Applied Math Capstone Projects

Blood coagulation is a series of biochemical reactions necessary to form a blood clot upon a vascular injury. The process occurs in three stages (initiation, amplification, and propagation) and in the presence of flow. To regulate bleeding disorders, the clotting system involves inhibition mechanisms at each stage. Initiation in the tissue factor pathway begins when clotting factor VIIa in the plasma binds its cofactor, tissue factor (TF) forming an active enzyme complex (TF:VIIa). Next, clotting factor X in the plasma binds with TF:VIIa and is enzymatically cleaved into activated factor X (Xa). Xa is required for other reactions as coagulation progresses.Tissue factor pathway inhibitor (TFPI) is known to be a strong inhibitor during the initiation phase, with the primary mechanism of binding to Xa in the plasma and then rebinding to TF:VIIa to form the quaternary complex TF:VIIa:Xa:TFPI. However, previous mathematical models of TFPI inhibition predict contradicting results. Some studies suggest that TFPI is a powerful inhibitor for Xa inhibition and others claim that it is a weak inhibitor because flow acts as a more potent inhibitor than TFPI. In this study, I reinvestigated the mechanisms of TFPI inhibition by considering a previous static experimental study of TFPI by Baugh et. al [2] where two inhibitory mechanisms were hypothesized to exist. The suggested reaction scheme, which incorporated both an Indirect Binding mechanism and a Direct Binding mechanism for TFPI inhibition, was never studied by Baugh et. al. [2]. I used a mathematical model based on this scheme and a constrained optimization framework to fit this proposed reaction scheme to multiple sets of data simultaneously. I found that this scheme for TFPI better fits the experimental data, explains the role of TFPI in regulating factor Xa under static conditions, and is consistent with the previously known kinetic rates and rate constants.Next, I studied the two mechanisms in the presence of flow to understand which mechanism can explain the role of TFPI in inhibiting the formation of Xa. I discovered that Direct Binding mechanism is essential for Xa inhibition by TFPI in the presence of flow.

Keywords: Mathematical modeling, TFPI, factor X, constrained optimization,parameter estimation.