A continuous-time Markov chain model of fibrosis progression in NAFLD and NASH.

The specific pathways, timescales, and dynamics driving the progression of fibrosis in NAFLD and NASH are not yet fully understood. Hence, a mechanistic model of the pathogenesis and treatment of fibrosis in NASH will necessarily have significant uncertainties. The rate of fibrosis progression and the heterogeneity of pathogenesis across patients are not thoroughly quantified. To address this problem, we have developed a continuous-time Markov chain model that is able to capture the heterogeneity of fibrosis progression observed in the clinic. We estimated the average time of disease progression through various stages of fibrosis using seven published clinical studies involving paired liver biopsies. Sensitivity analysis revealed therapeutic intervention at stage F1 or stage F2 results in greatest potential improvement in the average fibrosis scores for a typical patient cohort distribution. These results were in good agreement with a retrospective analysis of placebo-controlled pioglitazone clinical trials for the treatment of NAFLD and NASH. This model provides support for determining patient populations, duration, and potential successful endpoints for clinical trial design in the area of NAFLD and NASH.

A quantitative systems pharmacology model of the pathophysiology and treatment of COVID-19 predicts optimal timing of pharmacological interventions.

A quantitative systems pharmacology (QSP) model of the pathogenesis and treatment of SARS-CoV-2 infection can streamline and accelerate the development of novel medicines to treat COVID-19. Simulation of clinical trials allows in silico exploration of the uncertainties of clinical trial design and can rapidly inform their protocols. We previously published a preliminary model of the immune response to SARS-CoV-2 infection. To further our understanding of COVID-19 and treatment, we significantly updated the model by matching a curated dataset spanning viral load and immune responses in plasma and lung. We identified a population of parameter sets to generate heterogeneity in pathophysiology and treatment and tested this model against published reports from interventional SARS-CoV-2 targeting mAb and antiviral trials. Upon generation and selection of a virtual population, we match both the placebo and treated responses in viral load in these trials. We extended the model to predict the rate of hospitalization or death within a population. Via comparison of the in silico predictions with clinical data, we hypothesize that the immune response to virus is log-linear over a wide range of viral load. To validate this approach, we show the model matches a published subgroup analysis, sorted by baseline viral load, of patients treated with neutralizing Abs. By simulating intervention at different time points post infection, the model predicts efficacy is not sensitive to interventions within five days of symptom onset, but efficacy is dramatically reduced if more than five days pass post symptom onset prior to treatment.

Sources of inter-individual variability leading to significant changes in anti-PD-1 and anti-PD-L1 efficacy identified in mouse tumor models using a QSP framework.

While anti-PD-1 and anti-PD-L1 [anti-PD-(L)1] monotherapies are effective treatments for many types of cancer, high variability in patient responses is observed in clinical trials. Understanding the sources of response variability can help prospectively identify potential responsive patient populations. Preclinical data may offer insights to this point and, in combination with modeling, may be predictive of sources of variability and their impact on efficacy. Herein, a quantitative systems pharmacology (QSP) model of anti-PD-(L)1 was developed to account for the known pharmacokinetic properties of anti-PD-(L)1 antibodies, their impact on CD8+ T cell activation and influx into the tumor microenvironment, and subsequent anti-tumor effects in CT26 tumor syngeneic mouse model. The QSP model was sufficient to describe the variability inherent in the anti-tumor responses post anti-PD-(L)1 treatments. Local sensitivity analysis identified tumor cell proliferation rate, PD-1 expression on CD8+ T cells, PD-L1 expression on tumor cells, and the binding affinity of PD-1:PD-L1 as strong influencers of tumor growth. It also suggested that treatment-mediated tumor growth inhibition is sensitive to T cell properties including the CD8+ T cell proliferation half-life, CD8+ T cell half-life, cytotoxic T-lymphocyte (CTL)-mediated tumor cell killing rate, and maximum rate of CD8+ T cell influx into the tumor microenvironment. Each of these parameters alone could not predict anti-PD-(L)1 treatment response but they could shift an individual mouse's treatment response when perturbed. The presented preclinical QSP modeling framework provides a path to incorporate potential sources of response variability in human translation modeling of anti-PD-(L)1.

A Quantitative Systems Pharmacology Model of Liver Lipid Metabolism for Investigation of Non-Alcoholic Fatty Liver Disease.

Non-alcoholic fatty liver disease is a metabolic and inflammatory disease that afflicts many people worldwide and presently has few treatment options. To enhance the preclinical to clinical translation and the design of early clinical trials for novel therapeutics, we developed a Quantitative Systems Pharmacology model of human hepatocyte lipid metabolism. The intended application of the model is for simulating anti-steatotic therapies for reversing fatty liver. We parameterized the model using literature data from humans with both normal and elevated liver fat. We assessed that the model construct was sufficient to generate a virtual population of NAFLD patients that matched relevant statistics of a published clinical cohort, and then validated the model response to treatment by simulating pioglitazone and diet intervention in the virtual population. Finally, a sensitivity analysis was performed to determine the best points of intervention for reducing hepatic steatosis. Analysis of the model suggests the most potent method for reducing hepatic steatosis is by limiting non-esterified fatty acid flux from the adipose to the liver.

Pool size measurements improve precision of flux estimates but increase sensitivity to unmodeled reactions outside the core network in isotopically nonstationary metabolic flux analysis (INST-MFA).

Metabolic flux analysis (MFA) involves model-based estimation of metabolic reaction rates (i.e., fluxes) and, in some cases, metabolite content (i.e., pool sizes) from experimental measurements. Applying MFA to biological data helps determine the fate of substrates and the activity of specific pathways within metabolic networks. However, reliably estimating fluxes by using simplified "core" models to predict the dynamics of larger metabolic networks remains a challenge. One point of uncertainty relates to the advantages and potential pitfalls of including pool size measurements as experimental inputs for isotopically nonstationary MFA (INST-MFA). Here, we directly assessed the role of pool sizes using various core models and simulated datasets. To investigate the effects of pool size measurements on INST-MFA, we assessed the accuracy and precision of flux estimates obtained using different subsets of data (e.g., with or without pool size measurements) and simple network models that either matched or differed from the true network. The inclusion of pool size measurements provided incremental improvements to the precision of the flux estimates. However, adding pool size measurements increased the sensitivity of the flux solution to unmodeled reactions outside the core network. These results were confirmed using a large Escherichia coli model that is representative of realistic metabolic networks examined in MFA studies. Our findings indicate that accurate flux estimates can be obtained in the absence of pool size measurements, even when using core models that lack full network coverage. Addition of pool size measurements to INST-MFA datasets may reveal the activity of non-core reactions that influence the labeling dynamics and therefore necessitate network expansion in order to reconcile all available data to the model. Our findings also emphasize the key role that goodness-of-fit testing plays in assessing the quality of model fits obtained with INST-MFA.

FDA-Industry Scientific Exchange on assessing quantitative systems pharmacology models in clinical drug development: a meeting report, summary of challenges/gaps, and future perspective.

The pharmaceutical industry is actively applying quantitative systems pharmacology (QSP) to make internal decisions and guide drug development. To facilitate the eventual development of a common framework for assessing the credibility of QSP models for clinical drug development, scientists from US Food and Drug Administration and the pharmaceutical industry organized a full-day virtual Scientific Exchange on July 1, 2020. An assessment form was used to ensure consistency in the evaluation process. Among the cases presented, QSP was applied to various therapeutic areas. Applications mostly focused on phase 2 dose selection. Model transparency, including details on expert knowledge and data used for model development, was identified as a major factor for robust model assessment. The case studies demonstrated some commonalities in the workflow of QSP model development, calibration, and validation but differ in the size, scope, and complexity of QSP models, in the acceptance criteria for model calibration and validation, and in the algorithms/approaches used for creating virtual patient populations. Though efforts are being made to build the credibility of QSP models and the confidence is increasing in applying QSP for internal decisions at the clinical stages of drug development, there are still many challenges facing QSP application to late stage drug development. The QSP community needs a strategic plan that includes the ability and flexibility to Adapt, to establish Common expectations for model Credibility needed to inform drug Labeling and patient care, and to AIM to achieve the goal (ACCLAIM).

End-to-end application of model-informed drug development for ertugliflozin, a novel sodium-glucose cotransporter 2 inhibitor.

Model-informed drug development (MIDD) is critical in all stages of the drug-development process and almost all regulatory submissions for new agents incorporate some form of modeling and simulation. This review describes the MIDD approaches used in the end-to-end development of ertugliflozin, a sodium-glucose cotransporter 2 inhibitor approved for the treatment of adults with type 2 diabetes mellitus. Approaches included (1) quantitative systems pharmacology modeling to predict dose-response relationships, (2) dose-response modeling and model-based meta-analysis for dose selection and efficacy comparisons, (3) population pharmacokinetics (PKs) modeling to characterize PKs and quantify population variability in PK parameters, (4) regression modeling to evaluate ertugliflozin dose-proportionality and the impact of uridine 5'-diphospho-glucuronosyltransferase (UGT) 1A9 genotype on ertugliflozin PKs, and (5) physiologically-based PK modeling to assess the risk of UGT-mediated drug-drug interactions. These end-to-end MIDD approaches for ertugliflozin facilitated decision making, resulted in time/cost savings, and supported registration and labeling.

A Prototype QSP Model of the Immune Response to SARS-CoV-2 for Community Development.

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic requires the rapid development of efficacious treatments for patients with life-threatening coronavirus disease 2019 (COVID-19). Quantitative systems pharmacology (QSP) models are mathematical representations of pathophysiology for simulating and predicting the effects of existing or putative therapies. The application of model-based approaches, including QSP, have accelerated the development of some novel therapeutics. Nevertheless, the development of disease-scale mechanistic models can be a slow process, often taking years to be validated and considered mature. Furthermore, emerging data may make any QSP model quickly obsolete. We present a prototype QSP model to facilitate further development by the scientific community. The model accounts for the interactions between viral dynamics, the major host immune response mediators and tissue damage and regeneration. The immune response is determined by viral activation of innate and adaptive immune processes that regulate viral clearance and cell damage. The prototype model captures two physiologically relevant outcomes following infection: a "healthy" immune response that appropriately defends against the virus, and an uncontrolled alveolar inflammatory response that is characteristic of acute respiratory distress syndrome. We aim to significantly shorten the typical QSP model development and validation timeline by encouraging community use, testing, and refinement of this prototype model. It is our expectation that the model will be further advanced in an open science approach (i.e., by multiple contributions toward a validated quantitative platform in an open forum), with the ultimate goal of informing and accelerating the development of safe and effective treatment options for patients.

Quantitative analysis of variability in an integrated model of human ventricular electrophysiology and ß-adrenergic signaling.

In ventricular myocytes, stimulation of ß-adrenergic receptors activates critical cardiac signaling pathways, leading to shorter action potentials and increased contraction strength during the "fight-or-flight" response. These changes primarily result, at the cellular level, from the coordinated phosphorylation of multiple targets by protein kinase A. Although mathematical models of the intracellular signaling downstream of ß-adrenergic receptor activation have previously been described, only a limited number of studies have explored quantitative interactions between intracellular signaling and electrophysiology in human ventricular myocytes. Accordingly, our objective was to develop an integrative mathematical model of ß-adrenergic receptor signaling, electrophysiology, and intracellular calcium (Ca2+) handling in the healthy human ventricular myocyte. We combined published mathematical models of intracellular signaling and electrophysiology, then calibrated the model results against voltage clamp data and physiological changes occurring after stimulation of ß-adrenergic receptors with isoproterenol. We subsequently: (1) explored how molecular variability in different categories of model parameters translated into phenotypic variability; (2) identified the most important parameters determining physiological cellular outputs in the model before and after ß-adrenergic receptor stimulation; and (3) investigated which molecular level alterations can produce a phenotype indicative of heart failure with preserved ejection fraction (HFpEF). Major results included: (1) variability in parameters that controlled intracellular signaling caused qualitatively different behavior than variability in parameters controlling ion transport pathways; (2) the most important model parameters determining action potential duration and intracellular Ca2+ transient amplitude were generally consistent before and after ß-adrenergic receptor stimulation, except for a shift in the importance of K+ currents in determining action potential duration; and (3) decreased Ca2+ uptake into the sarcoplasmic reticulum, increased Ca2+ extrusion through Na+/Ca2+ exchanger and decreased Ca2+ leak from the sarcoplasmic reticulum may contribute to HFpEF. Overall, this study provided novel insight into the phenotypic consequences of molecular variability, and our integrated model may be useful in the design and interpretation of future experimental studies of interactions between ß-adrenergic signaling and cellular physiology in human ventricular myocytes.

Toward Progress in Quantitative Translational Medicine: A Call to Action.

Quantitative translational medicine (QTM) is envisioned as a multifaceted discipline that will galvanize the path from idea to medicine through quantitative translation across the discovery, development, regulatory, and utilization spectrum. Here, we summarize results of an American Society for Clinical Pharmacology and Therapeutics (ASCPT) survey on barriers relevant to the advancement of QTM and propose opportunities for its deployment. Importantly, we offer a call to action to break down these barriers through patient-centered stewardship, effective communication, cross-sector collaboration, and a modernized educational curriculum.

Analysis of compartments-in-series models of liver metabolism as partial differential equations: the effect of dispersion and number of compartments.

Non-alcoholic fatty liver disease is the most common cause of chronic liver disease. Precipitated by the build up of extra fat in the liver not caused by alcohol, it is still not understood why steatosis occurs where it does in the liver microstructure in non-alcoholic fatty liver disease. It is likely, however, that the location of steatosis is due, at least in part, to metabolic zonation (heterogeneity among liver cells in function and enzyme expression). Recently, there has been an influx of computational and mathematical models in order to investigate the relationship between metabolic zonation and steatosis in non-alcoholic fatty liver disease. Of interest among these models are "compartments-in-series" models. Compartments-in-series models include the spatial distribution of metabolite concentrations via series of compartments that are connected through some representation of blood flow. In this paper, we analyze one such model, focusing specifically at how the number of compartments and inclusion of dispersion in the flow affect simulation results. We find the number of compartments to have a much larger effect than the inclusion of dispersion, however this is likely due to numerical artifacts. Overall, we conclude that considering partial differential equations that are equivalent to compartments-in-series models would be beneficial both in computation and in theoretical analyses.

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.

Improving the generation and selection of virtual populations in quantitative systems pharmacology models.

Quantitative systems pharmacology (QSP) models aim to describe mechanistically the pathophysiology of disease and predict the effects of therapies on that disease. For most drug development applications, it is important to predict not only the mean response to an intervention but also the distribution of responses, due to inter-patient variability. Given the necessary complexity of QSP models, and the sparsity of relevant human data, the parameters of QSP models are often not well determined. One approach to overcome these limitations is to develop alternative virtual patients (VPs) and virtual populations (Vpops), which allow for the exploration of parametric uncertainty and reproduce inter-patient variability in response to perturbation. Here we evaluated approaches to improve the efficiency of generating Vpops. We aimed to generate Vpops without sacrificing diversity of the VPs' pathophysiologies and phenotypes. To do this, we built upon a previously published approach (Allen et al., 2016) by (a) incorporating alternative optimization algorithms (genetic algorithm and Metropolis-Hastings) or alternatively (b) augmenting the optimized objective function. Each method improved the baseline algorithm by requiring significantly fewer plausible patients (precursors to VPs) to create a reasonable Vpop.

Perspective on the State of Pharmacometrics and Systems Pharmacology Integration.

Reliance on modeling and simulation in drug discovery and development has dramatically increased over the past decade. Two disciplines at the forefront of this activity, pharmacometrics and systems pharmacology (SP), emerged independently from different fields; consequently, a perception exists that only few examples integrate these approaches. Herein, we review the state of pharmacometrics and SP integration and describe benefits of combining these approaches in a model-informed drug discovery and development framework.

A mathematical analysis of adaptations to the metabolic fate of fructose in essential fructosuria subjects.

Fructose is a major component of Western diets and is implicated in the pathogenesis of obesity and type 2 diabetes. In response to an oral challenge, the majority of fructose is cleared during "first-pass" liver metabolism, primarily via phosphorylation by ketohexokinase (KHK). A rare benign genetic deficiency in KHK, called essential fructosuria (EF), leads to altered fructose metabolism. The only reported symptom of EF is the appearance of fructose in the urine following either oral or intravenous fructose administration. Here we develop and use a mathematical model to investigate the adaptations to altered fructose metabolism in people with EF. First, the model is calibrated to fit available data in normal healthy subjects. Then, to mathematically represent EF subjects, we systematically implement metabolic adaptations such that model simulations match available data for this phenotype. We hypothesize that these modifications represent the major metabolic adaptations present in these subjects. This modeling approach suggests that several other aspects of fructose metabolism, beyond hepatic KHK deficiency, are altered and contribute to the etiology of this benign condition. Specifically, we predict that fructose absorption into the portal vein is altered, peripheral metabolism is slowed, renal reabsorption of fructose is mostly ablated, and alternate pathways for hepatic metabolism of fructose are upregulated. Moreover, these findings have implications for drug discovery and development, suggesting that the therapeutic targeting of fructose metabolism could lead to unexpected metabolic adaptations, potentially due to a physiological response to high-fructose conditions.

Modeling fructose-load-induced hepatic de-novo lipogenesis by model simplification.

Hepatic de-novo lipogenesis is a metabolic process implemented in the pathogenesis of type 2 diabetes. Clinically, the rate of this process can be ascertained by use of labeled acetate and stimulation by fructose administration. A systems pharmacology model of this process is desirable because it facilitates the description, analysis, and prediction of this experiment. Due to the multiple enzymes involved in de-novo lipogenesis, and the limited data, it is desirable to use single functional expressions to encapsulate the flux between multiple enzymes. To accomplish this we developed a novel simplification technique which uses the available information about the properties of the individual enzymes to bound the parameters of a single governing 'transfer function'. This method should be applicable to any model with linear chains of enzymes that are well stimulated. We validated this approach with computational simulations and analytical justification in a limiting case. Using this technique we generated a simple model of hepatic de-novo lipogenesis in these experimental conditions that matched prior data. This model can be used to assess pharmacological intervention at specific points on this pathway. We have demonstrated this with prospective simulation of acetyl-CoA carboxylase inhibition. This simplification technique suggests how the constituent properties of an enzymatic chain of reactions gives rise to the sensitivity (to substrate) of the pathway as a whole.