# THE EMERGING DISCIPLINE OF QUANTITATIVE SYSTEMS PHARMACOLOGY

EDITED BY: Tarek A. Leil and Sergey Ermakov PUBLISHED IN: Frontiers in Pharmacology

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## **THE EMERGING DISCIPLINE OF QUANTITATIVE SYSTEMS PHARMACOLOGY**

## Topic Editors:

**Tarek A. Leil,** Bristol-Myers Squibb, USA **Sergey Ermakov,** Bristol-Myers Squibb, USA

The promise of quantitative systems pharmacology: converting human physiology and pharmacology into computer models that can be used to generate insight into disease progression and therapeutic intervention. Copyright, Lightspring/Shutterstock.com

In 2011, the National Institutes of Health (NIH), in collaboration with leaders from the pharmaceutical industry and the academic community, published a white paper describing the emerging discipline of Quantitative Systems Pharmacology (QSP), and recommended the establishment of NIH-supported interdisciplinary research and training programs for QSP. QSP is still in its infancy, but has tremendous potential to change the way we approach biomedical research. QSP is really the integration of two disciplines that have been increasingly useful in biomedical research; "Systems Biology" and "Quantitative Pharmacology". Systems Biology is the field of biomedical research that seeks to understand the relationships between genes and biologically active molecules to develop qualitative models of these systems; and Quantitative Pharmacology is the field of biomedical research that seeks to use computer aided modeling and simulation to increase our

understanding of the pharmacokinetics (PK) and pharmacodynamics (PD) of drugs, and to aid in the design of pre-clinical and clinical experiments. The purpose of QSP modeling is to develop quantitative computer models of biological systems and disease processes, and the effects of drug PK and PD on those systems. QSP models allow testing of numerous potential experiments "in-silico" to eliminate those associated with a low probability of success, avoiding the potential costs of evaluating all of those failed experiments in the real world. At the same time, QSP models allow us to develop our understanding of the interaction between drugs and biological systems in a more systematic and rigorous manner. As the need to be more cost-efficient in the use of research funding increases, biomedical researchers will be required to gain the maximum insight from each experiment that is conducted. This need is even more acute in the pharmaceutical industry, where there is tremendous competition to develop innovative therapies in a highly regulated environment, combined with very high research and development (R&D) costs for bringing new drugs to market (~\$1.3 billion/drug). Analogous modeling & simulation approaches have been successfully integrated into other disciplines to improve the fundamental understanding of the science and to improve the efficiency of R&D (e.g., physics, engineering, economics, etc.). The biomedical research community has been slow to integrate computer aided modeling & simulation for many reasons: including the perception that biology and pharmacology are "too complex" and "too variable" to be modeled with mathematical equations; a lack of adequate graduate training programs; and the lack of support from government agencies that fund biomedical research. However, there is an active community of researchers in the pharmaceutical industry, the academic community, and government agencies that develop QSP and quantitative systems biology models and apply them both to better characterize and predict drug pharmacology and disease processes; as well as to improve efficiency and productivity in pharmaceutical R&D.

**Citation:** Leil, T. A., Ermakov, S., eds. (2015). The Emerging Discipline of Quantitative Systems Pharmacology. Lausanne: Frontiers Media. doi: 10.3389/978-2-88919-642-5

# Table of Contents

Athan Spiros, Patrick Roberts and Hugo Geerts

Sergey Ermakov, Peter Forster, Jyotsna Pagidala, Marko Miladinov, Albert Wang, Rebecca Baillie, Derek Bartlett, Mike Reed and Tarek A. Leil

## Editorial: The emerging discipline of quantitative systems pharmacology

Tarek A. Leil\* and Sergey Ermakov

*Bristol-Myers Squibb, Clinical Pharmacology and Pharmacometrics/Exploratory Clinical and Translational Research, Princeton, NJ, USA*

Keywords: systems pharmacology, systems biology, pharmacometrics, clinical pharmacology, modeling and simulation, in silico modeling, biomedical research

Quantitative Systems Pharmacology (QSP) has emerged recently as an approach that integrates knowledge coming from multiple disciplines including drug pharmacology, systems biology, physiology, mathematics and biochemistry. QSP was formally defined as a discipline and endorsed in the NIH White Paper (Sorger et al., 2011) in 2011. It has emerged at a time when the pharmaceutical industry is facing growing challenges in efficiency and productivity in R&D. QSP has the potential to help overcome some of these challenges. QSP models allow researchers to evaluate multiple hypotheses in-silico that would otherwise need to be evaluated experimentally. There is an expectation that the use of QSP will reduce the cost of R&D and the risks associated with uncertainties and gaps in our knowledge while bringing new therapies to patients.

QSP models are typically perceived as a research tool for hypothesis generation in drug discovery and exploratory clinical development; however, recently the US FDA used a QSP model to evaluate a proposed drug regimen for a new biologic therapy (Peterson and Riggs, 2015). In their communication with NPS Pharma, the FDA's Clinical Pharmacology division used a published QSP model of the calcium homeostasis system (Peterson and Riggs, 2010) to recommend an alternate dosing regimen for NATPARA, an injectable parathyroid hormone replacement drug used to control low blood calcium in patients with hypoparathyroidism. The use of a QSP model by the FDA to recommend an alternate dosing regimen to a sponsor highlights one of the important future applications of QSP models in regulatory interactions, and also represents an important milestone for the field. It is the first public instance of a QSP model being used by a regulatory agency to make a clinical recommendation to a sponsor. In the future, it is anticipated that it will be sponsors that leverage the utility of QSP models to support their own clinical decision making with regulatory agencies.

In the present research topic entitled, "The Emerging Discipline of Quantitative Systems Pharmacology," we provide an introduction to the developing field of QSP with a series of articles that describe models in different disease areas; showing how these models can be used to evaluate important research questions in pharmaceutical R&D. The research topic starts with a perspective article by Leil and Bertz (2014) that describes the history of how modeling tools where used in pharmacology and in drug development. The authors point out two major reasons for the growing importance of the QSP approach, (i) difficulty in finding new targets for therapies, and (ii) increasing cost and time required for developing a successful drug. Integrated into the drug development process, QSP modeling could become an effective tool to facilitate R&D; for example to translate knowledge between experimental systems (e.g., animal to human), and to predict the effects of multiple therapeutic interventions in combination; a task that would be inefficient using only clinical experimentation. The other articles in the research topic go on to demonstrate applications of QSP models to influence decision making in biomedical research.

One of the important applications of QSP modeling in pharmaceutical R&D is optimization of clinical dose and schedule. Oncology is one of the disease areas where the narrow therapeutic window of most therapeutics demands fine tuning of dose and schedule. Utilization of high doses

Edited and reviewed by: *Salvatore Salomone, Catania University, Italy*

> \*Correspondence: *Tarek A. Leil<EMAIL_ADDRESS>
#### Specialty section:

*This article was submitted to Experimental Pharmacology and Drug Discovery, a section of the journal Frontiers in Pharmacology*

> Received: *29 May 2015* Accepted: *12 June 2015* Published: *30 June 2015*

#### Citation:

*Leil TA and Ermakov S (2015) Editorial: The emerging discipline of quantitative systems pharmacology. Front. Pharmacol. 6:129. doi: 10.3389/fphar.2015.00129* of anti-angiogenesis therapy can result in rapid suppression of angiogenesis and hypoxia leading to tumor shrinkage. Paradoxically, this can subsequently lead to reduced drug delivery to the tumor and resumption in tumor angiogenesis, followed by progression of tumor growth. The paper by Sharan and Woo (2015) discusses how to delay or prevent this from happening by optimizing the dose and regimen of the anti-angiogenesis therapies with a QSP model of angiogenesis.

Another important application of QSP models is to provide mechanistic explanations for clinical data that are often counterintuitive to the perceived mechanism of action (MoA) of a drug. Despite the fact that two SGLT2 inhibitors are already approved for use in patients, questions remain regarding their MoA and why efficacy is lower than expected based on their high potency and selectivity for SGLT2. The papers by Demin et al. (2014) and Lu et al. (2014) explored this issue using mechanistic models of renal tubular filtration and transport, incorporating the PK and MoA of SGLT2 inhibitors. Lu et al. (2014) proposed two possible explanations for the lower than expected efficacy; the residual activity of SGLT2 following inhibition in the renal tubules, and the compensatory effect of SGLT1. Demin et al. (2014) supported this hypothesis, but also offered an alternative in which the sites of action of SGLT2 inhibitors are located not in the lumen of the kidney's proximal tubules where the concentration of SGLT2 inhibitor is high, but perhaps in the proximal tubule where the concentration of inhibitor is lower. Complex dose-response dependencies are often encountered in many disease areas, for instance, in treatments of schizophrenia as investigated by Spiros et al (Spiros et al., 2014). With the use of a sophisticated QSP model of cognitive impairment in schizophrenia, the authors predicted an inverse U-shape doseresponse with glycine that is a consequence of the shifting balance between excitation and inhibition in the cortical network.

The application of mechanistic models for prediction of target dependent or independent toxicity in secondary tissues has been the focus of QSP for many years, as this is the most common reason for termination of the development of otherwise efficacious therapies. In order to predict toxicity using a mechanistic model, it is useful to incorporate a physiologically based PK (PBPK) model to predict drug concentrations in the target organ. Woodhead et al. (2014) described the use of a PBPK/toxicity model of drug induced liver injury (DILI) to evaluate the impact of bile salt export pump (BSEP) inhibition on hepatotoxicity in rats and humans. The DILI model was used to predict the responses to BSEP inhibitors with and without clinical hepatotoxicity. In accordance with the observed

## References

clinical data, the model predicted that bosentan, but not telmisartan, will cause mild hepatocellular ATP decline and serum ALT elevation. Similar to the research by Woodhead et al. (2014), Chetty et al. also relied on PBPK to predict drug concentrations in tissue, linking these concentrations to targetmediated pharmacodynamic (PD) effects (Chetty et al., 2014). They did so using the Simcyp PBPK simulator, a tool that has a built-in PBPK model and allows users to input drug specific parameters that have been measured in-vitro to predict in-vivo plasma and tissue PK. Simcyp has become an important tool for pharmaceutical R&D and for communicating with regulatory agencies regarding the PK of investigational drugs and their potential PK-related drug-interactions. Chetty et al. described the use of Simcyp to predict the tissue concentrations of four different drugs, metoprolol, nifedipine, triazolam, and zolpidem (Chetty et al., 2014). They demonstrated how polymorphisms in drug metabolizing enzymes would have an effect on the concentration of drugs in the target tissue and the subsequent impact on pharmacodynamics.

One of the technical issues that potentially limit more widespread use of QSP in biomedical research is the lack of an accepted standard modeling tool to facilitate sharing of models between researchers. The tool should permit evaluation of experimental scenarios of interest in a flexible computational environment for conducting efficient high throughput simulation. A potential solution was implemented in the web-based virtual systems pharmacology (ViSP) platform described in the article by Ermakov et al. (2014). The salient feature of ViSP is the use of a model in the form of an executable file. Matched with a full set of model parameters this executable becomes independent of the model structure and the software that were used to develop the model while preserving flexibility in the input parameters. These characteristics could be useful in the future when the utilization and sharing of QSP models becomes more widespread.

In conclusion, we would like to emphasize the emerging potential that QSP holds for biomedical research and in particular to improve decision making in pharmaceutical R&D. In order for this to occur, QSP will need to present more examples of the value that it can bring to the process of hypothesis generation and testing; examples like those included in this research topic.

## Acknowledgments

We would like to thank the contributing authors to this research topic for providing interesting and relevant research articles.

SGLT2 in renal glucose reabsorption in humans. Front. Pharmacol. 5:274. doi: 10.3389/fphar.2014.00274

schizophrenia: exploring glycine modulation of excitation-inhibition balance. Front. Pharmacol. 5:229. doi: 10.3389/fphar.2014. 00229

Woodhead, J. L., Yang, K., Siler, S. Q., Watkins, P. B., Brouwer, K. L. R., Barton, H. A., et al. (2014). Exploring BSEP inhibition-mediated toxicity with a mechanistic model of drug-induced liver injury. Front. Pharmacol. 5:240. doi: 10.3389/fphar.2014.00240

**Conflict of Interest Statement:** Both of the authors are employees of Bristol-Myers Squibb. The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2015 Leil and Ermakov. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

## Quantitative Systems Pharmacology can reduce attrition and improve productivity in pharmaceutical research and development

## **Tarek A. Leil \* and Richard Bertz**

Clinical Pharmacology and Pharmacometrics, Exploratory Clinical and Translational Research, Bristol-Myers Squibb, Princeton, NJ, USA

#### **Edited by:**

Chiranjib Chakraborty, Galgotias University, India

#### **Reviewed by:**

Filippo Caraci, University of Catania, Italy Robert A. McArthur, McArthur and Associates GmbH, Switzerland

#### **\*Correspondence:**

Tarek A. Leil, Clinical Pharmacology and Pharmacometrics, Exploratory Clinical and Translational Research, Bristol-Myers Squibb, P.O. Box 4000, Princeton, NJ 08543-4000, USA e-mail<EMAIL_ADDRESS>
The empirical hypothesis generation and testing approach to pharmaceutical research and development (R&D), and biomedical research has proven very effective over the last half-century; resulting in tremendous increases productivity and the rates of approval for new drug applications at the Food and Drug Administration (FDA). However, as discovery of new therapeutic approaches for diseases with unmet medical need becomes more challenging, the productivity and efficiency of the traditional approach to drug discovery and development is diminishing. Innovative approaches are needed, such as those offered by Quantitative Systems Pharmacology (QSP) modeling and simulation. This "systems" approach to modeling and simulation can be used to guide the hypothesis generation and testing process in pharmaceutical R&D, in a manner similar to its adoption in other industries in the past. Embedding QSP into the existing processes within pharmaceutical discovery and development will be required in order to realize the full beneficial impact of this innovative approach.

**Keywords: Quantitative Systems Pharmacology, pharmaceutical R&D, modeling and simulation, Systems Biology, pharmacometrics, drug discovery and development**

## **INTRODUCTION**

One of the oldest documents recording the process of drug discovery is the Ancient Egyptian "materia medica" dating to the sixteenth century B.C. This approach to drug discovery, based on empirical evidence from the natural world, is known as Pharmacognosy (de Pasquale, 1984), and was the primary means of drug discovery until the middle of the twentieth century. Advances in biochemistry, molecular and cellular biology, and medicinal chemistry during middle of the twentieth century resulted in a shift to a more hypothesis driven, mechanism-based approach to drug discovery (Drews, 2000). This approach includes mining of data from human epidemiology studies, combined with nonclinical *in vitro* and *in vivo* experiments to demonstrate the validity of a therapeutic target. The addition of high throughput chemical synthesis and screening permits identification of target selective, high affinity compounds. This hypothesis driven approach to pharmaceutical research and development (R&D) has been a tremendous advance relative to the ancient methods of Pharmacognosy, and resulted in a dramatic increase in the percentage of new drug applications (NDAs) approved by the Food and Drug Administration (FDA) since the early 1960s (**Figure 1A**; U.S. Food and Drug Administration, 2013b). However, there appears to be a decrease in the productivity (**Figure 1B**) of this approach that appears to be due to at least two major factors. One being the increasing difficulty in finding novel therapeutic targets, either for diseases with well established standards of care or those with unmet medical need (Pammolli et al., 2011; Scannell et al., 2012), and the other being the increasing cost associated with discovery and drug development of new drugs. The current average cost to bring a drug to market is \$1.5 billion, over 10 times higher than the cost in the 1970s (DiMasi and Grabowski, 2007; Scannell et al., 2012). The need for improved productivity in the pharmaceutical industry has been recognized by the FDA, with the establishment of its "Critical Path Initiative" in 2004. This initiative was intended to improve the drug and medical device development processes, the quality of evidence generated during development, as well as the outcomes of clinical use of these products (Woodcock and Woosley, 2008).

## **COMPUTER MODELING AND SIMULATION AS TOOLS TO IMPROVE PRODUCTIVITY**

A decline in productivity is to be expected for any industry as it matures, and the competition from established products increases. This decline in productivity is typically associated with increasing development costs, partly due to the difficulty in differentiating one product from another in the marketplace. Industries must find innovative ways to increase the probability of commercial success while at the same time decreasing development costs. Most industries eventually realize the value of computer aided modeling and simulation as one of the means for achieving both of these objectives. Computer aided modeling and simulation allows testing of numerous potential scenarios "*in silico*" to eliminate those associated with a low probability of success, avoiding the tremendous costs of evaluating all of those failed scenarios in the real world. Today, aerospace, automotive,

electronics, and other industries routinely incorporate modeling and simulation into their R&D processes (Woltosz, 2012). The pharmaceutical industry has been slow to integrate computer aided modeling and simulation for many reasons: including the perception that biology and pharmacology are "too complex" to be modeled with mathematical equations; a lack of adequate graduate training programs for pharmaceutical modeling and simulation scientists; and the lack of support from government funding agencies for academic research in computer aided modeling and simulation approaches for biomedical research. However, in the last decade, both the FDA and National Institutes of Health (NIH) have recognized the value of modeling and simulation in increasing productivity in biomedical research and pharmaceutical R&D. The FDA established its Pharmacometrics Division in 2009 to promote and evaluate the use of modeling and simulation approaches in regulatory submissions to the agency (U.S. Food and Drug Administration, 2013a). In 2011, the NIH published a white paper describing the emerging discipline of Quantitative Systems Pharmacology (QSP) modeling, and recommended the establishment of NIH-supported interdisciplinary research and training programs for QSP (Sorger et al., 2011). QSP modeling and simulation is a new term to describe the integration of two disciplines that have been increasingly useful in biomedical research and pharmaceutical R&D; "Systems Biology" and "Quantitative Pharmacology." Systems Biology is the field of biomedical research that seeks to characterize biological networks of interactions, including those between genes and biologically active molecules to develop models of these systems that are usually qualitative in nature. Quantitative Pharmacology (a.k.a. Pharmacometrics) is the field of biomedical research that seeks to use computer aided modeling and simulation to increase our understanding of the pharmacokinetics (PK) and pharmacodynamics (PD) of drugs, and to aid in the design of pre-clinical and clinical experiments. The purpose of QSP modeling is to develop quantitative computer models of biological systems and disease processes; as well as the effects of drug PK and PD on those systems.

## **PHARMACEUTICAL R&D AND QUANTITATIVE SYSTEMS PHARMACOLOGY**

Pharmaceutical R&D is a stepwise process where investment in further characterizing the pharmacology of a candidate molecule is incrementally increased as confidence in the molecule's probability of regulatory and commercial success increases. Investment initially starts with *in vitro* biochemical and pharmacology studies; then moves to animal pharmacology and toxicology studies, then to human healthy volunteer pharmacology and toxicology studies; and finally to large and expensive patient efficacy and safety studies. QSP models are based on the fundamental understanding of biological pathways, disease processes, and drug mechanisms of action. Therefore, they are very effective tools for integration of prior collected biological/pharmacological knowledge, formulation of pharmacological hypotheses, and for efficient translation between the various experimental models within pharmaceutical R&D. Key milestones in R&D where QSP models will be critical to increasing the probability of success will be in the target identification stage, the transition from pre-clinical to first in man studies, the transition from healthy volunteer to patient studies, and the transition from adult to pediatric (**Figure 2A**). These milestones represent the point where knowledge from one set of experimental models (e.g., animal) must be effectively translated to another set (e.g., human). QSP can facilitate this translation by formal integration of the knowledge from the original experimental model and generation of hypotheses for potential outcomes in the next experimental model. Computer aided simulations to guide the design of experiments intended to test those hypotheses.

In addition to their utility in translation between experimental models, QSP allows prediction of the effects of multiple therapeutic interventions in combination. As it becomes clear in many therapeutic areas that modulation of single drug targets is less effective (e.g., oncology, virology), the cost of testing all of the potential combinations in the clinic is prohibitive. QSP can provide a framework in which to evaluate these potential combinations prior to testing in the clinic, by providing a fundamental

#### **FIGURE 2 | Continued**

**(A)** Incorporation of Quantitative Systems Pharmacology modeling and simulation in pharmaceutical R&D. Drug discovery and development is a long and complex process with numerous transition periods where effective translation from one experimental model to the next is a challenge. Major transitions occur when moving to first in man studies and first in pediatric studies. The cycles of application of QSP modeling and simulation are defined by (1) integration of experimental data and biological knowledge to develop QSP models; (2) generation of hypotheses for potential outcomes in future experiments; (3) testing of

systems and quantitative understanding of how these different mechanisms will interact.

## **PHARMACEUTICAL R&D AND QUANTITATIVE SYSTEMS PHARMACOLOGY**

Published examples describing the use of QSP modeling and simulation to facilitate biomedical research and pharmaceutical R&D have been increasing in recent years. Most of these publications have been focused on PK, since the processes that govern drug absorption, distribution, metabolism, and excretion are better established compared to those that govern disease biology and PD (Edginton et al., 2008). Strougo et al. (2012) demonstrated the use of these physiologically based PK (PBPK) models for prediction of PK in children prior to the conduct of the first pediatric clinical studies. There are software packages that can be licensed with PBPK models incorporated that allow prediction of *in vivo* drug PK based on the *in vitro* properties of the molecule (Kuentz et al., 2006; Jamei et al., 2009). QSP models that predict both PK and PD are much more complex, and tend to be disease area specific. Vega-Villa et al. (2013) published a QSP model of the nitric oxide metabolic pathways and demonstrated the models ability to predict toxic methemoglobin levels in humans treated with nitric oxide. Geerts et al. (2013a) published a QSP model of cognitive deficit in schizophrenia and were able to simulate the enhancement of cognition with clozapine and risperidone, as well as the worsening of cognition with γ -aminobutyric acid (GABA) modulators lorazepam and flumazenil. There are software packages that can be licensed that allow prediction of both PK and PD for a variety of drugs and mechanisms of action, but at much greater expense compared with those used for PBPK alone (Shoda et al., 2010; Eissing et al., 2011). Agoram and Demin (2011) reported on the development and application of a QSP model of the PD of the 5-lipoxygenase (5-LO) pathway. This QSP model has been used to explain the complex PK–PD relationship of zileuton, a marketed 5-LO inhibitor (Karelina et al., 2010). The model was able to demonstrate the mechanism behind the longer duration, but similar magnitude, of action with the 600 vs. 400 mg dose of zileuton. More important for its utility in drug discovery, this QSP model could be used to predict the PK and PD of a new molecule or combination of molecules intended to modulate another component of the 5-LO pathway based solely on the biophysical properties of the molecule and its potency at the target. One could then design a series of *in vivo* experiments to validate the hypotheses generated from these predictions.

those hypotheses with experiments that have been designed via simulation from QSP models. **(B)** Integration of QSP models in pharmaceutical R&D process. The model development team should be a sub-team of existing drug discovery and development teams. The goals of the model development team are to develop QSP models for their particular disease area and/or to apply existing QSP models to facilitate key milestones in discovery and development. The model development process should be rigorous and stepwise, so that models that are developed can used broadly in the disease area and can be used to communicate with regulatory agencies.

Quantitative Systems Pharmacology holds great promise in being able to uncover innovative therapeutic paradigms for complex multi-factorial diseases such as Alzheimer's and diabetes. Because these diseases involve multiple physiological processes and can affect multiple organs, QSP can provide an integrated understanding of the pathology as well as the possible complex counter-intuitive results of therapeutic intervention.

## **INTEGRATION OF QUANTITATIVE SYSTEMS PHARMACOLOGY INTO PHARMACEUTICAL R&D**

In order to leverage QSP to accomplish this, it must be properly integrated into the decision making process in pharmaceutical R&D. As mentioned above, it is possible to license PBPK and QSP models to facilitate decision making in pharmaceutical discovery and development. However, since licensing is often limited to a few specialized functions, this approach decreases the flexibility and utility of QSP across the different functions within R&D. QSP models should be integrated into the processes of discovery and development within pharmaceutical companies in order to maximize their potential benefit on R&D efficiency and productivity. To better integrate these models into the existing processes, they can be developed internally within the drug discovery and development teams. In addition, the teams must be organized and educated to support this integration. **Figure 2B** shows the integration of the QSP model development team with the drug discovery and development team. Development of a QSP model for prediction of clinical PK and PD should be a rigorous and stepwise process, with three main steps:

In addition to the modeling engineer, who will incorporate the equations into the model based on the agreed upon scope, critical individuals on the model development team include the following:

Once a QSP model is developed, it should be regularly updated with relevant internal and external research. In addition, it should be made available to all scientists in R&D that work in that particular disease area. The QSP model can be made flexible such that it can be readily adapted to other species that may be of interest in drug discovery (e.g., rat, monkey, rabbit, etc.). This would facilitate translation of experiments between these species and human.

## **OUTLOOK FOR QUANTITATIVE SYSTEMS PHARMACOLOGY IN PHARMACEUTICAL R&D**

Quantitative Systems Pharmacology holds great promise in being able to uncover innovative therapeutic paradigms for complex multi-factorial diseases such as Alzheimer's and multiple sclerosis. Because these diseases involve multiple physiological processes and can affect multiple organs, QSP can provide an integrated understanding of the pathology as well as the possible complex results of therapeutic intervention. QSP thus offers pharmaceutical R&D an innovative way to conduct at drug discovery and development, particularly in diseases that are poorly translated from animal disease models. Geerts et al. (2013b) recently published an article on how QSP, when combined with phenotypic screening and preclinical animal models, could be used to address the bottleneck in both cognitive and neuropsychiatric drug discovery and development for Alzheimer's disease. For such complex diseases that are poorly translated from animal disease models, target-focused drug discovery holds little promise for finding successful therapies. However, pharmaceutical companies are large and bureaucratic, and dramatic changes to the direction in which R&D is conducted may be adopted rather slowly.

There are smaller pharmaceutical and biotech companies that are fully integrating QSP into their biomedical R&D processes. One example is Merrimack Pharmaceuticals in Cambridge, MA, USA; founded by MIT professor of Biology and Biological Engineering Michael Yaffe. Merrimack states on their website, "We are a Systems Biology company. We believe that improving cancer care requires a systems-based understanding of the dynamic interactions within a cancer cell and its environment" (Merrimack Pharmaceuticals Inc., 2014). The scientific and financial communities will be watching these small companies, and if their model for a systems-based approach to R&D is successful, the pressure will be increased for "large pharma" to more fully adopt such innovative approaches into their discovery and development processes.

## **REFERENCES**

ofMedicalProductsandTobacco/CDER/ucm167032.htm [accessed October 13, 2014].

**Conflict of Interest Statement:** The authors are employees of Bristol-Myers Squibb.

*Received: 15 August 2014; accepted: 24 October 2014; published online: 10 November 2014.*

*Citation: Leil TA and Bertz R (2014) Quantitative Systems Pharmacology can reduce attrition and improve productivity in pharmaceutical research and development. Front. Pharmacol. 5:247. doi: 10.3389/fphar.2014.00247*

*This article was submitted to Experimental Pharmacology and Drug Discovery, a section of the journal Frontiers in Pharmacology.*

*Copyright © 2014 Leil and Bertz. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.*

## Systems pharmacology approaches for optimization of antiangiogenic therapies: challenges and opportunities

## **Satish Sharan and Sukyung Woo\***

Department of Pharmaceutical Sciences, College of Pharmacy, The University of Oklahoma Health Sciences Center, Oklahoma City, OK, USA

#### **Edited by:**

Tarek A. Leil, Bristol-Myers Squibb, USA

#### **Reviewed by:**

Xiaogang Wu, Institute for Systems Biology, USA Jeffrey S. Barrett, Sanofi Pharmaceuticals, USA

#### **\*Correspondence:**

Sukyung Woo, Department of Pharmaceutical Sciences, College of Pharmacy, The University of Oklahoma Health Sciences Center, CPB 331, 1110 N. Stonewall Avenue, Oklahoma City, OK 73117, USA e-mail<EMAIL_ADDRESS>
Targeted therapies have become an important therapeutic paradigm for multiple malignancies. The rapid development of resistance to these therapies impedes the successful management of advanced cancer. Due to the redundancy in angiogenic signaling, alternative proangiogenic factors are activated upon treatment with anti-VEGF agents. Higher doses of the agents lead to greater stimulation of compensatory proangiogenic pathways that limit the therapeutic efficacy of VEGF-targeted drugs and produce escape mechanisms for tumor. Evidence suggests that dose intensity and schedules affect the dynamics of the development of this resistance. Thus, an optimal dosing regimen is crucial to maximizing the therapeutic benefit of antiangiogenic agents and limiting treatment resistance. A systems pharmacology approach using multiscale computational modeling can facilitate a mechanistic understanding of these dynamics of angiogenic biomarkers and their impacts on tumor reduction and resistance. Herein, we discuss a systems pharmacology approach integrating the biology of VEGF-targeted therapy resistance, including circulating biomarkers, and pharmacodynamics to enable the optimization of antiangiogenic therapy for therapeutic gains.

**Keywords: systems pharmacology, biomarkers, dose selection, antiangiogenic therapy, resistance, targeted therapies, biologically effective dose, bed**

## **INTRODUCTION**

Therapeutic intervention in diseases takes place within a milieu of factors, including drug pharmacokinetics, signaling pathways, mechanisms of drug action, and compensatory processes. Studying any single pathway, mechanism of action, or interactive process in isolation has limited value in improving our understanding of the complexity of disease physiology. This is evident in the redundancy of signaling networks, feedback, and cross talk between multiple regulatory processes (Moriya et al., 1996; Pawson and Warner, 2007; Logue and Morrison, 2012). A systems approach is required to quantitatively integrate underlying disease and information contributing to treatment response and resistance. Systems pharmacology combines large scale experimental studies, pharmacokinetics, mechanisms of action, signaling pathways, adaptation mechanisms, biomarker, and pharmacodynamic data in a quantitative framework utilizing computational methods. This approach can facilitate understanding of disease systems, their mechanisms of action and pathways, and hypothesis development (Agoram, 2014). Systems pharmacology further offers a tool for translational considerations from non-clinical models to patients, realizing the bench to bedside paradigm (Allerheiligen, 2010; Kreeger and Lauffenburger, 2010; van der Graaf and Benson, 2011; Demin et al., 2013; Rogers et al., 2013; Vicini and van der Graaf, 2013; Visser et al., 2014). Herein we discuss systems pharmacology approaches to achieve a mechanistic understanding of the dynamics of circulatory biomarkers for antiangiogenic agents, thereby guiding selection of doses that can maximize the therapeutic benefits.

## **CHALLENGES IN ANTIANGIOGENIC THERAPIES**

Angiogenesis is critical for tumor growth and metastasis. VEGF signaling is an extensively studied pathway for blocking tumor angiogenesis. Several antiangiogenic agents targeting the VEGFpathways have been approved and are important modalities in the management of advanced cancers. Bevacizumab, a therapeutic antibody targeting VEGF and various VEGF receptor tyrosine kinase inhibitors (TKIs), have shown clinical benefit in solid tumors. However, the benefits of VEGF-targeted agents are shortlived and resistance to anti-VEGF agents rapidly emerges after an initial response phase, leading to restored tumor growth and progression. This rapid development of resistance to therapy constitutes a major clinical obstacle to providing extended therapeutic benefits with this class of drugs. Thus, effective strategies are needed to delay or prevent resistance to VEGF antiangiogenics.

Resistance to antiangiogenic agents arises through multiple mechanisms, including the activation of compensatory responses that are mediated by malignant cells and stroma cells within the microenvironment. Angiogenesis is a highly adaptive biological process. Tumors can resume angiogenesis and progress using diverse angiogenic signaling, including VEGF, FGF, HGF, PDGF, PlGF, and several proangiogenic cytokines. Numerous compensatory angiogenic factors are upregulated upon anti-VEGF therapy in a dose-dependent manner (Ebos et al., 2007), suggesting that dose intensity and frequency influence the development of therapy resistance. Higher doses of anti-VEGF therapy can create favorable conditions for metastasis by upregulating these growth factors (Ebos et al., 2009a). This emphasizes the importance of finding optimal dosing schedules for anti-VEGF therapy. The current dosing approach does not consider the best way to delay or prevent resistance to VEGF-targeted therapy, and thereby improve patient survival beyond a few months (Jubb et al., 2006; Azad et al., 2008; Cannistra, 2008).

## **BIOLOGICALLY EFFECTIVE DOSES OF ANTI-VEGF THERAPY**

Oncology drug development often involves the maximumtolerated dose (MTD)-based paradigm, even when data suggest that a drug maximally inhibits its target at lower doses. The recent analysis by the U.S. Food and Drug Administration (FDA) showed that inappropriate dose selection was the major cause of postmarketing requirements for oncology drugs approved between 2011 and 2013 (Prowell, 2014). Clinically recommended doses are often derived based on their safety profiles. Toxicity has been the primary end point for conventional dose-finding strategies (Parulekar and Eisenhauer, 2004; Le Tourneau et al., 2009). Since antiangiogenic therapies are mostly cytostatic in nature, they do not always conform to the concept that MTD produces maximum benefits (Sleijfer and Wiemer, 2008). Studies have revealed better therapeutic benefits when lower doses of antiangiogenic therapies were used in combination with other treatments (Kabbinavar et al., 2003; Huang et al., 2012). Similar results were observed with other targeted therapies, such as mammalian target of rapamycin kinase inhibitor, in which a lower dose of 25 mg was selected as the recommended dose for treatment after testing 25, 75, and 250 mg doses (Atkins et al., 2004). Likewise, in a study of 24 consecutive Phase I clinical trials, in which 97.7% of participants received targeted agents, patients receiving lower (≤25% MTD) doses responded as well as those patients receiving medium (25– 75% MTD) or high (≥75% MTD) doses (Jain et al., 2010). These findings support the concept that higher doses are not necessarily the most effective.

Higher doses of anti-VEGF therapies can lead to pronounced anti-vascular effects and, subsequently, hypoxia in the tumor, e.g., treatment-induced hypoxia. Treatment-induced hypoxia stimulates several compensatory biological processes to circumvent continued VEGF inhibition, leading to resistance to therapy (Harris, 2002; Casanovas et al., 2005; Drevs et al., 2005; Kerbel, 2005; Mizukami et al., 2005; Hendriksen et al., 2009; Casanovas, 2011). This excessive pruning also leads to reduced delivery of therapies into the tumor (Jain, 2005; Van der Veldt et al., 2012; Van der Veldt and Lammertsma, 2014). Tumors have abnormal vasculature, which leads to an abnormal blood supply that produces hypoxic regions in the tumor. Hypoxia has been also implicated in tumor progression by increasing genomic instability (Nelson et al., 2004) and selection of more malignant cancer stem cells with increased metastatic potential (Bottaro and Liotta, 2003; Conley et al., 2012). Therefore, antiangiogenic therapy can produce more challenges than benefits, if it is inappropriately administered (Huang et al., 2013b; Jain, 2013, 2014). This is consistent with RK Jain's vascular normalization concept, in which the judicious use of antiangiogenic drugs can lead to more efficient delivery of drugs and oxygen to the tumor cells (Jain, 2005). Utilization of the vascular normalization strategy has been shown to improve cancer immunotherapy (Huang et al., 2012, 2013a) and survival in glioblastoma patients (Sorensen et al., 2012; Emblem et al., 2013). Therefore, there is a critical need to find the biologically effective dose (BED) that balances between normalization and excessive anti-vascular effects from antiangiogenic agents, since suboptimal and higher doses can fail to alleviate hypoxia. Further, the BED can minimize stimulation of alternative, compensatory proangiogenic signals in response to treatment-induced hypoxia, and thus limit the rapid development of treatment resistance, extending the therapeutic benefits of antiangiogenic agents (Jubb et al., 2006; Azad et al., 2008; Cannistra, 2008).

## **DYNAMICS OF CIRCULATING ANGIOGENIC BIOMARKERS**

The transient effects of antiangiogenic therapy predominantly result from a redundancy in the angiogenesis signaling that mediates tumor escape from anti-VEGF therapy. Many of the signaling molecules (circulating angiogenic factors, or CAF) within these compensatory pathways can be detected systemically in patients treated with VEGF-targeting agents. For example, increases in VEGF and PlGF, and decreases in VEGFR2 can be observed. These changes are considered a "class" effect of VEGFtargeted therapies (Jain et al., 2009). Many of these observed CAF changes are recapitulated in tumor-bearing mice in a dosedependent manner, and are correlated with antitumor activity (Ebos et al., 2007). Thus, CAF are increasingly recognized as important pharmacodynamic biomarkers for better understanding the treatment response and aiding in the identification of the optimal dosing schedules for VEGF-targeted therapy (Huang et al., 2013b). Understanding the molecular interactions between therapy-induced CAFs and resistance to VEGF-targeted agents can inform the development of strategies to delay or overcome resistance to antiangiogenic therapy (Jain et al., 2009; Clarke and Hurwitz, 2013).

These circulating biomarkers are dynamic, altered over the course of treatment by variables including *in vivo* drug concentrations (PK), changes in the tumors (e.g., antitumor effect and disease progression), the biological turnover of signaling molecules, compensatory mechanisms, tumor-independent CAF induction by normal cells in the host body, and the development of resistance. These diverse contributing factors create uncertainty when attempting to use dynamic biomarkers. Mathematical modeling can play an important role in understanding and utilizing the biomarkers to find the optimum biological dose and schedule which can delay the onset of therapy resistance (Duda et al., 2013). A recent study showcased the utility of computational models in identifying dosing schedules to manipulate the dynamics of the development of resistance to EGFR-targeted therapy (Foo et al., 2012; Dolgin, 2014). A systems pharmacology approach using multiscale computational modeling offers a tool to integrate the biology of response and resistance to VEGF-targeted therapy, including circulatory biomarkers and the pharmacokinetics/pharmacodynamics of antiangiogenic drugs (**Figure 1**), to optimize therapeutic gains.

## **SYSTEMS PHARMACOLOGY APPROACH TO ANTIANGIOGENIC THERAPY**

The major challenge in developing a systems pharmacology model is how to integrate the dynamics outside the cell (phar macokinetics) with their downstream effects in terms of protein

formation or pharmacodynamic effects. PK/PD modeling has been used to explain the relationship between pharmacokinetics and the end downstream effects. What is missing is the mechanistic information in between. Limiting our investigation to antiangiogenic therapy, we anticipate three major challenges to filling this gap: (1) determining the interaction of ligands to their receptors and perturbation by drug molecules, (2) integrating the ensuing signal from these receptors with the downstream protein production machinery, and (3) accounting for interaction between various cell types, that produces pharmacodynamics responses and resistance.

## **DRUG-TARGET INTERACTION**

Receptor occupancy theory is well-developed and can be readily utilized to integrate this process (Black and Leff, 1983; Black et al., 1985; Mager and Jusko, 2008; Chen et al., 2009; Goodman and Redberg, 2014). We must be mindful that biology is complex and there are many subtypes of ligands, receptors, and coreceptors which have varying degrees of affinity and modulatory functions. Ligand-receptor interaction for angiogenesis involves the VEGF family of ligands (VEGF-A, B, C, D, and PlGF), three main receptors (VEGFR-1, -2, and -3), co-receptors NRP-1 and NRP-2, and heparan sulfate proteoglycans. NRP- and, -2 and proteoglycans play modulatory roles in ligand-receptor interaction; even VEGF-A is alternatively spliced to form VEGFA121, VEGFA145, VEGFA165, and VEGFA189 (Hoeben et al., 2004; Koch et al., 2011; Tugues et al., 2011). Popel and colleagues have contributed extensively to our understanding of the kinetics and interaction of VEGF ligands and receptors (Stefanini et al., 2010; Finley et al., 2011, 2013; Finley and Popel, 2012, 2013; Tan et al., 2013). Although a potential contribution of other ligand and receptor isoforms and families may be recognized, several studies have simplified these interactions by accounting for the most important VEGF ligand, VEGF-A (165), and receptor VEGFR-2 interaction as the major players in angiogenesis (Sharan and Woo, 2014; Zhang et al., 2014). The combination of competitive ligand receptor binding and an inhibitory Hill function model can be used to explain the VEGF-induced VEGFR activation and inhibitor-induced VEGFR inactivation (Sharan and Woo, 2014).

## **SIGNAL TRANSDUCTION**

Signaling pathways are an important component of a systems pharmacology model, which links receptor-ligand interaction to pharmacodynamic outputs (Iyengar et al., 2012). VEGF binding to its receptors led to the phosphorylation of the tyrosine kinase domain, which in turn initiated the canonical downstream signaling cascades involved in proliferation, migration, survival, and permeability (Tugues et al., 2011). Ordinary differential equation (ODE)-based models, also termed mechanistic or physicochemical models (Birtwistle et al., 2013; Zhang et al., 2014), are often used to describe the canonical signaling cascades. The advantage of this approach being more mechanistic can help a personalized medicine paradigm by incorporating information related to genomic variation and mutation (Iyengar et al., 2012). The limitation of this approach is the currently incomplete mechanistic knowledge of several mediators, signaling processes, and parameter identifiability. Given the incomplete mechanistic knowledge of several mediators and signaling processes, or in the absence of measurement of mediator signaling molecules, a more empirical quantitative logic (QL; Kirouac et al., 2013; Kirouac and Onsum, 2013) or transduction model (Mager and Jusko, 2001) can be utilized to characterize signal transduction. The QL approach has been elegantly explained by Kirouac and Onsum (2013) in building multiscale models which capture the features of oncogenic signaling networks. The transduction model has the flexibility of handling multiscale events with different transit time parameters to account for time needed for signal transduction from receptor-ligand interaction to nucleus, time for cell machinery to form proteins, and to show the pharmacodynamic effects on tumor growth. It is vital to take a balanced approach between mechanistic representation of the signaling pathway and the model's predictive power (Sharan and Woo, 2014).

## **THERAPEUTIC AND COMPENSATORY RESPONSES TO ANTI-VEGF THERAPY**

Ideally, signaling events are linked to tumor growth kinetics. Tumor inhibitory effects of anti-VEGF agents can be described by adapting well-established models (Simeoni et al., 2004, 2013; Ribba et al., 2014). In addition to tumor growth inhibition, systemically quantifiable biomarkers such as CAFs can serve as an important measurement to identify disease progression, make dose selections, or stratify patients. Indirect response models can be effectively used to capture inhibition, stimulation, and turnover rates of biomarkers modulation (Mager et al., 2003). We can use non-linear feedback regulation to account for compensatory increases in circulatory biomarkers in response to treatment-induced hypoxia by anti-VEGF agents.

The contributions of host cells and stroma cells within the tumor microenvironment have been increasingly recognized to play an important role in cancer progression and treatment (Ebos et al., 2007, 2009b; Kerbel and Ebos, 2010; Jain, 2013; Stroh et al., 2014). This should be explored using a systems pharmacology model. Antiangiogenic therapies have been shown to upregulate various growth factors in healthy cells and are dosedependent in non-tumor-bearing mice (Ebos et al., 2007). This dose-dependency is also observed in healthy human volunteers (Lindauer et al., 2010). Thus, it is important to characterize tumor and host cell contributions to CAF modulation and to provide mechanistic information for interpreting biomarker data in respect to antiangiogenic treatments.

## **APPLICATION OF A SYSTEMS PHARMACOLOGY MODEL OF CAFs FOR DOSE OPTIMIZATION**

We have recently developed a systems pharmacology model that uses sunitinib as the test drug to quantify the link between *in vivo* drug concentrations (PK), target–drug interactions, the biological target pathway, antitumor activity, and compensatory signals leading to treatment resistance (**Figure 1**). We used the most frequently studied CAFs, including VEGF, PlGF, and sVEGFR2. Our model predictions were consistent with the time- and dosedependent changes in these hypoxia-derived CAFs following sunitinib given to mice at various dosages (Ebos et al., 2007). We then tested our model within a clinical setting to explain VEGF changes in patients with cancer who experience different treatment outcomes; we found that our predictions were consistent with the observed VEGF changes in patients receiving sunitinib for the treatment of metastatic renal cancer (Kontovinis et al., 2009). The stimulation/inhibition capacity and the hill coefficients of VEGF, PlGF, and sVEGFR2 in mice were similar to those reported in humans, indicating that system-specific parameters for conserved physiological processes such as angiogenesis are comparable across species (Sharan and Woo, 2014).

**FIGURE 2 | (A)** Relationships of therapeutic efficacy and modulation of VEGF and PlGF biomarkers to sunitinib doses. Percentage reduction in tumor volume (•) and fold change in PlGF (N) and VEGF () are shown at various doses of sunitinib at the end of study. At the dose of 40 mg/kg/day, ∼75% of tumor volume was reduced, with minimal upregulation of hypoxia-dependent CAF. Further dose escalation resulted in marginal therapeutic gain (<5%), but significant upregulation of CAF, which may indicate excessive anti-vascular effects. **(B)** Utilization of CAF biomarkers in the selection of biological dose of antiangiogenic drugs. The fold change in VEGF and PlGF may serve as a surrogate marker for excessive anti-vascular effects and, in turn, potential for emerging resistance. This illustrates how the biologically effective dose may be selected in a manner which does not invoke significant hypoxia and involves little stimulation of hypoxia-dependent CAF. Monitoring multiple CAFs will be advantageous, as each factor has a different dynamic range. PlGF has a wider dynamic range than VEGF, and results in higher fold change at the same dose. This provides an advantage over VEGF, because PlGF changes are more likely detectable even at lower doses.

Our model allows us to delineate CAF changes in the tumor microenvironment and host body during VEGF-targeted therapy and to assess their impacts on tumor response and resistance to therapy. This provided insight into the possible ways to utilize the CAF for better dose guidance of these therapies, either alone or in combination. We found a relationship of tumor reduction and compensatory increase in VEGF and PlGF with increasing sunitinib doses in xenograft mice (**Figure 2A**). The increase in proangiogenic factors was directly related to the dose, suggesting that these CAF can be used as biomarkers to determine the optimal dose for antiangiogenic drugs. For example, in an A431 xenograft mouse model, the maximum benefit from sunitinib treatment may be achieved at a dose of 20–40 mg/kg/day of sunitinib, as such doses produce no significant changes in VEGF or PlGF levels. Further dose escalation resulted in marginal therapeutic gain (<5%), but significant upregulation of hypoxia-dependent CAF, which may indicate excessive anti-vascular effects. As such, these CAF could be used to construct a therapeutic index for antiangiogenic agents. **Figure 2B** illustrates this CAF biomarker-based paradigm for dose selections in particular, balancing between antitumor effects and CAF changes. The CAF modulation may serve as a surrogate marker reflecting the anti-vascular effects of antiangiogenic treatment. Ligands of tyrosine kinase receptors have been found to confer resistance by engaging survival signals redundant to those of targeted kinase (Wilson et al., 2012). If we assume that higher changes in compensatory signals are associated with higher likelihood of early onset of resistance, antiangiogenic doses may be increased up to the level at which the CAF increase from their baseline is minimal (e.g., <2-fold for VEGF).

Increasing sunitinib doses also led to VEGF and PlGF stimulation with different magnitudes (**Figure 2B**). This differential stimulation of pro-angiogenic factors can be exploited to facilitate dose finding. Given the inter-individual variability and heterogeneity in tumor response, monitoring multiple biomarkers, rather than relying on a single marker, would be advantageous. We found that PlGF changes were ∼2-fold higher than VEGF changes at the same dose (Sharan and Woo, 2014). This finding suggests that PlGF has a wider dynamic range than VEGF, and can ensure better detection of its change even at lower doses. Thus, monitoring PlGF and VEGF can aid in ensuring that the therapy does not fall below the minimum effective dose nor go above the excessive anti-vasculature dose. This finding is consistent with the recent study in which increased PlGF, but not VEGF, was associated with patients responding to cediranib (Batchelor et al., 2013). While we illustrated the CAF-based dose-finding strategy using VEGF and PlGF, other CAF could be used, as different tumor types and drug targets can invoke different CAF dynamics. Many concepts and the mathematical framework are broadly applicable among several tumor types and different antiangiogenic agents, and could serve as a paradigm for determining the optimal dose of targeted therapies.

Antiangiogenic therapies are often administered in combination with chemotherapy. There is increasing interest in combining antiangiogenics with other targeted therapies in order to improve therapeutic outcomes. However, since the clinical doses of many targeted therapies are determined based on MTD rather than BED, we cannot easily deduce the dosage and schedules of combinations from single agent studies. When antiangiogenic therapies are combined with drugs of same class, excessive overlapping toxicities have resulted (Azad et al., 2008, 2009). In addition, antiangiogenic therapies at higher doses could reduce the efficacy of concomitant cytotoxic agents, most likely due to reduced drug delivery by excessive vessel pruning (Van der Veldt et al., 2012). The CAF biomarker-based approach could also be useful for determining the optimal dose of combination therapy. In combination therapy, the role of antiangiogenic drugs may be focused on vascular normalization. Other therapeutics can be targeted toward killing tumor cells. In such cases, it is desirable for antiangiogenic drugs to be administered at lower doses at which the stimulation of compensatory signaling is minimal.

## **CONCLUSION**

Therapy-induced CAF can be effectively utilized as pharmacodynamic biomarkers to find the optimal biological dose for antiangiogenic drugs. This will ensure that the therapy maintains minimum effective dose levels, without invoking much compensatory response from the system. Routine incorporation of biomarkers into future clinical trials will be critical for the optimization of anti-VEGF agents and development of next generation of antiangiogenic regimens. Biomarker studies can be augmented by imaging studies, such as dynamic contrast-enhanced MRI (DCE-MRI), or other imaging techniques to monitor vessel integrity, permeability of blood vessels, and tumor perfusion (Murukesh et al., 2010). Thus, future strategies will require circulating biomarkers and imaging with an integrated multi-scale computational tool to guide optimal dose selection for antiangiogenic agents. As more data become available in the future, with the advance of high throughput methods like genomic data, the main challenge will be vertically integrating those data. Systems pharmacology will offer a tool to vertically integrate knowledge from pharmacokinetics, mechanisms of action, genomics, biomarkers, toxicokinetics, and pharmacodynamics. This approach yields an informed perspective from which we can streamline drug discovery and development. The knowledge gained from this approach can provide an in-depth understanding and, hence, a better approach for achieving enduring therapeutic benefits from antiangiogenic therapy.

## **ACKNOWLEDGMENT**

Research reported in this publication was supported by the National Institutes of General Medical Sciences of the National Institutes of Health under Award Number P20GM103639. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.

## **REFERENCES**

growth kinetics in xenograft models after administration of anticancer agents. *Cancer Res.* 64, 1094–1101. doi: 10.1158/0008-5472.CAN-03-2524

**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

*Received: 05 September 2014; accepted: 06 February 2015; published online: 20 February 2015.*

*Citation: Sharan S and Woo S (2015) Systems pharmacology approaches for optimization of antiangiogenic therapies: challenges and opportunities. Front. Pharmacol. 6:33. doi: 10.3389/fphar.2015.00033*

*This article was submitted to Experimental Pharmacology and Drug Discovery, a section of the journal Frontiers in Pharmacology.*

*Copyright* © *2015 Sharan and Woo. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.*

## Analysis of the efficacy of SGLT2 inhibitors using semi-mechanistic model

#### *Oleg Demin Jr. <sup>1</sup> \*, Tatiana Yakovleva1, Dmitry Kolobkov2 and Oleg Demin2*

*<sup>1</sup> Laboratory Alpha, Institute for Systems Biology Moscow, Moscow, Russia*

*<sup>2</sup> Institute for Systems Biology Moscow, Moscow, Russia*

### *Edited by:*

*Tarek A. Leil, Bristol-Myers Squibb, USA*

#### *Reviewed by:*

*Sukyung Woo, University of Oklahoma Health Science Center, USA Satyaprakash Nayak, Pfizer Inc., USA*

#### *\*Correspondence:*

*Oleg Demin Jr., Laboratory Alpha, Institute for Systems Biology Moscow, Nauchny proezd, 20, Bldg. 2, Technopark Slava, 117246 Moscow, Russia e-mail: demin\_<EMAIL_ADDRESS>
The Renal sodium-dependent glucose co-transporter 2 (SGLT2) is one of the most promising targets for the treatment of type 2 diabetes. Two SGLT2 inhibitors, dapagliflozin, and canagliflozin, have already been approved for use in USA and Europe; several additional compounds are also being developed for this purpose. Based on the *in vitro* IC50 values and plasma concentration of dapagliflozin measured in clinical trials, the marketed dosage of the drug was expected to almost completely inhibit SGLT2 function and reduce glucose reabsorption by 90%. However, the administration of dapagliflozin resulted in only 30–50% inhibition of reabsorption. This study was aimed at investigating the mechanism underlying the discrepancy between the expected and observed levels of glucose reabsorption. To this end, systems pharmacology models were developed to analyze the time profile of dapagliflozin, canagliflozin, ipragliflozin, empagliflozin, and tofogliflozin in the plasma and urine; their filtration and active secretion from the blood to the renal proximal tubules; reverse reabsorption; urinary excretion; and their inhibitory effect on SGLT2. The model shows that concentration levels of tofogliflozin, ipragliflozin, and empagliflozin are higher than levels of other inhibitors following administration of marketed SGLT2 inhibitors at labeled doses and non-marketed SGLT2 inhibitors at maximal doses (approved for phase 2/3 studies). All the compounds exhibited almost 100% inhibition of SGLT2. Based on the results of our model, two explanations for the observed low efficacy of SGLT2 inhibitors were supported: (1) the site of action of SGLT2 inhibitors is not in the lumen of the kidney's proximal tubules, but elsewhere (e.g., the kidneys proximal tubule cells); and (2) there are other transporters that could facilitate glucose reabsorption under the conditions of SGLT2 inhibition (e.g., other transporters of SGLT family).

**Keywords: SGLT-2, systems pharmacology modeling, Type 2 diabetes mellitus (T2DM), dapagliflozin**

## **INTRODUCTION**

Type 2 diabetes mellitus (T2DM) is a metabolic disorder that is characterized by hyperglycemia resulting from insulin resistance and relative lack of insulin. Current therapies for T2DM primarily address endocrine pathogenesis of insulin resistance and b-cell dysfunction. Consequently, many patients receive multiple glucose-lowering therapies and eventually require exogenous insulin administration. However, in clinical practice patients often fail to meet the targets for glycemic control (Ali et al., 2013), most frequently because of adverse effects–including hypoglycemia and weight gain–caused by therapeutic agents (Neumiller, 2014). Therefore, in order to avoid direct influence on insulin resistance and b-cell dysfunction, T2DM can be treated with inhibition of glucose reabsorption.

Glucose is reabsorbed to blood in the proximal tubules of the kidneys during the formation of primary urine. Where the reabsorption process is inhibited, glucose is excreted in urine and blood glucose concentration is reduced. Patients treated with inhibition of glucose reabsorption have a low risk of hypoglycemia because the mechanism of the treatment is independent of insulin release or endogenous glucose production (Misra, 2013). In the kidneys, families of glucose transporters and sodium-dependent glucose co-transporters are involved in glucose reabsorption. For example, sodium-dependent glucose cotransporter 2 (SGLT2) is thought to contribute to 90% of glucose reabsorption in kidneys (Liu et al., 2012), which makes it a promising target in T2DM therapy.

Currently, two SGLT2 inhibitors are marketed (dapagliflozin, canagliflozin) and several more are in development (e.g., empagliflozin, tofogliflozin). Based on inhibitory concentration 50% (IC50) values measured *in vitro* (Ohtake et al., 2012) and plasma concentrations measured in clinical trials (Yang et al., 2013), the marketed dosage of dapagliflozin was predicted to inhibit SGLT2 almost completely and thereby reduce glucose reabsorption by 90%. However, clinical trials demonstrated that dapagliflozin induced 50–80 g of urinary glucose excretion per day, which corresponded to only 30–50% inhibition of reabsorption (Komoroski et al., 2009a; Kasichayanula et al., 2011a). To explain these findings, several hypotheses were published (Liu et al., 2012). The following hypotheses explain the lower than predicted efficacy of SGLT2 inhibitors:

To explore these hypotheses further, it is possible to adopt a systems pharmacology modeling (SPM) approach.

Many mathematical models that describe development and treatment of T2DM appear in the literature, and Ajmera et al. (2013) present a detailed review of these models. Several mathematical models describing SGLT2 inhibitors are also presented. For example, three models describe the pharmacokinetics (PK) and pharmacodynamics (PD) of SGLT2 inhibitors in animals (Yamaguchi et al., 2011, 2012, 2013), two population PK models exist for empagliflozin (Riggs et al., 2013) and dapagliflozin (van der Walt et al., 2013), and Maurer et al. (2011) describes a PK/PD model for dapagliflozin in rats and humans. However, a model that describes the concentration of SGLT2 inhibitors at the potential site of action (i.e., the lumen of proximal tubule in the kidneys) is yet to be published. The level of a compound in plasma may differ significantly from that in the kidneys; therefore, prediction of the concentration of SGLT2 inhibitors in the lumen of the kidney's proximal tubules is important for understanding the PD effect of the drug.

The aim of this study was to construct a model that describes the active secretion of SGLT2 inhibitors from plasma into the lumen of the proximal tubules, reverse reabsorption, and urinary excretion. Using an SPM approach, our objective was to test the hypotheses used to explain the discrepancy between expected and observed levels of glucose reabsorption following administrations of SGLT2 inhibitors (see above). We also aimed to compare the efficacies of different SGLT2 inhibitors by simulating their concentration level in the lumen of the kidney's proximal tubules and estimating the level of inhibition produced during treatment in humans.

### **METHODS**

A family of semi-mechanistic PK/PD models was developed to describe administration, degradation, transport, glomerular filtration, active secretion, reverse reabsorption, and urinary excretion of 5 SGLT2 inhibitors (dapagliflozin, canagliflozin, ipragliflozin, empagliflozin, tofogliflozin). The assumptions used for model development are presented in **Table 1**. The models describe the PK of the drugs, inhibition of glucose reabsorption mediated by SGLT2, and levels of inhibition in transporters of the SGLT family. The models for dapagliflozin, ipragliflozin, and tofogliflozin, which have identical structures, include 4 compartments: plasma, peripheral compartment (tissues, organs), lumen of the kidney's proximal tubules, and urine. The models for canagliflozin and empagliflozin have the same structure and include 3 compartments: plasma, lumen of the kidney's proximal tubules, and urine. The rate equations for each model are similar, but many of the parameter values are specific to a particular drug. We chose to add the peripheral compartment, and a rate equation describing transport between plasma and peripheral compartment, to models describing activity of dapagliflozin, ipragliflozin, and tofogliflozin in order to achieve a better description of plasma PK data (see "Models verification strategy" Section in Supplementary Materials). The effects of compounds on SGLT2 and other transporters are described as functions of inhibitor concentration in the lumen of the kidney's proximal tubules. Schemes of the models are presented in **Figure 1**. Using the family of models, we were able to quantify, analyze, and compare PK and PD characteristics of the drugs. A system of ordinary differential equations, rate equations, and explicit functions are presented in **Table 2**. Model development and fitting procedures were performed using the DBSolve Optimum package (Gizzatkulov et al., 2010).

## **IDENTIFICATION OF MODEL PARAMETERS**

The strategy of model verification is presented in the Supplementary Materials. The dapagliflozin, ipragliflozin, and tofogliflozin models include 19 parameters: 4 physiological, 9 drug specific PK, and 6 drug specific PD. In the right hand side of canagliflozin or empagliflozin models, 17 parameters are included: 4 physiological, 7 drug specific PK, and 6 drug specific PD. The parameter values are specific to each SGLT2 inhibitor model, with the exception of 4 physiological parameters (*Vplasma*, *Vlumen*, *GFR*, and Q*urine*) that have equal values in each model. The physiological parameter values were taken (or calculated) from the literature, as were those for 2 PK parameters (*F* and *fup*) and 6 PD parameters (IC50 for SGLT1–6). The remaining 7 or 5 parameters were fitted against PK data on the dynamics of compounds in plasma and urine. The 95% confidence intervals

**Table 1 | Assumptions for models development.**

were calculated for fitted parameters. Parameter values, 95% confidence intervals, and the source of data for their identification are presented in Supplementary Table 1.

## **COMPARTMENT VOLUMES**

Volume of blood plasma was taken from the literature. The volume of the lumen of the kidney's proximal tubules was calculated using experimental data (see Supplementary Materials). In the models that described dapagliflozin, ipragliflozin, and tofogliflozin, distribution volume in peripheral compartments was fitted against PK data. Compartment volumes and the source of identification are presented in Supplementary Table 1.

## **SIMULATIONS**

Model simulations are presented as curves (simulated with optimal parameters values) with shadows (95% confidence bands) or as bars (simulated with optimal parameters values) with error bars (95% confidence bands). The description of simulating the 95% confidence bands is presented in the Supplementary Materials.

## **RESULTS**

All data available in the literature was used for model verification and validation (**Table 3**). Models were calibrated against clinical data obtained in trials where a single dose of SGLT2 inhibitor was administered. By applying the verification strategy described in the Supplementary Materials, we found that: (i) the active secretion of dapagliflozin, canagliflozin, and ipragliflozin from plasma to kidney lumen was equal to zero; (ii) the reabsorption of empagliflozin was equal to zero; and (iii) both active secretion and reabsorption of tofogliflozin were equal to zero. The appropriate choice of model parameters was validated against data obtained from single and multiple dose administration. **Figures 2**, **3** represent examples of dapagliflozin model calibration using plasma PK and urine recovery data respectively, where data was obtained from single dose trials. **Figures 4**, **5** also represent examples of dapagliflozin model validation against plasma PK and urine recovery data respectively, but data was obtained from multiple dose trials. The 95% confidence bands captured the variability in clinical data (**Figures 4**, **5**); therefore, we concluded that model validation was of satisfactory quality. Several additional figures demonstrating the quality of verification and validation in dapagliflozin, canagliflozin, ipragliflozin, empagliflozin, and tofogliflozin models are presented in the Supplementary Materials (Supplementary Figures 1–16). These figures demonstrate that the models enable a satisfactory description of plasma PK and recovery of SGLT2 inhibitors in urine.

## **CONCENTRATION OF SGLT2 INHIBITORS IN THE LUMEN OF THE KIDNEY'S PROXIMAL TUBULES**

To analyze and compare the concentration of drugs in the lumen of the kidney's proximal tubules–the predicted site of inhibition–we simulated time profiles of the drugs resulting

from oral administration at various dosages. **Figure 6** demonstrates that concentration levels of tofogliflozin, ipragliflozin, and empagliflozin are higher than levels of other inhibitors following administration of marketed SGLT2 inhibitors at labeled doses and non-marketed SGLT2 inhibitors at maximal doses (approved for phase 2/3 studies).

In order to investigate which of five compounds is most likely to accumulate at the potential site of action, we also simulated concentration levels of SGLT2 inhibitors in the lumen of the kidney's proximal tubules following a standardized dosage of the compounds equal to 20 mg. In this scenario, the model predicted that concentrations of empagliflozin and tofogliflozin were higher

than the levels of dapagliflozin, canagliflozin, and ipragliflozin (Supplementary Figure 17).

We also simulated and compared time profiles of SGLT2 inhibitor concentrations in plasma and lumen of the kidney. For all SGLT2 inhibitors, our model predicted that the concentration in the lumen of the kidneys was higher than in plasma (**Figures 7**, **8**, Supplementary Figures 18–20).

## **LEVELS OF SGLT2 INHIBITION DURING TREATMENT WITH SGLT2 INHIBITORS**

We simulated the average level of inhibition of glucose reabsorption mediated by SGLT2 and compared our findings with experimentally measured levels of glucose reabsorption inhibition following treatment with compounds (**Figures 9**, **10**, Supplementary Figures 21–23). In model simulations, the average level of inhibition of glucose reabsorption mediated by SGLT2 was higher than the

**FIGURE 3 | Example of verification of the dapagliflozin model using urine data.** Cumulative amount of dapagliflozin recovered in urine following simulation of a single administration of 50 mg. Curve represents model simulation and dots represent experimental data. Colors of dots correspond to different data sources: black—Obermeier et al. (2010); blue— Kasichayanula et al. (2011a); red—Kasichayanula et al. (2013).

**FIGURE 4 | Example of validation of the dapagliflozin model using plasma data.** Total level of dapagliflozin in plasma following simulation of a single administration, but at different doses (Yang et al., 2013). Curve represents model simulations and dots represent experimental data. Colors of curves and dots correspond to the different doses: black—5 mg, blue—10 mg. Model simulations are presented with 95% confidence bands.

level of total glucose reabsorption inhibition, and almost equal to 100%, following treatment with all experimental doses of SGLT2 inhibitors (**Figures 9**, **10**, Supplementary Figures 21–23).

To compare the efficacies of each compound, the level of SGLT2 inhibition was simulated after administration of equal doses (20 mg) (Supplementary Figure 24), labeled doses of marketed inhibitors, and maximal doses of other inhibitors approved for phase 2/3 studies (**Figure 11**). For all compounds, administration of equal or labeled/maximal approved doses resulted in almost 100% inhibition of SGLT2. Therefore, the difference in efficacy of the tested SGLT2 inhibitors was not significant.

## **EFFECT OF SGLT2 INHIBITORS ON OTHER TRANSPORTERS FROM THE SGLT FAMILY**

To predict the effect of dapagliflozin, canagliflozin, ipragliflozin, empagliflozin, and tofogliflozin on other members of the SGLT family, the inhibition level of these transporters in the lumen of the kidney's proximal tubules was simulated following administration of labeled doses of marketed inhibitors and maximal doses of other inhibitors approved for phase 2/3 studies. We found that the influence of the inhibitors on other transporters was substantial–approximately 50% or above for particular compounds (Supplementary Figure 25–29). The most effective inhibitor of SGLT1 was canagliflozin (Supplementary Figure 25), while ipragliflozin and tofogliflozin produced the strongest inhibition of SGLT3 (Supplementary Figure 26). While all other SGLT2 inhibitors have a similar effect on SGLT4, dapagliflozin is a weak inhibitor of this co-transporter (Supplementary Figure 27). Ipragliflozin and empagliflozin are the strongest SGLT5 inhibitors (Supplementary Figure 28), while canagliflozin has the strongest effect on SGLT6 (Supplementary Figure 29).

**FIGURE 6 | Concentration of SGLT2 inhibitors in the lumen of the kidney's proximal tubules.** Level of SGLT2 inhibitors in the lumen of the kidney's proximal tubules following simulation of multiple administrations of labeled doses of marketed SGLT2 inhibitors and maximal doses of other SGLT2 inhibitors approved for phase 2/3 studies. Colors of curves correspond to different compounds: black—10 mg QD dapagliflozin; blue—300 mg QD canagliflozin; red—25 mg QD empagliflozin; green—300 mg QD ipragliflozin; pink—40 mg QD tofogliflozin. Model simulations are presented with 95% confidence bands.

## **DISCUSSION**

SGLT2 is a promising target for the treatment of T2DM because its inhibition could lower glucose levels without directly influencing insulin resistance or b-cell function. However, in a

compartments following simulation of a single administration of 40 mg. Colors of curves correspond to various compartments. Black—total plasma concentration; blue—unbound plasma concentration; red—concentration in lumen. Model simulations are presented with 95% confidence bands.

previous study, administration of SGLT2 inhibitors resulted in only 30–50% inhibition of glucose reabsorption in human subjects even at high doses, which was in contrast to the expected inhibition of 90% based on *in vitro* potency and plasma levels (Liu et al., 2012). In our study, we applied a systems pharmacology modeling approach to test several hypotheses that attempt to explain the discrepancy between the expected and observed levels of glucose reabsorption following administration of SGLT2 inhibitors. We developed models, simulated concentrations of SGLT2 inhibitors in the lumen of the kidney's proximal tubules, and compared the efficacy of these compounds in terms of levels of *in vivo* SGLT2 inhibition.

Models for SGLT2 inhibitors were verified and validated against all available clinical data describing the PK of the compounds in plasma and urine. Similar to the model of Maurer et al. (2011), we introduced a peripheral compartment into our model of dapagliflozin. We also included this compartment for ipragliflozin and tofogliflozin models. Despite the inclusion of a peripheral compartment in a previously published model of empagliflozin (Riggs et al., 2013), we chose a model without peripheral compartment for empagliflozin based on Akaike Information Criterion (AIC) (Akaike, 1974). The AIC we calculated for the empagliflozin model without a peripheral compartment was lower than that of the model with peripheral compartment (343 vs. 345, respectively). Our canagliflozin model was also developed on the basis of one compartmental PK model.

Applying a verification strategy described in the Supplementary Materials, we were able to estimate the models' parameter values for active secretion of the drugs from plasma to urine and reabsorption from urine to plasma. Indeed, we found that the active secretion from plasma to the lumen of the

of different doses of dapagliflozin (Komoroski et al., 2009a). Model simulations are presented with 95% confidence bands.

**reabsorption inhibition levels during treatment with dapagliflozin.** Comparison of the average inhibition of glucose reabsorption mediated by

kidneys was equal to zero for dapagliflozin, canagliflozin, and ipragliflozin, but non-zero reabsorption should be taken into account to describe available clinical data. The reabsorption of empagliflozin was equal to zero, but non-zero secretion contributes substantially to the balance of the drug between plasma and urine. Both active secretion and reabsorption of tofogliflozin were equal to zero. Plasma and urine PK data are not sufficient to evaluate the unique values of the rate constants that are responsible for reabsorption and secretion simultaneously. These two parameters are correlated with each other. For tofogliflozin, there is lack of clinical data available to evaluate at least one of these parameters. To understand whether the uncertainty in these parameter values affects the description of clearance in the model, the total systemic and renal clearances measured in clinical trials were compared with those calculated in the model. The total systemic clearance of dapagliflozin was 265 mL/min in the model and 207 mL/min in clinical trials (Boulton et al., 2013). The renal clearance of dapagliflozin was 3.95 mL/min in the model and 3–5 mL/min in clinical trials (Komoroski et al., 2009a,b; Kasichayanula et al., 2011a). The renal clearances of empagliflozin and ipragliflozin in the model were 35 and 1.88 mL/min respectively, while they were 30–37 mL/min for empagliflozin (Heise et al., 2013a,b) and 1–3 mL/min for ipragliflozin (Veltkamp et al., 2011; Zhang et al., 2013) in clinical data. The total systemic clearance of tofogliflozin was equal to 9.9 L/h in the model and 10 L/h in clinical trials (Schwab et al., 2013). The renal clearance of tofogliflozin was equal to 20 mL/min in the model and 25.7 mL/min in clinical trials (Schwab et al., 2013). Therefore, the values produced by our models are similar to experimentally measured values.

Comparison of the average inhibition of glucose reabsorption mediated by

presented with 95% confidence bands.

**FIGURE 11 | Levels of SGLT2 inhibition after drug administration.** Levels of SGLT2 inhibition following simulation of multiple administrations of labeled doses of marketed SGLT2 inhibitors and maximal doses of other SGLT2 inhibitors approved for phase 2/3 studies. Colors of curves correspond to different compounds: black—10 mg QD dapagliflozin; blue—300 mg QD canagliflozin; red—25 mg QD empagliflozin; green—300 mg QD ipragliflozin; pink—40 mg QD tofogliflozin. Model simulations are presented with 95% confidence bands.

One hypothesis proposed by Liu et al. (2012) states that the low efficacy of SGLT2 inhibitors could be explained by the low concentration of compounds at the potential site of action–the lumen of kidney's proximal tubules. Our model suggests that concentrations of SGLT2 inhibitors in the lumen are higher than the corresponding unbound and total concentrations in plasma. This can be explained in terms of reabsorption of water in kidney's proximal tubules (Panchapakesan et al., 2009). A decrease in water volume in the lumen leads to an increase in the concentration of the compounds in lumen than in the plasma. In the model, this is reflected by the ratio of glomerular filtration and urine excretion (urine formation) rates. Thus, we conclude that the concentration of compounds in the lumen of the kidney's proximal tubules is actually relatively high, and we reject the hypothesis that the low efficacy of SGLT2 inhibitors is caused by their low concentration at the site of action. Our model predicts that concentrations of empagliflozin and tofogliflozin in kidney lumen are higher than concentrations of dapagliflozin, canagliflozin, and ipragliflozin following administration of equal doses. This prediction is supported by data obtained from clinical trials, which indicates that approximately 20% of the empagliflozin and tofogliflozin dose is recovered in urine (Brand et al., 2012; Zell et al., 2013) in comparison to about 1% for the other SGLT2 inhibitors (Kasichayanula et al., 2011a; Devineni et al., 2013; Zhang et al., 2013).

The model shows that administration of labeled doses of marketed inhibitors (dapagliflozin and canagliflozin) and of maximal doses approved for phase 2/3 studies of tofogliflozin, ipragliflozin, and empagliflozin leads to almost complete inhibition of SGLT2 *in vivo*. The average inhibition level of glucose reabsorption mediated by SGLT2 (the average SGLT2 inhibition level) predicted by the model is higher than glucose reabsorption inhibition level measured in clinical trials, and almost equal to 100%. Thus, if the lumen of the kidney's proximal tubules is indeed the site of action of SGLT2 inhibitors, and SGLT2 is the main transporter that facilitates reabsorption of glucose, then there is a contradiction between the simulations produced by the model and the clinical data. This contradiction leads us to support two hypotheses proposed by Liu et al. (2012). Firstly, that the potential site of action of SGLT2 inhibitors is not in the lumen of the kidney's proximal tubules, but in the proximal tubule cells. Secondly, that there are other transporters that could facilitate glucose reabsorption under the conditions of SGLT2 inhibition. Both hypotheses appear reasonable within the framework of our current model. To determine which of these two hypotheses is true, further modeling supported by additional experimental data is required.

The model was applied to compare the efficacy of different SGLT2 inhibitors in respect of inhibiting other transporters in the SGLT family that are expressed in kidneys. Simulating the administration of equal doses of compounds (20 mg), labeled doses of marketed inhibitors, and maximal doses of other inhibitors approved for phase 2/3 studies showed that levels of SGLT2 inhibition are similar for all compounds and almost equal to 100%. This is caused by high concentrations of SGLT2 inhibitors in the lumen of the kidneys and low *in vitro* IC50 values. The effect of SGLT2 inhibitors on other transporters is also rather strong because of its high concentration in kidney's lumen. Canagliflozin is the strongest SGLT1 and SGLT6 inhibitor, and this is caused by canagliflozin's low IC50 (the lowest of all the SGLT2 inhibitors considered here). The most effective SGLT3 inhibitors are ipragliflozin and tofogliflozin because of their high *in vitro* potencies. All compounds have similar effects on SGLT4, except dapagliflozin. Dapagliflozin has the weakest influence on SGLT4 because of its low concentration in the kidney's lumen. Ipragliflozin and empagliflozin are the strongest SGLT5 inhibitors because of their low IC50 of for SGLT5, and the high concentration of ipragliflozin in the lumen.

In conclusions, we have developed a systems pharmacology model for SGLT2 inhibitors that enables the estimation of its concentration in the lumen of the kidney's proximal tubules (the potential site of SGLT2 action) and the prediction of SGLT2 inhibition levels during treatment in humans. We have shown that the concentration of SGLT2 inhibitors in the lumen of the proximal tubules is high, and that the level of SGLT2 inhibition during treatment in humans is almost 100%. Based on the results of our model, two explanations for the observed low efficacy of SGLT2 inhibitors were supported: (1) the site of action of SGLT2 inhibitors is not in the lumen of the kidney's proximal tubules, but elsewhere (e.g., the kidneys proximal tubule cells); and (2) there are other transporters that could facilitate glucose reabsorption under the conditions of SGLT2 inhibition (e.g., other transporters of SGLT family). It was found that all SGLT2 inhibitors have similar efficacy.

## **SUPPLEMENTARY MATERIAL**

The Supplementary Material for this article can be found online at: http://www.frontiersin.org/journal/10.3389/fphar. 2014.00218/abstract

## **REFERENCES**

**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

*Received: 30 April 2014; accepted: 09 September 2014; published online: 13 October 2014.*

*Citation: Demin O Jr., Yakovleva T, Kolobkov D and Demin O (2014) Analysis of the efficacy of SGLT2 inhibitors using semi-mechanistic model. Front. Pharmacol. 5:218. doi: 10.3389/fphar.2014.00218*

*This article was submitted to Experimental Pharmacology and Drug Discovery, a section of the journal Frontiers in Pharmacology.*

*Copyright © 2014 Demin, Yakovleva, Kolobkov and Demin. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.*

## Use of systems pharmacology modeling to elucidate the operating characteristics of SGLT1 and SGLT2 in renal glucose reabsorption in humans

#### *Yasong Lu1 \*, Steven C. Griffen2†, David W. Boulton3 and Tarek A. Leil <sup>1</sup>*

*<sup>1</sup> Quantitative Clinical Pharmacology, Clinical Pharmacology and Pharmacometrics, Exploratory Clinical and Translational Research, Bristol-Myers Squibb, Princeton, NJ, USA*

*<sup>2</sup> Diabetes Development Center, Global Clinical Research, Bristol-Myers Squibb, Princeton, NJ, USA*

*<sup>3</sup> Clinical Pharmacology and Pharmacometrics, Exploratory Clinical and Translational Research, Bristol-Myers Squibb, Princeton, NJ, USA*

#### *Edited by:*

*Maria Angela Sortino, University of Catania, Italy*

#### *Reviewed by:*

*Volker Vallon, University of California San Diegio and VA San Diego Healthcare System, USA Robinson Sabino-Silva, Federal University of Uberlandia, Brazil*

#### *\*Correspondence:*

*Yasong Lu, Clinical Pharmacology and Pharmacometrics, Exploratory Clinical and Translational Research, Bristol-Myers Squibb, MS# E14-08, Route 206 and Province Line Road, Princeton, NJ 08543, USA e-mail<EMAIL_ADDRESS>
### *†Present address:*

*Steven C. Griffen, JDRF, New York, USA*

In the kidney, glucose in glomerular filtrate is reabsorbed primarily by sodium-glucose cotransporters 1 (SGLT1) and 2 (SGLT2) along the proximal tubules. SGLT2 has been characterized as a high capacity, low affinity pathway responsible for reabsorption of the majority of filtered glucose in the early part of proximal tubules, and SGLT1 reabsorbs the residual glucose in the distal part. Inhibition of SGLT2 is a viable mechanism for removing glucose from the body and improving glycemic control in patients with diabetes. Despite demonstrating high levels (in excess of 80%) of inhibition of glucose transport by SGLT2 *in vitro*, potent SGLT2 inhibitors, e.g., dapagliflozin and canagliflozin, inhibit renal glucose reabsorption by only 30–50% in clinical studies. Hypotheses for this apparent paradox are mostly focused on the compensatory effect of SGLT1. The paradox has been explained and the role of SGLT1 demonstrated in the mouse, but direct data in humans are lacking. To further explore the roles of SGLT1/2 in renal glucose reabsorption in humans, we developed a systems pharmacology model with emphasis on SGLT1/2 mediated glucose reabsorption and the effects of SGLT2 inhibition. The model was calibrated using robust clinical data in the absence or presence of dapagliflozin (DeFronzo et al., 2013), and evaluated against clinical data from the literature (Mogensen, 1971; Wolf et al., 2009; Polidori et al., 2013). The model adequately described all four data sets. Simulations using the model clarified the operating characteristics of SGLT1/2 in humans in the healthy and diabetic state with or without SGLT2 inhibition. The modeling and simulations support our proposition that the apparent moderate, 30–50% inhibition of renal glucose reabsorption observed with potent SGLT2 inhibitors is a combined result of two physiological determinants: SGLT1 compensation and residual SGLT2 activity. This model will enable *in silico* inferences and predictions related to SGLT1/2 modulation.

**Keywords: systems pharmacology model, SGLT, dapagliflozin, renal glucose reabsorption, glucosuria, diabetes mellitus**

## **INTRODUCTION**

In the kidney, plasma glucose is continuously filtered by glomeruli and reabsorbed along the proximal tubules. Under normal physiological conditions, the reabsorption is almost complete. The reabsorption is mediated primarily by two sodium-glucose cotransporters (SGLTs), SGLT1 and SGLT2. In the kidney, SGLT2 is located in the early part (S1/S2 segments) of the proximal tubules, and is recognized as a low affinity, high capacity pathway for renal glucose reabsorption. SGLT1, on the other hand, is located in the distal part (S3 segment) of the proximal tubules, and is characterized as a high affinity, low capacity pathway (Wright, 2001; Mather and Pollock, 2011). SGLT2 is believed responsible for 80–90% of renal glucose reabsorption, and SGLT1 for the rest (10–20%) in healthy humans under normal physiological conditions (DeFronzo et al., 2012). SGLT2 has been identified as a viable target for improving glycemic control in diabetes. Two potent and selective SGLT2 inhibitors, dapagliflozin and canagliflozin, have been approved by many regulatory agencies for treating type 2 diabetes mellitus (T2DM).

Given the overwhelming contribution (*>*80%) of SGLT2 to renal glucose reabsorption, it has been expected that SGLT2 inhibitors, at sufficient exposures, would reduce renal glucose reabsorption by over 80%. This expectation, however, appeared to be contradicted by the clinical observations that only 30–50% of inhibition in glucose reabsorption was achieved with dapagliflozin and canagliflozin (Komoroski et al., 2009a; Devineni et al., 2013; Washburn and Poucher, 2013). To explain this apparent contradiction, several hypotheses, from peculiar pharmacokinetics of an inhibitor in the kidney (Liu et al., 2012) to SGLT1 compensation (Haddish-Berhane et al., 2010; Maurer et al., 2011; Abdul-Ghani et al., 2013), have been proposed. These hypotheses are yet to be tested.

Recently, Hummel et al. (2011) used a quantitative *in vitro* electrophysiological study to generate hypotheses about the relative contributions of human SGLTs to renal glucose reabsorption. Hummel et al. found that the two human transporters have similar apparent affinity for D-glucose (5 mM for hSGLT2 vs. 2 mM for hSGLT1), and inferred that the capacity of hSGLT1 for renal glucose reabsorption may be over 50% of hSGLT2 under normal conditions in humans. As such, the difference in the contribution to renal glucose reabsorption between the two cotransporters may be less profound than previously perceived.

Despite a large body of research in SGLTs and renal glucose reabsorption, the quantitative understanding of the characteristics of these cotransporters in humans remains limited (Vallon, 2011). Assessments in this regard have largely relied on fragments of data, insufficient to account for all key variables (e.g., SGLTs activities, plasma glucose levels, pharmacokinetic profiles of SGLTs inhibitors), and empirical, static mathematical models that do not account for the dynamic processes of renal glucose filtration, reabsorption, and transfer along tubular lumen over time. Consequently, a quantitative, holistic characterization has not yet been formulated.

Systems pharmacology modeling is a powerful tool for data and knowledge integration and hypothesis testing, and for providing quantitative understanding of a pharmacological target or pathway and insights into "what-if" scenarios that may not be feasibly obtained experimentally. For SGLTs-mediated renal glucose reabsorption, Yamaguchi et al. reported simplified systems pharmacology models in mice (Yamaguchi et al., 2012) and rats (Yamaguchi et al., 2011), and Haddish-Berhane et al. (2010) presented a conference poster on a minimal systems pharmacology model in humans with limited evaluation against clinical data on dapagliflozin (Komoroski et al., 2009a).

This report presents a systems pharmacology model that was developed based on renal physiology and a robust clinical data set, with emphasis on SGLTs-mediated glucose reabsorption in the proximal tubules. The model was evaluated against several external clinical data sets. It is anticipated that the model will be valuable in:

## **MATERIALS AND METHODS**

### **STUDIES AND DATA SETS**

The studies and data sets used for model calibration and evaluation are listed in **Table 1**. For more details, the reader is referred to the original reports.

The DeFronzo et al. (2013), Polidori et al. (2013) and Wolf et al. (2009) studies employed stepped hyperglycemic clamp (SHC) procedures, and the Mogensen study (1971) was conducted at fixed, elevated plasma glucose levels. The clinical approach of artificially maintaining a constant plasma glucose concentration allowed us to ignore the potential impacts of renal glucose reabsorption on plasma glucose concentration, hence simplifying the process of model development. Simulations using the systems pharmacology model with fixed glucose levels will provide "clean" illustrations of SGLTs operating characteristics. A more comprehensive model integrating renal glucose reabsorption and glucose-insulin homeostasis will be reported elsewhere (Lu et al., 2014).

The mean data from each study were used for model calibration or evaluation. The data in DeFronzo et al. (2013) were available from an internal database owned by Bristol-Myers Squibb/AstraZeneca. We excluded from analysis those data points where the actual plasma glucose level deviated 25% or more from the corresponding group means. These data points appeared at the steps with target glucose level ≥450 mg/dL, and represented only 17% of total data points at those steps. This exclusion should abolish potential undue influences of excessive variability in the data on parameter estimation.

## **MODEL STRUCTURE**

The model structure, shown in **Figure 1**, was developed based on the renal physiology and pharmacological understanding of SGLTs inhibition. The model describes the disposition of glucose as well as SGLTs inhibitors, if applicable, with emphasis on glomerular filtration and tubular reabsorption. The proximal convoluted tubules (PCT) were divided equally into six sequential sub-segments (PCT1-6), and the proximal straight tubules (PST) were divided equally into three sub-segments (PST1-3). The division allowed a more accurate description of the luminal glucose concentration as the filtrate progresses through tubular segments and the amount of UGE over time. The number of sub-segments was chosen to achieve an approximate agreement between predicted and observed UGE in a healthy subject under normal conditions. The distal tubules were not included due to their irrelevance to glucose reabsorption. The glomerular filtrate flowed from PCT1 through PST3 and drained into the urinary bladder. A urine compartment was added for collecting urine and urinary glucose.

Along the proximal tubules, filtered glucose was continuously reabsorbed. It was assumed that the absorption was mediated by SGLT2 in the PCT (PCT1-6) and by SGLT1 in the PST (PST1-3). The maximum reabsorption rate of SGLT2 (Vmax2) was uniformly distributed among the PCT1-6 sub-segments, and likewise for the Vmax of SGLT1 (Vmax1) among the PST1-3 subsegments. In each sub-segment, glucose was reabsorbed via a Michaelis-Menten process as Equation (1):

$$R\_{\dot{\jmath}} = \frac{V\_{\text{max},\dot{\jmath}} \times C\_{\text{glu},\dot{\jmath}}}{K\_m + C\_{\text{glu},\dot{\jmath}}} \tag{1}$$

where the subscript j is an index for a tubular sub-segment, and for a given sub-segment, *R* is the glucose reabsorption rate

(mass/time), *K*<sup>m</sup> denotes glucose affinity for SGLT1 or SGLT2, and *Cglu* represents luminal glucose concentration.

The mass of reabsorbed glucose was directed to another compartment (glucose reabsorbed) instead of the plasma glucose compartment. This approach is appropriate for scenarios where renal glucose recovery does not affect plasma glucose level, such as: (1) experimental procedures that fix plasma glucose levels (Mogensen, 1971; Wolf et al., 2009; DeFronzo et al., 2013; Polidori et al., 2013), and (2) subjects with normal glucose tolerance who can efficiently dispose the absorbed mass to maintain plasma glucose constant at the fasting state.

In the case where an SGLTs inhibitor, e.g., dapagliflozin or canagliflozin, was administered, the unbound portion of the inhibitor in plasma was freely filtered via glomeruli. The inhibitor then traveled through the tubular sub-segments and the urinary bladder, and was excreted to the urine compartment, similar to glucose but without tubular reabsorption. Within each subsegment, the inhibitor competed with glucose for SGLT1/2, and hence competitively inhibited glucose reabsorption. The reabsorption rate (*R*∗ *<sup>j</sup>* ), with competitive inhibition of an inhibitor, in a given sub-segment became:

$$R\_j^\* = \frac{V\_{\text{max},j} \times C\_{\text{glu},j}}{K\_m \times \left(1 + \frac{C\_{d \text{reg},j}}{K\_i}\right) + C\_{\text{glu},j}} \tag{2}$$

where *Cdrug* denotes luminal SGLTs inhibitor concentration, and *K*<sup>i</sup> is the affinity of the inhibitor to SGLTs. [See Supplementary Materials for further expansion of Equations (1) and (2)].

To obtain a similar time course of plasma concentration of canagliflozin with the dosing regimen (100 mg QD for 8 days) described in Polidori et al. (2013), a two-compartment pharmacokinetic (PK) model was developed based on the mean PK data reported (Devineni et al., 2013). For dapagliflozin, observed mean PK after 10 mg, QD, for 7 days was reported in DeFronzo et al. (2013). Interpolation of the observed dapagliflozin PK provided an input into the plasma inhibitor compartment (**Figure 1**) to allow description of dapagliflozin inhibition of tubular glucose reabsorption.

## **MODEL PARAMETERS AND CALIBRATION**

The physiological parameters, such as volumes, flow rates, glucose affinity for SGLTs (Km), and glucose reabsorption capacities (Vmax) are listed in **Table 2**, and SGLT2 inhibitor physicochemical parameters and binding affinity for SGLTs (Ki) are in **Table 3**. Most of the parameters were from the literature, measured in each of the respective studies, or based on reasonable assumptions, except for Vmax, Km, and Ki, whose values were calibrated. For parameter calibration, literature values were taken as the starting points (see **Tables 2, 3**), and then fine-tuned to allow the model predictions to be consistent with the mean UGE data in DeFronzo et al. (2013). Because a satisfactory agreement between the predictions and the observations of UGE could not be achieved over the entire plasma glucose range of 100–550 mg/dL, the calibration was focused on the data in the clinically relevant range, 100–400 mg/dL. In the end, only the set of calibrated values were considered physiologically plausible and accepted if it adequately described the DeFronzo et al. (2013) as well as the other three data sets (Mogensen, 1971; Wolf et al., 2009; Polidori et al., 2013).

The potential influences of diabetes and SGLT2 inhibition on the parameters to be calibrated were considered during parameterization. Renal SGLTs expression and activity may change in response to SGLT2 inhibition and/or diabetes. In the wildtype mouse, SGLT2 protein expression was enhanced with the treatment of empagliflozin, a selective SGLT2 inhibitor, without upregulation of mRNA (Vallon et al., 2014). In the diabetic state, the expressions of SGLT2 mRNA and protein have been found upregulated significantly relative to the respective controls in genetically modified mice (Vallon et al., 2014), diabetic rats, (Freitas et al., 2008; Tabatabai et al., 2009), and humans (Rahmoune et al., 2005). For renal SGLT1, however, the response is more diverse, with increased, unchanged, or reduced expression and/or activity observed in animals (Vallon and Thomson, 2012; Vallon et al., 2014). It is challenging to incorporate these potential changes in SGLT activity in the model for two reasons: (i) limited quantitative understanding in humans regarding these changes, and (ii) adequate calibration of parameters for these changes is not supported by available data. For simplification, therefore, the Vmax1, Km, and Ki values were assumed consistent between the healthy and diabetics, and Vmax2 was allowed to adjust between the healthy and disease state. The Vmax2 in healthy subjects was estimated as a proportion of that in diabetics, and the value of the proportion was calibrated using the DeFronzo et al. (2013). The potential impact of SGLT2 inhibition on Vmax, Km, and Ki values was ignored.

Although Vmax in humans has generally been reported as the sum of Vmax1 and Vmax2, with difficulty in separating the two components, it is worth pointing out that in our study, quantitative separation of Vmax1 and Vmax2 was feasible without an assumption of the value of Vmax1/Vmax2 ratio, because the calibration data set (DeFronzo et al., 2013) encompassed scenarios with and without perturbation of SGLT2 activity. Such a separation was achieved previously in rats with the aid of mathematical modeling (Yamaguchi et al., 2011).

## **MODEL EVALUATION**

Once it was calibrated using the DeFronzo et al. (2013), the model was evaluated for its predictivity against three data sets from different sources (Mogensen, 1971; Wolf et al., 2009; Polidori et al., 2013). The parameters were held constant for the evaluation unless they were study specific, in which case they were adjusted per the study conditions as listed in **Tables 1, 2**. The Ki values of canagliflozin, necessary for simulating the Polidori et al., conditions (Polidori et al., 2013), are listed in **Table 3**.

#### **SIMULATIONS AND EXPLORATIONS**

## *Renal glucose reabsorption and UGE vs. loss-of-function mutation of SGLTs*

Numerous mutations in SGLT1 (Martin et al., 1996; Lam et al., 1999) and SGLT2 have been identified in humans (Santer et al., 2003; Kleta et al., 2004; Calado et al., 2008; Yu et al., 2011). The mutations in SGLT1 disrupt the trafficking of SGLT1 from the endoplasmic reticulum to the plasma membrane (Lam et al., 1999), and the mutations in SGLT2 reduce SGLT2 expression in the apical side of PCT (Yu et al., 2011). These mutations are likely to reduce the Vmax of these cotransporters. It is yet to be clarified to what extent the function of SGLTs in the kidney is affected by a given mutation. Simulations using our systems pharmacology model can provide theoretical, quantitative relationships between a reduction in Vmax and glucose reabsorption or UGE in an otherwise healthy person. To enable these simulations, the mean daily plasma glucose profile in the healthy subjects from Freckmann et al. (2007) was used as an input to the plasma glucose compartment of our model. The quantitative SGLTs function-UGE relationships will be instrumental to mapping renal SGLTs genotypes to their apparent functions.

## **Table 2 | Physiological parameters.**

## *Sensitivity of renal glucose reabsorption and UGE to SGLT1 kinetics (Vmax 1 and K<sup>i</sup> 1)*

The analysis of sensitivity of renal glucose reabsorption and UGE to SGLT1 kinetics will help clarify these questions: (1) How strong is the influence of an alteration of SGLT1 kinetics on renal glucose reabsorption and UGE in the healthy state? (2) How strong is the influence in the diabetic state? (3) From drug discovery perspective, without consideration of its effect on intestinal SGLT1, will an SGLT1/2 dual inhibitor induce stronger glucosuria than a highly selective SGLT2 inhibitor, e.g., dapagliflozin? The analysis was conducted with simulations in a naive healthy subject and a T2DM subject with or without SGLT2 inhibition under the SHC procedure used by DeFronzo et al. (2013) with a target plasma glucose range of 100–350 mg/dL. With all other parameters held constant, we first evaluated how a decrease in Vmax1 would affect renal glucose reabsorption and UGE; and likewise, we then evaluated how changes in Km1, or Ki1 with the presence of SGLTs inhibition, would affect renal glucose reabsorption and UGE.

## **SOFTWARE**

Processing of the raw data from the DeFronzo et al. study (2013) was conducted using S-PLUS 8.1 version 3.4 (TIBCO, Palo Alto,

**Table 3 | SGLT2 inhibitor-specific parameters.**

*\*Reference: Bristol-Myers Squibb/AstraZeneca report (2010): Summary of clinical pharmacology studies: Dapagliflozin (BMS-512148). BMS Document Control Number 930047848.*

CA) on a UNIX platform. Model development and simulations were performed using Berkeley Madonna version 8.3.18 (Berkeley Madonna Inc., Berkeley, CA).

## **RESULTS**

## **MODEL CALIBRATION USING DeFronzo et al. (2013)**

The UGE data from DeFronzo et al. (2013) allowed estimation of Vmax, glucose Km, and dapagliflozin Ki values for SGLTs in the healthy subjects and T2DM patients. In the model, the healthy and T2DM subjects were differentiated by their Vmax2 for describing the DeFronzo et al. conditions. The parameter estimates are presented in **Tables 2, 3**. The model performance is demonstrated in **Figure 2**. The model adequately described the cumulative (**Figures 2A,B**) and step-wise UGE data (**Figures 2C,D**) at baseline and in the first 4 h (where the target plasma glucose escalated from 100 to 350 mg/dL) after dapagliflozin treatment. From 4.67 h onward (where the target plasma glucose increased from 400 to 550 mg/dL), the model prediction of UGE in the dapagliflozin treated groups was slightly lower than the observed. The glucose concentrations in the tubular sub-segments PCT1-6 and PST1-3 in T2DM patients at baseline and treated with dapagliflozin are illustrated in Figure S1. At baseline, the tubular glucose concentration tapers along the proximal tubules with plasma glucose level up to 23 mM. With further increase in plasma glucose, the tubular glucose level becomes more uniform as the reabsorption approaches saturation. After dapagliflozin treatment, however, glucose is increasingly concentrated along the proximal tubules.

### **MODEL EVALUATION**

The calibrated model was evaluated for its predictive performance relative to three separate clinical data sets (Mogensen, 1971; Wolf et al., 2009; Polidori et al., 2013). The predictions are overlaid with corresponding observations in **Figure 3**. The predictions agreed well with the observed data, indicating that the model is plausible, has reasonable accuracy, and can be used for inference and prediction.

## **SGLTs OPERATING CHARACTERISTICS FOR THE DeFronzo et al. (2013) CONDITIONS**

### *SGLTs relative contributions to renal glucose reabsorption*

The model derived step-wise amount of glucose reabsorbed by renal SGLT1 and SGLT2 in the healthy subjects at baseline and after dapagliflozin treatment is shown in **Figures 4A,B**, and the relative contributions of the two pathways at each step are in **Figures 4C,D**. At near normal glycemic levels (∼100 mg/dL) at baseline (without SGLT2 inhibition), SGLT2 contributed to 90% of total reabsorption and SGLT1 10%. The 90%/10% split became 80%/20% with plasma glucose escalated to over 200 mg/dL. With the presence of dapagliflozin, the contribution of SGLT2 declined and SGLT1 became the more predominant reabsorption pathway; the relative contributions varied with plasma dapagliflozin concentration over time. Similar results were obtained in the T2DM patients, for whom the relative contributions of SGLT1 and SGLT2 before and after dapagliflozin treatment are illustrated in **Figures 4E,F**.

## *SGLTs operation efficiency*

The calculated operation efficiency (defined as reabsorption rate/Vmax × 100% for either SGLT1 or SGLT2) for both SGLTs in the healthy subjects is plotted in **Figure 5A**. At the plasma glucose level of ∼100 mg/dL, SGLT2 and SGLT1 were operating at ∼40 and 20% of their respective Vmax. The operation efficiency increased with plasma glucose (and thereby filtered glucose load) for both SGLTs, with the slope for SGLT1 being much steeper than for SGLT2. The operation efficiency at plasma glucose ≥400 mg/dL reached 97% for SGLT1 and 81% for SGLT2. Even with plasma glucose as high as 550 mg/dL, SGLT2 operated at just 89% of its capacity. Dapagliflozin treatment lowered SGLT2 operation efficacy to as low as 10%, and drove SGLT1 operation to over 90% of its capacity. Similar results were found in the T2DM patients (**Figure 5B**).

## **SIMULATIONS AND EXPLORATIONS**

## *Renal glucose reabsorption and UGE vs. loss-of-function mutation of SGLTs*

Simulations were conducted to establish quantitative relationships between loss of function (i.e., reduction in Vmax) of SGLT2 or SGLT1 and renal glucose reabsorption as well as UGE in an otherwise healthy subject with normoglycemia (plasma glucose ranging from 80 to 125 mg/dL with a time-weighted average of 90 mg/dL). The simulation results for SGLT2 are in **Figure 6A** and SGLT1 in **Figure 6B**. A 50% loss of function for SGLT2 caused UGE of 4.5 g per day, and 100% of loss of function resulted in 79 g UGE per day. The total glucose reabsorption was lowered by 17, 32, and 49% for a 75, 87.5, and 100% loss of SGLT2 function, respectively. Loss of SGLT1 function caused much less severe glucosuria, 1.2 g at 50% and 16 g at 100% of loss of function. The total glucose reabsorption was reduced by only 10% with complete loss of SGLT1 activity.

### *Sensitivity of renal glucose reabsorption and UGE to SGLT1 kinetics*

In a naive healthy subject with a plasma glucose level of ∼100 mg/dL, the elimination of SGLT1 activity, either through driving Vmax1 to zero or Km1 to infinity, inhibited renal glucose

reabsorption by only 10%. This was consistent with the result above for SGLT1 loss-of-function mutation (**Figure 6B**). In the diabetic state with a mean plasma glucose level up to 250 mg/dL, simulations suggested a slightly stronger influence (up to 20% lowering) on renal glucose reabsorption.

For simulations in the diabetic state with the presence of SGLT2 inhibition, the inhibitor was assumed identical to dapagliflozin, except that its Ki1 was allowed to change. The sensitivity of UGE to Vmax1 at 10, 14, 17, and 20 mmol/h (corresponding to a 50, 30, 15, and 0% reduction in SGLT1 capacity) is illustrated in **Figure 7A**. A mild to moderate, depending on the glucose level, increase in UGE was expected with reduction in Vmax1. At the plasma glucose level of 150–250 mg/dL, roughly equivalent to the range of average levels in real-life T2DM patients, a 30% reduction in Vmax1, presumed to be clinically well tolerated (Abdul-Ghani et al., 2013), augmented glucosuria by up to 30%. The sensitivity of UGE to Ki1 is depicted in **Figure 7B**. The tested Ki1 values ranged from 6 to 10,000 nM. The 6 nM represented a 20× selectivity (similar to the SGLT1/2 dual inhibitor LX4211 Zambrowicz et al., 2013) for SGLT2 (0.3 nM) vs. SGLT1 (6 nM) for an SGLTs inhibitor which is otherwise identical to dapagliflozin. UGE was found to be insensitive to Ki1.

## **DISCUSSION**

Highly selective and potent SGLT2 inhibitors, such as dapagliflozin and canagliflozin, have demonstrated significant and clinically meaningful effects on glycemic control in T2DM patients. It has been puzzling that SGLT2 inhibitors inhibit renal glucose reabsorption by only 30–50% clinically, despite the overwhelming contribution of SGLT2 to renal glucose reabsorption (80–90%) under normal conditions. Several hypotheses have been proposed for this apparently discrepant observation (Haddish-Berhane et al., 2010; Maurer et al., 2011; Pfister et al., 2011; Liu et al., 2012; Abdul-Ghani et al., 2013), and most of them are focused on the compensatory effect of SGLT1. The hypothesis of SGLT1 compensation has recently been confirmed in mice (Rieg et al., 2014). However, due to the differences in the experimental conditions in mice (Rieg et al., 2014) and in clinical trials (Komoroski et al., 2009a; Devineni et al., 2013; Heise et al., 2013; Washburn and Poucher, 2013) (see Table S1), extrapolation of the Rieg et al. (2014) finding to the clinic is not straightforward. As a whole, this situation indicates that, despite tremendous advances in the basic biology of SGLTs and pharmaceutical development targeting SGLT2, the roles of these transporters in renal glucose reabsorption, especially in humans, have yet to be clarified in a quantitative, mechanistic manner. To this end, we developed a systems pharmacology model for SGLT-mediated renal glucose reabsorption in humans with or without pharmacological modulation of SGLT2 activity. In general, this model adequately described four separate data sets from different study settings (Mogensen, 1971; Wolf et al., 2009; DeFronzo et al., 2013; Polidori et al., 2013) and replicated severe

glucosuria (79 g/day) in normoglycemic human subjects with homozygous SLGT2 mutations (Santer et al., 2003).

The prediction of UGE at the plasma glucose level of 400 mg/dL and higher in the subjects treated with dapagliflozin was lower than the observed data from DeFronzo et al., (**Figure 2**). This possibly results from compensatory effects in the renal tubules when glucose concentrations are drastically elevated. Bank and Aynedjian (1990) proposed that high glucose concentration in the proximal tubules would stimulate water reabsorption in the proximal portion and enhance compensatory water excretion in the more distal portion. In the DeFronzo et al. study (2013), an increase in urine volume was observed with escalation of plasma glucose level. This hydrodynamic change in response to glucose level may interfere with tubular glucose reabsorption. These processes, however, were not included in the model. Nevertheless, the unsatisfactory performance at high glucose levels (over 400 mg/dL) is unlikely to hamper the utility of the model because those glucose levels are irrelevant to most of normal or even diabetic conditions. Overall, the performance of the model suggests that the model is useful for mechanistically evaluating the roles of SGLT1 and SGLT2 in renal glucose reabsorption, and for predicting clinical pharmacodynamics of SGLT2 inhibitors.

## **CHARACTERIZATION OF SGLTs OPERATION WITHOUT THE PRESENCE OF SGLT2 INHIBITION**

The Vmax values of SGLT1 and SGLT2 were estimated to be 20 mmol/h and 94 (healthy)/110 (diabetic) mmol/h, respectively, and the glucose Km values for SGLT1 and SGLT2 were estimated to be 0.5 and 4 mM, respectively. The sum of the Vmax values (i.e., total reabsorption capacity) and the two Km estimates are similar to previously reported estimates (Mogensen, 1971; Diez-Sampedro et al., 2001; Chao and Henry, 2010; Hummel et al., 2011; DeFronzo et al., 2013). The Vmax2/Vmax1 ratio in the healthy subject (4.7) is consistent with that in the rat (5.4) (Yamaguchi et al., 2011).

Under near normoglycemic conditions (average plasma glucose ∼80–120 mg/dL) in both healthy and diabetic subjects, SGLT2 and SGLT1 are operating at about 40 and 20% of their respective capacities, and contributing to 90 and 10% of total glucose reabsorption, respectively. With the increase in plasma glucose concentration, SGLT2 operation efficiency steadily increases to near 90% of its capacity, whereas SGLT1 operation efficiency jumps sharply to over 80% of its capacity

and then steadily approaches to the maximum. The relative contributions of 90%/10% gradually becomes 80%/20% for SGLT2 and SGLT1 as plasma glucose rises. These results solidify the current characterization of the relative contributions of the two transporters to renal glucose reabsorptoin without the presence of SGLT2 inhibition (Chao and Henry, 2010; DeFronzo et al., 2012).

## **CHARACTERIZATION OF SGLT's OPERATION IN THE PRESENCE OF SGLT2 INHIBITION**