reactions $R1$, $R2$ and $R3$ (and indirectly $R4$). Another process omitted
from the diagram could be the ‘containment process’ ensuring that all
reactions take place in sufficient proximity such that their products are
accessible by the other reactions: this would have an ‘enables’ arrow to all
four reactions.

From the process graph in Fig. 2.4c, it is easiest to observe the feature of
(catalytic) closure, highlighted with thick black arrows. If reaction $R1$ is
taken out of the system indefinitely, reactions $R2$ and $R3$ can no longer
take place, as $R1$ was supplying the reactant a needed by both of them.
Likewise, if reaction $R2$ is stopped permanently then $R1$ cannot take place
as it’s catalyst $b$ is no longer produced and $R3$ also stops because $b$ was
required as a reactant. Finally, knocking out $R3$ will first stop $R2$
because catalyst $c$ is no longer produced, and this in turn will stop the
manufacture of catalyst $b$, halting $R1$.

Thus, given that a continual supply of food resources is available (i.e.
process $\\{F\\}$ is ‘on’), the closed set of reactions $\\{R1,R2,R3\\}$ in a
sense form a ‘strongly symbiotic’ group, producing the molecular and catalytic
requirements of each other, in a self-sustained manner. In the long term,
either all reactions $\\{R1,R2,R3\\}$ will be taking place together, or none
of them will be taking place. Reaction $R4$ is not in the catalytically closed
network, because it simply feeds off product $d$ made by reaction $R3$ (a
‘parasite’ or ‘side reaction’). Permanently disabling $R4$ has no effect on
the continuance of $\\{R1,R2,R3\\}$.333333The minimal example presented here
is engineered to convey the general idea of catalytic closure. Recent formal
treatment of the problem (?, ?, ?) has addressed detecting autocatalytic sets
in large randomly generated reaction systems. Typically, large AC sets exist
(maxRAFs), but these may be further composed of sub-networks which by
themselves are autocatalytic (subRAFs). In turn, subRAFs may be further
decomposed until minimal irreducible self-sustaining sets are reached
(irrRAFs). Therefore, in large systems, it is generally not the case that
permanently disabling one reaction leads to the disappearance of the entire
autocatalytic set.

Now returning to autopoiesis, ? (?, Ch7 therein) stated that autopoietic
machines implement organisational closure. He meant by this that, because an
autopoietic machine continually constructs its own material embodiment from
ambient nutrients, then every process in the system necessarily has to be made
possible from the actions of other processes in the system, and thus the group
of processes constituting the system are only viable collectively, just like
the closed set of reactions $\\{R1,R2,R3\\}$ in our autocatalytic example.
That is, if an autopoietic machine is taken apart or severely damaged, its
multimolecular, macromolecular and supramolecular components will disintegrate
quickly. An autopoietic machine can be depicted as a process closure diagram,
similar to Fig. 2.4c. Autopoietic machines however implement a specific type
of process closure, because one extra requirement is that some of the
processes must build a membrane and constitute the system as a unity in space
(part (ii) of the definition of autopoiesis).

Figure 2.5:  Autopoiesis as Organisational Closure. A cellular organism, such
as an amoeba (a) can be thought of as a special type of physico-chemical
system that exists because of a mutually supporting set of processes that form
a closed set (b). Closed set pictured in black. See text for discussion.

Figure 2.5 shows a single-celled amoeba both in physical space as we observe
it, and the autopoietic organisation giving rise to such a complex
physicochemical system represented (very) abstractly as a hypothetical graph
of closed process dependencies. Processes marked with $(m)$ are processes
concerned with the production of a semi-permeable membrane, or processes which
are made possible by the fact that a semi-permeable membrane is produced, such
as passive or active molecular diffusions across the membrane boundary. The
closed network of processes $\\{p1(m),p2,p3(m),p4\\}$, marked in black, has
the collective action to realise the same network over time, whilst also
materially constructing the amoeba in space. Dissecting the amoeba, disrupting
any one of the processes $\\{p1(m),p2,p3(m),p4\\}$ will eventually cause all
of the other processes in the closed network to stop, leading to the
irrecoverable disintegration of the amoeba.343434 Although there could be some
redundancy: if some processes are stopped, organisational closure could still
be ensured by other processes filling their role. Green process circles denote
events whose operation continues regardless of whether or not the amoeba
exists, but whose presence is required to create a niche in which the amoeba
can survive (e.g. by providing nutrients, or sunlight if the organism is
autotrophic). Blue process circles are events that the amoeba enables through
its operation, but are of no further consequence to the amoeba (like the
excretion of waste products). Red circles are processes entirely independent
of the amoeba, and their existence, or non-existence, is inconsequential for
the bug.

Processes and their closure in Fig. 2.5b are at a higher level of abstraction
than those in Fig. 2.4c. In the latter case, processes corresponded to
catalysed chemical reactions, and each process had its enabling conditions met
quite simply: i.e. when the required reactant and catalyst molecules were
present in the (well-stirred) reaction solution. The autopoietic machine of
Fig. 2.5, however, has a much richer set of physicochemical phenomena
simultaneously happening, not just catalysed reactions, but processes such as
solvent volume changes, the maintenance of molecular crowding, the use of pH
gradients to drive endergonic reactions, and the formation of supramolecular
structures. This dense web of entangled processes matter for the continuation
of the whole machine. As such, processes in Fig. 2.5b generally exist on
different levels of abstraction, run over different timescales, and are
generally only made possible by other processes constructing complicated
material constraints (for example, a supra-molecular membrane must be
constructed for an ion-pumping process to become possible). For this reason,
processes in Fig. 2.5b are harder to pinpoint exactly and are labelled more
anonymously as “p”.353535The difference in complexity between a cellular
organism represented as a closed set of processes, and an autocatalytic
reaction net represented in the same manner can be seen in a different way. An
autocatalytic set can bootstrap itself into existence from a food set, if some
of the initial reactions can proceed spontaneously at a slow rate, or if some
members of the food set catalyse the initial reactions. However, an
autopoietic machine cannot spontaneously emerge from a nutrient medium.
Rather, it has to come from an existing autopoietic machine, in an unbroken
lineage. The processes in the machine result from the build-up of complicated
material constraints. As such, the machine can self-maintain from a previous
functional state (and go on to divide, continuing the lineage), but its
complexity prohibits a full re-emergence of the system from the nutrients
alone.

Employing an organisational closure diagram to represent an autopoietic system
is beneficial in the following ways:

  1. 1)

The diagram gives a method to be specific about the closed set of processes
and map their relationships. This is one level of abstraction less than
autopoiesis, which does not detail particular process relationships but simply
requires that overall, the process network should continuously re-create
itself.

  2. 2)

The diagram makes clear that the closed set of processes constituting the
autopoietic system need not all necessarily take place within the physical
membrane of the system. In other words, the ‘frontier’ of the autopoietic
system is not the same as the membrane boundary (?, ?). Indeed, vital
processes in the organisational closure may take place across or even outside
the compartment boundary. An organism may fashion its environment into an
extension of itself, a niche necessary for its own self-maintenance (a spider
building a web, for example). Thus, it is more correct to consider the full
extent of an autopoietic system to include part of the environment as well.

  3. 3)

The diagram makes clear that organisational closure is a non-trivial concept.
Processes can have different types of enabling relationships. One process may
be a precondition for the existence of another, or it may simply just modify
its rate. Alternatively, there could be complicated enabling conditions for a
process, where different subsets of incoming arrows would equally serve to
enable it (?, ?).

####  2.2.3 Other Relational Biology Perspectives Similar to
Autopoiesis

Autopoiesis is not unique in providing a theory of the logical organisation of
biological systems. Other researchers have made different but closely related
attempts, and four of these are reviewed below. The four attempts focussed on,
excepting Kauffman, don’t tend to relate the logical organisation of a living
system with its autonomy like autopoiesis crucially does, but nevertheless,
they usefully illuminate the ideas in autopoiesis from different angles and
often in a less abstract language. In this way, they are useful to include in
this discussion to form a solid appreciation of what autopoiesis
means.363636Another cross-board comparison of organisational approaches to
life, with an emphasis on M-R systems, can be found in ? (?). After the
related theories have been reviewed, Section 2.3 then explains how an
autonomous systems perspective of life converts into a protocell research
program.

##### Kauffman’s Collectively Autocatalytic Sets and Work-Constraint Cycle

Autocatalytic sets were first proposed by Stuart Kauffman in 1986 as an
alternative paradigm to resolve both the emergence of complex polymers and the
appearance of connected chemical networks in the origin of life (?, ?, ?).
Already briefly reviewed in Section 2.2.2, the idea of an autocatalytic set is
a hypothetical network of (two or more) ongoing reactions that act to mutually
catalyse each other and sustain the reaction network as a whole. This is a
different idea to isolated catalysis, where the product of one reaction
catalyses another reaction, and also a different idea to isolated
autocatalysis, where a single reaction speeds itself up by making more of the
catalytic factor which is driving the reaction. Rather, catalysis is achieved
collectively: alone, the reactions would not proceed, but as a network with
catalytic closure, they can.

As well as having implications in the emergence of life373737Briefly, based on
the theory of phase transitions in random graphs, Kauffman and colleagues
argued that the sudden emergence of a large autocatalytic web of reactions
would be inevitable in prebiotic chemistry, given a sufficient diversity of
smaller molecules that could weakly catalyse the formation of other molecules,
including larger ones. The notion of an autocatalytic set is a general one,
not particularly restricted to certain molecule types, and such autocatalytic
sets were envisaged at different levels: between organic molecules and
unspecific catalysts, to explain how the first connected metabolisms emerged,
or between peptides and peptide catalysts to explain the appearance of complex
peptides., catalytic closure can be seen as a cornerstone feature of all
extant cellular life. In one sense, cellular metabolism can be viewed as a
complex autocatalytic set. Certainly, in order to function at all, protein
enzymes are required to selectively catalyse reactions that would otherwise
proceed extremely slowly, and the enzymes themselves are produced as part of
the whole metabolic network. In this regard, an autocatalytic set seems to
realise part (i) of the definition of autopoiesis: it forms a network (of
chemical reactions) whose operation (production of products and catalysts)
regenerates that same network (makes the catalysed chemical reactions
possible). From simple mycoplasma, to all instances of free living cells,
Kauffman remarked “The system as a whole is collectively autocatalytic. Every
molecular species has its formation catalysed by some molecular species in the
system, or else is supplied exogenously as food” (cited in ?, ?, p377).

In his subsequent work, Investigations (?, ?) and later, Kauffman appeared to
accept that autocatalytic chemical networks were a crucial part of cellular
operation, but not the whole story. Efficient channelling and synchronisation
of reaction pathways by highly specific enzymes is indeed a feature of cell
metabolism because without the influence of enzymes making specific reactions
occur rapidly in certain sequences, side reactions would ruin the organisation
of metabolism. But, another important feature of metabolism is that cells coax
non-spontaneous (endergonic) synthesis to occur overall by cleverly linking
spontaneous (exergonic) reactions, via various mechanisms. Living cells don’t
obtain all the high energy and structurally complex organic molecules they
require by simply absorbing them from the environment. Rather, they internally
synthesise the majority of these molecules by tapping an energy flow to piece
together smaller molecules into larger ones. Cells perform biosynthesis by
storing some of the energy released from the oxidation of food (spontaneous
reactions) in energy carrier molecules (ATP being the traditional example)
that diffuse throughout the cell. Such energy carriers then ‘power’ non-
spontaneous processes to convert smaller molecules into products with higher
energy (?, ?). Sometimes, energy carriers enable not only non-spontaneous
chemical transformations, but also non-spontaneous membrane transport
processes as well, like the pumping of ions against a gradient. However,
autocatalytic sets do not deal explicitly with the logistics of endergonic-
exergonic reaction couplings, and contain no notion of a surrounding membrane,
nor any concept of spatial organisation in fact.383838Also, whether non-
catalysed reactions are permitted by the definition is unclear.

Therefore, perhaps sensing a deeper problem, Kauffman started down the line of
developing a more abstract, more encompassing approach to investigate the
nature of autonomous agents in general, “that mysterious concatenation of
matter, energy, information and something more that we call life” (?, ?, p47).
Inspired by the example of a bacterium swimming up a glucose gradient to ‘get
food’, he asked what must a physical system be to constitute an autonomous
agent? and came up with a tentative answer: an autonomous agent is a self-
replicating system that is able to perform at least one thermodynamic work
cycle (?, ?).

The perspective on the logic of autonomous agents that Kauffman arrived at in
his book Investigations was similar in character to autopoiesis, but instead
of being purely relational, made more use of thermodynamic concepts. Rather
than talking about abstract ‘component production’, he instead looked at the
problem of cellular organisation through the lens of work and energy. Any
system able to do useful work has to set up some kind of constraints on a raw
energy flow, to channel this flow toward some specific means (Kauffman
followed ? (?) in seeing work as the “constrained release of energy into fewer
degrees of freedom”). Kauffman said that the work performed by cells was
indeed due to constraints existing on energy flows, but these constraints were
mostly not fixed, instead they were actually constructed or manipulated by the
cell itself as it performed work. So, the idea of a work-constraints (W-C)
cycle was born: in cells, work is made possible by a web of constraints, and
this web of constraints exists largely because work is done.393939 Cells also
directly use work, for movement, etc. This circular thinking has the same
flavour as autocatalytic sets, but is pitched at a higher level of
abstraction: instead of a network of reactions being maintained (that produce
species, enabling those same reactions), a network of constraints is
maintained (that enable work, remaking those same constraints).

Helping to understand the concept better, the following hypothetical example
of propagating work and constraint construction in the cell was given by ? (?,
p101). Firstly, lipid synthesis for the membrane takes work to accomplish i.e.
spontaneous catabolic reactions releasing energy from food need to have this
energy channelled into high energy carriers, which then permit the non-
spontaneous biosynthesis reactions making the lipids, to proceed. Once
produced, the lipids then incorporate into and maintain the bilayer membrane,
and this supramolecular structure provides an oily internal environment
favourable to some reactions, because it changes the translational,
vibrational and rotational motions of the reactant molecules. In other words,
the bilayer has modified the boundary conditions of those reactions (modified
the constraint acting upon them), so that they now take place. Products of
such reactions may go on to do more work and modify more constraints, like
diffusing across the cell, giving up vibrational energy to do work opening an
ion channel, and so on.

Therefore, apart from the ubiquitous use of specific catalysts to channel
reaction pathways, cells are generally also in the business of coupling
spontaneous processes to non-spontaneous ones in complex webs to synthesise
components (and also capitalise on the affordances offered by self-assembly
e.g. protein folding and spatial membrane formation), such that they can exist
as complex non-equilibrium systems. We have no theory, Kauffman claims, that
allows us to capture this kind of organisation where work propagates, makes
constraints, and these constraints enable further work to be done.

Figure 2.6:  A Rube Goldberg Machine is a comical device, but also serves well
in a more scholarly sense to convey the concept of propagating work, as
discussed by Kauffman (see text). Artwork Copyright © and TM Rube Goldberg
Inc. All Rights Reserved. RUBE GOLDBERG ® is a registered trademark of Rube
Goldberg Inc. All materials used with permission. rubegoldberg.com.

A useful metaphor employed by Kauffman to illustrate the concept of
propagating work are machines of the Rube Goldberg type (Fig. 2.6). These
machines consist of a series of stages where in each stage some kind of
potential energy is converted to work, and the work done triggers the next
stage. The machine is able to operate, because the constraints (i.e. the
positioning of the apparatus) have been carefully set up by a human
beforehand, and work propagates through the chain only once. An engine is a
machine at a higher level of organisation, able to bend a linear chain of work
tasks into a cycle, arriving back at its original configuration, because some
of the energy released during the spontaneous steps (gas explosion in the
cylinder head) is used to drive the non-spontaneous steps necessary to reset
the cycle (pumping of fuel, re-compression of cylinder). At a yet further
level of organisation lies a cell, able to perform continuous work like an
engine does, but additionally some of the work it continually produces is used
for its own means to actually remake the cellular structure (the crucial
constraints) in the process.404040Rube Goldberg machines and engines can also
dynamically build constraints, but to a much more limited extent than a cell
does. (For example, a step in a Rube Goldberg machine might spray a wall
white, and this act enables a subsequent step to reflect a beam of light from
that wall.)

Departing from autopoiesis, Kauffman cites ‘closure’ as having being achieved
when the cell divides ‘making a rough copy of itself’. For him, reproduction
is a vital aspect of an autonomous agent, and the final outcome of the web of
work and constraints.414141but some cells, like heart and brain cells do not
divide after their initial development phase, yet still constitute bonafide
autonomous living agents. Autopoietic theory, on the other hand, is typically
dismissive of cell division as a central feature of life, and instead uses
‘closure’ to mean the closure of processes allowing the continual re-synthesis
of the same system (because for Maturana & Varela, robust self-maintenance
logically preceded the ability to divide).

##### Rosen’s (M,R) Systems

In the late 1950’s, and preceding the notion of autocatalytic sets, relational
biologist Robert Rosen developed a mathematical framework called (M,R) or
metabolism-repair systems aimed at capturing the essential logic of life
(later summarised in ? (?); see ? (?) or ? (?) for introductory overviews).
Rosen observed that living organisms possess two distinct mechanisms, one for
the actual functioning, and another for the repair of the functional part.
Human-engineered machines, on the other hand, are different: they are
typically produced to execute a specific function, and have no (or extremely
limited) means for self-repair, instead relying on an external agency for this
task. Indeed, as ? (?) remark, a human-made machine even has difficulty
providing information to an external agency about the operational status of
all of its components, let alone having the capacity to repair them.

Rosen observed that every living cell is based on a metabolic network that
relies on catalysts for its operation, but rather than being given from the
outside, these catalysts are synthesised by the metabolic network itself.
Furthermore, Rosen observed that these catalysts (or as he saw them,
mathematical mappings from sets of reactants to sets of products) had a
tendency to become degraded by chemical transformations and/or diluted by
system growth, lessening their concentration, and so would continually need to
be ‘repaired’ by some mechanism. This set up the following conundrum that
Rosen tried to resolve with the mathematical machinery of functions and
category theory:

Catalysts (M) are required for the successful operation of a metabolic
network, but each catalyst inherently degrades and thus is required to be
continually ‘repaired’ by a subnetwork of reactions (R). In turn, the
subnetworks repairing each catalyst also rely on catalysts which also need to
be repaired, and so on.

Only two escape routes exist out of this puzzle; either an infinite regress
(not a valid solution), or catalytic closure, where it is the collective
action of the whole metabolic network that constitutes the repair mechanism
for the repair mechanisms. Rosen’s work was an abstract - some would argue
obscure - mathematical attempt to resolve how catalytic closure could be
realised by a metabolic network. Rosen additionally required the stronger
condition that this catalytic closure should only be realisable in a single,
unique way (so called ‘organisational invariance’ or ‘invertibility’).
Essentially, Rosen was seeking solutions to the equation

$f=f(f)$

which states that metabolism is effectively a mapping function $f$, which acts
on itself, to produce itself (?, ?).

At their core, both (M,R) systems and autopoiesis were theories emphasising
that the underlying cause for the existence of an organism is a closed network
of relations, and these relations remain invariant despite the flowing (far-
from-equilibrium) material structure of the system. Rosen expressed this idea
by saying that organisms were ‘closed to efficient causation’ but open to
material causation. Both autopoiesis and (M,R) were formulated in abstract
terms, at the systems level, in a true relational biology spirit without any
mention of material implementation nor thermodynamic considerations. However,
crucial differences also exist between the two theories. One difference is
that (M,R) systems only appeared to focus on the replacement of catalysts, not
all cellular structures and components as autopoiesis did. Another obvious
difference is that no notion of a membrane entered into (M,R) systems. Other
comparisons have been made by (?, ?).

Although effort has been made to make Rosen’s mathematical approach a little
more understandable (?, ?, ?), it is fair to say that his approach to
biological organisation remains the one most shrouded in mystery and
uncertainty. To the extent that (M,R) systems have been reviewed above, it
seems unclear how they are qualitatively different to autocatalytic sets.
Autocatalytic sets seem to trivially solve the issue of a catalysed reaction
network in which all catalysts are produced by the network itself, and thus
the recursive problem of ‘what repairs the repair system’ attacked by Rosen
seems irrelevant. (M,R) systems without the ‘organisational invariance’
property seem to be identical to autocatalytic sets which do not have
catalysts supplied in the food set424242For example, the (M,R) metabolic
system analysed in ? (?) could equally be labelled as an ‘autocatalytic set
that has none of the catalysts supplied in the food set’., and no concrete
chemical examples of (M,R) systems with the elusive ‘organisational
invariance’ property seem to exist. One extra puzzle is why Rosen himself
never discussed worked examples of (M,R) systems using abstract chemical
notation.

##### Gánti’s Chemoton

One intellectual contribution made by Tibor Gánti to clarify attempts at a
definition of life were his absolute and potential lists of life criteria,
already recited in the introduction of this chapter. However, these life
criteria formed just the starting point of Gánti’s research program. The
centrepiece was his Chemoton model, a kind of minimal blueprint for a
proliferating, instruction controlled and membrane-bound chemical system that
satisfied all the life criteria, and one which Gánti claimed captured the core
organisational logic of all living cells (?, ? see Fig. 2.7). Gánti developed
the chemoton to fill the role of the most fundamental and indivisible unit of
biology, in the hope of transforming the science into a more exact and well
grounded discipline like physics or chemistry.

Figure 2.7:  The Chemoton. The logical coupling of a metabolic, genetic and
membrane system, claimed by Tibor Gánti to minimally implement a program
controlled proliferating microsphere system. On this diagram, it should be
noted that the outer circle corresponds to actual physical organisation of
matter, i.e. a self-assembled physical membrane in space, whereas the inner
circles correspond only to relational organisations of processes, i.e. the
chemical cycles don’t actually occupy fixed spatial positions, able to
physically enclose other cycles: instead, reactions happen at all points in
the well-stirred interior. Reprinted from (?, ?).

The chemoton model can be seen as a culmination of some key observations made
by Gánti. First of all, he observed an abstract property shared by all
continuously operating machines, including all lifeforms: all must set up
constrained pathways on the flow of energy between a high energy and low
energy source, transforming part of this energy into useful work (an
observation not dissimilar to Kauffman’s, above). Secondly, he noted that
biological systems are unlike any technological machines that we can currently
produce, in that they manipulate chemical energy by chemical means. Biological
cells are ‘ticking chemical machines’, and because all parts are implemented
at the size scale of molecular and supramolecular chemistry, this endows they
with unique abilities, such as the ability to synthesise all of their own
components for repair, growth and eventual reproduction. Hence, he narrowed to
domain of living systems to that of fluid automata, remarking that “in looking
for the fundamental principle of life, we have to examine the nature and
organisation of ‘constrained paths’ involving chemical changes capable of work
performance, regulation and control in solutions” (?, ?, p74, emphasis added.
See also ?, ?). Finally, Gánti observed that it would make sense to base a
characterisation of life’s organisational logic at the level of the simplest
cells, the prokaryotes. He observed that all prokaryotes function by coupling
three distinct subsystems: a metabolic system converting energy and building
structures, a genetic information system that controls this metabolic system
and encodes heritable traits, and finally a membrane system keeping the whole
operation together and facilitating system reproduction.434343As remarked in
Chapter 1, this triad is currently used to guide protocell research, and back
in 1971, Gánti was quite unique amongst his peers (excepting Maturana and
Varela) in suggesting a bounding membrane as one of the necessary components
for life. Viruses are ruled out by this triad classification, because they
lack metabolism. Single replicating molecules are also ruled out as ‘living’
too. For Gánti, life was not embodied in single molecules, but was rather a
systemic property based on the tight integration of the latter three
subsystems.

With the chemoton model, Gánti essentially tried to solve the problem, to a
first approximation, of how a metabolic, genetic and membrane chemical system
must be stoichiometrically coupled together, in order to form the most basic
instance of a proliferating chemical microsphere system, whereby microsphere
reproduction was program controlled and sustainable.444444 ? (?) also
described a logic for a proliferating minimum protocell system, based on
realistic prebiotic considerations. Their hypothetical system did not have
template program control, but could still proliferate by capturing light
energy via pigment molecules in the membrane. This energy was stored in
electrochemical ion gradients across the membrane, which, in turn, could
enable internal lipid synthesis from a precursor, growing and proliferating
the system. Referring to Fig. 2.7, the chemoton functions as follows. The
autocatalytic metabolic cycle in the chemoton transforms high energy nutrient
$X$ into low energy waste product $Y$, and as it turns, produces template
monomers $V^{\prime}$ and membrane precursor $T^{\prime}$. The template
monomers $V^{\prime}$ accumulate inside the system until a threshold
concentration is reached. Once the threshold concentration is superseded, the
template molecule $pVn$ spontaneously ‘unzips’ into two complementary base
strands.454545Although the problem of non-enzymatic replication of nucleic
acids is actually far from being solved (?, ?). At this moment, monomers
$V^{\prime}$ start pairing to the base strands, constructing two new whole
template molecules, whilst also producing a byproduct $R$ in the process. This
byproduct combines with the membrane precursor $T^{\prime}$, creating new
amphiphilic molecules for the membrane, which grows, deforming in shape until
division is achieved. Therefore, the membrane grows in bursts, synchronised
with the replication of the template molecule inside the chemoton.464646Gánti
did not indicate how reliable spatial segregation of the newly formed template
molecules into the daughter chemotons was achieved. This could also be argued
as very relevant to the logic of proliferating life. The system is program
controlled by the template, in the minimal sense that the length of the
template (the template, after all, has no sequence data) affects the
reproduction time and thus the dynamics of the cell cycle of the
chemoton.474747 In order for a pattern to count as ‘information’, Gánti
required that another system existed capable of reading and interpreting the
pattern. The chemoton system read and interpreted the length of the template
to control the dynamics of the division cycle.  Crucially, all three
subsystems are mutually dependent on each other, and the program controlled
reproduction of the whole ‘super system’ is only possible when all three are
present and functioning. Notably, Gánti argued that correct functioning could
only be obtained if each of the three cycles was autocatalytic.484848 The
membrane growth process can be regarded as autocatalytic because the membrane
absorbs membrane monomers at a rate proportional to its surface area,
accelerating its growth as it grows larger. In the personal view of the
present author, the claim that all cycles require to be autocatalytic for
correct functioning is not immediately obvious.

To summarise, the chemoton system used chemical cycles to channel an energy
difference existing between nutrients and waste into the construction of more
program controlled micro-sized ‘ticking’ machines. Undoubtedly, the chemoton
is a false model of cellular life, for indeed no life form either directly
implements, nor could be artificially constructed using the exact chemical
sequences proposed by Gánti. However, Gánti’s objective was to propose a false
model which was nevertheless instructive or heuristic in understanding
something about the essence of living organisation. Gánti’s engineering
background gave him a practical approach to the problem of ‘what is life?’,
absent from the other more abstract relational biology approaches discussed in
this subsection. The emblematic schematic of the chemoton represents a visual
thinking point that has directly inspired a number of protocell simulation
studies (e.g. ?, ?, ?, ?, ?, ?, ?).

Similar to an autopoietic system, a chemoton operates in physical space,
synthesising its own components, including a bounding membrane that enables
the internal processes to keep running. Departing from autopoiesis (and the
other perspectives discussed here on biological organisation), the chemoton
also includes a heritable ‘genetic information’ system as an essential
participant in the organisational logic of life. The chemoton is constructed
to address Gánti’s absolute and potential life criteria, whereas autopoiesis
only targets the absolute criteria. In fact, the chemoton does not operate in
a stationary self-maintaining state, as an autopoietic system is envisaged to
do. Rather, to avoid an osmotic burst eventually caused by the exponential
accumulation of impermeable internal components, a functioning chemoton must
continuously synthesise membrane material and then divide. On this difference,
Gánti remarked that “living systems are fundamentally growing (accumulating)
systems, in which more matter enters than leaves. A growing system cannot be
in a stationary state” (?, ?, p73). Differing from autocatalytic sets and M-R
systems, the chemoton circuit diagram contains no chemical paths accelerated
by catalysts. Only spontaneous reactions are included. Rather than being
essential for life, Gánti argued that catalysts only speed up reactions that
can already occur spontaneously and don’t influence the stoichiometry of the
overall chemical change between reactants and products. Stoichiometric
coupling and not kinetics was the level of analysis that interested him. He
stated that “The truly fundamental elementary units of biology should not be
sought in the enzymatic regulation, but in the system regulated by the
enzymes” (?, ?, p63).

##### Constructive Dynamical Systems and Component Systems

Through a series of inspiring papers in the mid 90’s, Walter Fontana and Leo
Buss enquired into the shortcomings of the traditional dynamical systems
perspective as being able to represent biological organisation. They argued
that the way Newton taught us to formulate and solve dynamics problems was
correct, but did not reach far enough to describe the processes and material
transformations happening in whole organisms. What was needed, they said, was
a new theory of constructive dynamical systems (?, ?, ?).

Their essential point was as follows. Traditional dynamical models can only
capture change in the system they model by value changes in scalar state
variables. From the outset, the modeller is charged with identifying all of
the relevant variables and their coupling for the entire lifetime of the
system being modelled, such that the state space is of fixed size and
mathematical tools such as stability, sensitivity and bifurcation analysis can
be applied. However, this setup is quite brittle, for it cannot cope with more
profound changes in the system being modelled, such as the creation of
qualitatively new objects or new constraints (boundary conditions) which
emerge through the action of the system dynamics.494949It is true that some
finite amount of structural change in a system can be accommodated by using a
traditional dynamical system. For example, varying parameters can be handled
by making them state variables. Or, changing degrees of freedom can be
accommodated by starting with a high dimensional state space and specifying
dormant state variables that become active when necessary. However, most
systems with emergent constraints can outgrow a fixed description. Fontana and
Buss called this is the ‘object problem’ of dynamical systems (?,
?).505050Advances have been made in the analysis of hybrid dynamical systems
that combine continuous and discontinuous state changes (?, ?). But, such
hybrid systems still have a fixed equation structure, and thus still face the
object problem. The problem arises because converting a real world system into
a traditional dynamical model always loses a handle on the actual objects
which are interacting; these objects are instead dissolved into scalar state
variables. In the final dynamical equations, there exists no mechanism and no
information with which to construct new evolution equations if the underlying
objects represented by the system change, i.e. when the current state
variables fall into critical ranges or ratios. Indeed, this is by design, as
any dynamical model ‘freezes’ the problem domain, and it is assumed all that
is relevant about the problem has been included in the model.

However, the construction/destruction of objects and the
appearance/disappearance of constraints is a crucial feature in the
biochemical dynamics of living systems.515151Also, constraint construction via
dynamics is also feature of the operation of social insect systems, i.e. in
the concept of stigmergy (?, ?) whereby individual agents lay down structural
constraints in the environment as a cue to later guide the behaviour of other
passing agents. By this process, wasps are able to indirectly communicate and
build a honeycomb, and ants are e.g. able to organise collective cemeteries
for the dead. In response to perturbations, cells can synthesise new
components and radically change the properties of their embodiment,
effectively becoming a dynamical system with different relevant state
variables and evolution equations. Cells can do more than simply change their
state. Therefore, Fontana and Buss said that a new type of dynamical model
would be required to fully capture biological organisation: one that can move
in an object space (a structural space of evolution equations), as well as in
the standard phase space (a space of states possible with the current set of
evolution equations). This new type of dynamical system would not only flow in
phase space, but could also change the dimensionality and flow features of the
phase space, as it evolved along the state trajectory.

As a first example of a dynamical system able to deal with the object problem,
Fontana and Buss proposed a model artificial chemistry able to execute
reactions over a growing variety of chemical species (where molecules were
implemented as expressions in lambda calculus). This constituted a rudimentary
example of a dynamical system able to modify its object structure (the types
of species present: novel ones could appear) as well as changing its state
(the concentration of each species present). Appendix A of this thesis
presents a different approach to simulate general constructive dynamical
systems by using a framework based on petri nets.

From the dynamical systems viewpoint offered by Fontana and Buss, a self-
maintaining system is one whose equation structure is not fixed a priori, but
results as a stabilised aspect of the component dynamics it causes (i.e. the
system occupies a stable attractor in object space). This notion of biological
organisation can be seen as a more formal statement of autopoiesis. It differs
only in that there is no explicit mention of a bounding membrane.

Another proposal congruent to constructive dynamical systems is component
systems (?, ?). Component systems are made of interacting components able to
create an open-ended variety of new components, or destroy existing ones.
Therefore, they also constitute systems able to build their own internal
constraints and modify their governing dynamical description. Kampis holds the
view that component systems are only computable over the short term when their
dynamical description remains static. In the longer term, he says, they are
not computable because their changing description prohibits them from being
mapped to any single simulation algorithm.

###  2.3 Autonomy is a Missing Conceptual Backdrop
for Origins of Life Protocell Research

At this point, it is useful to recapitulate what has been said in this chapter
so far. Firstly, the introduction revealed that two distinct general
conceptions of life are followed by (and indeed partition most) scientists and
philosophers, in lieu of a unanimously agreed definition of life. The pair
were the ‘evolution’ and ‘autonomy’ conceptions of life.

Under the popular ‘evolution’ (or diachronic) conception of life, a cell is
primarily considered as a self-reproducing entity that evolves. This view
holds that the most significant feature of living systems is their genetic
information content (DNA) and the replication and passing on of this
information content to future generations. Through a pure evolutionary lens,
the origin of life is straightforwardly conceived as a continuum between
replicating ‘informational’ molecules at one end and more complex reproducing
living cells (that embed replicating informational molecules) at the other
end. The broad challenge of the evolutionary-based origins of life research
program is to decipher how the first self-replicating RNA molecules appeared
and then how they evolved, via natural selection at the level of chemical
assemblies, into membrane bound DNA-RNA-protein architectures (“cells”). The
current mainstream line of investigation in protocell research is located
firmly within the evolutionary view. Szostak’s ribocell thesis (Section 2.1.1)
posits that a major transition in prebiotic chemical evolution was the
insertion of RNA molecules into lipid compartments: this duo opened the
floodgates of evolution (leading onto the development of internal metabolism,
translation machinery, energetics etc.) as soon as the replication of the RNA
and the division of the compartment became synchronised. The long term goal of
the ribocell project is therefore to achieve a minimal synthetic system that
solves this synchronisation problem.

Conversely, under the marginalised ‘autonomy’ (or synchronic) conception of
life, a cell is primarily considered as an autonomous system that, through its
organisation, self-produces and self-maintains its own localised material
existence in space. This view holds that the most significant feature of
living systems is their system-level ‘autopoietic’ organisation that allows
for their continued existence and produces their outward purposive behaviour
(as reviewed in Section 2.2.2). The systems-oriented autonomy perspective does
not exclude that genetic molecules are important, but they are not the key
issue (see below).

As has been discussed, the evolutionary perspective is already heavily
embedded in research programs into origins of life. The questions that the
remainder of this section attempts to answer are: what alternative type of
research program into origins does an ‘autonomy’ conception of life propose?
what are its main claims? and why is such a program vital to develop protocell
research further?

A key point is that the autonomy conception of life instils a deep systemic
appreciation of the way molecules have to organise in space and time in order
to form a functional far-from-equilibrium biological cell. The autonomy
approach to origins projects these same systems-level considerations back onto
the protocells that proceeded the first cells. Although perhaps more difficult
to articulate than the evolutionary view, the autonomous systems view is
primarily concerned with explaining how protocells developed in organisation
up to the extremely complex autopoietic organisation of full-fledged cells.
The main question posed is along these lines: how did protocells transition
from more rudimentary self-maintaining chemical reactors into chemical
‘agents’ that are able to fabricate the majority of their components by
controlling energy/matter flow through a boundary that, also, is of their own
making?

The role of the protocell membrane is a crucial aspect in the autonomy view of
origins. Rather than being regarded simply as a secondary ‘container’ holding
things together, under the autonomy account, the membrane is regarded as a key
integrated part of the protocell system. The membrane is the primary interface
that controls energy and matter exchanges between a protocell and its
environment. Autonomy brings to the fore the fundamental issue of how
protocells were able to progressively take control of their membranes (by
effectively coupling internal metabolic networks with membrane production and
trans-membrane processes, see Chapter 3), first turning into basic autonomous
agents capable of robust far-from-equilibrium self-production in varied
environments, and then into more complex autonomous agents with reliable
division and heredity properties (?, ?, ?). The role of a self-assembled
membrane in channelling matter and energy flow through a protocell system only
becomes obvious from an autonomy perspective. Most evolutionary-based
protocell research does also see membranes as relevant, but not in such a
strong sense: here, membranes are simply passive structures that serve to
segregate molecular populations.

In trying to grasp the tenets of an autonomous system account of protocells,
it is revealing to compare it with the evolutionary ribocell approach. The
ribocell approach postulates that ‘limping’ protocells composed of naked RNA
genes in compartments, with the help of fortuitous environmental
conditions525252such as the availability of nucleic acid precursors, shear
forces to prompt compartment division and heat cycling to separate RNA
strands., managed to get onto the runway of evolution by natural selection.
Conveniently, evolution then solved all of the harder problems to make
functioning, fully integrated cellular systems. How evolution actually
achieved each stage of protocell integration is outside the scope of the
ribocell project. On the other hand, the autonomous systems perspective
directly confronts the hard issue of cellular integration. It tries to
explicitly explain how protocells incrementally developed in order to solve
the key problems of cellularity – such as problems of selective permeability
(adequate nutrient access and waste disposal from compartment), osmotic water
flow, and the harnessing and distribution of free energy resources – so that
they could eventually exist as robust and adaptive far-from-equilibrium
systems. Whilst postponed ‘for evolution to deal with’ by ribocell
project535353Although under criticism here, it should be noted that the
ribocell research program does not contradict the autonomous systems approach.
It is simply more of a shortcut towards integrated protocells. The ribocell
program does indeed see the linking of protocell metabolism and membrane as
relevant (see for example ?, ?, ?, ?). Additionally, the ribocell program is
generating a wealth of excellent data about lipid vesicles (e.g. permeability
measurements) and relevant physical effects (e.g. protocell competition)
within the origins of life field., the systems integration problem is the main
problem in the origins of cellular life and imperative to confront in detail
if a comprehensive account of origins is to be reached. This is the reason why
the autonomy perspective is the ‘big picture’ framework vital for protocell
research (even if the integration problem is a harder and more diffuse
scientific challenge than the well-defined synchronisation problem of the
ribocell).

Additionally, protocell behaviour (and how this stems from the chemical
organisation of a protocell) is also naturally included under an autonomous
systems account of protocell development. How protocells originated the
ability to act on their own behalf as agents, to adapt to new or varied
environments, or how they developed mechanisms to move in a more directed way
(other than just by brownian motion or convection) are important lines of
research that are not normally included under the evolutionary view. Recently,
an increasing number of studies are acknowledging that a protocell that only
replicates would be a poor mimic of cellular life. As ? (?) state, “life is
not simply a machine that divides. Instead, life is integrated with its
surroundings, both on a cellular and a chemical level.” (p591). Therefore,
there now exists a building inertia to investigate how the non-replicating’
aspects of cellular life could have had precursors in protocells too (?, ?, ?,
?, ?, ?, ?, ?).

Finally, on the controversial issue of genetic material, the autonomous
systems account favours the appearance of simpler self-maintaining protocell
systems first, followed by protocells with template-controlled metabolisms
later.545454In terms of the Template (T), Metabolism (M) and Compartment (C)
subsystems of protocells, the autonomy approach tends to favour the hypothesis
that M+C $\rightarrow$ T+M+C (far-from equilibrium self-maintaining reactor
systems later incorporated templates), and the ribocell approach supports the
hypothesis T+C $\rightarrow$ T+M+C (close to equilibrium ‘gene bags’ later
evolved metabolism). This is for the reason that protocells would first have
to become units of a basic complexity, adequately controlling energy and
matter flows, in order to be able to support a further increase of complexity
brought about by templates. As ? (?, p249) explain: “Before higher levels of
complexity (based on macromolecular mechanisms, e.g., genetic or enzymatic
mechanisms) are achieved, there has to be some self-constructing
organization…through which the material and energetic problems associated to
the actual capacity to generate that complexity are solved.”. Another, more
basic reason for considering templates after metabolism is that metabolism may
be necessary for assisting the fabrication and repair of the templates. Once
templates had successfully become incorporated into metabolism, they would
then open up new possibilities of metabolic control (e.g. enzymatic control of
metabolic pathways) and would enable the synthesis of new structural elements
not possible before. Additionally, templates would enter autonomous protocells
into an evolutionary dimension, allowing for the reliable division and
heredity of their complex organisations (discussed in ?, ?, ?).

Now that a broad outline has been sketched of how the autonomous systems
conception of life transfers into a protocells research agenda, Chapter 3 goes
into more detail about how the origin of autonomy in protocells can be
modelled and defines the area in which this thesis makes its contributions.
Later on, the discussion (Section 5.1) elaborates more on the arguments made
in this section.

##  Chapter 3 Autonomy in Protocells:
A Semi-Empirical Approach

The biological autonomy conception of life was introduced in detail in Chapter
2 as a constellation of ideas revolving around the abstract principle of
autopoiesis, and the conclusion of Chapter 2 started outlining how such an
autonomous perspective can transfer into an important systems-oriented
framework for research on protocells. This Chapter aims to bridge the
conceptual and scientific worlds by making more precise how the origin of
autonomy in protocells can be approached through a ‘semi-empirical’ scientific
research program based on theoretical modelling (Section 3.3) and goes on to
define the sub-area in which this thesis makes its primary contributions
(Section 3.4). To begin, however, it is explained why the theory of biological
autonomy fundamentally requires parallel efforts in theoretical and empirical
modelling in order to understand the origin of autonomy in protocells.

###  3.1 Perspective: The Development of Biological
Autonomy Theory

The concept of biological autonomy has undergone much development over the
past 40 years. This can be attested by comparing Francisco Varela’s original
abstract exposition of it, closely tied to autopoiesis (?, ?), to the state of
the art synthesis (?, ?), still conceptual and bearing the legacy of
autopoiesis, but considerably expanded (notably, reconciling autonomy with
evolution), and more closely linked to empirical examples.

Some of the key developments to biological autonomy will be briefly
recapitulated here, with pointers to the relevant literature for the
interested reader. To begin, one development has been the clarification of the
notion of organisational closure (discussed in Chapter 2), and how it maybe
more accurate to think of a closure of constraints operating in organisms,
when speaking of an organisational closure (?, ?, ?, ?).111‘Constraints’ are
boundary conditions that emerge through the dynamics of the system itself.
They are usually material configurations and in turn reduce the degrees of
freedom of certain components in the system. This work has helped sharpen what
separates autonomous biological systems from less complex physical systems
exhibiting closure, like the water cycle, or exhibiting self-organisation,
like dissipative structures such as candle flames or hurricanes (?, ?, ?).

Other developments to biological autonomy have involved identifying important
aspects that the theory of autopoiesis either missed out, or treated in an
inappropriately trivial way (?, ?). The role of the cell membrane was one
aspect not emphasised enough by autopoiesis. It has since been emphasised that
whilst the membrane does indeed bound an autonomous agent in space, it more
significantly serves as the interface through which the autonomous system
controls its relations with the outside world, including the energy-matter
flow through it (?, ?, ?). This shifted the perspective: autonomous systems
regarded before as systems ‘resisting perturbations and maintaining their
organisation’ became more regarded as systems that necessarily interacted with
the environment as agents as an essential part of their autonomy. Another
important aspect neglected by autopoiesis was the historical dimension of
autonomous agents, i.e. the relevance of genetic templates, populations and
evolution. Some recent work has indicated that genetic templates, being
dynamically decoupled from the self-maintaining organisation of an autonomous
system are a relevant addition to the theory of biological autonomy.222Under
this type of terminology, a ‘dynamically decoupled’ component or subsystem is
one that is “sufficiently independent of the processes of material and energy
flow that it can be varied without disrupting these basic processes, but still
able to be linked to parts of the mechanism so as to be able to modulate their
operations” (?, ?). Such templates grant a biological system capacities of
increased robustness (for example, by allowing the system to switch into
qualitatively different modes of self-maintenance; ?, ?), and they also open
the way for reliable heredity and the eventual open-ended evolution of
autonomous systems (?, ?, ?).

Further clarifications to the biological autonomy framework have consisted in
debates about about autopoiesis being necessary and sufficient (or just
necessary) to capture the phenomena of cognition and life (?, ?, ?, ?,
?).333‘Cognition’ roughly means the operation of acquiring, processing and
storing sensory inputs, and then using this information to guide successful
future actions in the environment. Whereas Maturana and Varela always held the
position that cognition and life were entailed by the implications of
autopoiesis, the consensus view emerging from these debates is that
autopoiesis is only necessary and not sufficient for cognition and life.

Yet other supplements to the theory of biological autonomy have dealt with
making the notion of ‘norms’ more concrete (?, ?) and research on how autonomy
could be extended beyond the paradigmatic case of the single cell towards
communities or aggregates like biofilms or multicellular organisms (?, ?).

Finally, a very important contribution to the theory of biological autonomy
has been the insistence that biological systems are physical systems (?, ?, ?,
?, ?, ?) and, therefore, should not be treated purely as abstract mathematical
objects implementing closure (i.e. as autopoiesis regards them). Rather,
organisms are constrained to further obey the laws of thermodynamics. This
realisation has helped to make a list of basic ingredients necessary for
achieving the synthesis of autonomous systems (e.g. semi-permeable membranes,
catalysts and energy currencies are required444Semi-permeable membranes are
necessary for any autopoietic system. If a membrane is fully permeable, then
there is no distinction between cellular system and environment. If a membrane
is completely impermeable, then the cell cytoplasm will settle to chemical
equilibrium. Catalysts in turn are necessary for the temporal coordination of
reaction pathways, and energy currencies are necessary to drive endothermic
processes at different sites around the cell.), and has also highlighted that
all autonomous systems necessarily require to be thermodynamically open
systems, continually traversed by a flow of matter and energy.

Therefore, the theory of biological autonomy has been quite fertile as regards
to developments in the past 40 years. However, whilst undoubtedly valuable,
these developments have not really ventured outside the domain of abstract
relational biology. Instead of modelling cellular autonomy in a concrete way,
they have been exercises in expanding, re-ordering and making more precise the
high-level characterisation of biological systems.

####  3.1.1 Why Biological Autonomy Needs Theoretical Models

Staying at the conceptual level is valid if the overall goal is to use
biological autonomy as a tool to define life, or to articulate alternative
general standpoints, for example as some authors have done in cognitive
science.555In cognitive science, autopoiesis underlies new currents of
thinking which links cognition in living systems with the fact that their
bodies are self-individuating and ‘flowing’ dynamic structures (?, ?, ?). This
position stands in contrast to previous views that saw embodiment as
irrelevant to cognition/intelligence, or only relevant in a limited role, i.e.
as just an interface getting inputs from and delivering outputs to the
environment). However, if the aim is to (i) develop a grounded account of how
autonomy is actually realised in specific instances of biological cells or
(ii) to develop an understanding of how autonomy first originated in protocell
systems (as is the aim in this thesis), then a level of analysis based at the
overall organisational logic of autonomous systems is inappropriate. Rather,
the level of analysis must be taken down towards the detailed molecular
structure of particular cell or protocell systems and theoretical models need
to be developed where time, states, frequencies, flow rates, spatial details,
molecular details, molecular interactions etc. are all returned to the
picture. An abstract theory of biological autonomy is able to discuss the
generic organisation of autonomous systems at length, but lacking empirically-
based models, it is prohibited from taking the further steps of being able to
accurately explore system dynamics and make predictions about the behaviour of
specific cells/protocells. Therefore, only theoretical/computational models,
mathematical systems-level analysis and targeted experiments will potentially
give insight into how autonomy is actually realised in living cells and how it
arose in protocells.

The main problem with modelling biological autonomy is that the goal of
autopoiesis (at the centre of the framework) was precisely the opposite: to
purposely throw away all of the structural details of the cell in order to
keep only the core organisational logic of the system. Autopoiesis and similar
relational biology approaches like Kauffman’s W-C cycle, or Rosen’s M-R
systems are hence - and unsurprisingly - not suggestive of immediate routes to
low-level cell dynamics models.666In general, high-level theoretical
frameworks give a hint of how a certain system operates overall, but no clue
as to the behaviour of specific instances (i.e. they underdetermine the
phenomena they relate to). In biological autonomy, autopoiesis broadly defines
global cellular logic, but does not determine the complex dynamic behaviour of
a particular cell. The theory of evolution by natural selection identifies the
general requirements for an evolving system, but does not determine which
lineages will develop in any particular population (or when increasing
complexity will result). Likewise, in physics, the second law of
thermodynamics states that entropy always increases in physical systems, but
this does not determine the ordered phenomena demonstrated in certain far-
from-equilibrium systems (dissipative systems). In fact, mathematically
speaking, relational models start from completely different primitives than
dynamical models do, as ? (?) has stated: “[Relational biology gives] a
different language talking about things, a language that does not translate to
‘ordinary’ mathematics. In other words, there is no road whatsoever from
relational models to differential equations or computer programs.” (p95).

One way out of the dilemma of modelling autonomous systems is to start by
constructing simple cell models that embody autopoiesis in the most reduced,
minimal way possible. Such models are reviewed in Section 3.2 to follow.
Before getting there, it is first worth commenting on the relationship between
modelling biological autonomy and Systems Biology, since the latter discipline
also takes an integrative approach to deal with the biological complexity of
the cell.

####  3.1.2 Systems Biology and Modelling Biological Autonomy

Systems biology, like biological autonomy, ultimately seeks an integrated
systems account of living organisms: that is, how their structure and function
emerges from a complex system of diverse components with various
interdependencies. Whereas biological autonomy comes from the top-down, from a
systems-theoretic account of cell organisation, systems biology works from the
bottom-up, iteratively developing and refining precise quantitative models of
organisms like E. coli or Mycoplasma Pneumoniae (for example, see ?, ?, ?, ?).
As such, it would appear that systems biology should be ultimately guided by,
and working towards, modelling the core concepts emerging from the theory of
biological autonomy. However, even though certain eminent systems biologists
have seen the work of Rosen, for example, as relevant to informing the field
of systems biology (?, ?), and indeed the definition of “Autopoietic Systems”
does exist in Springer’s Encyclopedia of Systems Biology (?, ?), in general,
mainstream systems biology is largely ignorant of (or agnostic to) the more
abstract system-theoretic approaches to living systems.

Why is this so? As ? (?) explain, “systems” biology can be interpreted in a
pragmatic way, or in a ‘hard line’ systems-theoretic way. Most practitioners
of systems biology are pragmatists. They are not so much concerned for
abstract principles and laws of cellular organisation, but rather they
perceive that an ‘understanding’ of a living system is reached through a
process of pooling all the empirical information sources available for a
particular organism (e.g. genome, transcriptome, proteome, metabolism, spatial
information etc.) and then creating a mathematical model that predicts some
aspects of its behaviour. The fundamental question of how cellular behaviour
is connected to the mode in which a cell fabricates its own embodiment – the
question that biological autonomy investigates – is not of immediate relevance
for a pragmatic systems biologist, whose principal task is instead to
construct an effective model777 Systems biology models have traditionally
focussed on simulating cells as ‘one pot’ metabolic networks. Other forces and
physical effects that come about through the embodiment of a chemical network
in space are often disregarded (but this is changing). of some sub-part of an
already living, already autopoietic cellular system. It is perhaps appropriate
that ‘cellular weather forecasting’ has been used to refer to the practice of
systems biology (?, ?).

Having made the critical observations above, it should be pointed out that
systems biology does include a more conceptual/theoretical strand which seeks
to identify more foundational principles defining the possible ‘design space’
of all living systems. The beginnings of a theory of biological robustness (?,
?, ?), for example, is located within this strand, and as ? (?) points out,
this theoretical framework has certain parallels to biological autonomy. The
theory of robustness generally tries to account for how organisms can survive
as invariants units, maintaining their core functions in the face of constant
internal changes and external environmental perturbations. Investigated under
this approach are the mechanisms that an organism employs to maintain a stable
overall presence, which can involve the organism switching into qualitatively
different dynamical regimes, such as entering a dormant state under extreme
dehydration. The idea of robustness is thus wider than that of homeostasis
(which is just maintaining a set of dynamical variables within bounds), and
could be seen under the light of biological autonomy as related to how
organisational closure is maintained. However, systems biology seems to have
been isolated from the systems-theoretic ideas and concepts in the biological
autonomy literature, and hence “curiously these two lines of discussion seem
to have no connection to each other” (?, ?, p625).

The concept of biological autonomy, in fact, has not percolated significantly
into biological science. One main reason could be that the framework has been
perceived as too abstract: whilst it offers insightful semi-formal concepts
about cellular organisation to ‘keep in the back of the mind’, these concepts
don’t easily translate into low-level concrete models that can be related to
real empirical examples of cells (as discussed above). As such, rather than
specifically aiming to model biological autonomy, systems biology instead
takes a low-level, practical, data-driven route to understanding the
complexity of the cell. Nevertheless, biological autonomy still stands at the
conceptual epicentre of systems biology, and its system-theoretic concepts
will be necessary to incorporate eventually if cells are ever to be understood
in their entirety.

###  3.2 Dynamic Models Capturing Minimal Autopoiesis

One start to modelling autonomy in cells or protocells could be argued to be
present in minimal models of autopoiesis which reduce cellular autopoiesis
down to its most nominal expression, and then try to implement this with
dynamical components either in-silico inside the computer, or in-vitro in real
chemistry. These models are critically reviewed below, leading on to Section
3.3 where a combined “semi-empirical” approach is put forward as a promising
route for modelling basic autonomy in protocells.

####  3.2.1 Computational Models of Autopoiesis in
Artificial Chemistry

The field of ‘computational autopoiesis’ (?, ?) is a distinctive sub-field of
Artificial Life, with the goal of simulating and formalising (minimal)
autopoiesis in abstract ‘cell-like’ models. Such models, typically implemented
as 2D lattice artificial chemistries, embed the circular logic of autopoiesis
by featuring a metabolism and membrane that co-support each other. The
metabolism synthesises the membrane (that would decay otherwise) whilst the
membrane encloses the metabolism and provides the correct conditions to
sustain it (e.g. by limiting the diffusion of metabolites). In addition to
being orders of magnitude more abstract, computational autopoiesis models
depart from systems biology models of cells because they explicitly account
for how the membrane of the cellular entity is produced and maintained as a
whole. In other words, the cellular membrane is not treated as a pre-given
boundary condition for the cell dynamics. Rather, the membrane is a boundary
condition that emerges through the dynamics of the system components, and
cannot be present without them.888‘Boundary conditions’ for a dynamical system
are here meant in the sense of (i) parameters used in the evolution equations,
or more generally (ii) factors affecting the algebraic structure of the
evolution equations. This is usage is different to what ‘boundary conditions’
refers to in boundary value problems in mathematics (i.e. solution of a
differential equation, subject to extra constraints). Confusing matters
further, ‘boundary’ is sometimes used to refer to the cellular membrane!

Models of computational autopoiesis bring autopoiesis out of the abstract
relational biology domain, and provide an experimental test bed to start
asking dynamical questions about organisational closure.999In a related field,
the kinetic modelling of autocatalytic sets (?, ?) aims to explore catalytic
closure in concrete instances of chemical reaction networks. Such questions
include: How does the cellular system respond to specific perturbations, of
specific durations? What type of perturbations is the system robust to? If
lesions are made to crucial pathways and/or some processes are temporarily
stopped, can the system recover from this interference, or does its
organisational closure break down permanently? To what extent is the agents
behaviour (e.g. movement) related to its continuing metabolic self-
maintenance? Generally, which are the open and unresolved issues in
autopoietic theory requiring further formalisation?

Computational autopoiesis models span from extremely abstract models running
on ‘toy’ physics, at one end, to more elaborate models with physically
justified component interactions at the other (Fig. 3.1). To give an idea, a
survey of notable models will be conducted below.

Figure 3.1:  Example Models of Computational Autopoiesis. Moving from more
abstract single molecule per lattice site models (a-e) toward more physically
realistic coarse grain models (f-h), including models based on reaction-
diffusion systems (g,h).  View Image Copyright Permissions.

Perhaps at the most abstract end of the computational autopoiesis spectrum
lies the analysis of recurrent spatiotemporal patterns in the Game of Life,
such as gliders (?, ?, ?; see Fig. 3.1a) and blocks and blinkers (?, ?). These
special patterns can be seen as autopoietic systems because they are entities
that produce and dynamically maintain their own bounded unity, albeit in a
universe ruled by “game-of-life physics”. Although as far from living cells as
one could imagine, the analysis of such mathematical patterns has helped
sharpen some of the autopoietic concepts outlined by Maturana and Varela, such
as the concept of a cognitive domain, and the dichotomy between organisation
and structure in an autopoietic system.

Similarly abstract was the the original model of computational autopoiesis,
presented as part of the first journal publication explaining the concept of
autopoiesis (?, ?, corrected in ?, ?; see Fig. 3.1b). In this model, three
types of chemical component - substrates, catalysts and links - randomly
floated around on a square lattice. The catalyst particles were able to
convert substrates into links which, when adjacent, bonded together into
larger membrane segments. Eventually, closed membranes would form around the
catalyst particles, and, even though the membrane links would spontaneously
decay, they would be continually re-synthesised by the entrapped catalyst.
Thus, ‘autopoietic’ self-maintaining entities were created.101010Technically,
the entrapped catalyst was not itself synthesised by the system, and so some
disputed the ‘autopoietic’ status of the cell-like entities formed. Variants
of the original 1974 model have since been implemented on hexagonal lattice
grids (?, ?, ?; see Fig. 3.1c), using mixed lattice/off-lattice simulations
(?, ?; see Fig. 3.1d), and even just in one dimension (?, ?).

One interesting extension to the ? (?) model, later made by ? (?), was to
modify the membrane link behaviour such that the autopoietic cell structure
became motile and gradient-climbing. Motivated by the general autonomy-related
question “When does a chemical network bounded by a membrane become a cell
that has its own intention?” (p59), the latter authors conjectured that self-
producing protocells could use their dynamic membrane shape to both sense
environmental conditions and produce motor movement of the whole system
(without the need for explicit sensors and effectors). Using a different cell-
like model, (?, ?; see Fig. 3.1e) similarly explored how chemotactic movement
and cell self-maintenance were related, and specifically the extent to which
the latter determined the former. In the Egbert & Di Paolo model, the membrane
of the cell was represented as a flexible loop of connected springs and the
whole cell translated to a new location determined by the overall direction of
force produced by locally activated membrane cilia. In the Suzuki & Ikegami
model, movement was produced by the gradual amoeba-like flowing and migration
of the membrane.

Moving onto more physically grounded models of computational autopoiesis, ?
(?) presented a model to investigate general conditions for the emergence of
membrane-bound protocells on a surface where there was a population of self-
replicating catalysts that could also synthesise membrane molecules (Fig.
3.1f). In this model, particles were designated as hydrophobic, hydrophilic or
neutral, and they followed random walks across a lattice biased by interaction
potentials between particles. Under the correct parameter regimes, the
emergence of connected membrane compartments could be observed on the lattice,
encapsulating the underlying chemistry and, in turn, produced and maintained
by it (even when resource gradients were present).

More recently, Agmon et al. (?, ?, ?; see Fig. 3.1g) have proposed a
computational autopoiesis model based on a modified reaction-diffusion (RD)
system. Reaction-diffusion systems simulate the time evolution of a smooth
concentration field rather than the time evolution of single molecules. The RD
system of Agmon et al. contains reacting and diffusing metabolic chemicals,
and these can produce amphiphilic molecules for the membrane with special
aggregation properties. The authors prime the two-dimensional model with an
initial self-maintaining ‘protocell’ configuration (a membrane surrounding a
concentration of metabolic chemicals), and then quantify the robustness of the
‘protocell’ configuration by systematically mapping how the configuration
responds to localised perturbations of its structure.

Finally, it should be noted that the standard reaction-diffusion systems of
physics have sometimes been considered as models of computational autopoiesis.
Under certain parameter settings, RD systems can exhibit a stable regime of
localised ‘spots’ with differing chemical concentrations to the surrounding
medium, both in still fluids (?, ?) and in fluids with convection (?, ?; see
Fig. 3.1h). Even though such spots have no surrounding membrane surfactant
layer, they are nevertheless distinguishable individuals that dynamically
maintain their own continued existence. They can also move, responding to
perturbations and following resource gradients. Therefore these ‘spot’
patterns have been argued to fulfil the autopoietic definition.111111? (?)
comments that dissipative structures lacking a topological membrane cannot
store energy in alternative reserves, and also require to exploit their energy
resource as is, with no energy transduction (p51).

On reflection, the field of computational autopoiesis has been most useful for
making more precise the abstract concepts of autopoiesis, and for outlining
where grey areas still remain.121212For example, through exploration with
their model ? (?) discuss the possibility that the network of process
dependencies implementing organisational closure in an autopoietic system is
not invariant, but can change over time, still retaining closure.
Additionally, computational autopoiesis models usually have a strong aesthetic
appeal (i.e. they depict colourful cellular systems moving around and
responding to environmental perturbations), and this quality helps them to
capture attention and articulate the theory of autopoiesis to a wider
audience. With regards to modelling autonomy, computational autopoiesis models
make a rudimentary start: there is the notion of a minimal organisational
closure wherein constraints emerge and support each other to create the cell
entity (i.e. the membrane supports the metabolism which in turn supports the
membrane).

However, the major shortcoming of computational autopoiesis models for
investigating the origin of autonomy in protocells (or cellular autonomy) is
that they bear only a very superficial resemblance to real protocells (or
cells). Beyond a weak qualitative correspondence, it is difficult to map such
models to empirical systems and experimental data. The computational models
usually have an unrealistic size scale, an undefined timescale, and some even
use implausible physics.131313Most models are single-molecule implementations,
meaning that the size scale of the membrane is unrealistically small with
respect to the metabolites. Other implausible physical aspects have included
membranes made from strong chemical bonds (whereas semi-permeable lipid
membranes are actually held together only by weak forces) and waste particles
magically disappearing in the cell interior. Also in all models described so
far, there is no account of osmosis. A main problem with computational
autopoiesis models is identifying what role contingency plays. Often a
circular collection of grid elements will be labelled as a ‘protocell’ and
then used as a vehicle to make claims about the origins of cellular life. But,
lacking any empirical grounding, it remains unclear to what extent the
behaviour and characteristics of the studied ‘protocell’ model are dependent
on the particular details of the computational implementation.

####  3.2.2 Experimental Models of Autopoietic Lipid Aggregates

In past years, there has also been interest in implementing chemical
aggregates that can be said to be ‘autopoietic’ (?, ?). The aim was to produce
a synthetic chemical system that shared, albeit in a minimal form, the same
fundamental chemical organisation implemented by all biological systems
(thereby, arguably creating a type of ‘living’ matter from inert components).
Before reading the following experimental descriptions, the reader may benefit
from reviewing Section 4.1.1.

At the end of the 1980s, ? (?) speculated that the implementation of minimal
autopoietic systems in real chemical media was indeed feasible, and suggested
reverse micelles as a candidate structure. They envisioned an organic (oily)
solvent containing dissolved precursors and also tiny water droplets each
wrapped by a single layer of surfactant (reverse micelles). The precursors
would diffuse into the small watery core of the micelles and subsequently
react to produce new amphiphiles for the micelle membrane. Each individual
micelle would hence be autopoietic in the following sense: the molecular
components forming the bounded micelle (a cluster of lipid amphiphiles) would
provide the adequate conditions for a simple metabolic process (a single
chemical reaction) that, in turn, would synthesise the components (lipid
amphiphiles) for the bounded micelle. A secondary effect resulting from this
process would be that the micelles would also grow and divide, self-
reproducing at the same time. Hence, the micelles were said to carry out
“autopoietic self-reproduction”.141414 In this low level of complexity, the
autopoietic network is incredibly minimal. It could be argued that the most
significant feature of the system is not the self-maintenance but the self-
reproduction of the micelle aggregates. Some authors have focussed just on
this latter aspect to develop thermodynamically grounded models of micelle
reproduction life cycles (?, ?, ?, ?).

The vision outlined by Luisi and Varela was empirically realised shortly
afterward by Bachmann and colleagues, initially for reverse micelles in
isooctane (?, ?), and then for normal aqueous micelles (?, ?). Two years
later, autopoietic self-reproducing vesicles were realised by ? (?). The
essential logic of the latter two experimental studies, without going into too
much chemical detail is depicted in Fig. 3.2a and can be summarised as
follows. Initially, a chemical mixture was prepared that consisted of two
immiscible phases: an aqueous phase and oily phase made of lipid precursor
(that floated on top, shown as dark blue in Fig. 3.2a). Along the interface of
these phases, the precursor would slowly be hydrolysed (e.g. split by
accepting a water molecule) to form the lipid surfactant and a side product.
The surfactant would slowly populate the interfacial area and exist in slowly
increasing concentration in the water phase until such a time that the
critical micelle concentration (or critical vesicle concentration) was reached
(see Section 4.1.1). At this point, micelles (or vesicles) would suddenly form
spontaneously in the water phase and they would start to sequester some of the
precursor inside their oily membranes. As a result, the contact area between
the precursor and the water phase would start to increase significantly and a
type of ‘physical autocatalysis’ would start to take hold: the increased
hydrolysis rate of precursor would create more micelles (or vesicles),
creating more interfacial surface area and thereby increasing the hydrolysis
rate of precursor yet further. This positive feedback effect is observed
experimentally as a sharp increase in the concentration of micelles (or
vesicles) after a long onset time, and ceases when all the precursor in the
closed system has been used up, leaving a single phase suspension of micelles
(or vesicles) in equilibrium.

Figure 3.2:  Minimal Autopoiesis in vitro. (a) ‘Autopoietic’ self-reproduction
of micelles. The self-reproduction of vesicles follows the similar logic.
Autocatalytic self-reproduction of supramolecular lipid aggregates has been
seen as an interesting alternative scenario to the self-replication of
template molecules, and strengthens the role of compartment systems in origins
of life. (b) Autopoietic self-maintenance of vesicles. In the homeostatic
regime, vesicles can maintain a constant size - but with a dynamically
changing structure - if the rate of surfactant production matches the rate of
surfactant destruction.

As a side note, ? (?) have lately reported on an experimental scheme for
autopoietic self-reproducing micelles closer in spirit to the original vision
of Luisi & Varela. In this scheme, the amphiphile for the micelle membrane is
synthesised from two simpler molecules, rather than being created by the
hydrolysation of a more complicated precursor which is more realistic from a
prebiotic point of view.

In another recent experimental work, the idea of the autopoietic self-
reproduction of vesicles has been extended to a system of phospholipid
vesicles able to grow and divide in an indefinite cycle (?, ?). Phospholipids
are more complicated two-tail lipids that form the basis of all modern cell
membranes. For their synthesis to be achieved, a more elaborate chemistry,
more like a minimal metabolism, had to be included onboard the vesicles.
Vesicles had to include a specific catalyst that joined a precursor
phospholipid to another molecule in order to synthesise the new phospholipids.
This requirement meant that, in order for daughter vesicles to go on growing
and re-producing themselves, the chemistry happening onboard the vesicles also
required an extra reaction pathway to produce more of the catalyst. Thus, two
reaction pathways took place on the vesicles (and three precursors were
required in the external solution). Generally, this study serves as a neat
illustration of an essential point: in order to be able to divide into
functional progeny, complex protocell systems would have to possess chemical
pathways to synthesise all of their key chemical components (e.g. have an
autopoietic organisation). In fact, this experimental work is an
implementation that comes very close to the original computational autopoiesis
model (?, ?). One difference is that, in the experimental system, all
chemistry happens on or inside the vesicle membrane, not in the internal
aqueous phase of the vesicles. In fact, the experimental system represents an
advance over the computational model scenario, since the catalyst can be
reproduced, permitting growing daughter cells.

Finally, another landmark study in the field of chemical autopoiesis is that
of ? (?). Here, the authors experimentally demonstrated that aggregates could
be made to simply self-maintain without necessarily entering into a self-
reproductive regime (Fig. 3.2b). Their experiment consisted of feeding a
suspension of vesicles not only with a precursor that hydrolysed to give
surfactant, but also with a second compound that had the opposite effect,
causing the oxidation (the loss of electrons) of existing surfactants. When
oxidised, the surfactants in the vesicle membranes transformed into a
molecular form which did not form vesicles (marked ‘NS’ in Fig. 3.2b).
Depending on the relative supply rates of the precursor and oxidising
compound, they showed vesicles could be placed in a growing/proliferating
regime (in the sense of Bachmann), in a homeostatic regime (closer to the
basic idea of autopoiesis), or in a decaying regime.

It can be observed that the experimental route for demonstrating minimal
chemical autopoiesis has a very different character from computational studies
on abstract ‘cell-like’ autopoietic systems. Real chemistry is difficult to
control (specific aspects cannot be fine-tuned, and all interactions are
frequently not known), and often the behaviour of aggregate chemistry at the
nm/$\mu$m size scale cannot be observed directly. Instead nano or micro-scale
mechanisms have to be carefully deduced by indirect means i.e. by making a
suitable hypothesis consistent with population-level behaviour (although
observation of single systems is now becoming possible with modern microscopy
and imaging techniques). On the other hand, to counter these drawbacks, real
chemical implementations of autopoiesis do not suffer the reality gap that
plagues computational autopoiesis simulations.

Minimal chemical models of ‘aggregate autopoiesis’ are relevant in the effort
of modelling autonomous protocells, because they represent an empirical start
in the direction of creating compartment-based systems where chemistry is
coupled with self-assembly processes. The criticism of chemical autopoiesis is
that it has not gone far enough to create elaborate self-maintaining chemical
aggregates. In particular, the concept of ‘metabolism’ was minimal and
chemistry always took place on the aggregate surface, rather than being a
complex aqueous-based chemistry inside a vesicle.151515Recently, ? (?) has
issued a challenge for future chemical autopoiesis attempts: “can one obtain
such a Zepik system… with other kind of organic chemistry reactions, and
possibly in a way that an internal mechanism – more than reactions at the
bilayer – are involved?”

###  3.3 A Scientific Research Program Toward
Basic Autonomous Protocells

In this thesis, the stages leading up to the first basic autonomous protocells
are investigated by modelling the co-evolution of protocell metabolism and
membrane through a ‘semi-empirical’ approach. These terms will be described in
due course. As compared to the minimal autopoiesis models of Section 3.2, this
approach entails constructing more chemically realistic (empirically based)
computational models of early protocells and considers that the protocell
metabolism, membrane and the coupling between metabolism and membrane can be
much more elaborate. In particular, rather than the protocell membrane just
serving to localise a metabolic network that in turn produces the membrane,
the membrane is instead regarded as an active interface controlling energy and
matter flow through the system (as explained in Section 2.3) and various
functional components for the membrane can be produced by the metabolism.
Hence, an ‘autopoietic’ systems perspective on protocell self-production and
function is maintained, but the development of models is not constrained to
the strict path of minimal autopoiesis.

The following section describes what a ‘co-evolution of protocell metabolism
and membrane’ approach entails, the rationale behind it, and why this approach
defines a scientific research program into the origin of the first basic
autonomous protocells. Then, Section 3.3.2 explains the ‘semi-empirical’
modelling approach followed to construct different protocell membrane-
metabolism couplings. Section 3.3.3 goes on to review two specific scenarios
of membrane-metabolism co-evolution explored with semi-empirical modelling.

####  3.3.1 Framework: Co-Evolution of Protocell Metabolism and Membrane

The early earth would have resembled a formidable cauldron; an expansive,
heterogeneous and certainly not well-mixed chemical environment whose
properties are nigh impossible to classify. Different chemical networks would
have likely existed on catalytic surfaces, in micro-enclosures (e.g. in porous
rocks), in water-oil emulsions, in spatially separated parts of solution, in
the atmospheric gas phase, and in complicated structured media (arrays of
interacting reaction zones, separated by, for example, self-assembled
supramolecular structures), to name but a few scenarios.161616Some constraints
could be placed upon chemical possibilities if the geography, climate and
chemical composition of the early earth was known, but this information is
unavailable. Rather, educated guesses have to be relied upon, see ? (?). There
would have been uncontrolled merging, mixing, and transfer between different
chemical collectives and assemblies, driven by energy fluxes such as thermal
and chemical gradients, lightening discharges, comet impacts, fluid
convections, volcanic activity and solar radiation. In solution, other free-
floating compartment systems apart from vesicles could have existed too, such
as coacervates (blobs of macromolecules and other organic ingredients held
together by electrostatic charges), and these could have also played a role in
promoting certain kinds of reactions and in establishing the first protocells.
Additionally, competition or symbiotic colony effects could have taken place
in some communities of chemical aggregates.

As for the development of protocells, given the chaotic prebiotic chemistry
conditions described above, it is certainly naive to assume that their lineage
comprised a smooth set of transformations whereby free-floating equilibrium
lipid vesicles gradually and elegantly became far-from-equilibrium biological
cellular systems. As ? (?) remark “the appearance of protocells was not likely
the consequence of a single system lineage that can be traced back to its
roots on the early Earth” (p1243). In the beginning, there could have been
several very discontinuous transitions leading up to functional protocells,
and indeed multiple scenarios can be envisaged for the creation of vesicle-
based chemical systems. One hypothesis, called the ‘obcell’, even advances
that vesicles developed metabolic systems on the outsides of their membranes
first, absorbing elements from a complex surrounding ‘protocytoplasm’, before
becoming inverted into protocells (?, ?, ?).

Such a state of affairs might seem to present an intractable starting point
for any investigation into the origin of autonomous protocells. It would seem
that a multitude of unknown and contingent pathways could have lead to the
first protocells. However, possibilities can be narrowed down. An important
bottleneck can be identified that fixes a waypoint through which prebiotic
protocell systems must have passed: the first functional or ‘basic autonomous’
protocells with the ability to robustly maintain themselves far-from-
equilibrium – and with the ability to divide in a controlled way into equally
functional progeny – could only have existed as such if their metabolic and
membrane systems were tightly integrated. This point is absolutely crucial.

Numerous times in prebiotic chemistry, there may have occurred the chance
insertion of complex reaction systems, developed in different chemical
contexts, into various self-assembled compartments (e.g. into the internal
aqueous phase and/or membrane of lipid vesicles). However, such structures
would have been unlikely to result in stable functional protocell systems
since the membrane would probably not possess the correct composition, nor
contain the correct molecular machinery (selective channels, carriers, ion
pumps, mechanisms to transduce external energy into a form usable by chemical
reactions etc) in order to meet the permeability, catalytic and energy
requirements to keep the metabolism running, and at the same time avoid e.g.
osmotic burst. Equally, the metabolic processes would probably not be able to
synthesise all of the key system components enabling division into equally
functional offspring.

The bottleneck arising from the need of tight membrane-metabolism integration
in protocells during origins of life is useful because it has implications for
the stages immediately preceding the bottleneck.171717However, the further
back from this bottleneck one goes, the less clear the scenario becomes. The
bottleneck implies that a co-evolution of membrane and metabolism must have
taken place over time in protocells, to ensure the high level of integration
required to pass through it. Even if metabolism first developed directly on
board protocell membranes, and not in their internal medium, then still an
integration of membrane and metabolism must have occurred. Pure chance
meetings of diverse chemical components would likely have produced complicated
conglomerates, but it would not be the type of organised complexity necessary
for functional protocells with the ability to proliferate into equally
functional protocells. Therefore, from a certain point, protocell membrane and
metabolism must have increased in complexity together, bootstrapping each
other’s functionality in a cyclic way so as to coordinate the dynamical
behaviour of their respective components at each stage.

The co-evolution of metabolism and membrane implication is able to define a
research program toward the first autonomous protocells. As (?, ?)
articulates, the problem is to investigate how simple ‘leaky’ protocells with
a strong heterotrophic requirement were able to become progressively
sequestered from their environments, turning into more impermeable and
selective autotrophic systems that used sophisticated means, such as internal
component synthesis, active transport and enzymatic metabolism, to stay far-
from-equilibrium.

####  3.3.2 Methodology: Semi-Empirical Modelling

The co-evolution of protocell metabolism and membrane scenario introduced
above is investigated in this thesis via a ‘semi-empirical’ modelling
approach. The semi-empirical approach aims to create a theoretical modelling
paradigm that goes some way to bridging the gap between pure in-silico and
pure in-vitro implementations of protocell systems, taking the best from both
worlds.

As discussed in Section 3.2.1, pure in-silico cell or protocell models can be
configured to an exact specification, directly monitored, and there is full
knowledge of all mechanisms. But, often, they lack physical and chemical
plausibility. Conversely, purely experimental protocell implementations
(Section 3.2.2) have the opposite problem; there is no reality gap, but it is
extremely difficult to construct nano-sized chemical aggregates to an exact
specification and often impossible to monitor their dynamic behaviour
directly. The goal of the semi-empirical approach is to create theoretical
protocell models able to incorporate realistic physical effects, empirical
constants, size scales and time scales such that they can be directly
interfaced to, and developed in parallel with, experimental research on lipid
aggregates. Having a hybrid experimental-theoretical approach has considerable
value. Realistic theoretical models can be suggestive of molecular mechanisms
underlying experimentally observed phenomena, and models can further guide new
experiments. Moreover, once validated experimentally, theoretical models can
be used in an extrapolative way, to test more complex protocell scenarios that
are difficult to construct directly in the lab.

The ideal semi-empirical protocell model would have a full representation of
space, be able to cover both short and long timescales, allow the inclusion of
empirical data and constants (granting quantitative comparison against
experiments) and would be amenable to full mathematical analysis to yield
elegant and human-intuitive solutions. Of course, no theoretical model
possesses all of these desirable qualities. Rather, the art is to reach a
suitable compromise dependent on the context.

The semi-empirical protocell model used in the scientific work of this thesis
is the kinetic vesicle model introduced by ? (?)181818The vesicle model can be
seen to have roots in earlier kinetics models designed to capture the
mechanisms of autopoietic self-reproduction of micelles and vesicles (Section
3.2.2), see ?, ?, ?, ?., summarised in its most basic mathematical form in Box
2.191919In Box 2, the model is stated in a deterministic formulation, in terms
of particle numbers. It is possible to express the model in different ways. A
deterministic formulation in terms of concentrations is given in ? (?) and the
original stochastic formulation, in terms of particle numbers, is best
summarised in ? (?, ?). This model represents a good compromise of the factors
mentioned above. The vesicle model is able to represent a protocell operating
far-from-equilibrium, where the protocell metabolism and protocell membrane
are both dynamic objects able to interact with each other. Many different
membrane-metabolism couplings can be dynamically tested on the kinetic vesicle
model, with the membrane able to admit different lipid compositions (e.g.
changing its permeability and fluidity) and able to embed various hydrophobic
molecules that further modify the membrane function (e.g. by making selective
channels). Most implementations of the model so far have been similar to
simulation models of Gánti’s Chemoton (see Section 2.2.3) but crucially differ
in some important aspects. Most notably, osmotic water flow is rigorously
included and the protocell has a variable volume interior aqueous pool. Volume
is independent from the surface area of the bilayer membrane, which means that
the protocell can assume different shapes, dependent on the volume-surface
area relationship at any given time.202020 Cell or protocell models that
consider surface area and volume as independent properties are quite rare.
Perhaps the closest current approach is the physicochemical cell model of ?
(?). Also, passive diffusion of solutes by Fick’s first law across the lipid
bilayer membrane is included (an obvious feature, curiously absent in all
Chemoton models so far). Moreover, the model incorporates realistic physical
features such as accurate surface areas and volumes of lipids, molecule
numbers, membrane thickness, membrane lipid exchange rates (to match the CVC -
see Section 4.1.1), concentration ranges and mass action kinetics of the
internal chemistry. Based at the coarse grain level of kinetics, the model is
able to directly incorporate rate constants from experimental papers (e.g.
solute permeability constants) and therefore, the model timescale is generally
well defined. The interested reader is directed to ? (?) for a recent review
of applications.

Box 2: Mavelli & Ruiz-Mirazo Unilamellar Vesicle Model

##### Vesicle reduced surface (scalar value representing vesicle shape)

$\Phi=S_{\mu}/\sqrt[3]{36\pi(\Omega/N_{A})^{2}}$ (3.1)

##### Lipid exchange kinetics for bilayer (of single lipid type)

$\frac{dL_{c}}{dt}=\Omega\textbf{r}_{L}({\vec{s}})+k_{out}L_{\mu}-k_{in}S_{\mu}l_{c}\textbf{u}(\Phi)$
(3.2) $\frac{dL_{\mu}}{dt}=-2k_{out}L_{\mu}+k_{in}S_{\mu}(l_{c}+l_{\cal
E})\textbf{u}(\Phi)$ (3.3) $S_{\mu}=\frac{1}{2}L_{\mu}\alpha$ (3.4)
$\textbf{u}(\Phi)=\begin{cases}\text{exp}\left(\frac{1}{\Phi}-1\right)&\text{if
}\Phi<1\\\ 1&\text{otherwise}\end{cases}$ (3.5)

##### Internal solute kinetics

$\frac{dS_{i}}{dt}=\Omega\textbf{r}_{i}({\vec{s}})+S_{\mu}D_{i}\left(\frac{s_{i}^{\cal
E}-s_{i}}{\lambda}\right)$ (3.6)

##### Internal aqueous volume changes

$\Omega=\frac{\sum_{N}S_{j}+B_{T}}{C_{\cal E}}\qquad\text{\footnotesize(if
water flow considered instantaneous)}$ (3.7)
$\frac{d\Omega}{dt}=N_{A}v_{aq}P_{aq}S_{\mu}\left(\sum_{N}s_{j}+b_{T}-C_{\cal
E}\right)\qquad\text{\footnotesize(if water flow considered finite)}$ (3.8)

Box 2 Continued: Mavelli & Ruiz-Mirazo Unilamellar Vesicle Model

##### Description of model constants and symbols*

Description Unit Value (typ) $N_{A}$ Avogadro’s constant $\text{mol}^{-1}$
$6.02214129\times 10^{23}$ ${\cal V}$ Litre volume of vesicle aqueous pool
$\ell$ ($\text{dm}^{3}$) $5.236\times 10^{-19}$ $\Omega$ Scaled vesicle
volume: $\Omega=N_{A}{\cal V}$ $\text{mol}^{-1}\text{dm}^{3}$ $S_{\mu}$
Bilayer surface area (equal for both leaflets) $\text{dm}^{2}$ $3.1416\times
10^{-12}$ $\lambda$ Bilayer thickness dm $4.0\times 10^{-8}$ $\alpha$ Lipid
$L$ head area $\text{dm}^{2}$ $3.0\times 10^{-17}$ $N$ Number of solute
species types inside vesicle $S_{i}$ Particle number of solute $i$ inside
vesicle $s_{i}$ Concentration of solute $i$ inside vesicle M up to mM
${\vec{s}}$ Vector of all solute concentrations ${\vec{s}}=[s_{1}\cdots
s_{N}]$ M $\textbf{r}_{i}({\vec{s}})$ MAK kinetics functions producing solute
$i$ $\text{M s}^{-1}$ $s_{i}^{\cal E}$ Concentration of solute $i$ in
environment M up to mM $D_{i}$ Diffusion constant for solute $i$
$\text{dm}^{2}\text{s}^{-1}\text{mol}^{-1}$ $2.65\times 10^{8}$ $L_{c}$ Free
lipid number inside vesicle $20$ $l_{c}$ Free lipid concentration inside
vesicle M $5.0\times 10^{-5}$ $\textbf{r}_{L}({\vec{s}})$ MAK kinetics
functions producing lipid $L$ $\text{M s}^{-1}$ $k_{out}$ Lipid desorption
rate constant $\text{s}^{-1}$ $7.6\times 10^{-2}$ $k_{in}$ Lipid absorption
rate constant $\text{s}^{-1}\text{M}^{-1}\text{dm}^{-2}$ $7.6\times 10^{19}$
$L_{\mu}$ Total lipid number in both bilayer leaflets $2\times 10^{5}$
$\textbf{u}(\Phi)$ Function accelerating lipid uptake when mem. tension
$l_{\cal E}$ Free lipid concentration in environment M $5.0\times 10^{-5}$
$C_{\cal E}$ Total concentration of all species in environment M $B_{T}$
Number of buffer particles trapped inside vesicle $6.3\times 10^{4}$ $b_{T}$
Concentration of buffer species inside vesicle M $0.2$ $v_{aq}$ Molar volume
of water at room temperature $\text{dm}^{3}\text{mol}^{-1}$ $1.8\times
10^{-2}$ $P_{aq}$ Macroscopic permeability constant for water $\text{dm
s}^{-1}$ $1.0\times 10^{-4}$ * Values typical for a 100nm diameter unilamellar
vesicle.

####  3.3.3 Semi-Empirical Models Toward Basic Autonomous
Protocells

In the co-evolution of metabolism and membrane research program toward
autonomous protocells, the vesicle model has so far been employed in two
distinct ways (Fig. 3.3).

Figure 3.3:  Semi-Empirical Protocell Models Toward Basic Autonomous Systems.
(a) Lipid-Peptide protocell (?, ?). (b) Hypothesised evolutionary development
of membrane protein channels, from ? (?). (c) Lipid-producing protocell (?,
?). See text for discussion.  View Image Copyright Permissions.

The first scenario, depicted in Fig. 3.3a, has been to model a ‘lipid-peptide’
protocell (?, ?). In this scenario, an autocatalytic reaction cycle inside the
protocell produced peptide monomers that assembled into short peptides in the
protocell interior (or inside the bilayer membrane itself), before orienting
and spanning across the membrane where they functioned as rudimentary
channels. Once in place, the peptide channels enhanced the permeability of
certain solutes across the bilayer membrane – including the waste made by the
metabolic cycle – and also contributed to the ‘elasticity’ of the membrane,
i.e. the range in which the membrane was stable. The logic was that by
producing rudimentary transport channels for the membrane interface, the
protocell system could gain some additional control over its own far-from-
equilibrium maintenance and become more robust to changes in external
conditions as a consequence. Preliminary results indicated that production of
membrane channels could prevent an osmotic burst from certain initial
conditions, but could also shorten the division time of the protocell system
by making the membrane more rigid.

Related to the lipid-peptide protocell, Fig. 3.3b shows some steps for the
evolution of protein channels in protocells hypothesised by one recent study
(?, ?; see also ?, ?). The authors hypothesised that membrane channels co-
evolved with protocell metabolism, initially starting from membrane-bound
oligopeptides (Fig. 3.3b, steps 1 and 2), which then became ion conducting
channels (step 3), turning into more rigid channels (step 4) and then,
finally, channels capable of energy transduction and the utilisation of energy
for active transport against concentration gradients (step 5). Contemporary
biological cells critically rely on the latter to remain in far-from-
equilibrium conditions.

The second scenario addressed with the semi-empirical vesicle model has been a
‘lipid-producing’ protocell (Fig. 3.3c). The aim was to start investigating
what advantages were brought to a protocell that could control its own
membrane lipid composition (and hence permeability, fluidity, elasticity) by
endogenously synthesising a more complex lipid type, like a two-tailed
phospholipid (?, ?, ?, ?). Internal synthesis of elaborate phospholipids to
compose a surrounding membrane is a critical operation that all living cells
perform. Given that primitive protocells would likely have self-assembled from
simpler lipids types that were locally available, the transition from self-
assembled to self-produced membranes (and its implications) is an important
avenue to research in the development of protocells.

In the model, the protocell reaction network consumed a simple single-tail
lipid ($l$) already present in the protocell membrane (supplied by the outside
medium), and by absorbing high energy precursors $X$ and $Y$, was able to
modify this lipid into a two-tail lipid ($L$) whilst also producing waste
products ($W$).212121? (?) explored a similar model, but changed the internal
metabolism from a Gánti autocatalytic cycle to an ‘M-R’ system (that did not
use the simple lipid type ($l$) as a precursor). On incorporating the two-tail
lipid, the membrane would become both less elastic, and less permeable to
solutes (see below). Preliminary results indicated that, dependent on
parameters, different asymptotic lipid-phospholipid membrane compositions
could be achieved. Also, the observation was made that by requiring simple
lipid ($l$), the metabolic reaction cycle naturally ran more slowly (hence
producing less waste) in cases when the membrane composition was dominated by
phospholipids and thus less permeable.

The ‘lipid-peptide’ and ‘lipid-producing’ protocell scenarios are models of
how simple protocells began coupling internal reactions with trans-membrane
processes or membrane composition respectively, in order to become more
elaborate and more robust. In fact, the two scenarios are quite related.
Protocells made of an increased phospholipid content would have faced a
‘sealing off’ problem, like all living cells do. The close-packing and the
long chain length of phospholipids grant liposomes with better stability
characteristics222222In terms of temperature range, pH range, and typically
lower CVC value (see Section 4.1.1)., but at the same time make membranes that
are quite impermeable to solutes. Cells solve the ‘sealing off’ problem (and
even take advantage of it232323A closed membrane barrier with permeability
controlled solely by transport mechanisms can allow selective and controlled
molecular trans-membrane movement. The cell decides what is transported in and
out, even against concentration gradients. On the other hand, a permeable
membrane barrier that permits passive diffusions cannot be so selective, and
it is actually the molecular properties of the solutes that determine what is
transported in and out. ) by employing specialised machinery like channels to
selectively move molecules across their phospholipid membranes. Hence, as
protocell membranes became increasingly based on more elaborate lipid types
like phospholipids, membrane protein machineries like channels would have
likely co-evolved so that protocells could maintain their metabolic function
(?, ?).

One can imagine many immediate extensions to the ‘lipid-peptide’ and ‘lipid-
producing’ protocell scenarios that would explore the co-evolution of the
metabolism-membrane coupling further, hence moving the model closer toward
basic autonomous protocells. For example, the two approaches could be combined
to explore the dynamics of protocells that could synthesise impermeable
‘sealed’ membranes that were nevertheless made selectively permeable through
the parallel synthesis of peptide channels (a scenario closer to real
biological membranes). Also, a start in modelling the active transport of
solutes across the protocell membrane could be made to see what general
stability and control advantages the non-spontaneous molecular movement
against concentration gradients could bring to the protocell system.
Furthermore, a plethora of metabolic networks could be investigated beyond
Gánti’s autocatalytic cycles or Rosen’s M-R systems. See Section 5.2.3 for a
discussion of the challenges associated with extending the semi-empirical
protocell research program.

The scientific modelling work carried out in this thesis actually constitutes
a prequel rather than a sequel to the existing ‘lipid-peptide’ and ‘lipid-
producing’ protocell schemes. As the following section explains, there exists
rich protocell scenario to investigate before protocells started producing
complex components such as lipids and membrane proteins.

###  3.4 Before Basic Autonomous Protocells: Modelling the Early Interplay of
Chemical Reactions and Dynamic Compartments

Both of the protocell models proposed as getting closer to basic autonomous
protocells in the preceding Section 3.3.3 were ‘self-producing’ protocells.
Inside the lipid-peptide protocell, an autocatalytic reaction cycle produced
peptide monomers that eventually assembled into membrane channels and also
produced simple membrane lipids. Inside the lipid-producing protocell, a
reaction cycle instead manufactured a complex two-tail lipid. Rather than
extending these models further, a valid argument can be made for rigorously
investigating more simple protocells instead, that did not synthesise their
own membranes, nor complex membrane proteins.

Jumping straight into modelling lipid-synthesising protocells in fact brings
some problems. A first issue is that, in cells, fatty acids and phospholipids
are synthesised from small molecule precursors in a long sequence of linked
reaction steps, where some steps require specific organic catalysts to
proceed, or energy input from e.g. ATP in order to become spontaneous, or both
factors. Realistically, lipid synthesis (fatty acids, or even more difficult,
phospholipids) from small molecule precursors is not a trivial task, and would
not be achievable by a simple chemical cycle. In early protocells that likely
operated at a strongly reduced level of molecular and organisational
complexity, it can be questioned whether ‘bottom up’ lipid synthesis from
small molecules was feasible, given the advanced catalytic and energetic
requirements, or whether this was a relatively late addition. Incidentally,
the chemical autopoiesis approaches in Section 3.3.2 did not solve the issue
of prebiotic lipid synthesis, but rather used a shortcut to bypass this
problem. This shortcut, available to human synthetic biologists but not
necessarily to prebiotic protocells, involved supplying the self-
sustaining/replicating system with precursors that were already structurally
very close to being amphiphilic aggregate-forming molecules. These precursors
typically required just a slight modification, often performed by just a
single reaction, in order to make them amphiphilic.

A second issue with modelling internal lipid synthesis is that internal
synthesis can have various biophysical effects on a vesicle. Some experimental
studies with giant unilamellar vesicles have shown that in cases where lipid
synthesis inside vesicles has been achieved artificially, the newly produced
lipids don’t always behave in an expected way i.e. they don’t always grow the
existing membrane uniformly. Rather, it has been observed that internal lipid
synthesis can lead to multiple new vesicles self-assembling inside the water
pool of the parent vesicle instead (?, ?).242424Also, in ? (?), the
phospholipid vesicle grows not by enlarging a single membrane, but by folding
into a multilamellar vesicle. Other have noted that asymmetries in area of the
inner and outer leaflet of a vesicle bilayer – as could take place when
internally produced lipids associate with the inner leaflet – can lead to
vesicle morphology transformations (?, ?). These findings point to the need
for non-trivial theoretical models to accurately account for the effects of
internal lipid synthesis.

In any case, an under-explored protocell area exists before reaching a
scenario of protocells which endogenously produce complex components like
lipids, or peptides: far-from-equilibrium chemistry in dynamic lipid
compartments. In this early protocell scenario, chemical networks could be
envisaged to interact with semi-permeable membranes, not by producing them,
but in more indirect ways, to form protocell aggregates or ‘reactors’ with
interesting non-linear dynamics, and possibly adaptive behaviours.

Figure 3.4:  Chemistry in Dynamic Lipid Compartments. Before the development
of protocells that internally synthesised complex components, a more simple
protocell scenario can be postulated, consisting of chemistry interacting with
dynamic lipid compartments. In this scenario, even though the protocell
membrane is not produced by the internal metabolism, non-linear protocell
dynamics can still result from various factors (a)-(d). See text for
discussion.

Figure 3.4 gives four examples of factors that can potentially lead to
interesting emergent chemical behaviour in a purely self-assembled protocell
chemical reactor, based on a vesicle, that does not have lipid or peptide
synthesis capability.

First of all, surface interactions can serve as an indirect coupling between
metabolism and membrane (Fig. 3.4a). The interior surface of a vesicle (or
alternatively the hydrophobic interior of its bilayer membrane) can provide an
environment that favours certain types of chemical reactions. As such, a
vesicle membrane is able to act as a promoter or regulator to certain
reactions in the protocell metabolism (?, ?). Moreover, surface chemistry has
often been found to accelerate reactions inside small compartments with a high
surface-to-volume ratio (?, ?, ?).

Secondly, vesicles have a semi-permeable and elastic membrane enclosing an
aqueous volume, and for these reasons, the internal aqueous volume can be
significantly variable due to osmosis (Fig. 3.4b). This variation in the size
of the molecular collision space can have various ramifications for the
dynamics of an encapsulated chemistry (?, ?, ?. See also Section 4.3.2 for a
detailed discussion).

Thirdly, vesicles are not just spheres that divide. Rather, vesicles exhibit a
rich variety of morphological transformations, triggered by changes in
membrane composition, osmosis and external forces (Fig. 3.4c). For example,
vesicles can grow into long filaments, and then divide (?, ?), or
alternatively can reach a ‘pearling’ instability whereby they rapidly convert
into a beaded string (?, ?). Also, vesicles can undergo oscillatory dynamics
when placed in a hypotonic (diluted) environment, swelling with water, and
then transiently bursting to release contents before resealing – iterating the
cycle until solute gradients are equalised (?, ?, ?, ?). Vesicles can fuse
together, mixing chemical contents and membrane composition, and increasing
their surface-to-volume ratio (?, ?). Furthermore, vesicles can bud smaller
vesicles both externally and internally (?, ?), and often exist in a range of
multilamellar and nested structures (vesicles within vesicles, like Russian
dolls) that provide an interesting compartmented scenario for reactions.

Fourth and finally, dynamical effects can be provoked in vesicles by the
presence of external forces, energy sources (e.g. ?, ?), and changing
environmental concentrations which may also originate from neighbouring
vesicles (Fig. 3.4d).

In summary, there exists a huge landscape of interesting possibilities for the
interaction of chemical networks with the self-assembly physics of vesicles,
well before vesicles would have started to produce important components
internally. Even vesicle growth, which would seem to require an internal lipid
production, could potentially have been achieved by other means, such as by
vesicle fusion, lipid competition (see Section 4.2.1) or by increased lipid
uptake rate in osmotic stress conditions (?, ?, ?). Therefore, before jumping
ahead to modelling self-producing protocell scenarios, a proper consolidation
of more basic scenarios where protocell membrane and metabolism are more
indirectly coupled is required.

The scientific contributions of this thesis, outlined in Chapter 4 to follow,
can be seen as contributions to the (wide) area of modelling chemistry in
dynamic compartments.

##  Chapter 4 Overview of
Scientific Contributions

This chapter summarises, in a simplified and largely non-technical way, the
main scientific contributions made by this thesis. Chapter 5 to follow
discusses in more detail how these results fit into the theme of modelling
chemistry inside dynamic lipid compartments (the research area explained in
Section 3.4), and into the overarching problem of modelling the appearance of
autonomy in protocells.

The published papers on which this chapter reports are included as Appendix D.
Material in Section 4.2 was published in Scientific Reports as “Modelling
Lipid Competition Dynamics in Heterogeneous Protocell Populations” (?, ?).
Material in Section 4.3 was published in Life as “Emergent Chemical Behaviour
in Variable-Volume Protocells” (?, ?). Material in Section 4.4 was published
in the Proceedings of the Twelfth European Conference of Artificial Life as
“Steady state analysis of a vesicle bioreactor with mechanosensitive channels”
(?, ?).

###  4.1 Prelude: The Equilibrium Self-Assembly of
Amphiphiles

As described in Chapter 1, a protocell is a far-from-equilibrium chemical
system embodied in a supra-molecular membrane structure which self-assembles
through the action of weak forces. A good departure point on the path toward
modelling protocells, like for modelling any phenomena, is to start simple: in
this case, to develop intuition for how protocell compartments can self-
assemble in an equilibrium setting without internal or external chemistry
taking place. As ? (?) underlines, “Self-assembly is an essential component in
the path towards cellular systems.” (p283).

In this regard, as a prelude to the scientific contributions to follow, the
first scientific contribution presented below details a spatial lattice model
developed to capture the self-assembly of amphiphile molecules, when these
molecules form part of complex mixtures containing water and/or oil. Before
the lattice model results are presented, Section 4.1.1 creates the context by
recapitulating the basic principles underlying the self-assembly of lipids
into micelles and vesicles.

####  4.1.1 Basic Principles of Micelle and Vesicle Self-Assembly

Liquid water is a vital pre-requisite for life as we know it. One of the
reasons why water is so important is due to the particular structure of water
molecules: they are polar and attract each other.111Polar molecules have no
overall charge, but their balance of charge throughout space is unequal and
leads to localised regions of attraction and repulsion. Ionic molecules (ions)
instead have an overall charge because they carry a surplus or absence of
electrons. In fact, water molecules engage in a highly dynamic network where
hydrogen bonds between neighbouring molecules are continuously broken and re-
established in another arrangement.222A hydrogen bond is the name given to the
electrostatic attraction between polar molecules. Hydrogen bonds are stronger
than Van der Waals forces, but weaker than covalent and ionic bonds. This
dynamic network of bonds leads to an important effect called the hydrophobic
effect. In living systems, this effect drives the folding of proteins into
functional three dimensional structures and is key to the formation of bilayer
cell membranes.

So, what is the hydrophobic effect? When molecules unable to form hydrogen
bonds are put into water, like oily hydrocarbon chains for example, they
restrict the hydrogen-bonding possibilities that the adjacent water molecules
can engage in. This makes the bonding network more ordered as a whole. The
hydrophobic effect is the name given to the water system striving to return to
a more disordered (or maximal entropy) state again. It does this by
aggregating non-polar molecules together, minimising their interface with the
water hydrogen bonding network. This is the reason why oil and water don’t
mix. Figure 4.1a illustrates the hydrophobic effect, using black rods to
represent oil hydrocarbons and red lines to signify minimisation of the oil-
water interface.

The hydrophobic effect becomes even more interesting when amphiphiles are
added to water. Amphiphiles are molecules composed of two parts: a polar or
ionic head part that can participate in the water hydrogen bonding network
(‘water loving’ or hydrophilic), and a non-polar hydrocarbon tail that cannot
(‘water hating’ or hydrophobic). An amphiphilic lipid molecule is drawn Fig.
4.1b. In water, the dual hydrophilic-hydrophobic personality of amphiphiles
(also called surfactants) means that they orient themselves such that the head
parts contact the water interface whilst the tail parts are sequestered away
together. This unique behaviour means that mixtures of amphiphiles, water and
oil can display a huge diversity of self-assembled microstructures. Figure
4.1c shows a so-called phase diagram that systematically maps how a three-part
mixture (called a ternary mixture) of amphiphile, water and oil can transition
between different regimes of self-assembly, dependent on the proportion of
each of the three components in the mixture.333 The phase diagram is drawn as
an equilateral triangle and uses a barycentric coordinate system. Each point
on the triangle surface has the same total concentration of amphiphiles, water
and oil; just their mix ratio is different. The vertices of the triangle
represent 100% concentration of amphiphile, water or oil respectively. Only a
single amphiphile type is allowed. Cleverly, the area inside the triangle
represents all the three-part (ternary) mixtures possible and the edges of the
triangle represent all the two-part (binary) mixtures possible. Although this
phase diagram is only illustrative, it conveys well the rich variety of
supramolecular structures that are able to exist in ternary mixtures under
suitable conditions. Further, the diagram highlights that the transitions
between different self-assembly regimes are often abrupt, and the transitions
carve up the phase space in a non-trivial way. Phase diagrams can become
extremely complex when other factors affecting self-assembly (like
temperature, pH, or the presence of multiple amphiphile types) are also taken
into account.

For protocells, the most relevant supra-molecular structures that amphiphiles
self-assemble into are micelles and vesicles. As was shown in Fig. 1.1d of
Chapter 1, micelles are small ordered clusters of relatively few amphiphiles,
whereas vesicles represent much larger structures formed of thousands of
amphiphiles arranged in a spherical (or quasi-spherical) bilayer. Micelles and
vesicles are not static, but very dynamic structures, constantly exchanging
lipids with the surrounding solution. As such, one of the key conditions for
the self-assembly of micelles and vesicles is the presence of a critical
concentration of free amphiphile monomer in the surrounding solution. This
concentration is termed the critical micelle concentration (CMC) or critical
vesicle concentration (CVC). Figure 4.1d illustrates the CMC behaviour for
micelles. When amphiphiles are initially added to water solvent (x-axis), they
exist as free monomers in the solvent. However, steady addition of amphiphiles
does not lead to the free amphiphile concentration increasing linearly.
Rather, the amphiphiles start becoming clustered into micellar aggregates, and
addition of more amphiphiles to the system results in more aggregates being
formed instead of an increase in the free monomer concentration (which stays
constant at the CMC). The same type of behaviour is observed in the case of
vesicles. Typically, the critical concentration depends on the chain length of
the amphiphiles forming the aggregates, decreasing as the hydrophobic chain
length increases.444 Amphiphiles with longer hydrophobic chains exchange more
slowly between aggregates and solution because of the higher energetic cost of
exposing their hydrophobic chain. This translates to a lower critical
concentration.

An additional factor determining whether micelles or vesicles (or indeed other
supra-molecular structures) assemble is the effective shape of the amphiphiles
concerned. The packing parameter is a useful quantity characterising how bulky