Proteolytic reactions on the phospholipid membrane surface, so-called "membrane-dependent" reactions, play central role in the process of blood clotting. One particularly important example is FX activation by the extrinsic tenase (VIIa/TF). Here we constructed three mathematical models of FX activation by VIIa/TF: (A) a homogeneous "well-mixed" model, (B) a two-compartment "well-mixed" model, (C) a heterogeneous model with diffusion, to investigate the impact and importance of inclusion of each complexity level. All models provided good description of the reported experimental data and were equivalently applicable for <40 μM of phospholipids. Model C provided better predictions than A, B in the presence of TF-negative phospholipid microparticles. Models predicted that for high TF surface density (STF ) and FX deficiency the FX activation rate was limited by the rate of FX binding to the membrane. For low STF and excess of FX the reaction rate was limited by the tenase formation rate. The analysis of the substrate delivery pathways revealed that FX bound to VIIa/TF predominantly from solution for STF >2.8 × 10-3 nmol/cm2 and from the membrane for lower STF . We proposed the experimental setting to distinguish between the collision-limited and non-collision-limited binding. The analysis of models in flow and non-flow conditions revealed that the model of a vesicle in flow might be substituted by model C in the absence of the substrate depletion. Together, this study was the first which provided the direct comparison of more simple and more complex models. The reaction mechanisms were studied in a wide range of conditions.
Keywords: blood clotting; computational modeling; initiation; reaction mechanisms.
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