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Blood coagulation is a vital physiological process involving a complex network of biochemical reactions, which converge to form a blood clot that repairs vascular injury. This process unfolds in three phases: initiation, amplification, and propagation, ultimately leading to thrombin formation. Coagulation begins when tissue factor (TF) is exposed on an injured vessel’s wall. The first step is when activated factor VII (VIIa) in the plasma binds to TF, forming complex TF:VIIa, which activates factor X. Activated factor X (Xa) is necessary for coagulation, so the regulation of its activation is crucial. Tissue Factor Pathway Inhibitor (TFPI) is a critical regulator of the initiation phase as it inhibits the activation of factor X. While previous studies have proposed two pathways—direct and indirect binding—for TFPI’s inhibitory role, the specific biochemical reactions and their rates remain ambiguous. Many existing mathematical models only assume an indirect pathway, which may be less effective under physiological flow conditions. In this study, we revisit datasets from two experiments focused on activated factor X formation in the presence of TFPI. We employ an adaptive Metropolis method for parameter estimation to reinvestigate a previously proposed biochemical scheme and corresponding rates for both inhibition pathways. Our findings show that both pathways are essential to replicate the static experimental results. Previous studies have suggested that flow itself makes a significant contribution to the inhibition of factor X activation. We added flow to this model with our estimated parameters to determine the contribution of the two inhibition pathways under these conditions. We found that direct binding of TFPI is necessary for inhibition under flow. The indirect pathway has a weaker inhibitory effect due to removal of solution phase inhibitory complexes by flow. 

Thrombin is an enzyme produced during blood coagulation that is crucial to the formation of a stable clot. Thrombin cleaves soluble fibrinogen into fibrin, which polymerizes and forms an insoluble, stabilizing gel around the growing clot. A small fraction of circulating fibrinogen is the variant γ A / γ ′, which has been associated with high-affinity thrombin binding and implicated as a risk factor for myocardial infarctions, deep vein thrombosis, and coronary artery disease. Thrombin is also known to be strongly sequestered by polymerized fibrin for extended periods of time in a way that is partially regulated by γ A / γ ′. However, the role of γ A / γ ′-thrombin interactions during fibrin polymerization is not fully understood. Here, we present a mathematical model of fibrin polymerization that considered the interactions between thrombin, fibrinogen, and fibrin, including those with γ A / γ ′. In our model, bivalent thrombin-fibrin binding greatly increased thrombin residency times and allowed for thrombin-trapping during fibrin polymerization. Results from the model showed that early in fibrin polymerization, γ ′ binding to thrombin served to localize the thrombin to the fibrin(ogen), which effectively enhanced the enzymatic conversion of fibrinogen to fibrin. When all the fibrin was fully generated, however, the fibrin-thrombin binding persisted but the effect of fibrin on thrombin switched quickly to serve as a sink, essentially removing all free thrombin from the system. This dual role for γ ′-thrombin binding during polymerization led to a paradoxical decrease in trapped thrombin as the amount of γ ′ was increased. The model highlighted biochemical and biophysical roles for fibrin-thrombin interactions during polymerization and agreed well with experimental observations. 

Abstract Computational models of various facets of hemostasis and thrombosis have increased substantially in the last decade. These models have the potential to make predictions that can uncover new mechanisms within the complex dynamics of thrombus formation. However, these predictions are only as good as the data and assumptions they are built upon, and therefore model building requires intimate coupling with experiments. The objective of this article is to guide the reader through how a computational model is built and how it can inform and be refined by experiments. This is accomplished by answering six questions facing the model builder: (1) Why make a model? (2) What kind of model should be built? (3) How is the model built? (4) Is the model a “good” model? (5) Do we believe the model? (6) Is the model useful? These questions are answered in the context of a model of thrombus formation that has been successfully applied to understanding the interplay between blood flow, platelet deposition, and coagulation and in identifying potential modifiers of thrombin generation in hemophilia A.