A Model for the Stoichiometric Regulation of Blood Coagulation

Abstract

We have developed a model of the extrinsic blood coagulation system that includes the stoichiometric anticoagulants. The model accounts for the formation, expression, and propagation of the vitamin K-dependent procoagulant complexes and extends our previous model by including: (a) the tissue factor pathway inhibitor (TFPI)-mediated inactivation of tissue factor (TF)⅐VIIa and its product complexes; (b) the antithrombin-III (AT-III)-mediated inactivation of IIa, mIIa, factor VIIa, factor IXa, and factor Xa; (c) the initial activation of factor V and factor VIII by thrombin generated by factor Xa-membrane; (d) factor VIIIa dissociation/activity loss; (e) the binding competition and kinetic activation steps that exist between TF and factors VII and VIIa; and (f) the activation of factor VII by IIa, factor Xa, and factor IXa. These additions to our earlier model generate a model consisting of 34 differential equations with 42 rate constants that together describe the 27 independent equilibrium expressions, which describe the fates of 34 species. Simulations are initiated by "exposing" picomolar concentrations of TF to an electronic milieu consisting of factors II, IX, X, VII, VIIa, V, and VIIII, and the anticoagulants TFPI and AT-III at concentrations found in normal plasma or associated with coagulation pathology. The reaction followed in terms of thrombin generation, proceeds through phases that can be operationally defined as initiation, propagation, and termination. The generation of thrombin displays a nonlinear dependence upon TF, AT-III, and TFPI and the combination of these latter inhibitors displays kinetic thresholds. At subthreshold TF, thrombin production/ expression is suppressed by the combination of TFPI and AT-III; for concentrations above the TF threshold, the bolus of thrombin produced is quantitatively equivalent. A comparison of the model with empirical laboratory data illustrates that most experimentally observable parameters are captured, and the pathology that results in enhanced or deficient thrombin generation is accurately described.

Structural Requirements for Expression of Factor Va Activity

“…The apparent activity of single chain factor V is a consequence of a limited amount of cleavage, which produces the active cofactor during the initial phase of the assay (63,64). In experiments using purified factor Xa, prothrombin, and phospholipid in the presence of the fluorescent thrombin inhibitor DAPA, which prevents feedback activation of single chain factor V, measurements of factor V activity give results that are 400-fold lower than for thrombin-activated factor V (3).…”

A Model Incorporating Some of the Mechanical and Biochemical Factors Underlying Clot Formation and Dissolution in Flowing Blood

“…This trend has continued with the emergence of models characterized by extremely large systems of equations (ODEs or reaction-diffusion equations) with inclusion of a greater number of aspects (flow rates, membrane binding site densities, availability of phospholipid sites, concentration of calcium, extent of activating stimulus, etc.) like those in Liepold et al (1995), Zarnitsina et al (1996a,b), Kuharsky and Fogelson (2001), Ataullakhanov et al (2002a,b), Hockin et al (2002) and Bungay et al (2003). At this stage, investigators are also beginning to consider whether these model systems can effectively capture the growth of clots or thrombi; our model is a step in this direction.…”

“…They also reported that the responses of their models are conditioned by the enzyme kinetics, the presence of feed back loops, and the extent of inhibition. Jones and Mann (1994) presented an early large scale model for thrombin generation via the extrinsic pathway, and extended it to include the role of inhibitors (Hockin et al, 2002). Basmadjian and coworkers investigated the possible steady states of their models, and also studied the regulation of the activation threshold by flow rate, surface area (of injury, say) and the type of surface (Baldwin and Basmadjian, 1994;Gregory and Basmadjian, 1994;Basmadjian et al, 1997).…”

Calibrating Thrombin Generation in Different Samples: Less Effort with a Less Efficient Substrate

“…Although it was developed half a century ago [1,2], it is only during the last one and a half decade that the thrombin generation test has attracted increasing attention. It appears that this test may replace coagulation based tests in many cases in the future [3,4], more so as computer aided models of the events leading to coagulation have been developed and been shown to correlate well with biochemical observations [5,6].…”