A Review of Quantitative Systems Pharmacology Models of the Coagulation Cascade: Opportunities for Improved Usability

A mathematical model for activated platelet-dependent activation of coagulation factor X by factor IXa

Membrane-dependent enzymatic reactions are central in many signaling and regulatory biological networks. Activation of blood coagulation factor X by activated factor IXa is a classical example, which retains many mysteries and controversies. Here we developed a novel non-stationary two-compartment computational model of this reaction on the physiological membrane of activated platelets (rather than phospholipid vesicles) within a wide platelet concentration range up to the intra-thrombus conditions, which took into account novel essential revisions in the mechanisms on factor IXa interactions with platelets. The set of ordinary differential equations (ODEs) was based on the laws of mass action and included several possible pathways of the complex formation. Sensitivity analysis was employed to identify critical points in the regulation. The model was able to describe the available experimental data and suggested that the major pathways of the enzyme-substrate complex assembly were membrane-dependent and solution-dependent enzyme delivery, with comparable contributions. The dependence of factor Xa formation on the activated procoagulant platelet concentration was predicted to be bell-shaped with the peak at (1.5-2)·106 platelets/μL, which is similar to the expected intra-thrombus concentration. The modeling of the kinetics of all model variables demonstrated two-phase kinetics. With increasing platelet concentration in the system, the transition time after which a stationary concentration is reached increases to approximately 5 min.

The Role of Cross-Institutional and Interdisciplinary Collaboration in Defining and Executing a Quantitative Systems Pharmacology Strategy

The application of quantitative systems pharmacology (QSP) has enabled substantial progress and impact in many areas of therapeutic discovery and development. This new technology is increasingly accepted by industry, academia, and solution providers, and is enjoying greater interest from regulators. In this chapter, we summarize key aspects regarding how effective collaboration among institutions and disciplines can support the growth of QSP and expand its application domain. We exemplify these considerations through a selection of successful cross-institutional or cross-functional collaborations, which resulted in reuse, repurposing, or extension of QSP modeling results or infrastructure, with important and novel results.

Quantitative Systems Pharmacology Models: Potential Tools for Advancing Drug Development for Rare Diseases

Rare diseases, affecting millions globally, present significant drug development challenges. This is due to the limited patient populations and the unique pathophysiology of these diseases, which can make traditional clinical trial designs unfeasible. Quantitative Systems Pharmacology (QSP) models offer a promising approach to expedite drug development, particularly in rare diseases. QSP models provide a mechanistic representation of the disease and drug response in virtual patients that can complement routinely applied empirical modeling and simulation approaches. QSP models can generate digital twins of actual patients and mechanistically simulate the disease progression of rare diseases, accounting for phenotypic heterogeneity. QSP models can also support drug development in various drug modalities, such as gene therapy. Impactful QSP models case studies are presented here to illustrate their value in supporting various aspects of drug development in rare indications. As these QSP model applications continue to mature, there is a growing possibility that they could be more widely integrated into routine drug development steps. This integration could provide a robust framework for addressing some of the inherent challenges in rare disease drug development.

Kinetic analysis of prothrombinase assembly and substrate delivery mechanisms

Prothrombinase complex, composed of coagulation factors Xa (FXa) and Va (FVa) is a major enzyme of the blood coagulation network that produces thrombin via activation of its inactive precursor prothrombin (FII) on the surface of phospholipid membranes. However, pathways and mechanisms of prothrombinase formation and substrate delivery are still discussed. Here we designed a novel mathematical model that considered different potential pathways of FXa or FII binding (from the membrane or from solution) and analyzed the kinetics of thrombin formation in the presence of a wide range of reactants concentrations. We observed the inhibitory effect of large FVa concentrations and this effect was phospholipid concentration-dependent. We predicted that efficient FII activation occurred via formation of the ternary complex, in which FVa, FXa and FII were in the membrane-bound state. Prothrombin delivery was mostly membrane-dependent, but delivery from solution was predominant under conditions of phospholipid deficiency or FXa/FVa excess. Likewise, FXa delivery from solution was predominant in the case of FVa excess, but high FII did not switch the FXa delivery to the solution-dependent one. Additionally, the FXa delivery pathway did not depend on the phospholipid concentration, being the membrane-dependent one even in case of the phospholipid deficiency. These results suggest a flexible mechanism of prothrombinase functioning which utilizes different complex formation and even inhibitory mechanisms depending on conditions.

Mechanistic modeling of cell viability assays with in silico lineage tracing

Data from cell viability assays, which measure cumulative division and death events in a population and reflect substantial cellular heterogeneity, are widely available. However, interpreting such data with mechanistic computational models is hindered because direct model/data comparison is often muddled. We developed an algorithm that tracks simulated division and death events in mechanistically detailed single-cell lineages to enable such a model/data comparison and suggest causes of cell-cell drug response variability. Using our previously developed model of mammalian single-cell proliferation and death signaling, we simulated drug dose response experiments for four targeted anti-cancer drugs (alpelisib, neratinib, trametinib and palbociclib) and compared them to experimental data. Simulations are consistent with data for strong growth inhibition by trametinib (MEK inhibitor) and overall lack of efficacy for alpelisib (PI-3K inhibitor), but are inconsistent with data for palbociclib (CDK4/6 inhibitor) and neratinib (EGFR inhibitor). Model/data inconsistencies suggest (i) the importance of CDK4/6 for driving the cell cycle may be overestimated, and (ii) that the cellular balance between basal (tonic) and ligand-induced signaling is a critical determinant of receptor inhibitor response. Simulations show subpopulations of rapidly and slowly dividing cells in both control and drug-treated conditions. Variations in mother cells prior to drug treatment all impinging on ERK pathway activity are associated with the rapidly dividing phenotype and trametinib resistance. This work lays a foundation for the application of mechanistic modeling to large-scale cell viability assay datasets and better understanding determinants of cellular heterogeneity in drug response.

A physiologically-based pharmacokinetic/pharmacodynamic modeling approach for drug-drug-gene interaction evaluation of S-warfarin with fluconazole

Warfarin is a widely used anticoagulant, and its S-enantiomer has higher potency compared to the R-enantiomer. S-warfarin is mainly metabolized by cytochrome P450 (CYP) 2C9, and its pharmacological target is vitamin K epoxide reductase complex subunit 1 (VKORC1). Both CYP2C9 and VKORC1 have genetic polymorphisms, leading to large variations in the pharmacokinetics (PKs) and pharmacodynamics (PDs) of warfarin in the population. This makes dosage management of warfarin difficult, especially in the case of drug-drug interactions (DDIs). This study provides a whole-body physiologically-based pharmacokinetic/PD (PBPK/PD) model of S-warfarin for predicting the effects of drug-drug-gene interactions on S-warfarin PKs and PDs. The PBPK/PD model of S-warfarin was developed in PK-Sim and MoBi. Drug-dependent parameters were obtained from the literature or optimized. Of the 34 S-warfarin plasma concentration-time profiles used, 96% predicted plasma concentrations within twofold range compared to observed data. For S-warfarin plasma concentration-time profiles with CYP2C9 genotype, 364 of 386 predicted plasma concentration values (~94%) fell within the twofold of the observed values. This model was tested in DDI predictions with fluconazole as CYP2C9 perpetrators, with all predicted DDI area under the plasma concentration-time curve to the last measurable timepoint (AUClast) ratio within twofold of the observed values. The anticoagulant effect of S-warfarin was described using an indirect response model, with all predicted international normalized ratio (INR) within twofold of the observed values. This model also incorporates a dose-adjustment method that can be used for dose adjustment and predict INR when warfarin is used in combination with CYP2C9 perpetrators.

Kinetics and regulation of coagulation factor X activation by intrinsic tenase on phospholipid membranes

BACKGROUND

Factor X activation by the phospholipid-bound intrinsic tenase complex is a critical membrane-dependent reaction of blood coagulation. Its regulation mechanisms are unclear, and a number of questions regarding diffusional limitation, pathways of assembly and substrate delivery remain open.

METHODS

We develop and analyze here a detailed mechanism-driven computer model of intrinsic tenase on phospholipid surfaces. Three-dimensional reaction-diffusion-advection and stochastic simulations were used where appropriate.

RESULTS

Dynamics of the system was predominantly non-stationary under physiological conditions. In order to describe experimental data, we had to assume both membrane-dependent and solution-dependent delivery of the substrate. The former pathway dominated at low cofactor concentration, while the latter became important at low phospholipid concentration. Factor VIIIa-factor X complex formation was the major pathway of the complex assembly, and the model predicted high affinity for their lipid-dependent interaction. Although the model predicted formation of the diffusion-limited layer of substrate for some conditions, the effects of this limitation on the fXa production were small. Flow accelerated fXa production in a flow reactor model by bringing in fIXa and fVIIIa rather than fX.

CONCLUSIONS

This analysis suggests a concept of intrinsic tenase that is non-stationary, employs several pathways of substrate delivery depending on the conditions, and is not particularly limited by diffusion of the substrate.

Critical evaluation of kinetic schemes for coagulation

Two well-established numerical representations of the coagulation cascade either initiated by the intrinsic system (Chatterjee et al., PLOS Computational Biology 2010) or the extrinsic system (Butenas et al., Journal of Biological Chemistry, 2004) were compared with thrombin generation assays under realistic pathological conditions. Biochemical modifications such as the omission of reactions not relevant to the case studied, the modification of reactions related to factor XI activation and auto-activation, the adaptation of initial conditions to the thrombin assay system, and the adjustment of some of the model parameters were necessary to align in vitro and in silico data. The modified models are able to reproduce thrombin generation for a range of factor XII, XI, and VIII deficiencies, with the coagulation cascade initiated either extrinsically or intrinsically. The results emphasize that when existing models are extrapolated to experimental parameters for which they have not been calibrated, careful adjustments are required.