A model for the tissue factor pathway to thrombin. II. A mathematical simulation.

A mathematical simulation of the tissue factor pathway to the generation of thrombin has been developed using a combination of empirical, estimated, and deduced rate constants for reactions involving the activation of factor IX, X, V, and VIII, in the formation of thrombin, as well as rate constants for the assembly of the coagulation enzyme complexes which involve factor VIIIa-factor IXa (intrinsic tenase) and factor Va-Xa (prothrombinase) assembled on phospholipid membrane. Differential equations describing the fate of each species in the reaction were developed and solved using an interactive procedure based upon the Runge-Kutta technique. In addition to the theoretical considerations involving the reactions of the tissue factor pathway, a physical constraint associated with the stability of the factor VIIIa-factor IXa complex has been incorporated into the model based upon the empirical observations associated with the stability of this complex. The model system provides a realistic accounting of the fates of each of the proteins in the coagulation reaction through a range of initiator (factor VIIa-tissue factor) concentrations ranging from 5 pM to 5 nM. The model is responsive to alterations in the concentrations of factor VIII, factor V, and their respective activated species, factor VIIIa and factor Va, and overall provides a reasonable approximation of empirical data. The computer model permits the assessment of the reaction over a broad range of conditions and provides a useful tool for the development and management of reaction studies.