A mathematical model for activated platelet-dependent activation of coagulation factor X by factor IXa

Membrane-dependent enzymatic reactions are central in many signaling and regulatory biological networks. Activation of blood coagulation factor X by activated factor IXa is a classical example, which retains many mysteries and controversies. Here we developed a novel non-stationary two-compartment computational model of this reaction on the physiological membrane of activated platelets (rather than phospholipid vesicles) within a wide platelet concentration range up to the intra-thrombus conditions, which took into account novel essential revisions in the mechanisms on factor IXa interactions with platelets. The set of ordinary differential equations (ODEs) was based on the laws of mass action and included several possible pathways of the complex formation. Sensitivity analysis was employed to identify critical points in the regulation. The model was able to describe the available experimental data and suggested that the major pathways of the enzyme-substrate complex assembly were membrane-dependent and solution-dependent enzyme delivery, with comparable contributions. The dependence of factor Xa formation on the activated procoagulant platelet concentration was predicted to be bell-shaped with the peak at (1.5-2)·10⁶ platelets/μL, which is similar to the expected intra-thrombus concentration. The modeling of the kinetics of all model variables demonstrated two-phase kinetics. With increasing platelet concentration in the system, the transition time after which a stationary concentration is reached increases to approximately 5 min.