,<a href="#ref-CR49">49</a>,<a href="#ref-CR50">50</a>,<a href="#ref-CR51">51</a>,<a href="#ref-CR52">52</a>,<a href="/articles/s41467-019-13232-z#ref-CR53">53</a></sup> and computation in cells appears to share some properties with these less conventional models. With this in mind, the application of theoretical computer science to cellular computation may still present routes to cellular supremacy in those areas where the properties of cellular and traditional computation differ.</p><p>Here, we introduce a selection of theoretical aspects of computing that impact significantly upon the nature of computation, all of which seem to be exploited in the cell for processing information, but whose theoretical implications may not be familiar to those outside the field of computer science.</p></div></div><div><h2>Computational states for computations over time</h2><div><p>Not all models of computation are equally powerful, that is, they are not equivalent in terms of the range of computations they can possibly describe. By this metric, combinatorial logic circuits are extremely weak, since the output of a circuit is purely a function of its current inputs (that is, there is no “memory”), and this severely restricts the range of computations that are possible with a single circuit. Clearly, there are models of computation more powerful than combinatorial logic, that is, models which can describe all computations that are possible with combinatorial logic circuits and more. In this regard, two extremely powerful models of computation, the Lambda calculus<sup><a href="/articles/s41467-019-13232-z#ref-CR54">54</a></sup> and the Turing Machine<sup><a href="/articles/s41467-019-13232-z#ref-CR42">42</a></sup> are particularly important. These two models are both equally powerful, but quite different in their formulation—the Lambda calculus is a model of functional computation, while the Turing Machine models stateful computation. Here we focus on stateful computation, as states enable functions that operate over time, such as memory, learning and adaptation.</p><p>The output of stateful computations depends not only on the current input, but also on the current state, which encodes information about previous inputs that are no longer present. Models of computation such as finite state machines (FSMs) (shown in Fig. <a href="/articles/s41467-019-13232-z#Fig2">2</a>) exceed the capabilities of combinatorial logic, and are extremely powerful models of computation—the central processing units of modern digital computers are built from sequential logic circuits, which are implementations of FSMs. Even so, they cannot describe all computations that are available to the Turing Machine model, since they have only a bounded number of states. Turing machines are similar to FSMs, but have an unbounded memory (commonly conceptualized as a tape), which endows them with an unbounded computational state space (number of distinct configurations). Consequently, Turing Machines can compute anything that any real computer can, and in fact, computer science starts from the notion that Turing Machines (TMs) demarcate what is (and is not) computable<sup><a href="/articles/s41467-019-13232-z#ref-CR42">42</a></sup>. From a practical perspective, these considerations of the limits of computability might be of less conceptual value than the strategy that TMs employ to decouple the complexity of the machine from the number of states on which they can operate.</p><div><figure><figcaption><b>Fig. 2</b></figcaption><div><div><a href="/articles/s41467-019-13232-z/figures/2"></a></div><p>Cells could provide more than logic circuits. Computer science has developed models of computation that are far more powerful than combinatorial logic, such as finite-state machines or the Turing Machine. These models are more powerful in that they allow processing of a wider range of inputs into outputs, and in many more ways, than are admissible by combinatorial logic. Similarly, living systems have evolved a variety of computational processes to allow cells to process information. A simple model, used extensively as the basis for engineering combinatorial logic circuits in cells, is the standard representation of the central dogma (CD) of molecular biology. However, this model does not incorporate core cellular mechanisms such as metabolism, or processes such as evolution, which may provide possibilities for building more powerful, but as yet unknown, models</p></div><p><a href="/articles/s41467-019-13232-z/figures/2">Full size image</a></p></figure></div><p>Modern digital computers, as with any real physical system<sup><a href="/articles/s41467-019-13232-z#ref-CR55">55</a></sup>, lack the unbounded state space required for implementing a Turing Machine. However, their state space is so vast as to make them practically indistinguishable from implementations of Turing Machines (consider that even systems with an extremely modest 1 MB of storage have at least \(2^{10^6 \!\times\! 8}\) states). It is therefore unlikely that cellular computing will outperform silicon purely on the basis of enabling more complex stateful computations. Nevertheless, synthetic biology has already engineered successful in vivo implementations of stateful computations<sup><a href="/articles/s41467-019-13232-z#ref-CR10">10</a>,<a href="/articles/s41467-019-13232-z#ref-CR56">56</a>,<a href="/articles/s41467-019-13232-z#ref-CR57">57</a></sup>, and there also exists significant theoretical work linking stateful models of computation to biological implementations<sup><a href="/articles/s41467-019-13232-z#ref-CR58">58</a>,<a href="/articles/s41467-019-13232-z#ref-CR59">59</a></sup>. This work is undoubtedly of considerable importance for a broad range of synthetic biology applications, and since biological systems naturally engage in stateful computation<sup><a href="#ref-CR60">60</a>,<a href="#ref-CR61">61</a>,<a href="/articles/s41467-019-13232-z#ref-CR62">62</a></sup>, statefulness or “memory” will likely be a key component in future engineered biocomputations of any significant complexity.</p></div></div><div><h2>Noise permits stochastic and non-deterministic computations</h2><div><p>Combinatorial logic circuits, FSMs and TMs model deterministic computations, which are essentially step-wise descriptions of mathematical functions that map inputs to outputs, where each step follows in a predetermined way from the previous step. Deterministic computation can be generalised to include stochastic and non-deterministic computation. Stochastic (or probabilistic, or randomised) computing refers to algorithms which can make random choices during their execution. Specifically, a given input may generate a number of different computational paths, each with some probability, and the cumulative probability of all such paths is equal to one. Probabilistic algorithms are a cornerstone of computer science<sup><a href="/articles/s41467-019-13232-z#ref-CR63">63</a></sup>, and are used to solve approximately, but efficiently, hard optimisation problems for which deterministic algorithms would be intractable. One of the most important algorithms in systems biology, the Gillespie algorithm, is stochastic. Gillespie showed from basic quantum mechanics that a set of biochemical reactions must be understood as a stochastic process<sup><a href="/articles/s41467-019-13232-z#ref-CR64">64</a></sup>, and offered an efficient way for simulating (sampling) its dynamics<sup><a href="/articles/s41467-019-13232-z#ref-CR65">65</a></sup>. Therefore, cells may already be seen as “stochastic processors” that could provide a substrate for implementing probabilistic algorithms. Indeed, the utility of stochastic processors has already been recognised in the silicon world<sup><a href="/articles/s41467-019-13232-z#ref-CR50">50</a>,<a href="/articles/s41467-019-13232-z#ref-CR66">66</a></sup>.</p><p>In non-deterministic models of computation, as in stochastic ones, there may be many computational paths from input to output, but crucially each of these computational paths is explored simultaneously by the algorithm, with a result analogous to parallel execution of multiple distinct deterministic algorithms. While non-determinism has considerable impact on theoretical computer science, practical implementations of non-deterministic computation remain elusive. Nevertheless, algorithmic solutions to some computational tasks can be significantly easier to express as non-deterministic, and biological systems extensively exploit non-determinism, both at the population level<sup><a href="/articles/s41467-019-13232-z#ref-CR67">67</a>,<a href="/articles/s41467-019-13232-z#ref-CR68">68</a></sup> and at the scale of evolution<sup><a href="/articles/s41467-019-13232-z#ref-CR69">69</a></sup>. Perhaps more speculatively, we might also consider the role of quantum effects in biology<sup><a href="/articles/s41467-019-13232-z#ref-CR70">70</a></sup>, and whether or not these may be harnessed for the purposes of non-deterministic algorithms in biological systems.</p></div></div><div><h2>Distributed computing can exploit concurrency</h2><div><p>For some models of computation, the definition of an algorithm is “sequential”, and implies an ordering of the computational steps. Implementations of these models enforce these “sequential semantics”, because sequential execution may be a strict requirement to ensure the correctness of an algorithm. However, for certain computations, algorithms exist in which the ordering of computational steps may be relaxed, or abandoned entirely—in computer science terms, the algorithm displays a level of concurrency. In such situations, if multiple computing devices may interact and coordinate their efforts as a “distributed system”, concurrent parts of an algorithm may be executed in parallel, potentially speeding up computations significantly.</p><p>The utility of such distributed computing is not limited to performance advantages. For some problems, sequentiality is desirable, but the nature of the computing substrate makes it impractical (or even impossible) to enforce<sup><a href="/articles/s41467-019-13232-z#ref-CR71">71</a></sup>. For instance, at a fundamental level, and even within a single cell, natural cellular computation is concurrent and distributed. Computation is performed by stochastic biochemical processes—the probabilistic interactions of spatially separated molecular computing “agents”, many of which can happen in any order. Computer science has long used distributed and concurrent models of computation such as actors<sup><a href="/articles/s41467-019-13232-z#ref-CR49">49</a></sup>, Petri nets<sup><a href="/articles/s41467-019-13232-z#ref-CR51">51</a></sup>, process algebras<sup><a href="/articles/s41467-019-13232-z#ref-CR72">72</a></sup> and population protocols<sup><a href="/articles/s41467-019-13232-z#ref-CR52">52</a></sup> to describe computations in just these situations.</p></div></div><div><h2>Analogue computing allows for continuous non-binary inputs</h2><div><p>The nature of computation described so far has been digital; that is, information is represented using a set of discrete values. However, many physically relevant quantities vary continuously. Even the signals that encode binary values in electronic logic circuits are, in reality, stored as continuous-valued voltages. Such signals must be discretised in order to represent digital values. In contrast, analogue computation allows continuous signals to be used directly in the computational steps of an algorithm, and for representation of information as continuous values.</p><p>Although many cellular computations involving binary “yes/no” decisions may be interpreted as digital computations, and digital logic computations are certainly suited to applications such as biosensors, cells often exhibit graded responses to stimuli that are more appropriately viewed as analogue computations<sup><a href="/articles/s41467-019-13232-z#ref-CR62">62</a>,<a href="/articles/s41467-019-13232-z#ref-CR73">73</a></sup>. Furthermore, the biochemical processes responsible for cellular computations involve discrete interactions of discrete molecules, but are also inherently stochastic. Cellular computing may, therefore, be viewed as both digital and stochastic, or as analogue computation with noise<sup><a href="/articles/s41467-019-13232-z#ref-CR74">74</a></sup>, and the viability of the cell as a substrate for synthetic analogue computations has already been demonstrated<sup><a href="/articles/s41467-019-13232-z#ref-CR75">75</a></sup>.</p><p>Whilst some models of analogue computation such as the Blum-Shub-Smale machine<sup><a href="/articles/s41467-019-13232-z#ref-CR53">53</a></sup> or neural networks<sup><a href="/articles/s41467-019-13232-z#ref-CR46">46</a></sup>, use arbitrary precision signals to perform super-Turing computation, it is not clear whether realisations of analogue computation will be able to provide more computational power than digital computation, since physical laws forbid the existence of such an idealised computer<sup><a href="/articles/s41467-019-13232-z#ref-CR55">55</a>,<a href="/articles/s41467-019-13232-z#ref-CR76">76</a></sup>. However, for digital models of computation, the abstraction of continuous signals into digital represents a semantic gap between the formal definition and implementation of a computation. Models of analogue computation admit continuous signals, which not only narrows this semantic gap, but also allows more powerful computational primitives to be used for defining algorithms<sup><a href="/articles/s41467-019-13232-z#ref-CR77">77</a></sup>. Consequently, depending on the computation and the computing substrate, an analogue algorithm might have a more intuitive implementation, require fewer components to implement, and be considerably more energy-efficient than its digital counterpart<sup><a href="/articles/s41467-019-13232-z#ref-CR74">74</a>,<a href="/articles/s41467-019-13232-z#ref-CR75">75</a></sup>.</p></div></div><div><h2>Engineering complex cellular computing systems</h2><div><p>There are certainly deep physical connections between chemistry and electronics<sup><a href="/articles/s41467-019-13232-z#ref-CR78">78</a></sup>, but the fact remains that the cellular environment is a radically different computing substrate than silicon. Although this difference might make cells unsuitable for computational tasks traditionally dominated by conventional computers, it could also offer opportunities to explore more unconventional models of computation. Aside from gene regulation, which has been useful for engineering biological logic circuits, a number of processes and features exist in natural systems which may offer computational capabilities. Here, we identify four such resources as promising in terms of their information-processing capabilities (Fig. <a href="/articles/s41467-019-13232-z#Fig3">3</a>).</p><div><figure><figcaption><b>Fig. 3</b></figcaption><div><div><a href="/articles/s41467-019-13232-z/figures/3"></a></div><p>Cellular information-processing fundamentals that go beyond combinatorial logic circuits. <b>a</b> Whole-cell computations, merging genetic and metabolic circuits, could achieve more ambitious goals than genetic circuits alone. Cells have evolved intricate networks that make simultaneous use of the varied features of both genetic and metabolic processes. In terms of information storage, metabolism presents a volatile memory, while DNA sequences are able to store information in a more stable fashion. Coordinating the use of different types of memory is a fundamental aspect of complex computer architectures. The dynamic difference is also a potential source of complexity if coupled; metabolic reactions operate on a faster timescale relative to genetic regulatory networks. <b>b</b> Multicellular computing (right) is currently implemented by connecting the output of one strain to the input of another. Social interactions among cells (left), such as cooperation, mutualism, competition or commensalism, are not considered in general. However, social interactions are fundamental in natural communities—they provide stable architectures executing a desired computation. <b>c</b> Gene expression noise is intrinsic to living systems; the panel figure shows different patterns for gene expression. Despite the fact that all are described as being on, there are different types of expression—thus different on/off standards. <b>d</b> The cell as a general-purpose machine. As the basis for a model of computation, the central dogma of molecular biology can be expanded to include metabolism. Evolutionary processes may also be included as major forces guiding information-processing in cells, since they allow the purpose of cellular computations to adapt over time</p></div><p><a href="/articles/s41467-019-13232-z/figures/3">Full size image</a></p></figure></div></div></div><div><h2>Towards whole-cell computation</h2><div><p>Synthetic cellular computing systems have generally focussed on DNA components that are isolated from the many other processes within a cell<sup><a href="/articles/s41467-019-13232-z#ref-CR79">79</a>,<a href="/articles/s41467-019-13232-z#ref-CR80">80</a></sup>. However, evolution has shaped intricate information-processing networks whose function emerges from the interplay between many layers of the cellular machinery<sup><a href="/articles/s41467-019-13232-z#ref-CR81">81</a></sup>. For example, bacteria adapt to nutrient fluctuations by sensing extracellular cues, transducing such signals to the genetic machinery, and ultimately adapting their metabolic state to make maximal use of carbon sources. This requires a careful whole-cell orchestration of trafficking processes at the levels of membrane, cellular signalling pathways, gene expression programmes and metabolic activity.</p><p>In a similar fashion, synthetic systems that exploit whole-cell interactions offer exciting opportunities to expand the range of computational tasks that can be achieved with living systems. Metabolic circuits, in particular, produce analogue dynamics that could allow us to move beyond basic Boolean operations<sup><a href="/articles/s41467-019-13232-z#ref-CR82">82</a></sup>. Circuits integrating genetic programs with metabolic activity have been successfully engineered to improve the productivity of microbial cell factories<sup><a href="#ref-CR83">83</a>,<a href="#ref-CR84">84</a>,<a href="/articles/s41467-019-13232-z#ref-CR85">85</a></sup>, but their potential goes far beyond simple production. Notably, retrobiosynthesis approaches based on generic representations of reactions, known as reaction rules, expand the design space of metabolic circuits by predicting novel synthetic pathways connecting metabolism and gene expression<sup><a href="#ref-CR86">86</a>,<a href="#ref-CR87">87</a>,<a href="/articles/s41467-019-13232-z#ref-CR88">88</a></sup>. Machine-learning is increasingly being applied by such retrosynthesis algorithms to select the best candidate reactions in the search through the chemical space<sup><a href="/articles/s41467-019-13232-z#ref-CR89">89</a>,<a href="/articles/s41467-019-13232-z#ref-CR90">90</a></sup>.</p><p>Moreover, experimental and theoretical work has shown that gene expression noise can permeate to metabolism<sup><a href="/articles/s41467-019-13232-z#ref-CR68">68</a>,<a href="/articles/s41467-019-13232-z#ref-CR91">91</a></sup>, suggesting the possibility of processing information using metabolic heterogeneity. The interplay between gene expression and metabolism can be conceptualised in terms of memory systems employed in most computer architectures. These have a long-term static memory, conceptually similar to information stored in DNA, and a short-term volatile memory, akin to the fast dynamics of metabolism (Fig. <a href="/articles/s41467-019-13232-z#Fig3">3a</a>). Computer science has developed efficient techniques for managing data flows across these two memories to exploit their characteristic timescales. There is some evidence that cells also exploit such differing timescales to their benefit<sup><a href="/articles/s41467-019-13232-z#ref-CR62">62</a></sup>, and, ultimately, the ability to encode signals in different frequency domains may allow us to move from classic Boolean abstractions to more complex coding systems.</p><p>Whole-cell computation presents major challenges because, as the size of synthetic circuit grows, so does their footprint on the cellular host. Synthetic circuits do not work in isolation, but continuously draw resources away from vital functions of the host<sup><a href="/articles/s41467-019-13232-z#ref-CR92">92</a></sup>. These resources include energy, polymerases for transcription, ribosomes for translation, enzymatic co-factors, and so on, the depletion of which has a negative impact on native processes. This is commonly known as the cellular burden, and has gathered substantial attention in the community<sup><a href="/articles/s41467-019-13232-z#ref-CR93">93</a></sup>. Recent work has aimed at identifying relevant sources of burden imposed by synthetic constructs<sup><a href="/articles/s41467-019-13232-z#ref-CR94">94</a>,<a href="/articles/s41467-019-13232-z#ref-CR95">95</a></sup>. Together with increasingly powerful mathematical models for cell physiology<sup><a href="/articles/s41467-019-13232-z#ref-CR96">96</a>,<a href="/articles/s41467-019-13232-z#ref-CR97">97</a></sup>, these experimental efforts are paving the way for accurate prediction<sup><a href="/articles/s41467-019-13232-z#ref-CR98">98</a></sup> and control of burden<sup><a href="/articles/s41467-019-13232-z#ref-CR99">99</a></sup>, which will enable the construction of complex circuitry that takes full advantage of the cellular machinery<sup><a href="/articles/s41467-019-13232-z#ref-CR100">100</a></sup>.</p></div></div><div><h2>The power of multicellular consortia</h2><div><p>The burden imposed by synthetic biological constructs places a fundamental ceiling on the information processing capacity of a single cell. In order to execute larger and more complex computations, living systems harness the capabilities of multicellular ensembles, such as the vast neural networks in the brain. Distributing computational demands across a population of specialised cells lowers the burden on each individual cell, and offers a way to more easily scale the complexity of the computations being performed. Such scalability is uniquely fostered in biological systems by the inherent ability of living cells to self-replicate. Similar distributed approaches have been employed in engineered biological systems, where an algorithm is spread across a consortium of different microbes that are able to communicate and interact (Fig. <a href="/articles/s41467-019-13232-z#Fig3">3b</a>). Many theoretical<sup><a href="#ref-CR101">101</a>,<a href="#ref-CR102">102</a>,<a href="#ref-CR103">103</a>,<a href="#ref-CR104">104</a>,<a href="/articles/s41467-019-13232-z#ref-CR105">105</a></sup> and experimental<sup><a href="#ref-CR106">106</a>,<a href="#ref-CR107">107</a>,<a href="#ref-CR108">108</a>,<a href="#ref-CR109">109</a>,<a href="#ref-CR110">110</a>,<a href="#ref-CR111">111</a>,<a href="/articles/s41467-019-13232-z#ref-CR112">112</a></sup> examples demonstrate the benefits of distributing computation in this way, as well as a growing number of tools for their simulation<sup><a href="#ref-CR113">113</a>,<a href="#ref-CR114">114</a>,<a href="#ref-CR115">115</a>,<a href="#ref-CR116">116</a>,<a href="#ref-CR117">117</a>,<a href="#ref-CR118">118</a>,<a href="#ref-CR119">119</a>,<a href="/articles/s41467-019-13232-z#ref-CR120">120</a></sup> and assembly in living cells<sup><a href="/articles/s41467-019-13232-z#ref-CR121">121</a>,<a href="/articles/s41467-019-13232-z#ref-CR122">122</a></sup>.</p><p>Although the development of engineered multicellular consortia is possible with current technologies, their structure is often fragile, and their information-processing capabilities are dwarfed by microbial communities found in nature<sup><a href="/articles/s41467-019-13232-z#ref-CR123">123</a></sup>. A key difference in naturally-occurring systems is that extensive resources and diverse mechanisms are used to establish and coordinate the complex social behaviours of a communityʼs participants<sup><a href="/articles/s41467-019-13232-z#ref-CR123">123</a></sup>. Social relationships such as cooperation, mutualism, competition and commensalism are used concurrently to drive a required community structure that can potentially change over time in response to the environment. Advances in our ability to control cell-to-cell interactions, either through spatial patterning of cell populations<sup><a href="/articles/s41467-019-13232-z#ref-CR112">112</a></sup> and/or orthogonal communication channels<sup><a href="/articles/s41467-019-13232-z#ref-CR121">121</a>,<a href="/articles/s41467-019-13232-z#ref-CR124">124</a></sup>, will be crucial to future developments in this area.</p><p>A feature of multicellular consortia that pushes us beyond the capabilities of classical electronic computers is their highly flexible and re-configurable nature<sup><a href="/articles/s41467-019-13232-z#ref-CR125">125</a></sup>. In computer science, a computer architecture describes the structural relationship between different components of a system (e.g. the processor and memory) and constrains how algorithms run on the system. A program compiled for one type of computer architecture may not be executable by another due to these physical differences. The architecture of most electronic computers is fixed during a computation and has been honed to perform primitive digital operations in quick succession, guided by a set of instructions (the code). While this architecture is general enough for tackling many types of task, its static architecture makes it sub-optimal for most of them. In a cellular consortium, such a severe trade-off between flexibility and optimality (e.g. in regards to energy consumption or speed) need not exist, as the cellular community can dynamically change its physical composition and the interactions present to produce a “living architecture” that better matches the problem at hand. Furthermore, such reconfiguration is possible even during a computation itself, offering a level of control and flexibility that electronic computers are unable to match. Harnessing these unique capabilities will offer synthetic biologists new approaches to solving problems and require us to rethink what a computer architecture can be<sup><a href="/articles/s41467-019-13232-z#ref-CR126">126</a></sup>.</p></div></div><div><h2>Encoding signals using gene expression noise</h2><div><p>Combinatorial logic, which relies on well separated on/off signals to encode information, constitutes a valuable framework with which to understand and build genetic circuits. Even if molecular signals (for example, a transcription factor that down-regulates a promoter) do not have absolute and constant values, the notion of a promoter being repressed or not (thus being binary) is intuitive. Nevertheless, the use of Boolean logic for engineering cellular circuits is often challenged by the fact that molecular signals are intrinsically noisy, and therefore stochastic. Each signal will have different on/off values (Fig. <a href="/articles/s41467-019-13232-z#Fig3">3c</a>), and not all are compatible, which makes building a large combinatorial circuit a significant challenge<sup><a href="/articles/s41467-019-13232-z#ref-CR127">127</a></sup>. Combinatorial logic is, therefore, a good example of how a given theoretical model of computation may be easily implemented with one physical toolkit (electronic), but not with another (molecular).</p><p>The voltage that runs through electronic wires is also noisy, but computer engineers overcame this problem by arranging for thresholds at the input and output of logic gates, so that analogue values could be abstracted into two unique values: 0 and 1. In contrast to this, living systems have evolved to benefit from signal variability. Stochasticity has been shown to be useful in coordinating the expression of large sets of genes<sup><a href="/articles/s41467-019-13232-z#ref-CR128">128</a></sup>, in producing the phenotypic variability that allows for bet-hedging strategies that promote survival in fluctuating environments<sup><a href="/articles/s41467-019-13232-z#ref-CR67">67</a>,<a href="/articles/s41467-019-13232-z#ref-CR129">129</a></sup>, and as a key component of evolution under tight selection criteria<sup><a href="/articles/s41467-019-13232-z#ref-CR69">69</a></sup>. Therefore, models of computation incorporating stochasticity would seem to be necessary to best fit the intrinsic properties of living systems.</p><p>Unlike silicon computing devices, where noise is a consequence of random signal fluctuations, cellular systems are capable of encoding important information into noise patterns. For example, the change in gene expression noise according to intracellular physical distances<sup><a href="/articles/s41467-019-13232-z#ref-CR130">130</a></sup> reveals information about the structural architecture of the cell. Also, noisy patterns in the cellular machinery of <i>Staphylococcus aureus</i> (that lead to different infectious cell types) originate in upstream molecular events<sup><a href="/articles/s41467-019-13232-z#ref-CR131">131</a></sup>. These examples, among others<sup><a href="/articles/s41467-019-13232-z#ref-CR75">75</a></sup>, highlight the fact that the shape of non-digital biological signals is used to effectively transmit information. Therefore, the challenge is to use noise for implementing computations — an area where cellular computers clearly outperform conventional ones. In the meantime, current efforts in the discretisation<sup><a href="/articles/s41467-019-13232-z#ref-CR132">132</a></sup>, stabilisation<sup><a href="/articles/s41467-019-13232-z#ref-CR133">133</a>,<a href="/articles/s41467-019-13232-z#ref-CR134">134</a></sup> and reusability<sup><a href="/articles/s41467-019-13232-z#ref-CR135">135</a></sup> of noisy signals may help to understand, and harness, the dynamic complexity of molecular interactions.</p></div></div><div><h2>Evolution as an information-processing mechanism</h2><div><p>Evolutionary computing is a field within computer science that develops and applies algorithms inspired by Darwinian evolution<sup><a href="/articles/s41467-019-13232-z#ref-CR136">136</a></sup>. Different implementations of this idea exist, such as genetic algorithms, evolutionary strategies or genetic programming, but the underlying principles are similar: a set of candidate solutions to a problem (an initial population) compete under some pre-defined fitness criteria, and the fittest individuals are selected to form the next generation (via crossover and/or mutation). An important advantage of these techniques is that they allow for the dynamic optimisation of solutions throughout potentially vast search spaces.</p><p>Both computer scientists and living systems use evolutionary algorithms to generate algorithmic solutions. Evolutionary processes have also been used to design biomolecules<sup><a href="/articles/s41467-019-13232-z#ref-CR137">137</a>,<a href="/articles/s41467-019-13232-z#ref-CR138">138</a></sup>, libraries of biological components<sup><a href="/articles/s41467-019-13232-z#ref-CR139">139</a></sup> and even to evolve non-functional genetic circuits into functional ones<sup><a href="/articles/s41467-019-13232-z#ref-CR140">140</a></sup>. Despite this, evolutionary processes are often omitted when engineering computing circuits in living cells. Harnessing the power of such information-processing mechanisms for predefined functions seems to be difficult, and the rational engineering of autonomous evolutionary computing in living cells is still an overarching challenge.</p><p>In order to start addressing this challenge, it will be important to formalise the effects of evolutionary dynamics on the flow of genetic information. A potential initial step would be to expand on the standard representation of the central dogma (CD) of molecular biology to include evolutionary dynamics, in an attempt to describe the model of computation of a living cell (Fig. <a href="/articles/s41467-019-13232-z#Fig3">3d</a>). Expansion of the CD-based model is not a new idea; for example, the inclusion of metabolic processes has previously been suggested<sup><a href="/articles/s41467-019-13232-z#ref-CR141">141</a></sup>, since, as evidenced above in “Towards whole-cell computation”, metabolism is a crucial omission from the point of view of information processing. A complete model of the flow of genetic information at a given point in time needs to include both genetic and metabolic processes, and dynamic models of computation inside living cells should include evolutionary processes that operate on genetic information.</p><p>Theoretical models of computation may find valuable and perhaps novel implementations within this dynamic representation of the CD. Recent developments in optogenetics are promising to this end, since these show how genetic elements dynamically shape their response in relation to external signals<sup><a href="/articles/s41467-019-13232-z#ref-CR142">142</a></sup>. Importantly, these studies linking environmental signals to intracellular responses in a predictable way, as well as directed evolution efforts<sup><a href="/articles/s41467-019-13232-z#ref-CR143">143</a></sup>, are undertaken in tightly controlled systems. However, the mechanisms that allow a cell to thrive in challenging and dynamic environments are largely unpredictable. For problems like bio-remediation which intrinsically involve ever-changing environments, natural cellular computers clearly show superiority compared to conventional ones.</p></div></div><div><h2>Applications of cellular computing systems</h2><div><p>As already discussed, cellular computing is unlikely to compete with conventional computers in domains for which the latter are specifically engineered. Although future biological systems may offer competitive performance in related areas such as data storage<sup><a href="/articles/s41467-019-13232-z#ref-CR144">144</a></sup>, the benefits are largely limited to the exploitation of material factors such as miniaturisation and longevity of components.</p><p>The identification of promising applications for cellular computing has been largely guided by the observation that living systems operate best in application domains that are not easily reachable by conventional computers. Successes in bio-remediation<sup><a href="/articles/s41467-019-13232-z#ref-CR145">145</a></sup>, bio-production<sup><a href="/articles/s41467-019-13232-z#ref-CR146">146</a></sup> and targeted therapeutics<sup><a href="/articles/s41467-019-13232-z#ref-CR147">147</a></sup> indicate that this is indeed a fruitful line of inquiry. Nevertheless, the implementation of conventional computations with unconventional computing substrates does not, in and of itself, constitute cellular supremacy. Rather, supremacy must be derived from the fact that the type of computation performed by a conventional computer is qualitatively different to that executed by living systems. Current implementations of computations within living cells are generally based on combinatorial or sequential logic circuits mapped onto equivalent genetic circuits; while these are useful metaphors for both understanding and engineering living systems, digital logic is not easily implemented using a cellular substrate. Furthermore, logic circuits offer a relatively bland computational palette compared to the richness of biology. For this reason, future developments in cellular computing should focus on models of computation that both accommodate and exploit the natural abilities of the cell, and avoid forcing biological systems into artificial (and often unsuitable) architectures<sup><a href="/articles/s41467-019-13232-z#ref-CR148">148</a></sup>.</p><p>This does not mean that cellular computing must necessarily “reinvent the wheel” when it comes to models of computation. Living systems share many characteristics with in vitro platforms for computation, and as well as the considerable body of theoretical work concerning molecular computing, cellular computing may draw on cell-free systems as a practical resource for faster prototyping with a greater degree of control<sup><a href="#ref-CR149">149</a>,<a href="#ref-CR150">150</a>,<a href="/articles/s41467-019-13232-z#ref-CR151">151</a></sup>. Furthermore, the relationship between computer science and natural computing is often synergistic. As described earlier, models of computation that transcend logic circuits are available which have yet to be explored by cellular computing to any great extent. In return, biological systems offer computational features that are (and are expected to remain) unavailable to silicon implementations of existing computational models. It is at this intersection that exciting opportunities for cellular supremacy emerge. For example, in the past decade it has become increasingly clear that a number of biological processes show quantum mechanical properties<sup><a href="/articles/s41467-019-13232-z#ref-CR152">152</a>,<a href="/articles/s41467-019-13232-z#ref-CR153">153</a></sup>. In particular, there is strong experimental evidence that long-lived quantum coherence is involved in photosynthesis<sup><a href="/articles/s41467-019-13232-z#ref-CR154">154</a></sup>, and that quantum tunnelling is active in enzyme catalysis<sup><a href="/articles/s41467-019-13232-z#ref-CR155">155</a></sup>. Since most quantum computing devices are built and run under stringent environmental conditions (at temperatures approaching absolute zero), the opportunity to control quantum effects in a biological system that “runs” at room temperature, through the emergence of a “quantum synthetic biology”, could turn out to be a game changer in the quantum supremacy race. More to the point, realising models of quantum computation<sup><a href="/articles/s41467-019-13232-z#ref-CR156">156</a></sup> using quantum biology could yield a cellular computer capable of a radically different kind of computation than silicon<sup><a href="/articles/s41467-019-13232-z#ref-CR153">153</a></sup>.</p><p>Although we have, until now, focussed primarily on bacterial cells, there does, of course, exist a multiplicity of cell types that possess rich and complex computational capabilities. For example, plants can respond to environmental signals and stresses in a way that is reminiscent of signal processing in neural networks (the so-called “plant perceptron”)<sup><a href="/articles/s41467-019-13232-z#ref-CR157">157</a></sup>. Cultured neuronal cells have been used to control flight simulators<sup><a href="/articles/s41467-019-13232-z#ref-CR158">158</a></sup> and robots<sup><a href="/articles/s41467-019-13232-z#ref-CR159">159</a></sup>, and slime mould has a rich repertoire of spatial computing capabilities<sup><a href="/articles/s41467-019-13232-z#ref-CR160">160</a></sup>. Additionally, we do not dismiss the possibility of “hybrid” architectures, in which cellular systems are interfaced to more traditional, silicon-based machines. Such connections may allow for subtle and sensitive adjustments to cell state, for example<sup><a href="/articles/s41467-019-13232-z#ref-CR161">161</a></sup>, but these hybrid systems will still fundamentally rely on the properties of the living material.</p><p>As we have already argued, natural cellular computing operates at vast scales, in a distributed manner, and in the presence of considerable noise. Consequently, biological metaphors have served as inspirations for models of amorphous computation, for which cellular computing is a promising implementation technology<sup><a href="/articles/s41467-019-13232-z#ref-CR162">162</a></sup>, especially at scales inaccessible to silicon. Robotics has also drawn inspiration from biological computation, particularly in relation to morphological computing, which takes advantage of the physical properties of computing agents in order to achieve more efficient computations<sup><a href="/articles/s41467-019-13232-z#ref-CR163">163</a></sup>. By using intrinsic physical properties of the computational substrate to “outsource” parts of the computation, increasingly complex computations can be carried out whilst maintaining relatively simplistic control structures<sup><a href="/articles/s41467-019-13232-z#ref-CR164">164</a></sup>. Living systems are an ideal implementation technology for morphological computation, since they not only compute solutions to individual instances of problems, but continuously compute and adapt in order to embody an efficient general solution. As we have previously argued, conventional silicon computers have inflexible architectures by comparison, which must sacrifice efficiency for generality. These qualitative differences between cellular and conventional computing suggest that applications such as terraforming and smart material production may remain beyond the reach of silicon computers, but in contrast, strategies for both applications based on living technologies have already been proposed<sup><a href="/articles/s41467-019-13232-z#ref-CR165">165</a>,<a href="/articles/s41467-019-13232-z#ref-CR166">166</a></sup>.</p><p>In this perspective, we have championed the notion of cellular supremacy in an attempt to focus attention on the high-impact areas in which synthetic biology can have a truly transformational effect. We call on the community to consider cellular supremacy as a framing device for future work, and to explore in a systematic fashion how it may be established. By accepting the idea of cellular supremacy, we naturally acknowledge the richness and power of living systems. And by ceding a degree of control to biology, we may yet open up a much wider range of applications and perspectives on information processing in nature.</p></div></div>
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 <i>Nat Commun</i> <b>10</b>, 5250 (2019). https://doi.org/10.1038/s41467-019-13232-z</p><p><a href="https://citation-needed.springer.com/v2/references/10.1038/s41467-019-13232-z?format=refman&amp;flavour=citation">Download citation</a></p><ul><li><p>Received: <time>08 July 2019</time></p></li><li><p>Accepted: <time>29 October 2019</time></p></li><li><p>Published: <time>20 November 2019</time></p></li><li><p><abbr>DOI</abbr>: https://doi.org/10.1038/s41467-019-13232-z</p></li></ul></div></div></div>
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 * Published: 20 November 2019

 Pathways to cellular supremacy in biocomputing

 * Lewis Grozinger1,
 * Martyn Amos ORCID: orcid.org/0000-0003-1680-55352,
 * Thomas E. Gorochowski ORCID: orcid.org/0000-0003-1702-786X3,4,
 * Pablo Carbonell ORCID: orcid.org/0000-0002-0993-56255,
 * Diego A. Oyarzún ORCID: orcid.org/0000-0002-0381-52786,7,
 * Ruud Stoof ORCID: orcid.org/0000-0001-9456-99751,
 * Harold Fellermann ORCID: orcid.org/0000-0001-5861-19451,
 * Paolo Zuliani1,
 * Huseyin Tas ORCID: orcid.org/0000-0003-4804-22378 &
 * …
 * Angel Goñi-Moreno ORCID: orcid.org/0000-0002-2097-25071
 Show authors

 Nature Communications volume 10, Article number: 5250 ( 2019 ) Cite this article

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 * DNA computing and cryptography
 * Synthetic biology

 Abstract

 Synthetic biology uses living cells as the substrate for performing human-defined computations. Many current implementations of cellular computing are based on the “genetic circuit” metaphor, an approximation of the operation of silicon-based computers. Although this conceptual mapping has been relatively successful, we argue that it fundamentally limits the types of computation that may be engineered inside the cell, and fails to exploit the rich and diverse functionality available in natural living systems. We propose the notion of “cellular supremacy” to focus attention on domains in which biocomputing might offer superior performance over traditional computers. We consider potential pathways toward cellular supremacy, and suggest application areas in which it may be found.

 Introduction

 Synthetic biology1,2 is a rapidly growing field of research which applies engineering concepts and principles to the rational engineering of living systems, such as bacteria and yeast. The promise of synthetic biology lies in its potential to provide new substrates for computation3, production4, pollution control5 and medical diagnosis6 (among many areas), and to harness the “wetware”7 inside the living cell for human-defined purposes. Synthetic biology is set to become a significant component of the multi-billion dollar bio-economy8, but, in addition to tangible benefits such as cheaper drug production or more precise bio-sensing, many researchers in the field believe that the very process of re-engineering life will both require and inform a reexamination of our fundamental understanding of cellular processes9. This position underpins the current paper.

 Much existing work in synthetic biology is concerned with the construction of “circuits” of biological components (such as genes and proteins) that receive some input (either endogenous, or exogenous), perform some transformation of that input, and produce a result determined by the “rules” encoded in the circuit. This input-transform-output pipeline is entirely consistent with the notion of a computation, as traditionally defined, and it is wholly unsurprising that synthetic biology has, so far, largely adhered to the genetic “logic circuit” model (groundbreaking examples include the genetic toggle switch10 and the “repressilator”11).

 The roots of this biological circuit metaphor date back to the mechanistic view of the cell; the idea that living systems may be viewed as machines, which, in turn, can be traced as far back as Descartes (and beyond). Characterisations of the cell as a “factory”, a “little engine”, and a “chemical machine” dominated early discourse in cell biology, and the post-war development of cybernetics and computer science, combined with the emergence of molecular biology, provided significant support for this conceptual interpretation of living systems12.

 The “machine model” of the cell was further cemented by the pioneering work of Jacob and Monod, which established that the lac operon13 facilitates metabolic switching within E. coli in a manner that may be interpreted as a simple Boolean circuit. In his highly influential popular book, Chance and Necessity (a chapter of which is titled “Microscopic Cybernetics”), Monod made explicit the connection between biological processes and the basis of electronic circuits:

 “The logic of biological regulatory systems abides not by Hegelian laws but, like the workings of computers, by the propositional algebra of George Boole.”14

 Since the discovery of the lac operon, the machine model has largely dominated molecular biology15, and the notion of the genome serving as a “genetic program” is still relatively common16. Of course, abstracting biological processes to the level of circuits (Boolean or otherwise) or even programs may be a necessary step in terms of making sense of their operation. Conversely, in the context of engineered biological systems, the availability of a set of well-characterised, modular and tunable components are perhaps necessary for creating controllable and predictable systems17. We emphasise here that we do not seek to overturn or abandon an extremely powerful and useful metaphor. However, it may give a misleading impression regarding the reliability and predictability of genetic circuits, compared to their electronic counterparts18. Moreover, as we argue in this paper, by restricting ourselves to the computational palette offered by (Boolean) combinatorial logic, we inherently (and seriously) limit the power and scope of synthetic biology.

 It is perhaps instructive at this point to discuss the field of molecular computing19, which many see as a conceptual precursor to synthetic biology, if not a direct predecessor. Although the notion of computing with individual atoms and molecules was attributed to Richard Feynman as early as the 1950s20, the field was only reified in 1994, when Leonard Adleman published his groundbreaking paper on computing solutions to the Hamiltonian Circuit Problem using molecular operations with strands of DNA21. At the time, a commonly-held belief was that the future promise of DNA computation22 lay in solving instances of hard computational problems that were beyond the capabilities of traditional silicon-based computers23. Much early work on producing general DNA-based computational models focussed on molecular emulation of the Boolean circuit model24,25. Discussion of the field’s overall direction was, for a time, dominated by the quest for the “killer application”, the application of DNA computing that would establish its superiority over existing computational substrates26,27. In some ways, this may be viewed as a restricted form of the search for so-called “quantum supremacy” in the quantum computing domain28.

 As the field of molecular computing evolved, it rapidly became clear that the killer application would not be found by solving large instances of computationally hard problems using any variant of Adleman’s original model. The elegance of the original solution derived from the encoding used to construct all possible paths through a given graph; vertices and edges were represented as strands of DNA that self-assembled into a collection of paths, which was then rapidly filtered in parallel using molecular manipulations to gradually extract valid solutions. Crucially, this reasonable run-time required the entire solution space for a given problem instance to be represented in an initial “test tube” at the start of the computation; the problem was to find the “needle” (valid solution(s)) in a molecular “haystack”. Essentially, the entire space of solutions was tested in polynomial time using molecular operations, but this came at the cost of having to represent the whole solution set in a single volume of liquid22. For even small problem instances, the amount of DNA required to represent all possible solutions would be astronomical; Hartmanis calculated that if Adleman’s experiment were scaled up from 7 to 200 vertices, the amount of DNA required would weigh more than the Earth29. We note, however, that this inherent time-space tradeoff would appear to hold regardless of whether the underlying substrate is DNA, silicon, or a more exotic material (with the possible exception of substrates for quantum computers30).

 Importantly, this assessment emphasised the fact that the killer application would probably not be derived from single-use, finite DNA-based systems (albeit ones that were large and potentially massively-parallel in nature). Subsequent influential work on DNA self-assembly31 and strand displacement architectures32 emulated traditional computational models such as cellular automata33 and artificial neurons34, but also took advantage of biochemical processes that provided power beyond mere miniaturisation. That is, rather than simply harnessing the potential for massively-parallel laboratory operations on large (but finite) numbers of molecules, these systems co-opted specific physical and chemical properties of the underlying substrate to generate the potential for autonomous operation and dynamic behaviour. In the context of synthetic biology, we suggest the killer application for engineered living systems will be similarly derived; one that will use features of the living system that are unavailable via traditional silicon-based substrates, for the purposes of applications that exploit autonomy and the ability to perform in uncertain environments.

 The search for cellular supremacy

 If we accept that a driving motivation for synthetic biology should be the search for a killer application, then this naturally leads to a consideration of the class of problems in which engineered living systems might offer what we call cellular supremacy (deliberately echoing the well-established notion of quantum supremacy28,35,36,37). That is, we seek a set of problem domains in which cell-based systems will offer capabilities beyond the reach of existing computers, due to cost or technological constraints. Simply put, cellular supremacy will be determined by the set of problems that biocomputers can practically solve that traditional microprocessor-based devices cannot. To identify this set of problems, we naturally focus on the “added value” that living systems offer beyond silicon-based hardware. In the following sections, we discuss a number of features of living systems that we believe give synthetic biology-based solutions a distinct “edge” over traditional computers. Importantly, we focus on aspects of computation and information transformation, rather than simply on the ability of the cell to act as a micro-scale drug precursor “production plant” or miniaturised bio-sensor. While these applications are important and valuable, they are not the main focus of the current discussion, which centres on the general computational capabilities of living systems if we go beyond the limitations of Boolean logic-based systems. In what follows, we use the term “cellular computing”38,39 to emphasise this focus on computation.

 When assessing cellular computing against traditional computing, it may be useful to frame the comparison using a scheme that emerged from an exercise on roadmapping the so-called “unconventional computation” domain. The authors identified a number of criteria or benchmarks against which emerging computational models may be measured, each accompanied by its own motivating question40. In what follows, we focus on the quality criterion, which asks the following question: Does the alternative model offer qualitatively different computation to traditional models? The authors define “quality” in terms of precision, richness, stochasticity and repeatability. Quality is concerned with the ability of the system to provide an analysis of inputs that is different to that offered by a traditional computer. If we focus on problems that fall within the remit of traditional silicon-based machines, and use existing metrics, then cellular computing will inevitably fall short on some of the other criteria identified40, such as speed and cost. However, we would argue that the real power of cell-based systems derives from the richness of their internal (and collective) architectures, and on their inherent stochasticity.

 This leads us to a consideration of the specific computationally expressive mechanisms that are available to us, and which act both inside and between living cells. In what follows we focus on five (non-exclusive) features of living cells that (we believe) offer the most potential in terms of the search for cellular supremacy; these are reconfigurability (that is, the ability to change internal state/structure in response to signals), noise (the ability to not only tolerate but to harness and exploit biological “messiness”), concurrency (the multitude and richness of inter-cellular processes that facilitate massively-parallel communication and coordination), representation (the ability to use non-binary representations for signals), and evolution (the population-level ability to seek out novel solutions to problems over time). By harnessing these capabilities, we will obtain bio-computing systems that are self-organising, self-repairing, resilient, distributed, and adaptive41.

 First, we consider aspects of computational theory that suggest how cellular computers may out-perform traditional machines. We then describe a number of features of biological systems that lend themselves to non-standard computation. Taken together, these two perspectives point towards a number of possible areas for investigation in which the killer application for cellular computing may reside.

 Information processing beyond digital logic

 The current definition of digital computation is based on the abstract model defined by Turing in the 1930s42, and the von Neumann architecture43 used to implement the types of computations performed by the Turing Machine. Although Turing’s model provides a framework for answering fundamental questions about computation, “…as soon as one leaves the comfort provided by the abundance of mathematical machinery used to describe digital computation, the world seems to be packed with paradoxes.”44.

 The important thing to note here is that although genetic circuits may appear to behave digitally, it is only the collective behaviour of a large number of inherently analogue components that give rise to this property. The fact remains that we still currently lack any formal framework within which to argue that a cell computes, according to any understood model of computation (although recent work has started to address this45).

 The nature of computation is not of purely theoretical interest. Mathematical models of computation and their properties inform the engineering of their physical manifestations (Fig. 1). Many such implementations may be possible, but all inherit the characteristics of their abstract counterparts—both their abilities and their limitations. The fact that the nature of computation within a given model is independent of its implementation allows the application of theoretical computer science to all kinds of physical systems, including cells. However, the cost of this generality is a semantic gap between the model and the physical processes that actually perform the computation. That is, mapping computations from an abstract model to a real system may be more or less difficult, depending on the model chosen. The cellular computing substrate is quite different from that of silicon computers, offering opportunities for implementing some models with a narrower semantic gap. Practical considerations such as these could guide future applications of cellular computing.

 Fig. 1

 The cell as a “physical” computer. A model of computation formally defines inputs and outputs, as well as how an algorithm processes inputs into outputs. Though the same theoretical model of computation can be physically implemented in many different ways, the nature of computation remains the same. Electronic implementations receive electronic data for inputs/outputs, while cells are able to sense/deliver a wide range of physical, chemical and biological inputs/outputs. The encoding of information into inputs can be done in different ways. Temperature, for instance, can be encoded as the height of mercury in a tube, the voltage of an electronic thermometer or the state of a DNA thermosensor

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 Conventional silicon computers are fundamentally implementations of a deterministic, centralised and digital model of computation, and they excel at computational tasks which are easily described by such models. In contrast, cellular computing has been optimised over billions of years of evolution to perform very different computational tasks, and we are unlikely to find cellular supremacy in applications such as discrete mathematics, sending emails or reading documents. However, computer science has developed models in which the nature of computation is quite different to that of the Turing Machine46,47,48,49,50,51,52,53 and computation in cells appears to share some properties with these less conventional models. With this in mind, the application of theoretical computer science to cellular computation may still present routes to cellular supremacy in those areas where the properties of cellular and traditional computation differ.

 Here, we introduce a selection of theoretical aspects of computing that impact significantly upon the nature of computation, all of which seem to be exploited in the cell for processing information, but whose theoretical implications may not be familiar to those outside the field of computer science.

 Computational states for computations over time

 Not all models of computation are equally powerful, that is, they are not equivalent in terms of the range of computations they can possibly describe. By this metric, combinatorial logic circuits are extremely weak, since the output of a circuit is purely a function of its current inputs (that is, there is no “memory”), and this severely restricts the range of computations that are possible with a single circuit. Clearly, there are models of computation more powerful than combinatorial logic, that is, models which can describe all computations that are possible with combinatorial logic circuits and more. In this regard, two extremely powerful models of computation, the Lambda calculus54 and the Turing Machine42 are particularly important. These two models are both equally powerful, but quite different in their formulation—the Lambda calculus is a model of functional computation, while the Turing Machine models stateful computation. Here we focus on stateful computation, as states enable functions that operate over time, such as memory, learning and adaptation.

 The output of stateful computations depends not only on the current input, but also on the current state, which encodes information about previous inputs that are no longer present. Models of computation such as finite state machines (FSMs) (shown in Fig. 2) exceed the capabilities of combinatorial logic, and are extremely powerful models of computation—the central processing units of modern digital computers are built from sequential logic circuits, which are implementations of FSMs. Even so, they cannot describe all computations that are available to the Turing Machine model, since they have only a bounded number of states. Turing machines are similar to FSMs, but have an unbounded memory (commonly conceptualized as a tape), which endows them with an unbounded computational state space (number of distinct configurations). Consequently, Turing Machines can compute anything that any real computer can, and in fact, computer science starts from the notion that Turing Machines (TMs) demarcate what is (and is not) computable42. From a practical perspective, these considerations of the limits of computability might be of less conceptual value than the strategy that TMs employ to decouple the complexity of the machine from the number of states on which they can operate.

 Fig. 2

 Cells could provide more than logic circuits. Computer science has developed models of computation that are far more powerful than combinatorial logic, such as finite-state machines or the Turing Machine. These models are more powerful in that they allow processing of a wider range of inputs into outputs, and in many more ways, than are admissible by combinatorial logic. Similarly, living systems have evolved a variety of computational processes to allow cells to process information. A simple model, used extensively as the basis for engineering combinatorial logic circuits in cells, is the standard representation of the central dogma (CD) of molecular biology. However, this model does not incorporate core cellular mechanisms such as metabolism, or processes such as evolution, which may provide possibilities for building more powerful, but as yet unknown, models

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 Modern digital computers, as with any real physical system55, lack the unbounded state space required for implementing a Turing Machine. However, their state space is so vast as to make them practically indistinguishable from implementations of Turing Machines (consider that even systems with an extremely modest 1 MB of storage have at least \(2^{10^6 \!\times\! 8}\) states). It is therefore unlikely that cellular computing will outperform silicon purely on the basis of enabling more complex stateful computations. Nevertheless, synthetic biology has already engineered successful in vivo implementations of stateful computations10,56,57, and there also exists significant theoretical work linking stateful models of computation to biological implementations58,59. This work is undoubtedly of considerable importance for a broad range of synthetic biology applications, and since biological systems naturally engage in stateful computation60,61,62, statefulness or “memory” will likely be a key component in future engineered biocomputations of any significant complexity.

 Noise permits stochastic and non-deterministic computations

 Combinatorial logic circuits, FSMs and TMs model deterministic computations, which are essentially step-wise descriptions of mathematical functions that map inputs to outputs, where each step follows in a predetermined way from the previous step. Deterministic computation can be generalised to include stochastic and non-deterministic computation. Stochastic (or probabilistic, or randomised) computing refers to algorithms which can make random choices during their execution. Specifically, a given input may generate a number of different computational paths, each with some probability, and the cumulative probability of all such paths is equal to one. Probabilistic algorithms are a cornerstone of computer science63, and are used to solve approximately, but efficiently, hard optimisation problems for which deterministic algorithms would be intractable. One of the most important algorithms in systems biology, the Gillespie algorithm, is stochastic. Gillespie showed from basic quantum mechanics that a set of biochemical reactions must be understood as a stochastic process64, and offered an efficient way for simulating (sampling) its dynamics65. Therefore, cells may already be seen as “stochastic processors” that could provide a substrate for implementing probabilistic algorithms. Indeed, the utility of stochastic processors has already been recognised in the silicon world50,66.

 In non-deterministic models of computation, as in stochastic ones, there may be many computational paths from input to output, but crucially each of these computational paths is explored simultaneously by the algorithm, with a result analogous to parallel execution of multiple distinct deterministic algorithms. While non-determinism has considerable impact on theoretical computer science, practical implementations of non-deterministic computation remain elusive. Nevertheless, algorithmic solutions to some computational tasks can be significantly easier to express as non-deterministic, and biological systems extensively exploit non-determinism, both at the population level67,68 and at the scale of evolution69. Perhaps more speculatively, we might also consider the role of quantum effects in biology70, and whether or not these may be harnessed for the purposes of non-deterministic algorithms in biological systems.

 Distributed computing can exploit concurrency

 For some models of computation, the definition of an algorithm is “sequential”, and implies an ordering of the computational steps. Implementations of these models enforce these “sequential semantics”, because sequential execution may be a strict requirement to ensure the correctness of an algorithm. However, for certain computations, algorithms exist in which the ordering of computational steps may be relaxed, or abandoned entirely—in computer science terms, the algorithm displays a level of concurrency. In such situations, if multiple computing devices may interact and coordinate their efforts as a “distributed system”, concurrent parts of an algorithm may be executed in parallel, potentially speeding up computations significantly.

 The utility of such distributed computing is not limited to performance advantages. For some problems, sequentiality is desirable, but the nature of the computing substrate makes it impractical (or even impossible) to enforce71. For instance, at a fundamental level, and even within a single cell, natural cellular computation is concurrent and distributed. Computation is performed by stochastic biochemical processes—the probabilistic interactions of spatially separated molecular computing “agents”, many of which can happen in any order. Computer science has long used distributed and concurrent models of computation such as actors49, Petri nets51, process algebras72 and population protocols52 to describe computations in just these situations.

 Analogue computing allows for continuous non-binary inputs

 The nature of computation described so far has been digital; that is, information is represented using a set of discrete values. However, many physically relevant quantities vary continuously. Even the signals that encode binary values in electronic logic circuits are, in reality, stored as continuous-valued voltages. Such signals must be discretised in order to represent digital values. In contrast, analogue computation allows continuous signals to be used directly in the computational steps of an algorithm, and for representation of information as continuous values.

 Although many cellular computations involving binary “yes/no” decisions may be interpreted as digital computations, and digital logic computations are certainly suited to applications such as biosensors, cells often exhibit graded responses to stimuli that are more appropriately viewed as analogue computations62,73. Furthermore, the biochemical processes responsible for cellular computations involve discrete interactions of discrete molecules, but are also inherently stochastic. Cellular computing may, therefore, be viewed as both digital and stochastic, or as analogue computation with noise74, and the viability of the cell as a substrate for synthetic analogue computations has already been demonstrated75.

 Whilst some models of analogue computation such as the Blum-Shub-Smale machine53 or neural networks46, use arbitrary precision signals to perform super-Turing computation, it is not clear whether realisations of analogue computation will be able to provide more computational power than digital computation, since physical laws forbid the existence of such an idealised computer55,76. However, for digital models of computation, the abstraction of continuous signals into digital represents a semantic gap between the formal definition and implementation of a computation. Models of analogue computation admit continuous signals, which not only narrows this semantic gap, but also allows more powerful computational primitives to be used for defining algorithms77. Consequently, depending on the computation and the computing substrate, an analogue algorithm might have a more intuitive implementation, require fewer components to implement, and be considerably more energy-efficient than its digital counterpart74,75.

 Engineering complex cellular computing systems

 There are certainly deep physical connections between chemistry and electronics78, but the fact remains that the cellular environment is a radically different computing substrate than silicon. Although this difference might make cells unsuitable for computational tasks traditionally dominated by conventional computers, it could also offer opportunities to explore more unconventional models of computation. Aside from gene regulation, which has been useful for engineering biological logic circuits, a number of processes and features exist in natural systems which may offer computational capabilities. Here, we identify four such resources as promising in terms of their information-processing capabilities (Fig. 3).

 Fig. 3

 Cellular information-processing fundamentals that go beyond combinatorial logic circuits. a Whole-cell computations, merging genetic and metabolic circuits, could achieve more ambitious goals than genetic circuits alone. Cells have evolved intricate networks that make simultaneous use of the varied features of both genetic and metabolic processes. In terms of information storage, metabolism presents a volatile memory, while DNA sequences are able to store information in a more stable fashion. Coordinating the use of different types of memory is a fundamental aspect of complex computer architectures. The dynamic difference is also a potential source of complexity if coupled; metabolic reactions operate on a faster timescale relative to genetic regulatory networks. b Multicellular computing (right) is currently implemented by connecting the output of one strain to the input of another. Social interactions among cells (left), such as cooperation, mutualism, competition or commensalism, are not considered in general. However, social interactions are fundamental in natural communities—they provide stable architectures executing a desired computation. c Gene expression noise is intrinsic to living systems; the panel figure shows different patterns for gene expression. Despite the fact that all are described as being on, there are different types of expression—thus different on/off standards. d The cell as a general-purpose machine. As the basis for a model of computation, the central dogma of molecular biology can be expanded to include metabolism. Evolutionary processes may also be included as major forces guiding information-processing in cells, since they allow the purpose of cellular computations to adapt over time

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 Towards whole-cell computation

 Synthetic cellular computing systems have generally focussed on DNA components that are isolated from the many other processes within a cell79,80. However, evolution has shaped intricate information-processing networks whose function emerges from the interplay between many layers of the cellular machinery81. For example, bacteria adapt to nutrient fluctuations by sensing extracellular cues, transducing such signals to the genetic machinery, and ultimately adapting their metabolic state to make maximal use of carbon sources. This requires a careful whole-cell orchestration of trafficking processes at the levels of membrane, cellular signalling pathways, gene expression programmes and metabolic activity.

 In a similar fashion, synthetic systems that exploit whole-cell interactions offer exciting opportunities to expand the range of computational tasks that can be achieved with living systems. Metabolic circuits, in particular, produce analogue dynamics that could allow us to move beyond basic Boolean operations82. Circuits integrating genetic programs with metabolic activity have been successfully engineered to improve the productivity of microbial cell factories83,84,85, but their potential goes far beyond simple production. Notably, retrobiosynthesis approaches based on generic representations of reactions, known as reaction rules, expand the design space of metabolic circuits by predicting novel synthetic pathways connecting metabolism and gene expression86,87,88. Machine-learning is increasingly being applied by such retrosynthesis algorithms to select the best candidate reactions in the search through the chemical space89,90.

 Moreover, experimental and theoretical work has shown that gene expression noise can permeate to metabolism68,91, suggesting the possibility of processing information using metabolic heterogeneity. The interplay between gene expression and metabolism can be conceptualised in terms of memory systems employed in most computer architectures. These have a long-term static memory, conceptually similar to information stored in DNA, and a short-term volatile memory, akin to the fast dynamics of metabolism (Fig. 3a). Computer science has developed efficient techniques for managing data flows across these two memories to exploit their characteristic timescales. There is some evidence that cells also exploit such differing timescales to their benefit62, and, ultimately, the ability to encode signals in different frequency domains may allow us to move from classic Boolean abstractions to more complex coding systems.

 Whole-cell computation presents major challenges because, as the size of synthetic circuit grows, so does their footprint on the cellular host. Synthetic circuits do not work in isolation, but continuously draw resources away from vital functions of the host92. These resources include energy, polymerases for transcription, ribosomes for translation, enzymatic co-factors, and so on, the depletion of which has a negative impact on native processes. This is commonly known as the cellular burden, and has gathered substantial attention in the community93. Recent work has aimed at identifying relevant sources of burden imposed by synthetic constructs94,95. Together with increasingly powerful mathematical models for cell physiology96,97, these experimental efforts are paving the way for accurate prediction98 and control of burden99, which will enable the construction of complex circuitry that takes full advantage of the cellular machinery100.

 The power of multicellular consortia

 The burden imposed by synthetic biological constructs places a fundamental ceiling on the information processing capacity of a single cell. In order to execute larger and more complex computations, living systems harness the capabilities of multicellular ensembles, such as the vast neural networks in the brain. Distributing computational demands across a population of specialised cells lowers the burden on each individual cell, and offers a way to more easily scale the complexity of the computations being performed. Such scalability is uniquely fostered in biological systems by the inherent ability of living cells to self-replicate. Similar distributed approaches have been employed in engineered biological systems, where an algorithm is spread across a consortium of different microbes that are able to communicate and interact (Fig. 3b). Many theoretical101,102,103,104,105 and experimental106,107,108,109,110,111,112 examples demonstrate the benefits of distributing computation in this way, as well as a growing number of tools for their simulation113,114,115,116,117,118,119,120 and assembly in living cells121,122.

 Although the development of engineered multicellular consortia is possible with current technologies, their structure is often fragile, and their information-processing capabilities are dwarfed by microbial communities found in nature123. A key difference in naturally-occurring systems is that extensive resources and diverse mechanisms are used to establish and coordinate the complex social behaviours of a communityʼs participants123. Social relationships such as cooperation, mutualism, competition and commensalism are used concurrently to drive a required community structure that can potentially change over time in response to the environment. Advances in our ability to control cell-to-cell interactions, either through spatial patterning of cell populations112 and/or orthogonal communication channels121,124, will be crucial to future developments in this area.

 A feature of multicellular consortia that pushes us beyond the capabilities of classical electronic computers is their highly flexible and re-configurable nature125. In computer science, a computer architecture describes the structural relationship between different components of a system (e.g. the processor and memory) and constrains how algorithms run on the system. A program compiled for one type of computer architecture may not be executable by another due to these physical differences. The architecture of most electronic computers is fixed during a computation and has been honed to perform primitive digital operations in quick succession, guided by a set of instructions (the code). While this architecture is general enough for tackling many types of task, its static architecture makes it sub-optimal for most of them. In a cellular consortium, such a severe trade-off between flexibility and optimality (e.g. in regards to energy consumption or speed) need not exist, as the cellular community can dynamically change its physical composition and the interactions present to produce a “living architecture” that better matches the problem at hand. Furthermore, such reconfiguration is possible even during a computation itself, offering a level of control and flexibility that electronic computers are unable to match. Harnessing these unique capabilities will offer synthetic biologists new approaches to solving problems and require us to rethink what a computer architecture can be126.

 Encoding signals using gene expression noise

 Combinatorial logic, which relies on well separated on/off signals to encode information, constitutes a valuable framework with which to understand and build genetic circuits. Even if molecular signals (for example, a transcription factor that down-regulates a promoter) do not have absolute and constant values, the notion of a promoter being repressed or not (thus being binary) is intuitive. Nevertheless, the use of Boolean logic for engineering cellular circuits is often challenged by the fact that molecular signals are intrinsically noisy, and therefore stochastic. Each signal will have different on/off values (Fig. 3c), and not all are compatible, which makes building a large combinatorial circuit a significant challenge127. Combinatorial logic is, therefore, a good example of how a given theoretical model of computation may be easily implemented with one physical toolkit (electronic), but not with another (molecular).

 The voltage that runs through electronic wires is also noisy, but computer engineers overcame this problem by arranging for thresholds at the input and output of logic gates, so that analogue values could be abstracted into two unique values: 0 and 1. In contrast to this, living systems have evolved to benefit from signal variability. Stochasticity has been shown to be useful in coordinating the expression of large sets of genes128, in producing the phenotypic variability that allows for bet-hedging strategies that promote survival in fluctuating environments67,129, and as a key component of evolution under tight selection criteria69. Therefore, models of computation incorporating stochasticity would seem to be necessary to best fit the intrinsic properties of living systems.

 Unlike silicon computing devices, where noise is a consequence of random signal fluctuations, cellular systems are capable of encoding important information into noise patterns. For example, the change in gene expression noise according to intracellular physical distances130 reveals information about the structural architecture of the cell. Also, noisy patterns in the cellular machinery of Staphylococcus aureus (that lead to different infectious cell types) originate in upstream molecular events131. These examples, among others75, highlight the fact that the shape of non-digital biological signals is used to effectively transmit information. Therefore, the challenge is to use noise for implementing computations — an area where cellular computers clearly outperform conventional ones. In the meantime, current efforts in the discretisation132, stabilisation133,134 and reusability135 of noisy signals may help to understand, and harness, the dynamic complexity of molecular interactions.

 Evolution as an information-processing mechanism

 Evolutionary computing is a field within computer science that develops and applies algorithms inspired by Darwinian evolution136. Different implementations of this idea exist, such as genetic algorithms, evolutionary strategies or genetic programming, but the underlying principles are similar: a set of candidate solutions to a problem (an initial population) compete under some pre-defined fitness criteria, and the fittest individuals are selected to form the next generation (via crossover and/or mutation). An important advantage of these techniques is that they allow for the dynamic optimisation of solutions throughout potentially vast search spaces.

 Both computer scientists and living systems use evolutionary algorithms to generate algorithmic solutions. Evolutionary processes have also been used to design biomolecules137,138, libraries of biological components139 and even to evolve non-functional genetic circuits into functional ones140. Despite this, evolutionary processes are often omitted when engineering computing circuits in living cells. Harnessing the power of such information-processing mechanisms for predefined functions seems to be difficult, and the rational engineering of autonomous evolutionary computing in living cells is still an overarching challenge.

 In order to start addressing this challenge, it will be important to formalise the effects of evolutionary dynamics on the flow of genetic information. A potential initial step would be to expand on the standard representation of the central dogma (CD) of molecular biology to include evolutionary dynamics, in an attempt to describe the model of computation of a living cell (Fig. 3d). Expansion of the CD-based model is not a new idea; for example, the inclusion of metabolic processes has previously been suggested141, since, as evidenced above in “Towards whole-cell computation”, metabolism is a crucial omission from the point of view of information processing. A complete model of the flow of genetic information at a given point in time needs to include both genetic and metabolic processes, and dynamic models of computation inside living cells should include evolutionary processes that operate on genetic information.

 Theoretical models of computation may find valuable and perhaps novel implementations within this dynamic representation of the CD. Recent developments in optogenetics are promising to this end, since these show how genetic elements dynamically shape their response in relation to external signals142. Importantly, these studies linking environmental signals to intracellular responses in a predictable way, as well as directed evolution efforts143, are undertaken in tightly controlled systems. However, the mechanisms that allow a cell to thrive in challenging and dynamic environments are largely unpredictable. For problems like bio-remediation which intrinsically involve ever-changing environments, natural cellular computers clearly show superiority compared to conventional ones.

 Applications of cellular computing systems

 As already discussed, cellular computing is unlikely to compete with conventional computers in domains for which the latter are specifically engineered. Although future biological systems may offer competitive performance in related areas such as data storage144, the benefits are largely limited to the exploitation of material factors such as miniaturisation and longevity of components.

 The identification of promising applications for cellular computing has been largely guided by the observation that living systems operate best in application domains that are not easily reachable by conventional computers. Successes in bio-remediation145, bio-production146 and targeted therapeutics147 indicate that this is indeed a fruitful line of inquiry. Nevertheless, the implementation of conventional computations with unconventional computing substrates does not, in and of itself, constitute cellular supremacy. Rather, supremacy must be derived from the fact that the type of computation performed by a conventional computer is qualitatively different to that executed by living systems. Current implementations of computations within living cells are generally based on combinatorial or sequential logic circuits mapped onto equivalent genetic circuits; while these are useful metaphors for both understanding and engineering living systems, digital logic is not easily implemented using a cellular substrate. Furthermore, logic circuits offer a relatively bland computational palette compared to the richness of biology. For this reason, future developments in cellular computing should focus on models of computation that both accommodate and exploit the natural abilities of the cell, and avoid forcing biological systems into artificial (and often unsuitable) architectures148.

 This does not mean that cellular computing must necessarily “reinvent the wheel” when it comes to models of computation. Living systems share many characteristics with in vitro platforms for computation, and as well as the considerable body of theoretical work concerning molecular computing, cellular computing may draw on cell-free systems as a practical resource for faster prototyping with a greater degree of control149,150,151. Furthermore, the relationship between computer science and natural computing is often synergistic. As described earlier, models of computation that transcend logic circuits are available which have yet to be explored by cellular computing to any great extent. In return, biological systems offer computational features that are (and are expected to remain) unavailable to silicon implementations of existing computational models. It is at this intersection that exciting opportunities for cellular supremacy emerge. For example, in the past decade it has become increasingly clear that a number of biological processes show quantum mechanical properties152,153. In particular, there is strong experimental evidence that long-lived quantum coherence is involved in photosynthesis154, and that quantum tunnelling is active in enzyme catalysis155. Since most quantum computing devices are built and run under stringent environmental conditions (at temperatures approaching absolute zero), the opportunity to control quantum effects in a biological system that “runs” at room temperature, through the emergence of a “quantum synthetic biology”, could turn out to be a game changer in the quantum supremacy race. More to the point, realising models of quantum computation156 using quantum biology could yield a cellular computer capable of a radically different kind of computation than silicon153.

 Although we have, until now, focussed primarily on bacterial cells, there does, of course, exist a multiplicity of cell types that possess rich and complex computational capabilities. For example, plants can respond to environmental signals and stresses in a way that is reminiscent of signal processing in neural networks (the so-called “plant perceptron”)157. Cultured neuronal cells have been used to control flight simulators158 and robots159, and slime mould has a rich repertoire of spatial computing capabilities160. Additionally, we do not dismiss the possibility of “hybrid” architectures, in which cellular systems are interfaced to more traditional, silicon-based machines. Such connections may allow for subtle and sensitive adjustments to cell state, for example161, but these hybrid systems will still fundamentally rely on the properties of the living material.

 As we have already argued, natural cellular computing operates at vast scales, in a distributed manner, and in the presence of considerable noise. Consequently, biological metaphors have served as inspirations for models of amorphous computation, for which cellular computing is a promising implementation technology162, especially at scales inaccessible to silicon. Robotics has also drawn inspiration from biological computation, particularly in relation to morphological computing, which takes advantage of the physical properties of computing agents in order to achieve more efficient computations163. By using intrinsic physical properties of the computational substrate to “outsource” parts of the computation, increasingly complex computations can be carried out whilst maintaining relatively simplistic control structures164. Living systems are an ideal implementation technology for morphological computation, since they not only compute solutions to individual instances of problems, but continuously compute and adapt in order to embody an efficient general solution. As we have previously argued, conventional silicon computers have inflexible architectures by comparison, which must sacrifice efficiency for generality. These qualitative differences between cellular and conventional computing suggest that applications such as terraforming and smart material production may remain beyond the reach of silicon computers, but in contrast, strategies for both applications based on living technologies have already been proposed165,166.

 In this perspective, we have championed the notion of cellular supremacy in an attempt to focus attention on the high-impact areas in which synthetic biology can have a truly transformational effect. We call on the community to consider cellular supremacy as a framing device for future work, and to explore in a systematic fashion how it may be established. By accepting the idea of cellular supremacy, we naturally acknowledge the richness and power of living systems. And by ceding a degree of control to biology, we may yet open up a much wider range of applications and perspectives on information processing in nature.

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 Acknowledgements

 A.G.-M. was supported by the SynBio3D project of the UK Engineering and Physical Sciences Research Council (EP/R019002/1) and the European CSA on biological standardization BIOROBOOST (EU grant number 820699). T.E.G. was supported by a Royal Society University Research Fellowship (grant UF160357) and BrisSynBio, a BBSRC/EPSRC Synthetic Biology Research Centre (grant BB/L01386X/1). P.Z. was supported by the EPSRC Portabolomics project (grant EP/N031962/1). P.C. was supported by SynBioChem, a BBSRC/EPSRC Centre for Synthetic Biology of Fine and Specialty Chemicals (grant BB/M017702/1) and the ShikiFactory100 project of the European Union’s Horizon 2020 research and innovation programme under grant agreement 814408.

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 1. School of Computing, Newcastle University, Newcastle Upon Tyne, NE4 5TG, UK

 Lewis Grozinger, Ruud Stoof, Harold Fellermann, Paolo Zuliani & Angel Goñi-Moreno

 2. Department of Computer and Information Sciences, Northumbria University, Newcastle upon Tyne, NE1 8ST, UK

 Martyn Amos

 3. BrisSynBio, University of Bristol, Tyndall Avenue, Bristol, BS8 1TQ, UK

 Thomas E. Gorochowski

 4. School of Biological Sciences, University of Bristol, Tyndall Avenue, Bristol, BS8 1TQ, UK

 Thomas E. Gorochowski

 5. Manchester Synthetic Biology Research Centre for Fine and Speciality Chemicals (SYNBIOCHEM), Manchester Institute of Biotechnology and School of Chemistry, University of Manchester, Manchester, M1 7DN, UK

 Pablo Carbonell

 6. School of Informatics, University of Edinburgh, Edinburgh, EH8 9AB, UK

 Diego A. Oyarzún

 7. School of Biological Sciences, University of Edinburgh, Edinburgh, EH9 3BF, UK

 Diego A. Oyarzún

 8. Systems and Synthetic Biology Program, Centro Nacional de Biotecnologí­a (CNB-CSIC), Campus de Cantoblanco, 28049, Madrid, Spain

 Huseyin Tas

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 L.G., M.A. and A. G.-M. conceived the study. L.G., M.A., T.E.G., P.C., D.A.O., R.S., H.F., P.Z., H.T. and A.G.-M. contributed to the writing and editing of the paper.

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 Grozinger, L., Amos, M., Gorochowski, T.E. et al. Pathways to cellular supremacy in biocomputing. Nat Commun 10, 5250 (2019). https://doi.org/10.1038/s41467-019-13232-z

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  Published: 20 November 2019  
 
 
 
 
 
 
  Nature Communications 
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  Abstract Synthetic biology uses living cells as the substrate for performing human-defined computations. Many current implementations of cellular computing are based on the “genetic circuit” metaphor, an approximation of the operation of silicon-based computers. Although this conceptual mapping has been relatively successful, we argue that it fundamentally limits the types of computation that may be engineered inside the cell, and fails to exploit the rich and diverse functionality available in natural living systems. We propose the notion of “cellular supremacy” to focus attention on domains in which biocomputing might offer superior performance over traditional computers. We consider potential pathways toward cellular supremacy, and suggest application areas in which it may be found. 
 
 
 
 
  Introduction  Synthetic biology 1,2  is a rapidly growing field of research which applies engineering concepts and principles to the rational engineering of living systems, such as bacteria and yeast. The promise of synthetic biology lies in its potential to provide new substrates for computation 3 , production 4 , pollution control 5  and medical diagnosis 6  (among many areas), and to harness the “wetware” 7  inside the living cell for human-defined purposes. Synthetic biology is set to become a significant component of the multi-billion dollar bio-economy 8 , but, in addition to tangible benefits such as cheaper drug production or more precise bio-sensing, many researchers in the field believe that the very process of re-engineering life will both require and inform a reexamination of our fundamental understanding of cellular processes 9 . This position underpins the current paper. Much existing work in synthetic biology is concerned with the construction of “circuits” of biological components (such as genes and proteins) that receive some input (either endogenous, or exogenous), perform some transformation of that input, and produce a result determined by the “rules” encoded in the circuit. This input-transform-output pipeline is entirely consistent with the notion of a computation, as traditionally defined, and it is wholly unsurprising that synthetic biology has, so far, largely adhered to the genetic “logic circuit” model (groundbreaking examples include the genetic toggle switch 10  and the “repressilator” 11 ). The roots of this biological circuit metaphor date back to the mechanistic view of the cell; the idea that living systems may be viewed as machines, which, in turn, can be traced as far back as Descartes (and beyond). Characterisations of the cell as a “factory”, a “little engine”, and a “chemical machine” dominated early discourse in cell biology, and the post-war development of cybernetics and computer science, combined with the emergence of molecular biology, provided significant support for this conceptual interpretation of living systems 12 . The “machine model” of the cell was further cemented by the pioneering work of Jacob and Monod, which established that the lac operon 13  facilitates metabolic switching within E. coli in a manner that may be interpreted as a simple Boolean circuit. In his highly influential popular book, Chance and Necessity (a chapter of which is titled “Microscopic Cybernetics”), Monod made explicit the connection between biological processes and the basis of electronic circuits: “The logic of biological regulatory systems abides not by Hegelian laws but, like the workings of computers, by the propositional algebra of George Boole.” 14   Since the discovery of the lac operon, the machine model has largely dominated molecular biology 15 , and the notion of the genome serving as a “genetic program” is still relatively common 16 . Of course, abstracting biological processes to the level of circuits (Boolean or otherwise) or even programs may be a necessary step in terms of making sense of their operation. Conversely, in the context of engineered biological systems, the availability of a set of well-characterised, modular and tunable components are perhaps necessary for creating controllable and predictable systems 17 . We emphasise here that we do not seek to overturn or abandon an extremely powerful and useful metaphor. However, it may give a misleading impression regarding the reliability and predictability of genetic circuits, compared to their electronic counterparts 18 . Moreover, as we argue in this paper, by restricting ourselves to the computational palette offered by (Boolean) combinatorial logic, we inherently (and seriously) limit the power and scope of synthetic biology. It is perhaps instructive at this point to discuss the field of molecular computing 19 , which many see as a conceptual precursor to synthetic biology, if not a direct predecessor. Although the notion of computing with individual atoms and molecules was attributed to Richard Feynman as early as the 1950s 20 , the field was only reified in 1994, when Leonard Adleman published his groundbreaking paper on computing solutions to the Hamiltonian Circuit Problem using molecular operations with strands of DNA 21 . At the time, a commonly-held belief was that the future promise of DNA computation 22  lay in solving instances of hard computational problems that were beyond the capabilities of traditional silicon-based computers 23 . Much early work on producing general DNA-based computational models focussed on molecular emulation of the Boolean circuit model 24,25 . Discussion of the field’s overall direction was, for a time, dominated by the quest for the “killer application”, the application of DNA computing that would establish its superiority over existing computational substrates 26,27 . In some ways, this may be viewed as a restricted form of the search for so-called “quantum supremacy” in the quantum computing domain 28 . As the field of molecular computing evolved, it rapidly became clear that the killer application would not be found by solving large instances of computationally hard problems using any variant of Adleman’s original model. The elegance of the original solution derived from the encoding used to construct all possible paths through a given graph; vertices and edges were represented as strands of DNA that self-assembled into a collection of paths, which was then rapidly filtered in parallel using molecular manipulations to gradually extract valid solutions. Crucially, this reasonable run-time required the entire solution space for a given problem instance to be represented in an initial “test tube” at the start of the computation; the problem was to find the “needle” (valid solution(s)) in a molecular “haystack”. Essentially, the entire space of solutions was tested in polynomial time using molecular operations, but this came at the cost of having to represent the whole solution set in a single volume of liquid 22 . For even small problem instances, the amount of DNA required to represent all possible solutions would be astronomical; Hartmanis calculated that if Adleman’s experiment were scaled up from 7 to 200 vertices, the amount of DNA required would weigh more than the Earth 29 . We note, however, that this inherent time-space tradeoff would appear to hold regardless of whether the underlying substrate is DNA, silicon, or a more exotic material (with the possible exception of substrates for quantum computers 30 ). Importantly, this assessment emphasised the fact that the killer application would probably not be derived from single-use, finite DNA-based systems (albeit ones that were large and potentially massively-parallel in nature). Subsequent influential work on DNA self-assembly 31  and strand displacement architectures 32  emulated traditional computational models such as cellular automata 33  and artificial neurons 34 , but also took advantage of biochemical processes that provided power beyond mere miniaturisation. That is, rather than simply harnessing the potential for massively-parallel laboratory operations on large (but finite) numbers of molecules, these systems co-opted specific physical and chemical properties of the underlying substrate to generate the potential for autonomous operation and dynamic behaviour. In the context of synthetic biology, we suggest the killer application for engineered living systems will be similarly derived; one that will use features of the living system that are unavailable via traditional silicon-based substrates, for the purposes of applications that exploit autonomy and the ability to perform in uncertain environments.    The search for cellular supremacy  If we accept that a driving motivation for synthetic biology should be the search for a killer application, then this naturally leads to a consideration of the class of problems in which engineered living systems might offer what we call cellular supremacy (deliberately echoing the well-established notion of quantum supremacy 28,35,36,37 ). That is, we seek a set of problem domains in which cell-based systems will offer capabilities beyond the reach of existing computers, due to cost or technological constraints. Simply put, cellular supremacy will be determined by the set of problems that biocomputers can practically solve that traditional microprocessor-based devices cannot. To identify this set of problems, we naturally focus on the “added value” that living systems offer beyond silicon-based hardware. In the following sections, we discuss a number of features of living systems that we believe give synthetic biology-based solutions a distinct “edge” over traditional computers. Importantly, we focus on aspects of computation and information transformation, rather than simply on the ability of the cell to act as a micro-scale drug precursor “production plant” or miniaturised bio-sensor. While these applications are important and valuable, they are not the main focus of the current discussion, which centres on the general computational capabilities of living systems if we go beyond the limitations of Boolean logic-based systems. In what follows, we use the term “cellular computing” 38,39  to emphasise this focus on computation. When assessing cellular computing against traditional computing, it may be useful to frame the comparison using a scheme that emerged from an exercise on roadmapping the so-called “unconventional computation” domain. The authors identified a number of criteria or benchmarks against which emerging computational models may be measured, each accompanied by its own motivating question 40 . In what follows, we focus on the quality criterion, which asks the following question: Does the alternative model offer qualitatively different computation to traditional models? The authors define “quality” in terms of precision, richness, stochasticity and repeatability. Quality is concerned with the ability of the system to provide an analysis of inputs that is different to that offered by a traditional computer. If we focus on problems that fall within the remit of traditional silicon-based machines, and use existing metrics, then cellular computing will inevitably fall short on some of the other criteria identified 40 , such as speed and cost. However, we would argue that the real power of cell-based systems derives from the richness of their internal (and collective) architectures, and on their inherent stochasticity. This leads us to a consideration of the specific computationally expressive mechanisms that are available to us, and which act both inside and between living cells. In what follows we focus on five (non-exclusive) features of living cells that (we believe) offer the most potential in terms of the search for cellular supremacy; these are reconfigurability (that is, the ability to change internal state/structure in response to signals), noise (the ability to not only tolerate but to harness and exploit biological “messiness”), concurrency (the multitude and richness of inter-cellular processes that facilitate massively-parallel communication and coordination), representation (the ability to use non-binary representations for signals), and evolution (the population-level ability to seek out novel solutions to problems over time). By harnessing these capabilities, we will obtain bio-computing systems that are self-organising, self-repairing, resilient, distributed, and adaptive 41 . First, we consider aspects of computational theory that suggest how cellular computers may out-perform traditional machines. We then describe a number of features of biological systems that lend themselves to non-standard computation. Taken together, these two perspectives point towards a number of possible areas for investigation in which the killer application for cellular computing may reside.    Information processing beyond digital logic  The current definition of digital computation is based on the abstract model defined by Turing in the 1930s 42 , and the von Neumann architecture 43  used to implement the types of computations performed by the Turing Machine. Although Turing’s model provides a framework for answering fundamental questions about computation, “…as soon as one leaves the comfort provided by the abundance of mathematical machinery used to describe digital computation, the world seems to be packed with paradoxes.” 44 . The important thing to note here is that although genetic circuits may appear to behave digitally, it is only the collective behaviour of a large number of inherently analogue components that give rise to this property. The fact remains that we still currently lack any formal framework within which to argue that a cell computes, according to any understood model of computation (although recent work has started to address this 45 ). The nature of computation is not of purely theoretical interest. Mathematical models of computation and their properties inform the engineering of their physical manifestations (Fig. 1). Many such implementations may be possible, but all inherit the characteristics of their abstract counterparts—both their abilities and their limitations. The fact that the nature of computation within a given model is independent of its implementation allows the application of theoretical computer science to all kinds of physical systems, including cells. However, the cost of this generality is a semantic gap between the model and the physical processes that actually perform the computation. That is, mapping computations from an abstract model to a real system may be more or less difficult, depending on the model chosen. The cellular computing substrate is quite different from that of silicon computers, offering opportunities for implementing some models with a narrower semantic gap. Practical considerations such as these could guide future applications of cellular computing.    Fig. 1       The cell as a “physical” computer. A model of computation formally defines inputs and outputs, as well as how an algorithm processes inputs into outputs. Though the same theoretical model of computation can be physically implemented in many different ways, the nature of computation remains the same. Electronic implementations receive electronic data for inputs/outputs, while cells are able to sense/deliver a wide range of physical, chemical and biological inputs/outputs. The encoding of information into inputs can be done in different ways. Temperature, for instance, can be encoded as the height of mercury in a tube, the voltage of an electronic thermometer or the state of a DNA thermosensor   Full size image    Conventional silicon computers are fundamentally implementations of a deterministic, centralised and digital model of computation, and they excel at computational tasks which are easily described by such models. In contrast, cellular computing has been optimised over billions of years of evolution to perform very different computational tasks, and we are unlikely to find cellular supremacy in applications such as discrete mathematics, sending emails or reading documents. However, computer science has developed models in which the nature of computation is quite different to that of the Turing Machine 46,47,48,49,50,51,52,53  and computation in cells appears to share some properties with these less conventional models. With this in mind, the application of theoretical computer science to cellular computation may still present routes to cellular supremacy in those areas where the properties of cellular and traditional computation differ. Here, we introduce a selection of theoretical aspects of computing that impact significantly upon the nature of computation, all of which seem to be exploited in the cell for processing information, but whose theoretical implications may not be familiar to those outside the field of computer science.    Computational states for computations over time  Not all models of computation are equally powerful, that is, they are not equivalent in terms of the range of computations they can possibly describe. By this metric, combinatorial logic circuits are extremely weak, since the output of a circuit is purely a function of its current inputs (that is, there is no “memory”), and this severely restricts the range of computations that are possible with a single circuit. Clearly, there are models of computation more powerful than combinatorial logic, that is, models which can describe all computations that are possible with combinatorial logic circuits and more. In this regard, two extremely powerful models of computation, the Lambda calculus 54  and the Turing Machine 42  are particularly important. These two models are both equally powerful, but quite different in their formulation—the Lambda calculus is a model of functional computation, while the Turing Machine models stateful computation. Here we focus on stateful computation, as states enable functions that operate over time, such as memory, learning and adaptation. The output of stateful computations depends not only on the current input, but also on the current state, which encodes information about previous inputs that are no longer present. Models of computation such as finite state machines (FSMs) (shown in Fig. 2) exceed the capabilities of combinatorial logic, and are extremely powerful models of computation—the central processing units of modern digital computers are built from sequential logic circuits, which are implementations of FSMs. Even so, they cannot describe all computations that are available to the Turing Machine model, since they have only a bounded number of states. Turing machines are similar to FSMs, but have an unbounded memory (commonly conceptualized as a tape), which endows them with an unbounded computational state space (number of distinct configurations). Consequently, Turing Machines can compute anything that any real computer can, and in fact, computer science starts from the notion that Turing Machines (TMs) demarcate what is (and is not) computable 42 . From a practical perspective, these considerations of the limits of computability might be of less conceptual value than the strategy that TMs employ to decouple the complexity of the machine from the number of states on which they can operate.    Fig. 2       Cells could provide more than logic circuits. Computer science has developed models of computation that are far more powerful than combinatorial logic, such as finite-state machines or the Turing Machine. These models are more powerful in that they allow processing of a wider range of inputs into outputs, and in many more ways, than are admissible by combinatorial logic. Similarly, living systems have evolved a variety of computational processes to allow cells to process information. A simple model, used extensively as the basis for engineering combinatorial logic circuits in cells, is the standard representation of the central dogma (CD) of molecular biology. However, this model does not incorporate core cellular mechanisms such as metabolism, or processes such as evolution, which may provide possibilities for building more powerful, but as yet unknown, models   Full size image    Modern digital computers, as with any real physical system 55 , lack the unbounded state space required for implementing a Turing Machine. However, their state space is so vast as to make them practically indistinguishable from implementations of Turing Machines (consider that even systems with an extremely modest 1 MB of storage have at least \(2^{10^6 \!\times\! 8}\) states). It is therefore unlikely that cellular computing will outperform silicon purely on the basis of enabling more complex stateful computations. Nevertheless, synthetic biology has already engineered successful in vivo implementations of stateful computations 10,56,57 , and there also exists significant theoretical work linking stateful models of computation to biological implementations 58,59 . This work is undoubtedly of considerable importance for a broad range of synthetic biology applications, and since biological systems naturally engage in stateful computation 60,61,62 , statefulness or “memory” will likely be a key component in future engineered biocomputations of any significant complexity.    Noise permits stochastic and non-deterministic computations  Combinatorial logic circuits, FSMs and TMs model deterministic computations, which are essentially step-wise descriptions of mathematical functions that map inputs to outputs, where each step follows in a predetermined way from the previous step. Deterministic computation can be generalised to include stochastic and non-deterministic computation. Stochastic (or probabilistic, or randomised) computing refers to algorithms which can make random choices during their execution. Specifically, a given input may generate a number of different computational paths, each with some probability, and the cumulative probability of all such paths is equal to one. Probabilistic algorithms are a cornerstone of computer science 63 , and are used to solve approximately, but efficiently, hard optimisation problems for which deterministic algorithms would be intractable. One of the most important algorithms in systems biology, the Gillespie algorithm, is stochastic. Gillespie showed from basic quantum mechanics that a set of biochemical reactions must be understood as a stochastic process 64 , and offered an efficient way for simulating (sampling) its dynamics 65 . Therefore, cells may already be seen as “stochastic processors” that could provide a substrate for implementing probabilistic algorithms. Indeed, the utility of stochastic processors has already been recognised in the silicon world 50,66 . In non-deterministic models of computation, as in stochastic ones, there may be many computational paths from input to output, but crucially each of these computational paths is explored simultaneously by the algorithm, with a result analogous to parallel execution of multiple distinct deterministic algorithms. While non-determinism has considerable impact on theoretical computer science, practical implementations of non-deterministic computation remain elusive. Nevertheless, algorithmic solutions to some computational tasks can be significantly easier to express as non-deterministic, and biological systems extensively exploit non-determinism, both at the population level 67,68  and at the scale of evolution 69 . Perhaps more speculatively, we might also consider the role of quantum effects in biology 70 , and whether or not these may be harnessed for the purposes of non-deterministic algorithms in biological systems.    Distributed computing can exploit concurrency  For some models of computation, the definition of an algorithm is “sequential”, and implies an ordering of the computational steps. Implementations of these models enforce these “sequential semantics”, because sequential execution may be a strict requirement to ensure the correctness of an algorithm. However, for certain computations, algorithms exist in which the ordering of computational steps may be relaxed, or abandoned entirely—in computer science terms, the algorithm displays a level of concurrency. In such situations, if multiple computing devices may interact and coordinate their efforts as a “distributed system”, concurrent parts of an algorithm may be executed in parallel, potentially speeding up computations significantly. The utility of such distributed computing is not limited to performance advantages. For some problems, sequentiality is desirable, but the nature of the computing substrate makes it impractical (or even impossible) to enforce 71 . For instance, at a fundamental level, and even within a single cell, natural cellular computation is concurrent and distributed. Computation is performed by stochastic biochemical processes—the probabilistic interactions of spatially separated molecular computing “agents”, many of which can happen in any order. Computer science has long used distributed and concurrent models of computation such as actors 49 , Petri nets 51 , process algebras 72  and population protocols 52  to describe computations in just these situations.    Analogue computing allows for continuous non-binary inputs  The nature of computation described so far has been digital; that is, information is represented using a set of discrete values. However, many physically relevant quantities vary continuously. Even the signals that encode binary values in electronic logic circuits are, in reality, stored as continuous-valued voltages. Such signals must be discretised in order to represent digital values. In contrast, analogue computation allows continuous signals to be used directly in the computational steps of an algorithm, and for representation of information as continuous values. Although many cellular computations involving binary “yes/no” decisions may be interpreted as digital computations, and digital logic computations are certainly suited to applications such as biosensors, cells often exhibit graded responses to stimuli that are more appropriately viewed as analogue computations 62,73 . Furthermore, the biochemical processes responsible for cellular computations involve discrete interactions of discrete molecules, but are also inherently stochastic. Cellular computing may, therefore, be viewed as both digital and stochastic, or as analogue computation with noise 74 , and the viability of the cell as a substrate for synthetic analogue computations has already been demonstrated 75 . Whilst some models of analogue computation such as the Blum-Shub-Smale machine 53  or neural networks 46 , use arbitrary precision signals to perform super-Turing computation, it is not clear whether realisations of analogue computation will be able to provide more computational power than digital computation, since physical laws forbid the existence of such an idealised computer 55,76 . However, for digital models of computation, the abstraction of continuous signals into digital represents a semantic gap between the formal definition and implementation of a computation. Models of analogue computation admit continuous signals, which not only narrows this semantic gap, but also allows more powerful computational primitives to be used for defining algorithms 77 . Consequently, depending on the computation and the computing substrate, an analogue algorithm might have a more intuitive implementation, require fewer components to implement, and be considerably more energy-efficient than its digital counterpart 74,75 .    Engineering complex cellular computing systems  There are certainly deep physical connections between chemistry and electronics 78 , but the fact remains that the cellular environment is a radically different computing substrate than silicon. Although this difference might make cells unsuitable for computational tasks traditionally dominated by conventional computers, it could also offer opportunities to explore more unconventional models of computation. Aside from gene regulation, which has been useful for engineering biological logic circuits, a number of processes and features exist in natural systems which may offer computational capabilities. Here, we identify four such resources as promising in terms of their information-processing capabilities (Fig. 3).    Fig. 3       Cellular information-processing fundamentals that go beyond combinatorial logic circuits. a Whole-cell computations, merging genetic and metabolic circuits, could achieve more ambitious goals than genetic circuits alone. Cells have evolved intricate networks that make simultaneous use of the varied features of both genetic and metabolic processes. In terms of information storage, metabolism presents a volatile memory, while DNA sequences are able to store information in a more stable fashion. Coordinating the use of different types of memory is a fundamental aspect of complex computer architectures. The dynamic difference is also a potential source of complexity if coupled; metabolic reactions operate on a faster timescale relative to genetic regulatory networks. b Multicellular computing (right) is currently implemented by connecting the output of one strain to the input of another. Social interactions among cells (left), such as cooperation, mutualism, competition or commensalism, are not considered in general. However, social interactions are fundamental in natural communities—they provide stable architectures executing a desired computation. c Gene expression noise is intrinsic to living systems; the panel figure shows different patterns for gene expression. Despite the fact that all are described as being on, there are different types of expression—thus different on/off standards. d The cell as a general-purpose machine. As the basis for a model of computation, the central dogma of molecular biology can be expanded to include metabolism. Evolutionary processes may also be included as major forces guiding information-processing in cells, since they allow the purpose of cellular computations to adapt over time   Full size image       Towards whole-cell computation  Synthetic cellular computing systems have generally focussed on DNA components that are isolated from the many other processes within a cell 79,80 . However, evolution has shaped intricate information-processing networks whose function emerges from the interplay between many layers of the cellular machinery 81 . For example, bacteria adapt to nutrient fluctuations by sensing extracellular cues, transducing such signals to the genetic machinery, and ultimately adapting their metabolic state to make maximal use of carbon sources. This requires a careful whole-cell orchestration of trafficking processes at the levels of membrane, cellular signalling pathways, gene expression programmes and metabolic activity. In a similar fashion, synthetic systems that exploit whole-cell interactions offer exciting opportunities to expand the range of computational tasks that can be achieved with living systems. Metabolic circuits, in particular, produce analogue dynamics that could allow us to move beyond basic Boolean operations 82 . Circuits integrating genetic programs with metabolic activity have been successfully engineered to improve the productivity of microbial cell factories 83,84,85 , but their potential goes far beyond simple production. Notably, retrobiosynthesis approaches based on generic representations of reactions, known as reaction rules, expand the design space of metabolic circuits by predicting novel synthetic pathways connecting metabolism and gene expression 86,87,88 . Machine-learning is increasingly being applied by such retrosynthesis algorithms to select the best candidate reactions in the search through the chemical space 89,90 . Moreover, experimental and theoretical work has shown that gene expression noise can permeate to metabolism 68,91 , suggesting the possibility of processing information using metabolic heterogeneity. The interplay between gene expression and metabolism can be conceptualised in terms of memory systems employed in most computer architectures. These have a long-term static memory, conceptually similar to information stored in DNA, and a short-term volatile memory, akin to the fast dynamics of metabolism (Fig. 3a). Computer science has developed efficient techniques for managing data flows across these two memories to exploit their characteristic timescales. There is some evidence that cells also exploit such differing timescales to their benefit 62 , and, ultimately, the ability to encode signals in different frequency domains may allow us to move from classic Boolean abstractions to more complex coding systems. Whole-cell computation presents major challenges because, as the size of synthetic circuit grows, so does their footprint on the cellular host. Synthetic circuits do not work in isolation, but continuously draw resources away from vital functions of the host 92 . These resources include energy, polymerases for transcription, ribosomes for translation, enzymatic co-factors, and so on, the depletion of which has a negative impact on native processes. This is commonly known as the cellular burden, and has gathered substantial attention in the community 93 . Recent work has aimed at identifying relevant sources of burden imposed by synthetic constructs 94,95 . Together with increasingly powerful mathematical models for cell physiology 96,97 , these experimental efforts are paving the way for accurate prediction 98  and control of burden 99 , which will enable the construction of complex circuitry that takes full advantage of the cellular machinery 100 .    The power of multicellular consortia  The burden imposed by synthetic biological constructs places a fundamental ceiling on the information processing capacity of a single cell. In order to execute larger and more complex computations, living systems harness the capabilities of multicellular ensembles, such as the vast neural networks in the brain. Distributing computational demands across a population of specialised cells lowers the burden on each individual cell, and offers a way to more easily scale the complexity of the computations being performed. Such scalability is uniquely fostered in biological systems by the inherent ability of living cells to self-replicate. Similar distributed approaches have been employed in engineered biological systems, where an algorithm is spread across a consortium of different microbes that are able to communicate and interact (Fig. 3b). Many theoretical 101,102,103,104,105  and experimental 106,107,108,109,110,111,112  examples demonstrate the benefits of distributing computation in this way, as well as a growing number of tools for their simulation 113,114,115,116,117,118,119,120  and assembly in living cells 121,122 . Although the development of engineered multicellular consortia is possible with current technologies, their structure is often fragile, and their information-processing capabilities are dwarfed by microbial communities found in nature 123 . A key difference in naturally-occurring systems is that extensive resources and diverse mechanisms are used to establish and coordinate the complex social behaviours of a communityʼs participants 123 . Social relationships such as cooperation, mutualism, competition and commensalism are used concurrently to drive a required community structure that can potentially change over time in response to the environment. Advances in our ability to control cell-to-cell interactions, either through spatial patterning of cell populations 112  and/or orthogonal communication channels 121,124 , will be crucial to future developments in this area. A feature of multicellular consortia that pushes us beyond the capabilities of classical electronic computers is their highly flexible and re-configurable nature 125 . In computer science, a computer architecture describes the structural relationship between different components of a system (e.g. the processor and memory) and constrains how algorithms run on the system. A program compiled for one type of computer architecture may not be executable by another due to these physical differences. The architecture of most electronic computers is fixed during a computation and has been honed to perform primitive digital operations in quick succession, guided by a set of instructions (the code). While this architecture is general enough for tackling many types of task, its static architecture makes it sub-optimal for most of them. In a cellular consortium, such a severe trade-off between flexibility and optimality (e.g. in regards to energy consumption or speed) need not exist, as the cellular community can dynamically change its physical composition and the interactions present to produce a “living architecture” that better matches the problem at hand. Furthermore, such reconfiguration is possible even during a computation itself, offering a level of control and flexibility that electronic computers are unable to match. Harnessing these unique capabilities will offer synthetic biologists new approaches to solving problems and require us to rethink what a computer architecture can be 126 .    Encoding signals using gene expression noise  Combinatorial logic, which relies on well separated on/off signals to encode information, constitutes a valuable framework with which to understand and build genetic circuits. Even if molecular signals (for example, a transcription factor that down-regulates a promoter) do not have absolute and constant values, the notion of a promoter being repressed or not (thus being binary) is intuitive. Nevertheless, the use of Boolean logic for engineering cellular circuits is often challenged by the fact that molecular signals are intrinsically noisy, and therefore stochastic. Each signal will have different on/off values (Fig. 3c), and not all are compatible, which makes building a large combinatorial circuit a significant challenge 127 . Combinatorial logic is, therefore, a good example of how a given theoretical model of computation may be easily implemented with one physical toolkit (electronic), but not with another (molecular). The voltage that runs through electronic wires is also noisy, but computer engineers overcame this problem by arranging for thresholds at the input and output of logic gates, so that analogue values could be abstracted into two unique values: 0 and 1. In contrast to this, living systems have evolved to benefit from signal variability. Stochasticity has been shown to be useful in coordinating the expression of large sets of genes 128 , in producing the phenotypic variability that allows for bet-hedging strategies that promote survival in fluctuating environments 67,129 , and as a key component of evolution under tight selection criteria 69 . Therefore, models of computation incorporating stochasticity would seem to be necessary to best fit the intrinsic properties of living systems. Unlike silicon computing devices, where noise is a consequence of random signal fluctuations, cellular systems are capable of encoding important information into noise patterns. For example, the change in gene expression noise according to intracellular physical distances 130  reveals information about the structural architecture of the cell. Also, noisy patterns in the cellular machinery of Staphylococcus aureus (that lead to different infectious cell types) originate in upstream molecular events 131 . These examples, among others 75 , highlight the fact that the shape of non-digital biological signals is used to effectively transmit information. Therefore, the challenge is to use noise for implementing computations — an area where cellular computers clearly outperform conventional ones. In the meantime, current efforts in the discretisation 132 , stabilisation 133,134  and reusability 135  of noisy signals may help to understand, and harness, the dynamic complexity of molecular interactions.    Evolution as an information-processing mechanism  Evolutionary computing is a field within computer science that develops and applies algorithms inspired by Darwinian evolution 136 . Different implementations of this idea exist, such as genetic algorithms, evolutionary strategies or genetic programming, but the underlying principles are similar: a set of candidate solutions to a problem (an initial population) compete under some pre-defined fitness criteria, and the fittest individuals are selected to form the next generation (via crossover and/or mutation). An important advantage of these techniques is that they allow for the dynamic optimisation of solutions throughout potentially vast search spaces. Both computer scientists and living systems use evolutionary algorithms to generate algorithmic solutions. Evolutionary processes have also been used to design biomolecules 137,138 , libraries of biological components 139  and even to evolve non-functional genetic circuits into functional ones 140 . Despite this, evolutionary processes are often omitted when engineering computing circuits in living cells. Harnessing the power of such information-processing mechanisms for predefined functions seems to be difficult, and the rational engineering of autonomous evolutionary computing in living cells is still an overarching challenge. In order to start addressing this challenge, it will be important to formalise the effects of evolutionary dynamics on the flow of genetic information. A potential initial step would be to expand on the standard representation of the central dogma (CD) of molecular biology to include evolutionary dynamics, in an attempt to describe the model of computation of a living cell (Fig. 3d). Expansion of the CD-based model is not a new idea; for example, the inclusion of metabolic processes has previously been suggested 141 , since, as evidenced above in “Towards whole-cell computation”, metabolism is a crucial omission from the point of view of information processing. A complete model of the flow of genetic information at a given point in time needs to include both genetic and metabolic processes, and dynamic models of computation inside living cells should include evolutionary processes that operate on genetic information. Theoretical models of computation may find valuable and perhaps novel implementations within this dynamic representation of the CD. Recent developments in optogenetics are promising to this end, since these show how genetic elements dynamically shape their response in relation to external signals 142 . Importantly, these studies linking environmental signals to intracellular responses in a predictable way, as well as directed evolution efforts 143 , are undertaken in tightly controlled systems. However, the mechanisms that allow a cell to thrive in challenging and dynamic environments are largely unpredictable. For problems like bio-remediation which intrinsically involve ever-changing environments, natural cellular computers clearly show superiority compared to conventional ones.    Applications of cellular computing systems  As already discussed, cellular computing is unlikely to compete with conventional computers in domains for which the latter are specifically engineered. Although future biological systems may offer competitive performance in related areas such as data storage 144 , the benefits are largely limited to the exploitation of material factors such as miniaturisation and longevity of components. The identification of promising applications for cellular computing has been largely guided by the observation that living systems operate best in application domains that are not easily reachable by conventional computers. Successes in bio-remediation 145 , bio-production 146  and targeted therapeutics 147  indicate that this is indeed a fruitful line of inquiry. Nevertheless, the implementation of conventional computations with unconventional computing substrates does not, in and of itself, constitute cellular supremacy. Rather, supremacy must be derived from the fact that the type of computation performed by a conventional computer is qualitatively different to that executed by living systems. Current implementations of computations within living cells are generally based on combinatorial or sequential logic circuits mapped onto equivalent genetic circuits; while these are useful metaphors for both understanding and engineering living systems, digital logic is not easily implemented using a cellular substrate. Furthermore, logic circuits offer a relatively bland computational palette compared to the richness of biology. For this reason, future developments in cellular computing should focus on models of computation that both accommodate and exploit the natural abilities of the cell, and avoid forcing biological systems into artificial (and often unsuitable) architectures 148 . This does not mean that cellular computing must necessarily “reinvent the wheel” when it comes to models of computation. Living systems share many characteristics with in vitro platforms for computation, and as well as the considerable body of theoretical work concerning molecular computing, cellular computing may draw on cell-free systems as a practical resource for faster prototyping with a greater degree of control 149,150,151 . Furthermore, the relationship between computer science and natural computing is often synergistic. As described earlier, models of computation that transcend logic circuits are available which have yet to be explored by cellular computing to any great extent. In return, biological systems offer computational features that are (and are expected to remain) unavailable to silicon implementations of existing computational models. It is at this intersection that exciting opportunities for cellular supremacy emerge. For example, in the past decade it has become increasingly clear that a number of biological processes show quantum mechanical properties 152,153 . In particular, there is strong experimental evidence that long-lived quantum coherence is involved in photosynthesis 154 , and that quantum tunnelling is active in enzyme catalysis 155 . Since most quantum computing devices are built and run under stringent environmental conditions (at temperatures approaching absolute zero), the opportunity to control quantum effects in a biological system that “runs” at room temperature, through the emergence of a “quantum synthetic biology”, could turn out to be a game changer in the quantum supremacy race. More to the point, realising models of quantum computation 156  using quantum biology could yield a cellular computer capable of a radically different kind of computation than silicon 153 . Although we have, until now, focussed primarily on bacterial cells, there does, of course, exist a multiplicity of cell types that possess rich and complex computational capabilities. For example, plants can respond to environmental signals and stresses in a way that is reminiscent of signal processing in neural networks (the so-called “plant perceptron”) 157 . Cultured neuronal cells have been used to control flight simulators 158  and robots 159 , and slime mould has a rich repertoire of spatial computing capabilities 160 . Additionally, we do not dismiss the possibility of “hybrid” architectures, in which cellular systems are interfaced to more traditional, silicon-based machines. Such connections may allow for subtle and sensitive adjustments to cell state, for example 161 , but these hybrid systems will still fundamentally rely on the properties of the living material. As we have already argued, natural cellular computing operates at vast scales, in a distributed manner, and in the presence of considerable noise. Consequently, biological metaphors have served as inspirations for models of amorphous computation, for which cellular computing is a promising implementation technology 162 , especially at scales inaccessible to silicon. Robotics has also drawn inspiration from biological computation, particularly in relation to morphological computing, which takes advantage of the physical properties of computing agents in order to achieve more efficient computations 163 . By using intrinsic physical properties of the computational substrate to “outsource” parts of the computation, increasingly complex computations can be carried out whilst maintaining relatively simplistic control structures 164 . Living systems are an ideal implementation technology for morphological computation, since they not only compute solutions to individual instances of problems, but continuously compute and adapt in order to embody an efficient general solution. As we have previously argued, conventional silicon computers have inflexible architectures by comparison, which must sacrifice efficiency for generality. These qualitative differences between cellular and conventional computing suggest that applications such as terraforming and smart material production may remain beyond the reach of silicon computers, but in contrast, strategies for both applications based on living technologies have already been proposed 165,166 . In this perspective, we have championed the notion of cellular supremacy in an attempt to focus attention on the high-impact areas in which synthetic biology can have a truly transformational effect. We call on the community to consider cellular supremacy as a framing device for future work, and to explore in a systematic fashion how it may be established. By accepting the idea of cellular supremacy, we naturally acknowledge the richness and power of living systems. And by ceding a degree of control to biology, we may yet open up a much wider range of applications and perspectives on information processing in nature.  
 
 
 
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     Download references     Acknowledgements A.G.-M. was supported by the SynBio3D project of the UK Engineering and Physical Sciences Research Council (EP/R019002/1) and the European CSA on biological standardization BIOROBOOST (EU grant number 820699). T.E.G. was supported by a Royal Society University Research Fellowship (grant UF160357) and BrisSynBio, a BBSRC/EPSRC Synthetic Biology Research Centre (grant BB/L01386X/1). P.Z. was supported by the EPSRC Portabolomics project (grant EP/N031962/1). P.C. was supported by SynBioChem, a BBSRC/EPSRC Centre for Synthetic Biology of Fine and Specialty Chemicals (grant BB/M017702/1) and the ShikiFactory100 project of the European Union’s Horizon 2020 research and innovation programme under grant agreement 814408.   Author information  Authors and Affiliations   School of Computing, Newcastle University, Newcastle Upon Tyne, NE4 5TG, UK Lewis Grozinger, Ruud Stoof, Harold Fellermann, Paolo Zuliani &amp; Angel Goñi-Moreno   Department of Computer and Information Sciences, Northumbria University, Newcastle upon Tyne, NE1 8ST, UK Martyn Amos   BrisSynBio, University of Bristol, Tyndall Avenue, Bristol, BS8 1TQ, UK Thomas E. Gorochowski   School of Biological Sciences, University of Bristol, Tyndall Avenue, Bristol, BS8 1TQ, UK Thomas E. Gorochowski   Manchester Synthetic Biology Research Centre for Fine and Speciality Chemicals (SYNBIOCHEM), Manchester Institute of Biotechnology and School of Chemistry, University of Manchester, Manchester, M1 7DN, UK Pablo Carbonell   School of Informatics, University of Edinburgh, Edinburgh, EH8 9AB, UK Diego A. Oyarzún   School of Biological Sciences, University of Edinburgh, Edinburgh, EH9 3BF, UK Diego A. Oyarzún   Systems and Synthetic Biology Program, Centro Nacional de Biotecnologí­a (CNB-CSIC), Campus de Cantoblanco, 28049, Madrid, Spain Huseyin Tas    Authors  Lewis Grozinger You can also search for this author in
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 PubMed Google Scholar      Contributions L.G., M.A. and A. G.-M. conceived the study. L.G., M.A., T.E.G., P.C., D.A.O., R.S., H.F., P.Z., H.T. and A.G.-M. contributed to the writing and editing of the paper. Corresponding author Correspondence to
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  Reprints and Permissions     About this article       Cite this article Grozinger, L., Amos, M., Gorochowski, T.E. et al. Pathways to cellular supremacy in biocomputing.
 Nat Commun 10, 5250 (2019). https://doi.org/10.1038/s41467-019-13232-z  Download citation    Received: 08 July 2019    Accepted: 29 October 2019    Published: 20 November 2019     DOI: https://doi.org/10.1038/s41467-019-13232-z     
 
 
 
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Pathways to cellular supremacy in biocomputing - Nature Communications
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