Our group develops mechanistic models to understand how therapeutic agents alter thrombin generation and clot formation. These models combine biochemical reaction networks, platelet activation, lipid-surface reactions, flow-mediated transport, and drug-target binding kinetics to predict how treatments reshape the coagulation response.

A major current focus is modeling non-factor therapies for hemophilia. For anti-TFPI therapy, we developed models of concizumab to examine downstream effects in hemophilia A, including effects that are difficult to isolate experimentally. For FVIII-mimetic therapy, we developed mathematical models of emicizumab that analyze affinity-driven complex formation and lipid-surface reactions. These projects ask how drug mechanism, inhibitor kinetics, platelet count, lipid availability, and coagulation factor levels combine to determine thrombin generation and treatment efficacy.

This research is motivated by the changing treatment landscape for hemophilia and related bleeding disorders. Mathematical modeling gives us a way to explore therapeutic and physiologic parameter ranges, compare mechanisms across drugs, and generate hypotheses for experiments and translational studies.

Relevant recent publications:

• Miyazawa et al., "Examining downstream effects of concizumab in hemophilia A with a mathematical modeling approach," Journal of Thrombosis and Haemostasis, 2025.

• Madrigal et al., "Mathematical analysis of emicizumab: affinity-driven complex formation and lipid-surface reactions," Journal of Thrombosis and Haemostasis, 2025.

Patients with the same clinical category of hemophilia or factor deficiency can have very different bleeding phenotypes. Our group uses mechanistic modeling, virtual patient populations, global sensitivity analysis, and experimental collaborations to identify biological modifiers that may help explain this variability.

We vary coagulation factor and inhibitor levels across physiologic ranges and use model outputs as quantitative surrogates for thrombin generation, clot formation, and bleeding risk. This approach has helped identify factor V and combinations of coagulation factors as potential modifiers of thrombin generation in factor VIII, IX, and XI deficient blood.

The long-term goal is to understand how biochemical variation, surface-mediated reactions, and treatment mechanisms combine to shape patient-specific hemostatic response. These models support a more individualized view of bleeding disorders and provide experimentally testable hypotheses about why some patients bleed more than others.

Many key coagulation reactions occur on biological surfaces, including activated platelets, lipid vesicles, and other phosphatidylserine-rich membranes. These surfaces do more than provide a passive platform: surface area, binding-site density, enzyme distribution, and molecular localization can change reaction rates and alter the overall coagulation response.

Our group develops continuum, stochastic, and discrete models of lipid-surface and platelet-surface reactions. Recent work has focused on how enzyme distributions on lipid vesicles affect surface-mediated coagulation reactions, how binding-site distributions shape reaction outcomes, and how TFPI, protein S, and TFPIalpha-fVshort-protein S complexes regulate thrombin generation.

These models help connect biochemical rate measurements to the spatial and surface-dependent reality of coagulation. They also provide a foundation for understanding drug action, because therapies such as concizumab and emicizumab act in networks where surface localization and binding kinetics strongly influence outcome.

Relevant recent publications:

• Madrigal et al., "Modeling the distribution of enzymes on lipid vesicles: A novel framework for surface-mediated reactions in coagulation," Mathematical Biosciences, 2024.

• Cao, Sen Gupta, and Leiderman, "Continuum and discrete modeling of binding-site distribution-mediated reactions on lipid surfaces," Biophysical Journal, 2026.

• Ginsberg et al., "Mechanisms of thrombin inhibition by protein S and the TFPIalpha-fVshort-protein S complex," Biophysical Journal, 2026.

• Santiago et al., "A new look at TFPI inhibition of factor X activation," PLOS Computational Biology, 2024.

Thrombin is central to clot formation, but its role is shaped by interactions with fibrin and by the evolving structure of the clot itself. Our group develops mathematical models of thrombin-fibrin binding and fibrin polymerization to understand how biochemical binding, physical trapping, and polymer structure regulate clot growth and stability.

Our models have suggested that part of thrombin's long-lived association with fibrin may arise from physical trapping within fibrin fibers during polymerization. We also study how bivalent thrombin-fibrin binding and fibrinogen variants may regulate thrombin localization, sequestration, and downstream coagulation.

This work connects molecular-scale binding mechanisms to larger questions about clot stability, fibrinolysis, and therapeutic modulation of coagulation.

Relevant recent publications:

• Kelley and Leiderman, "A mathematical model of bivalent binding suggests physical trapping of thrombin within fibrin fibers," Biophysical Journal, 2019.

• Kelley and Leiderman, "Mathematical modeling to understand the role of bivalent thrombin-fibrin binding during polymerization," PLOS Computational Biology, 2022.

• Nelson, Kelley, Haynes, and Leiderman, "Mathematical models of fibrin polymerization: Past, present, and future," Current Opinion in Biomedical Engineering, 2021.