Mathematical modeling to understand the role of bivalent thrombin-fibrin binding during polymerization

Abstract

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 γA/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 γA/γ′. However, the role of γA/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 γA/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. Author summary We developed a mathematical model of fibrin polymerization that explicitly incorporated thrombin-fibrin(ogen) interactions, including the γ′ variant of fibrin(ogen). This variant is associated with clots that are more resistant to fibrinolysis and is therefore implicated as a risk factor in cardiovascular disease. However, the underlying mechanism it is not completely understood. We previously modeled γ′-thrombin interactions in a preformed fibrin clot and hypothesized that some thrombin became physically trapped within the clot during its formation (fibrin polymerization). We developed the model in this study to test that hypothesis and determine the role of γ′ during polymerization. The new model showed the plausibility of large amounts of thrombin being trapped within fibrin fibers during polymerization and suggested a dual role for γ′ during polymerization: localization of thrombin to the fibrin(ogen) during an initial early phase of polymerization and sequestration of thrombin during the later phase. The model results suggested a new regulatory mechanism for fibrin polymerization.