A mathematical model of plasmin-mediated fibrinolysis of single fibrin fibers

Fibrinolysis, the plasmin-mediated degradation of the fibrin mesh that stabilizes blood clots, is an important physiological process, and understanding mechanisms underlying lysis is critical for improved stroke treatment. Experimentalists are now able to study lysis on the scale of single fibrin fibers, but mathematical models of lysis continue to focus mostly on fibrin network degradation. Experiments have shown that while some degradation occurs along the length of a fiber, ultimately the fiber is cleaved at a single location. We built a 2-dimensional stochastic model of a fibrin fiber cross-section that uses the Gillespie algorithm to study single fiber lysis initiated by plasmin. We simulated the model over a range of parameter values to learn about patterns and rates of single fiber lysis in various physiological conditions. We also used epifluorescent microscopy to measure the cleavage times of fibrin fibers with different apparent diameters. By comparing our model results to the laboratory experiments, we were able to: 1) suggest value ranges for unknown rate constants(namely that the degradation rate of fibrin by plasmin should be ≤ 10 s−1 and that if plasmin crawls, the rate of crawling should be between 10 s−1 and 60 s−1); 2) estimate the fraction of fibrin within a fiber cross-section that must be degraded for the fiber to cleave in two; and 3) propose that that fraction is higher in thinner fibers and lower in thicker fibers. Collectively, this information provides more details about how fibrin fibers degrade, which can be leveraged in the future for a better understanding of why fibrinolysis is impaired in certain disease states, and could inform intervention strategies.Author summary: Fibrinolysis, the enzymatic degradation of the fibrin fibers that stabilize blood clots, plays an important role in preventing heart attacks and strokes during wound healing. Because blood clots exhibit multiscale structural features, a wholistic understanding of clot degradation requires knowledge of how single enzymatic reactions propagate through the larger-scale clot features. Limitations of experimental techniques typically restrict their results to one spatial scale, so mathematical models have the potential to explain the origins of experimental results and act as a bridge that connect results across spatial scales. Recent experimental results have probed mechanisms regulating the digestion of individual fibrin fibers, however mathematical models of fibrinolysis continue to focus mostly on the degradation of full fibrin clots. We built a 2-dimensional stochastic fibrinolysis model to interrogate the digestion of single fibrin fibers by plasmin, the primary fibrinolytic enzyme. By comparing our model results to laboratory experiments of fiber degradation, we estimated previously unmeasurable lysis rates, demonstrated that plasmin likely crawls between protofibrils, and approximated the fraction of a fiber that must be degraded prior to cleavage. This foundational mathematical model could be leveraged in the future to determine mechanistic origins of certain disease states and could inform intervention strategies.