Mathematical Model of Serine Protease Inhibition in the Tissue Factor Pathway to Thrombin

Abstract

A mathematical model has been developed to simulate the generation of thrombin by the tissue factor pathway. The model gives reasonable predictions of published experimental results without the adjustment of any parameter values. The model also accounts explicitly for the effects of serine protease inhibitors on thrombin generation. Simulations to define the optimum affinity profile of an inhibitor in this system indicate that for an inhibitor simultaneously potent against VIIa, IXa, and Xa, inhibition of thrombin generation decreases dramatically as the affinity for thrombin increases. Additional simulations show that the reason for this behavior is the sequestration of the inhibitor by small amounts of thrombin generated early in the reaction. This model is also useful for predicting the potency of compounds that inhibit thrombosis in rats. We believe that this is the first mathematical model of blood coagulation that considers the effects of exogenous inhibitors. Such a model, or extensions thereof, should be useful for evaluating targets for therapeutic intervention in the processes of blood coagulation.The clotting of blood is an exquisitely complex process. The simultaneous requirements for the free flow of blood under normal conditions and rapid clotting to prevent blood loss in the case of injury require a delicate balance between clot formation and clot lysis. Taken together, these processes involve more than 30 proteins, at least 10 of which are serine proteases. Inhibitors of serine proteases occur as natural anticoagulants, and natural and synthetic inhibitors have been widely studied for therapeutic applications in the prevention of thrombosis (1).When choosing candidate serine protease inhibitors for therapeutic use, the choice of a target enzyme may be less than obvious. Many of the enzymes have multiple activities, there is positive and negative feedback regulation, and there are alternative pathways for activation and inactivation. In addition, serine protease inhibitors (especially synthetic compounds) generally have a spectrum of activities due to the high degrees of homology among the blood coagulation factors. This raises the question of whether the best antithrombotic compound would be specific for a single enzyme or show affinities for several serine proteases (2).Mathematical modeling can help us understand such complex systems, but published models of blood coagulation suffer from the following limitations: consideration of only a small part of the coagulation cascade (3-7), empirical description of interactions for which molecular mechanisms were known (3, 8, 9), determination of some (4, 9, 10) or all (3, 11) of the parameter values from the experimental data to which the model predictions were then compared (curve fitting), and the absence of comparisons of model predictions to experimental data (6,(12)(13)(14). In the best of these studies (4, 5, 7), most or all of the parameter values were independently determined, model predictions were compared to experimental results that had not...

Studies on the Different Modes of Action of the Anticoagulant Protease Inhibitors DX-9065a and Argatroban

“…The Mathematical Model-The enzyme reactions used in the current model are similar to those described earlier for the mathematical modeling of extrinsically triggered blood coagulation (7,8), except that antithrombin-III and fibrinogen/fibrin are additionally incorporated into the model, but the involvement of meizothrombin described in the previous literatures (7,8) is not considered in the current study. The reaction scheme used in the current model is summarized in Fig.…”

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Mathematical Models of Blood Coagulation and Platelet Adhesion: Clinical Applications

“…The mathematical model of TF-initiated thrombin generation in reconstituted systems developed by Jones and Mann [17] was used with modifications by other groups to study the effects of various therapeutic agents and mechanisms of their action. Leipold et al [57] advanced this model to include exogenous serine protease inhibitors with affinity for any or all of coagulation factors VIIa, IXa, Xa, and IIa. Application of the revised model for predicting the affinity profile of the optimal inhibitor and the inhibitory potency of several compounds revealed the following: 1) The predicted thrombin generation times are mostly insensitive to changes in the affinity at the inhibition constant K i >1 nM; 2) However, for compounds with high affinity for both FVIIa and FIXa, inhibition of thrombin generation decreases as the affinity for thrombin increases (K i from 1000 to 5 nM); 3) Inhibitors with affinity for a single serine protease are less potent compared to inhibitors with a spectrum of affinities; 4) Compounds with high affinity for FVIIa, FXa and thrombin are predicted to be highly-potent, regardless of their affinity for FIXa.…”

Dynamic Modeling of the Human Coagulation Cascade Using Reduced Order Effective Kinetic Models

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