A Mathematical Model of Bivalent Binding Suggests Physical Trapping of Thrombin within Fibrin Fibers

Abstract

Thrombin is an enzyme that plays many important roles in the blood clotting process; it activates platelets, cleaves coagulation proteins within feedback loops, and cleaves fibrinogen into fibrin, which polymerizes into fibers to form a stabilizing gel matrix in and around growing clots. Thrombin also binds to the formed fibrin matrix, but this interaction is not well understood. Thrombin-fibrin binding is often described as two independent, single-step binding events, one high-affinity and one low-affinity. However, kinetic schemes describing these single-step binding events do not explain experimentally-observed residency times of fibrin-bound thrombin. In this work, we study a bivalent, sequential-step binding scheme as an alternative to the high-affinity event and, in addition to the low-affinity one. We developed mathematical models for the single- and sequential-step schemes consisting of reaction-diffusion equations to compare to each other and to experimental data. We then used Bayesian inference, in the form of Markov chain Monte Carlo, to learn model parameter distributions from previously published experimental data. For the model to best fit the data, we made an additional assumption that thrombin was irreversibly sequestered; we hypothesized that this could be due to thrombin becoming physically trapped within fibrin fibers as they formed. We further estimated that ∼30% of thrombin in the experiments to which we compare our model output became physically trapped. The notion of physically trapped thrombin may provide new insights into conflicting observations regarding the speed of fibrinolysis. Finally, we show that our new model can be used to further probe scenarios dealing with thrombin allostery.