Integrating Epidemiological Data into a Mechanistic Model of Type 2 Diabetes: Validating the Prevalence of Virtual Patients

Assessing the performance of QSP models: biology as the driver for validation

Validation of a quantitative model is a critical step in establishing confidence in the model's suitability for whatever analysis it was designed. While processes for validation are well-established in the statistical sciences, the field of quantitative systems pharmacology (QSP) has taken a more piecemeal approach to defining and demonstrating validation. Although classical statistical methods can be used in a QSP context, proper validation of a mechanistic systems model requires a more nuanced approach to what precisely is being validated, and what role said validation plays in the larger context of the analysis. In this review, we summarize current thoughts of QSP validation in the scientific community, contrast the aims of statistical validation from several contexts (including inference, pharmacometrics analysis, and machine learning) with the challenges faced in QSP analysis, and use examples from published QSP models to define different stages or levels of validation, any of which may be sufficient depending on the context at hand.

An industry perspective on current QSP trends in drug development

2023 marks the 10th anniversary of Natpara's submission to the US FDA, which led to the first recorded regulatory interaction where a decision was supported by Quantitative and Systems Pharmacology (QSP) simulations. It had taken about 5 years for the timid QSP discipline to emerge as an effective Model-Informed Drug Development (MIDD) tool with visible impact in the pharmaceutical industry. Since then, the presence of QSP in the regulatory environment has continued to increase, to the point that the Agency reported 60 QSP submissions in 2020 alone, representing ~ 4% of their annual IND submissions [1]. What sort of industry mindset has enabled QSP to reach this level of success? How does QSP fit within the MIDD paradigm? Does QSP mean the same to Discovery and to Clinical Development projects? How do 'platforms' compare to 'fit-for-purpose' QSP models in an industrial setting? Can QSP and empirical Pharmacokinetic-Pharmacodynamic (PKPD) modelling be complementary? What level of validation is required to inform drug development decisions? This article reflects on all these questions, in particular addressing those audiences with limited line-of-sight into the drug industry decision-making machinery.

Assessing the Role of Patient Generation Techniques in Virtual Clinical Trial Outcomes

Virtual clinical trials (VCTs) are growing in popularity as a tool for quantitatively predicting heterogeneous treatment responses across a population. In the context of a VCT, a plausible patient is an instance of a mathematical model with parameter (or attribute) values chosen to reflect features of the disease and response to treatment for that particular patient. A number of techniques have been introduced to determine the set of model parametrizations to include in a virtual patient cohort. These methodologies generally start with a prior distribution for each model parameter and utilize some criteria to determine whether a parameter set sampled from the priors should be included or excluded from the plausible population. No standard technique exists, however, for generating these prior distributions and choosing the inclusion/exclusion criteria. In this work, we rigorously quantify the impact that VCT design choices have on VCT predictions. Rather than use real data and a complex mathematical model, a spatial model of radiotherapy is used to generate simulated patient data and the mathematical model used to describe the patient data is a two-parameter ordinary differential equations model. This controlled setup allows us to isolate the impact of both the prior distribution and the inclusion/exclusion criteria on both the heterogeneity of plausible populations and on predicted treatment response. We find that the prior distribution, rather than the inclusion/exclusion criteria, has a larger impact on the heterogeneity of the plausible population. Yet, the percent of treatment responders in the plausible population was more sensitive to the inclusion/exclusion criteria utilized. This foundational understanding of the role of virtual clinical trial design should help inform the development of future VCTs that use more complex models and real data.

Quantitative systems pharmacology model of erythropoiesis to simulate therapies targeting anemia due to chronic kidney disease

Anemia induced by chronic kidney disease (CKD) has multiple underlying mechanistic causes and generally worsens as CKD progresses. Erythropoietin (EPO) is a key endogenous protein which increases the number of erythrocyte progenitors that mature into red blood cells that carry hemoglobin (Hb). Recombinant human erythropoietin (rHuEPO) in its native and re-engineered forms is used as a therapeutic to alleviate CKD-induced anemia by stimulating erythropoiesis. However, due to safety risks associated with erythropoiesis-stimulating agents (ESAs), a new class of drugs, prolyl hydroxylase inhibitors (PHIs), has been developed. Instead of administering exogenous EPO, PHIs facilitate the accumulation of HIF-α, which results in the increased production of endogenous EPO. Clinical trials for ESAs and PHIs generally involve balancing decisions related to safety and efficacy by carefully evaluating the criteria for patient selection and adaptive trial design. To enable such decisions, we developed a quantitative systems pharmacology (QSP) model of erythropoiesis which captures key aspects of physiology and its disruption in CKD. Furthermore, CKD virtual populations of varying severities were developed, calibrated, and validated against public data. Such a model can be used to simulate alternative trial protocols while designing phase 3 clinical trials, as well as an asset for reverse translation in understanding emerging clinical data.

In silico cancer immunotherapy trials uncover the consequences of therapy-specific response patterns for clinical trial design and outcome

Late-stage cancer immunotherapy trials often lead to unusual survival curve shapes, like delayed curve separation or a plateauing curve in the treatment arm. It is critical for trial success to anticipate such effects in advance and adjust the design accordingly. Here, we use in silico cancer immunotherapy trials - simulated trials based on three different mathematical models - to assemble virtual patient cohorts undergoing late-stage immunotherapy, chemotherapy, or combination therapies. We find that all three simulation models predict the distinctive survival curve shapes commonly associated with immunotherapies. Considering four aspects of clinical trial design - sample size, endpoint, randomization rate, and interim analyses - we demonstrate how, by simulating various possible scenarios, the robustness of trial design choices can be scrutinized, and possible pitfalls can be identified in advance. We provide readily usable, web-based implementations of our three trial simulation models to facilitate their use by biomedical researchers, doctors, and trialists.

Modeling Clinical Phenotype Variability: Consideration of Genomic Variations, Computational Methods, and Quantitative Proteomics

Advances in biomedical and computer technologies have presented the modeling community the opportunity for mechanistically modeling and simulating the variability in a disease phenotype or in a drug response. The capability to quantify response variability can inform a drug development program. Quantitative systems pharmacology scientists have published various computational approaches for creating virtual patient populations (VPops) to model and simulate drug response variability. Genomic variations can impact disease characteristics and drug exposure and response. Quantitative proteomics technologies are increasingly used to facilitate drug discovery and development and inform patient care. Incorporating variations in genomics and quantitative proteomics may potentially inform creation of VPops to model and simulate virtual patient trials, and may help account for, in a predictive manner, phenotypic variations observed clinically.

Virtual clinical trials of anti-PD-1 and anti-CTLA-4 immunotherapy in advanced hepatocellular carcinoma using a quantitative systems pharmacology model

BACKGROUND

Hepatocellular carcinoma (HCC) is the most common form of primary liver cancer and is the third-leading cause of cancer-related death worldwide. Most patients with HCC are diagnosed at an advanced stage, and the median survival for patients with advanced HCC treated with modern systemic therapy is less than 2 years. This leaves the advanced stage patients with limited treatment options. Immune checkpoint inhibitors (ICIs) targeting programmed cell death protein 1 (PD-1) or its ligand, are widely used in the treatment of HCC and are associated with durable responses in a subset of patients. ICIs targeting cytotoxic T-lymphocyte-associated protein 4 (CTLA-4) also have clinical activity in HCC. Combination therapy of nivolumab (anti-PD-1) and ipilimumab (anti-CTLA-4) is the first treatment option for HCC to be approved by Food and Drug Administration that targets more than one immune checkpoints.

METHODS

In this study, we used the framework of quantitative systems pharmacology (QSP) to perform a virtual clinical trial for nivolumab and ipilimumab in HCC patients. Our model incorporates detailed biological mechanisms of interactions of immune cells and cancer cells leading to antitumor response. To conduct virtual clinical trial, we generate virtual patient from a cohort of 5,000 proposed patients by extending recent algorithms from literature. The model was calibrated using the data of the clinical trial CheckMate 040 (ClinicalTrials.gov number, NCT01658878).

RESULTS

Retrospective analyses were performed for different immune checkpoint therapies as performed in CheckMate 040. Using machine learning approach, we predict the importance of potential biomarkers for immune blockade therapies.

CONCLUSIONS

This is the first QSP model for HCC with ICIs and the predictions are consistent with clinically observed outcomes. This study demonstrates that using a mechanistic understanding of the underlying pathophysiology, QSP models can facilitate patient selection and design clinical trials with improved success.

Mathematical Modeling of Complement Pathway Dynamics for Target Validation and Selection of Drug Modalities for Complement Therapies

Motivation: The complement pathway plays a critical role in innate immune defense against infections. Dysregulation between activation and regulation of the complement pathway is widely known to contribute to several diseases. Nevertheless, very few drugs that target complement proteins have made it to the final regulatory approval because of factors such as high concentrations and dosing requirements for complement proteins and serious side effects from complement inhibition.

Methods: A quantitative systems pharmacology (QSP) model of the complement pathway has been developed to evaluate potential drug targets to inhibit complement activation in autoimmune diseases. The model describes complement activation via the alternative and terminal pathways as well as the dynamics of several regulatory proteins. The QSP model has been used to evaluate the effect of inhibiting complement targets on reducing pathway activation caused by deficiency in factor H and CD59. The model also informed the feasibility of developing small-molecule or large-molecule antibody drugs by predicting the drug dosing and affinity requirements for potential complement targets.

Results: Inhibition of several complement proteins was predicted to lead to a significant reduction in complement activation and cell lysis. The complement proteins that are present in very high concentrations or have high turnover rates (C3, factor B, factor D, and C6) were predicted to be challenging to engage with feasible doses of large-molecule antibody compounds (≤20 mg/kg). Alternatively, complement fragments that have a short half-life (C3b, C3bB, and C3bBb) were predicted to be challenging or infeasible to engage with small-molecule compounds because of high drug affinity requirements (>1 nM) for the inhibition of downstream processes. The drug affinity requirements for disease severity reduction were predicted to differ more than one to two orders of magnitude than affinities needed for the conventional 90% target engagement (TE) for several proteins. Thus, the QSP model analyses indicate the importance for accounting for TE requirements for achieving reduction in disease severity endpoints during the lead optimization stage.

Virtual Populations for Quantitative Systems Pharmacology Models

Quantitative systems pharmacology (QSP) places an emphasis on dynamic systems modeling, incorporating considerations from systems biology modeling and pharmacodynamics. The goal of QSP is often to quantitatively predict the effects of clinical therapeutics, their combinations, and their doses on clinical biomarkers and endpoints. In order to achieve this goal, strategies for incorporating clinical data into model calibration are critical. Virtual population (VPop) approaches facilitate model calibration while faced with challenges encountered in QSP model application, including modeling a breadth of clinical therapies, biomarkers, endpoints, utilizing data of varying structure and source, capturing observed clinical variability, and simulating with models that may require more substantial computational time and resources than often found in pharmacometrics applications. VPops are frequently developed in a process that may involve parameterization of isolated pathway models, integration into a larger QSP model, incorporation of clinical data, calibration, and quantitative validation that the model with the accompanying, calibrated VPop is suitable to address the intended question or help with the intended decision. Here, we introduce previous strategies for developing VPops in the context of a variety of therapeutic and safety areas: metabolic disorders, drug-induced liver injury, autoimmune diseases, and cancer. We introduce methodological considerations, prior work for sensitivity analysis and VPop algorithm design, and potential areas for future advancement. Finally, we give a more detailed application example of a VPop calibration algorithm that illustrates recent progress and many of the methodological considerations. In conclusion, although methodologies have varied, VPop strategies have been successfully applied to give valid clinical insights and predictions with the assistance of carefully defined and designed calibration and validation strategies. While a uniform VPop approach for all potential QSP applications may be challenging given the heterogeneity in use considerations, we anticipate continued innovation will help to drive VPop application for more challenging cases of greater scale while developing new rigorous methodologies and metrics.

Beyond the single average tumor: Understanding IO combinations using a clinical QSP model that incorporates heterogeneity in patient response

A quantitative systems pharmacology model for metastatic melanoma was developed for immuno‐oncology with the goal of predicting efficacy of combination checkpoint therapy with pembrolizumab and ipilimumab. This literature‐based model is developed at multiple scales: (i) tumor and immune cell interactions at a lesion level; (ii) multiple heterogeneous target lesions, nontarget lesion growth, and appearance of new metastatic lesion at a patient level; and (iii) interpatient differences at a population level. The model was calibrated to pembrolizumab and ipilimumab monotherapy in patients with melanoma from Robert et al., specifically, waterfall plot showing target lesion response and overall response rate (Response Evaluation Criteria in Solid Tumors [RECIST] version 1.1), which additionally considers nontarget lesion growth and appearance of new metastatic lesions. We then used the model to predict waterfall and RECIST version 1.1 for combination treatment reported in Long et al. A key insight from this work was that nontarget lesions growth and appearance of new metastatic lesion contributed significantly to disease progression, despite reduction in target lesions. Further, the lesion level simulations of combination therapy show substantial efficacy in warm lesions (intermediary immunogenicity) but limited advantage of combination in both cold and hot lesions (low and high immunogenicity). Because many patients with metastatic disease are expected to have a mixture of these lesions, disease progression in such patients may be driven by a subset of cold lesions that are unresponsive to checkpoint inhibitors. These patients may benefit more from the combinations which include therapies to target cold lesions than double checkpoint inhibitors.

Translational approaches to treating dynamical diseases through in silico clinical trials

The primary goal of drug developers is to establish efficient and effective therapeutic protocols. Multifactorial pathologies, including dynamical diseases and complex disorders, can be difficult to treat, given the high degree of inter- and intra-patient variability and nonlinear physiological relationships. Quantitative approaches combining mechanistic disease modeling and computational strategies are increasingly leveraged to rationalize pre-clinical and clinical studies and to establish effective treatment strategies. The development of clinical trials has led to new computational methods that allow for large clinical data sets to be combined with pharmacokinetic and pharmacodynamic models of diseases. Here, we discuss recent progress using in silico clinical trials to explore treatments for a variety of complex diseases, ultimately demonstrating the immense utility of quantitative methods in drug development and medicine.

QSP-IO: A Quantitative Systems Pharmacology Toolbox for Mechanistic Multiscale Modeling for Immuno-Oncology Applications

Immunotherapy has shown great potential in the treatment of cancer; however, only a fraction of patients respond to treatment, and many experience autoimmune‐related side effects. The pharmaceutical industry has relied on mathematical models to study the behavior of candidate drugs and more recently, complex, whole‐body, quantitative systems pharmacology (QSP) models have become increasingly popular for discovery and development. QSP modeling has the potential to discover novel predictive biomarkers as well as test the efficacy of treatment plans and combination therapies through virtual clinical trials. In this work, we present a QSP modeling platform for immuno‐oncology (IO) that incorporates detailed mechanisms for important immune interactions. This modular platform allows for the construction of QSP models of IO with varying degrees of complexity based on the research questions. Finally, we demonstrate the use of the platform through two example applications of immune checkpoint therapy.

gQSPSim: A SimBiology-Based GUI for Standardized QSP Model Development and Application

Quantitative systems pharmacology (QSP) models are often implemented using a wide variety of technical workflows and methodologies. To facilitate reproducibility, transparency, portability, and reuse for QSP models, we have developed gQSPSim, a graphical user interface–based MATLAB application that performs key steps in QSP model development and analyses. The capabilities of gQSPSim include (i) model calibration using global and local optimization methods, (ii) development of virtual subjects to explore variability and uncertainty in the represented biology, and (iii) simulations of virtual populations for different interventions. gQSPSim works with SimBiology‐built models using components such as species, doses, variants, and rules. All functionalities are equipped with an interactive visualization interface and the ability to generate presentation‐ready figures. In addition, standardized gQSPSim sessions can be shared and saved for future extension and reuse. In this work, we demonstrate gQSPSim’s capabilities with a standard target‐mediated drug disposition model and a published model of anti‐proprotein convertase subtilisin/kexin type 9 (PCSK9) treatment of hypercholesterolemia.

Exploration of sexual dimorphism and inter-individual variability in multivariate parameter spaces for a pharmacokinetic compartment model

Pharmacokinetic models are particularly useful to study the underlying and complex physiological mechanisms contributing to clinical differences across patient subgroups or special populations. Unfortunately, the inherent variability of biological systems and knowledge gaps in physiological data limit confidence in model predictions for special populations. Sourcing data to reflect the desired physiologies can be resource intensive, particularly for a larger model. Thus, a critical step in model development for special populations involves an in-depth analysis of model inputs, which can be guided by Monte Carlo simulations. Such an approach enables the generation of parameter values by stochastic sampling that are subsequently restricted to the combinations that describe biologically plausible or target model output. Our approach utilized a published pharmacokinetic compartmental model to demonstrate how sampling in conjunction with global sensitivity analysis can be used to explore sexual dimorphism and inter-individual variability in multivariate parameter spaces for differentiation of model input and behavior across phenotypes. Despite limiting the model output to relatively narrow ranges, male and female phenotypes were associated with wide variability in both individual parameter values and combinations of parameters. Through an integrated approach using a support vector machine, principal component analysis and global sensitivity analysis, our approach revealed that specific combinations of parameters gave rise to a certain phenotype, while individual parameters influenced the shape of plasma concentration profile. Augmenting analysis of the model input with global sensitivity analysis enabled an understanding of both sexual dimorphism and inter-individual variability in pharmacokinetics. While the current study revealed how model input could be separated by sex for a simple compartment model, the approach could be extended to other patient factors, such as age or disease, and to a more complex physiologically-based model that describes absorption, distribution, metabolism, and elimination with more detail.

A Survey of Software Tool Utilization and Capabilities for Quantitative Systems Pharmacology: What We Have and What We Need

Quantitative systems pharmacology (QSP) is a rapidly emerging discipline with application across a spectrum of challenges facing the pharmaceutical industry, including mechanistically informed prioritization of target pathways and combinations in discovery, target population, and dose expansion decisions early in clinical development, and analyses for regulatory authorities late in clinical development. QSP's development has influences from physiologic modeling, systems biology, physiologically‐based pharmacokinetic modeling, and pharmacometrics. Given a varied scientific heritage, a variety of tools to accomplish the demands of model development, application, and model‐based analysis of available data have been developed. We report the outcome from a community survey and resulting analysis of how modelers view the impact and growth of QSP, how they utilize existing tools, and capabilities they need improved to further accelerate their impact on drug development. These results serve as a benchmark and roadmap for advancements to the QSP tool set.

Linear-In-Flux-Expressions Methodology: Toward a Robust Mathematical Framework for Quantitative Systems Pharmacology Simulators

Quantitative Systems Pharmacology (QSP) modeling is increasingly used as a quantitative tool for advancing mechanistic hypotheses on the mechanism of action of a drug, and its pharmacological effect in relevant disease phenotypes, to enable linking the right drug to the right patient. Application of QSP models relies on creation of virtual populations for simulating scenarios of interest. Creation of virtual populations requires 2 important steps, namely, identification of a subset of model parameters that can be associated with a phenotype of disease and development of a sampling strategy from identified distributions of these parameters. We improve on existing sampling methodologies by providing a means of representing the structural relationship across model parameters and describing propagation of variability in the model. This gives a robust, systematic method for creating a virtual population. We have developed the Linear-In-Flux-Expressions (LIFE) method to simulate variability in patient pharmacokinetics and pharmacodynamics using relationships between parameters at baseline to create a virtual population. We demonstrate the importance of this methodology on a model of cholesterol metabolism. The LIFE methodology brings us a step closer toward improved QSP simulators through enhanced capture of the observed variability in drug and disease clinical data.

Evaluating optimal therapy robustness by virtual expansion of a sample population, with a case study in cancer immunotherapy

Cancer is a highly heterogeneous disease, exhibiting spatial and temporal variations that pose challenges for designing robust therapies. Here, we propose the VEPART (Virtual Expansion of Populations for Analyzing Robustness of Therapies) technique as a platform that integrates experimental data, mathematical modeling, and statistical analyses for identifying robust optimal treatment protocols. VEPART begins with time course experimental data for a sample population, and a mathematical model fit to aggregate data from that sample population. Using nonparametric statistics, the sample population is amplified and used to create a large number of virtual populations. At the final step of VEPART, robustness is assessed by identifying and analyzing the optimal therapy (perhaps restricted to a set of clinically realizable protocols) across each virtual population. As proof of concept, we have applied the VEPART method to study the robustness of treatment response in a mouse model of melanoma subject to treatment with immunostimulatory oncolytic viruses and dendritic cell vaccines. Our analysis (i) showed that every scheduling variant of the experimentally used treatment protocol is fragile (nonrobust) and (ii) discovered an alternative region of dosing space (lower oncolytic virus dose, higher dendritic cell dose) for which a robust optimal protocol exists.

QSP Toolbox: Computational Implementation of Integrated Workflow Components for Deploying Multi-Scale Mechanistic Models

Quantitative systems pharmacology (QSP) modeling has become increasingly important in pharmaceutical research and development, and is a powerful tool to gain mechanistic insights into the complex dynamics of biological systems in response to drug treatment. However, even once a suitable mathematical framework to describe the pathophysiology and mechanisms of interest is established, final model calibration and the exploration of variability can be challenging and time consuming. QSP models are often formulated as multi-scale, multi-compartment nonlinear systems of ordinary differential equations. Commonly accepted modeling strategies, workflows, and tools have promise to greatly improve the efficiency of QSP methods and improve productivity. In this paper, we present the QSP Toolbox, a set of functions, structure array conventions, and class definitions that computationally implement critical elements of QSP workflows including data integration, model calibration, and variability exploration. We present the application of the toolbox to an ordinary differential equations-based model for antibody drug conjugates. As opposed to a single stepwise reference model calibration, the toolbox also facilitates simultaneous parameter optimization and variation across multiple in vitro, in vivo, and clinical assays to more comprehensively generate alternate mechanistic hypotheses that are in quantitative agreement with available data. The toolbox also includes scripts for developing and applying virtual populations to mechanistic exploration of biomarkers and efficacy. We anticipate that the QSP Toolbox will be a useful resource that will facilitate implementation, evaluation, and sharing of new methodologies in a common framework that will greatly benefit the community.

Efficient Generation and Selection of Virtual Populations in Quantitative Systems Pharmacology Models

Quantitative systems pharmacology models mechanistically describe a biological system and the effect of drug treatment on system behavior. Because these models rarely are identifiable from the available data, the uncertainty in physiological parameters may be sampled to create alternative parameterizations of the model, sometimes termed "virtual patients." In order to reproduce the statistics of a clinical population, virtual patients are often weighted to form a virtual population that reflects the baseline characteristics of the clinical cohort. Here we introduce a novel technique to efficiently generate virtual patients and, from this ensemble, demonstrate how to select a virtual population that matches the observed data without the need for weighting. This approach improves confidence in model predictions by mitigating the risk that spurious virtual patients become overrepresented in virtual populations.

Enhancing the discovery and development of immunotherapies for cancer using quantitative and systems pharmacology: Interleukin-12 as a case study

Recent clinical successes of immune checkpoint modulators have unleashed a wave of enthusiasm associated with cancer immunotherapy. However, this enthusiasm is dampened by persistent translational hurdles associated with cancer immunotherapy that mirror the broader pharmaceutical industry. Specifically, the challenges associated with drug discovery and development stem from an incomplete understanding of the biological mechanisms in humans that are targeted by a potential drug and the financial implications of clinical failures. Sustaining progress in expanding the clinical benefit provided by cancer immunotherapy requires reliably identifying new mechanisms of action. Along these lines, quantitative and systems pharmacology (QSP) has been proposed as a means to invigorate the drug discovery and development process. In this review, I discuss two central themes of QSP as applied in the context of cancer immunotherapy. The first theme focuses on a network-centric view of biology as a contrast to a "one-gene, one-receptor, one-mechanism" paradigm prevalent in contemporary drug discovery and development. This theme has been enabled by the advances in wet-lab capabilities to assay biological systems at increasing breadth and resolution. The second theme focuses on integrating mechanistic modeling and simulation with quantitative wet-lab studies. Drawing from recent QSP examples, large-scale mechanistic models that integrate phenotypic signaling-, cellular-, and tissue-level behaviors have the potential to lower many of the translational hurdles associated with cancer immunotherapy. These include prioritizing immunotherapies, developing mechanistic biomarkers that stratify patient populations and that reflect the underlying strength and dynamics of a protective host immune response, and facilitate explicit sharing of our understanding of the underlying biology using mechanistic models as vehicles for dialogue. However, creating such models require a modular approach that assumes that the biological networks remain similar in health and disease. As oncogenesis is associated with re-wiring of these biological networks, I also describe an approach that combines mechanistic modeling with quantitative wet-lab experiments to identify ways in which malignant cells alter these networks, using Interleukin-12 as an example. Collectively, QSP represents a new holistic approach that may have profound implications for how translational science is performed.

Bridging Systems Medicine and Patient Needs

While there is widespread consensus on the need both to change the prevailing research and development (R&D) paradigm and provide the community with an efficient way to personalize medicine, ecosystem stakeholders grapple with divergent conceptions about which quantitative approach should be preferred. The primary purpose of this position paper is to contrast these approaches. The second objective is to introduce a framework to bridge simulation outputs and patient outcomes, thus empowering the implementation of systems medicine.

A mathematical model of the human metabolic system and metabolic flexibility

In healthy subjects some tissues in the human body display metabolic flexibility, by this we mean the ability for the tissue to switch its fuel source between predominantly carbohydrates in the postprandial state and predominantly fats in the fasted state. Many of the pathways involved with human metabolism are controlled by insulin and insulin-resistant states such as obesity and type-2 diabetes are characterised by a loss or impairment of metabolic flexibility. In this paper we derive a system of 12 first-order coupled differential equations that describe the transport between and storage in different tissues of the human body. We find steady state solutions to these equations and use these results to nondimensionalise the model. We then solve the model numerically to simulate a healthy balanced meal and a high fat meal and we discuss and compare these results. Our numerical results show good agreement with experimental data where we have data available to us and the results show behaviour that agrees with intuition where we currently have no data with which to compare.

Systems biology for simulating patient physiology during the postgenomic era of medicine

Systems pharmacology models capable of accurately recapitulating sophisticated patient phenotypes have enabled the investigation of mechanisms responsible for therapeutic efficacy. Although omics data sets are capable of characterizing the operation of subcellular networks, their utility in mechanistically predicting quantitative, clinically accessible outcome measures has been limited. Developing insights into clinical outcomes from omics data sets will benefit from modeling approaches that can integrate molecular networks mechanistically with simulations of patient pathophysiology across compartments and scales.

A conceptual review on systems biology in health and diseases: from biological networks to modern therapeutics

Human physiology is an ensemble of various biological processes spanning from intracellular molecular interactions to the whole body phenotypic response. Systems biology endures to decipher these multi-scale biological networks and bridge the link between genotype to phenotype. The structure and dynamic properties of these networks are responsible for controlling and deciding the phenotypic state of a cell. Several cells and various tissues coordinate together to generate an organ level response which further regulates the ultimate physiological state. The overall network embeds a hierarchical regulatory structure, which when unusually perturbed can lead to undesirable physiological state termed as disease. Here, we treat a disease diagnosis problem analogous to a fault diagnosis problem in engineering systems. Accordingly we review the application of engineering methodologies to address human diseases from systems biological perspective. The review highlights potential networks and modeling approaches used for analyzing human diseases. The application of such analysis is illustrated in the case of cancer and diabetes. We put forth a concept of cell-to-human framework comprising of five modules (data mining, networking, modeling, experimental and validation) for addressing human physiology and diseases based on a paradigm of system level analysis. The review overtly emphasizes on the importance of multi-scale biological networks and subsequent modeling and analysis for drug target identification and designing efficient therapies.

Alternate virtual populations elucidate the type I interferon signature predictive of the response to rituximab in rheumatoid arthritis

Background

Mechanistic biosimulation can be used in drug development to form testable hypotheses, develop predictions of efficacy before clinical trial results are available, and elucidate clinical response to therapy. However, there is a lack of tools to simultaneously (1) calibrate the prevalence of mechanistically distinct, large sets of virtual patients so their simulated responses statistically match phenotypic variability reported in published clinical trial outcomes, and (2) explore alternate hypotheses of those prevalence weightings to reflect underlying uncertainty in population biology. Here, we report the development of an algorithm, MAPEL (Mechanistic Axes Population Ensemble Linkage), which utilizes a mechanistically-based weighting method to match clinical trial statistics. MAPEL is the first algorithm for developing weighted virtual populations based on biosimulation results that enables the rapid development of an ensemble of alternate virtual population hypotheses, each validated by a composite goodness-of-fit criterion.

Results

Virtual patient cohort mechanistic biosimulation results were successfully calibrated with an acceptable composite goodness-of-fit to clinical populations across multiple therapeutic interventions. The resulting virtual populations were employed to investigate the mechanistic underpinnings of variations in the response to rituximab. A comparison between virtual populations with a strong or weak American College of Rheumatology (ACR) score in response to rituximab suggested that interferon β (IFNβ) was an important mechanistic contributor to the disease state, a signature that has previously been identified though the underlying mechanisms remain unclear. Sensitivity analysis elucidated key anti-inflammatory properties of IFNβ that modulated the pathophysiologic state, consistent with the observed prognostic correlation of baseline type I interferon measurements with clinical response. Specifically, the effects of IFNβ on proliferation of fibroblast-like synoviocytes and interleukin-10 synthesis in macrophages each partially counteract reductions in synovial inflammation imparted by rituximab. A multianalyte biomarker panel predictive for virtual population therapeutic responses suggested population dependencies on B cell-dependent mediators as well as additional markers implicating fibroblast-like synoviocytes.

Conclusions

The results illustrate how the MAPEL algorithm can leverage knowledge of cellular and molecular function through biosimulation to propose clear mechanistic hypotheses for differences in clinical populations. Furthermore, MAPEL facilitates the development of multianalyte biomarkers prognostic of patient responses in silico.

Insulin signaling - mathematical modeling comes of age

Signaling pathways that only a few years ago appeared simple and understandable, albeit far from complete, have evolved into very complex multi-layered networks of cellular control mechanisms, which in turn are integrated in a similarly complex whole-body level of control mechanisms. This complexity sets limits for classical biochemical reasoning, such that a correct and complete analysis of experimental data while taking the full complexity into account is not possible. In this Opinion we propose that mathematical modeling can be used as a tool in insulin signaling research, and we demonstrate how recent developments in modeling - and the integration of modeling in the experimental process - provide new possibilities to approach and decipher complex biological systems more efficiently.

A multiscale systems perspective on cancer, immunotherapy, and Interleukin-12

Monoclonal antibodies represent some of the most promising molecular targeted immunotherapies. However, understanding mechanisms by which tumors evade elimination by the immune system of the host presents a significant challenge for developing effective cancer immunotherapies. The interaction of cancer cells with the host is a complex process that is distributed across a variety of time and length scales. The time scales range from the dynamics of protein refolding (i.e., microseconds) to the dynamics of disease progression (i.e., years). The length scales span the farthest reaches of the human body (i.e., meters) down to the range of molecular interactions (i.e., nanometers). Limited ranges of time and length scales are used experimentally to observe and quantify changes in physiology due to cancer. Translating knowledge obtained from the limited scales observed experimentally to predict patient response is an essential prerequisite for the rational design of cancer immunotherapies that improve clinical outcomes. In studying multiscale systems, engineers use systems analysis and design to identify important components in a complex system and to test conceptual understanding of the integrated system behavior using simulation. The objective of this review is to summarize interactions between the tumor and cell-mediated immunity from a multiscale perspective. Interleukin-12 and its role in coordinating antibody-dependent cell-mediated cytotoxicity is used illustrate the different time and length scale that underpin cancer immunoediting. An underlying theme in this review is the potential role that simulation can play in translating knowledge across scales.

Validating a dimensionless number for glucose homeostasis in humans

Understanding type 2 diabetes is challenged by the diversity of patient phenotypes. Translating data across species and among individuals is a barrier for understanding the genetic loci that underpin this multifactorial disease. Dynamic scaling, based upon dimensional analysis, is a common technique in engineering used to translate data among different systems. The objective of this study was to gain insight using dimensional analysis into the relative changes in insulin production capacity vs. insulin-dependent glucose metabolism in patient groups that represent distinct stages of disease progression. A dimensionless number was derived using variables involved in the production of insulin and in the sensitivity of glucose metabolism to insulin. The resulting dynamic scaling relationship was validated against patient data obtained for over 2000 individuals that range in phenotype from normal to severe type 2 diabetes. Individuals were identified in the third National Health and Nutrition Evaluation Survey. Patient groups clustered in different regions based upon the severity of clinical symptoms. The cross-sectional comparison among patient groups shows that progression from normal to clinical onset of type 2 diabetes exhibits a non-linear change in the ratio of insulin production to insulin-dependent glucose metabolism: normals are balanced, pre-diabetic individuals exhibit an increase, and individuals with clinical type 2 diabetes exhibit a decrease in this ratio. This dimensionless number provides a method for discriminating between patient groups from first principles. By analogy with other dimensionless numbers, this number may be used to monitor basic physiological variables responsible for glucose homeostasis. In addition, a similar dynamic trajectory to the clinical populations could provide a criterion for selecting relevant animal models for diabetes.

Robust signaling networks of the adipose secretome

Type 2 diabetes is a prototypical complex systems disease that has a strong hereditary component and etiologic links with a sedentary lifestyle, overeating and obesity. Adipose tissue has been shown to be a central driver of type 2 diabetes progression, establishing and maintaining a chronic state of low-level inflammation. The number and diversity of identified endocrine factors from adipose tissue (adipokines) is growing rapidly. Here, I argue that a systems biology approach to understanding the robust multi-level signaling networks established by the adipose secretome will be crucial for developing efficient type 2 diabetes treatment. Recent advances in whole-genome association studies, global molecular profiling and quantitative modeling are currently fueling the emergence of this novel research strategy.