A kinetic model for simulation of blood coagulation and inhibition in the intrinsic path

A Review of Quantitative Systems Pharmacology Models of the Coagulation Cascade: Opportunities for Improved Usability

Despite the numerous therapeutic options to treat bleeding or thrombosis, a comprehensive quantitative mechanistic understanding of the effects of these and potential novel therapies is lacking. Recently, the quality of quantitative systems pharmacology (QSP) models of the coagulation cascade has improved, simulating the interactions between proteases, cofactors, regulators, fibrin, and therapeutic responses under different clinical scenarios. We aim to review the literature on QSP models to assess the unique capabilities and reusability of these models. We systematically searched the literature and BioModels database reviewing systems biology (SB) and QSP models. The purpose and scope of most of these models are redundant with only two SB models serving as the basis for QSP models. Primarily three QSP models have a comprehensive scope and are systematically linked between SB and more recent QSP models. The biological scope of recent QSP models has expanded to enable simulations of previously unexplainable clotting events and the drug effects for treating bleeding or thrombosis. Overall, the field of coagulation appears to suffer from unclear connections between models and irreproducible code as previously reported. The reusability of future QSP models can improve by adopting model equations from validated QSP models, clearly documenting the purpose and modifications, and sharing reproducible code. The capabilities of future QSP models can improve from more rigorous validation by capturing a broader range of responses to therapies from individual patient measurements and integrating blood flow and platelet dynamics to closely represent in vivo bleeding or thrombosis risk.

Effect of Australian elapid venoms on blood coagulation: Australian Snakebite Project (ASP-17)

Snake venoms contain toxins that activate the coagulation network and cause venom-induced consumption coagulopathy. A previously developed mathematical model of the coagulation network was refined and used to describe and predict the time course of changes in the coagulation factors following envenomation by Brown snake (Pseudonaja spp.), Tiger snake (Notechis scutatus), Rough-scaled snake (Tropidechis carinatus) and Hoplocephalus spp. (Stephens banded, Pale headed and Broad headed). Simulations of the time course of the change in coagulation factors were compared to data obtained from a large prospective study of Australian snake bites - the Australian Snakebite Project. The model predictions were also compared against data for partial and complete VICC obtained from the same study. The model simulations were used to understand the differences in consumption and recovery of clotting factors in partial versus complete VICC as well as among bites from different snake types. The model suggested that the venoms were absorbed almost instantaneously and provided a reasonable prediction of the observed concentration of clotting factors over time in patients bitten by Australian elapid snakes. The model predictions suggested a higher consumption of factors (fibrinogen, II and IX in particular) in patients with complete VICC compared to those with partial VICC. The model also predicted that snakes with "Xa-like" venoms may produce a less severe VICC than snakes with "Xa:Va-like" venoms.

Modeling of human factor Va inactivation by activated protein C

BACKGROUND

Because understanding of the inventory, connectivity and dynamics of the components characterizing the process of coagulation is relatively mature, it has become an attractive target for physiochemical modeling. Such models can potentially improve the design of therapeutics. The prothrombinase complex (composed of the protease factor (F)Xa and its cofactor FVa) plays a central role in this network as the main producer of thrombin, which catalyses both the activation of platelets and the conversion of fibrinogen to fibrin, the main substances of a clot. A key negative feedback loop that prevents clot propagation beyond the site of injury is the thrombin-dependent generation of activated protein C (APC), an enzyme that inactivates FVa, thus neutralizing the prothrombinase complex. APC inactivation of FVa is complex, involving the production of partially active intermediates and "protection" of FVa from APC by both FXa and prothrombin. An empirically validated mathematical model of this process would be useful in advancing the predictive capacity of comprehensive models of coagulation.

RESULTS

A model of human APC inactivation of prothrombinase was constructed in a stepwise fashion by analyzing time courses of FVa inactivation in empirical reaction systems with increasing number of interacting components and generating corresponding model constructs of each reaction system. Reaction mechanisms, rate constants and equilibrium constants informing these model constructs were initially derived from various research groups reporting on APC inactivation of FVa in isolation, or in the presence of FXa or prothrombin. Model predictions were assessed against empirical data measuring the appearance and disappearance of multiple FVa degradation intermediates as well as prothrombinase activity changes, with plasma proteins derived from multiple preparations. Our work integrates previously published findings and through the cooperative analysis of in vitro experiments and mathematical constructs we are able to produce a final validated model that includes 24 chemical reactions and interactions with 14 unique rate constants which describe the flux in concentrations of 24 species.

CONCLUSION

This study highlights the complexity of the inactivation process and provides a module of equations describing the Protein C pathway that can be integrated into existing comprehensive mathematical models describing tissue factor initiated coagulation.

Blood coagulation dynamics: mathematical modeling and stability results

The hemostatic system is a highly complex multicomponent biosystem that under normal physiologic conditions maintains the fluidity of blood. Coagulation is initiated in response to endothelial surface vascular injury or certain biochemical stimuli, by the exposure of plasma to Tissue Factor (TF), that activates platelets and the coagulation cascade, inducing clot formation, growth and lysis. In recent years considerable advances have contributed to understand this highly complex process and some mathematical and numerical models have been developed. However, mathematical models that are both rigorous and comprehensive in terms of meaningful experimental data, are not available yet. In this paper a mathematical model of coagulation and fibrinolysis in flowing blood that integrates biochemical, physiologic and rheological factors, is revisited. Three-dimensional numerical simulations are performed in an idealized stenosed blood vessel where clot formation and growth are initialized through appropriate boundary conditions on a prescribed region of the vessel wall. Stability results are obtained for a simplified version of the clot model in quiescent plasma, involving some of the most relevant enzymatic reactions that follow Michaelis-Menten kinetics, and having a continuum of equilibria.

The limits of simulation of the clotting system

OBJECTIVE

To investigate in how far successful simulation of a thrombin generation (TG) curve gives information about the underlying biochemical reaction mechanism.

RESULTS

The large majority of TG curves do not contain more information than can be expressed by four parameters. A limited kinetic mechanism of six reactions, comprising proteolytic activation of factor (F) X and FII, feedback activation of FV, a cofactor function of FVa and thrombin inactivation by antithrombin can simulate any TG curve in a number of different ways. The information content of a TG curve is thus much smaller than the information required to describe a physiologically realistic reaction scheme of TG. Consequently, much of the input information is irrelevant for the output. FVIII deficiency or activation of protein C can, for example, be simulated by a reaction mechanism in which these factors do not occur.

CONCLUSION

A model that comprises not more than six reactions can simulate the same TG curve in a number of possible ways. The possibilities increase exponentially as the model grows more realistic. Successful simulation of experimental data therefore does not validate the underlying assumptions. A fortiori, simulation that is not checked against experimental data lacks any probative force. Simulation can be of use, however, to detect mistaken hypotheses and for parameter estimation in systems with fewer than five free parameters.

Mathematical modeling of material-induced blood plasma coagulation

Contact activation of the intrinsic pathway of the blood coagulation cascade is initiated when a procoagulant material interacts with coagulation factor XII, (FXII) yielding a proteolytic enzyme FXIIa. Procoagulant surface properties are thought to play an important role in activation. To study the mechanism of interaction between procoagulant materials and blood plasma, a mathematical model that is similar in form and in derivation to Michaelis-Menten enzyme kinetics was developed in order to yield tractable relationships between dose (surface area and energy) and response (coagulation time (CT)). The application of this model to experimental data suggests that CT is dependent on the FXIIa concentration and that the amount of FXIIa generated can be analyzed using a model that is linearly dependent on contact time. It is concluded from these experiments and modeling analysis that the primary mechanism for activation of coagulation involves autoactivation of FXII by the procoagulant surface or kallikrein-mediated reciprocal activation of FXII. FXIIa-induced self-amplification of FXII is insignificant.