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Mathematical modeling of fibrin-thrombin interactions: from bivalent binding to polymerization
Kelley, Michael A.
Kelley, Michael A.
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2022
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Blood clotting is the natural response to injury to seal a wound or damaged blood vessel and prevent bleeding. During the clotting process, the enzyme thrombin is produced and cleaves fibrinogen into fibrin, a protein that polymerizes to form a stabilizing fiber meshwork around the clot. A small fraction of circulating fibrinogen is the variant $\gamma_A/\gamma'$, 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 potentially regulated by $\gamma_A/\gamma'$, but the mechanism is not fully understood. This research was motivated by the questions: (1) what is the mechanism underlying sequestration of thrombin by polymerized fibrin? (2) what is the role of $\gamma_A/\gamma'$-thrombin interactions during fibrin polymerization? A mathematical modeling approach was used to address these questions. A kinetic scheme for bivalent thrombin-fibrin binding was hypothesized and verified using a reaction-diffusion model and experimental data. That model led to a further hypothesis that thrombin becomes physically and irreversibly trapped inside of fibrin fibers during polymerization. Since that model did not describe polymerization events, a new ordinary differential equation model of polymerization that incorporated thrombin-fibrin interactions was developed to test the hypothesis. Bivalent thrombin-fibrin binding was found to greatly increase thrombin residency times, which allowed for thrombin-trapping as the fibrin polymerized, validating the hypothesis. Additionally, during early fibrin polymerization, $\gamma'$-binding to thrombin served to localize thrombin to the fibrin(ogen), effectively enhancing enzymatic conversion of fibrinogen to fibrin. Once all fibrin was fully produced, the fibrin-thrombin binding persisted but switched roles to become a thrombin sink, essentially removing all of the thrombin from the system. This two-phase role for $\gamma'$-thrombin binding during polymerization led to a paradoxical decrease in trapped thrombin as the number of $\gamma'$-binding sites were increased, as is observed experimentally. These novel mathematical models highlight biochemical and biophysical roles for fibrin-thrombin interactions during and after fibrin polymerization and agree well with experimental observations.
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