Coagulation Makes Waves

Human life depends on the fact that blood remains fluid while it is in the vessels, but clots promptly when released by injury. Nature accomplishes this balancing act by means of a collection of a dozen or so proteases and cofactors, arranged in a reaction network, as described formally in Panteleev et al. (1xTask-oriented modular decomposition of biological networks: trigger mechanism in blood coagulation. Panteleev, M.A., Balandina, A.N...., and Ataullakhanov, F.I. Biophys. J. 2010; 98: 1751–1761Abstract | Full Text | Full Text PDF | PubMed | Scopus (19)See all References1). The proteases normally circulate in the form of inactive pro-enzymes that can be activated by proteolytic cleavage. Once activated, they cleave and activate other proteases, forming a cascade that powerfully amplifies the initial signal. The cascade begins with so-called “tissue factors,” substances that are exposed to blood when tissues are injured. The end of the cascade is activated factor II (IIa, aka thrombin), which cleaves fibrinogen to form fibrin—the protein polymer that forms the physical body of the clot.Dashkevich et al. (2xThrombin activity propagates in space during blood coagulation as an excitation wave. Dashkevich, N.M., Ovanesov, M.V...., and Ataullakhanov, F.I. Biophys. J. 2012; 103: 2233–2240Abstract | Full Text | Full Text PDF | PubMed | Scopus (24)See all References2) in this issue took note of the fact that this highly nonlinear process contains a positive feedback loop because thrombin can also cleave factor XI, higher up in the cascade (3xFeedback activation of factor XI by thrombin in plasma results in additional formation of thrombin that protects fibrin clots from fibrinolysis. von dem Borne, P.A., Meijers, J.C., and Bouma, B.N. Blood. 1995; 86: 3035–3042PubMedSee all References3). This suggested that the coagulation system might function as an excitable medium, able to propagate autonomous waves of activation in the same way that a nerve fiber conducts an action potential. To test this hypothesis, they devised an apparatus in which a one-dimensional clotting reaction—instigated by tissue factor at x = 0—could be monitored optically.Thrombin itself is invisible, so the investigators devised a peptide that can be cleaved by thrombin, releasing a fluorophore. To work backward from the fluorescence image to the thrombin distribution, they had to reverse-engineer the reaction-diffusion equation describing this process. Despite the well-known numerical difficulties in inverting such equations, they achieved a usable thrombin image, and demonstrated that the clotting process can, in fact, propagate as an autonomous wave front at the constant—if snail-like—velocity of 20–50 μm/min.To further understand the mechanism, they modified their previous mathematical model of the coagulation cascade (1xTask-oriented modular decomposition of biological networks: trigger mechanism in blood coagulation. Panteleev, M.A., Balandina, A.N...., and Ataullakhanov, F.I. Biophys. J. 2010; 98: 1751–1761Abstract | Full Text | Full Text PDF | PubMed | Scopus (19)See all References1) by adding diffusion terms and the presence of the fluorogenic peptide. This gave a system of 24 partial and two ordinary differential equations, which they numerically integrated. The resulting simulation successfully recapitulated the experimental results, and confirmed that the positive feedback loop from thrombin to factor XI was critical for propagation.To test this conclusion, they repeated the experiment using plasma from patients with hemophilia C, a rare genetic bleeding disorder in which factor XI is absent. As predicted, a sustained, autonomous wave did not form. It has been a long-standing puzzle why hemophilia C causes serious bleeding—particularly from large wounds—when factor XI is only a relatively minor component of the clotting cascade, and one that can be bypassed by other pathways. Based on their experimental and theoretical results, the authors hypothesize that the importance of factor XI lies precisely in its ability to propagate the clotting front far from the injured tissue surface, in order to seal large wounds. They also found that propagation depends on the presence of the cofactor factor VIII, shedding further light on the pathophysiology of the more common Hemophilia A in which that factor is deficient.This work is especially notable for the integration (no pun intended) of theoretical, methodological, and experimental studies. Those of us who do modeling are often tempted simply to demonstrate that a certain mechanism is possible and leave it to others to relate the work to the real world. By intertwining experimental, theoretical, and numerical techniques, these investigators were able to go from a mathematical curiosity to an established mechanism and a proposed solution of a riddle of clinical importance. This is an exemplar of how biophysics should work.