Understanding blood clot formation could lead to new strategies to effectively control bleeding

Developing computational tools to understand the molecular basis of human disease is a grand challenge facing systems biology. Many have suggested that the integration of experimental and computational research is required to unravel critical questions facing molecular medicine. Despite this, mechanistic network modeling has not played a significant role in the development of new therapies for cancer, cardiovascular diseases or for acute events like thrombosis during surgery. A critical limiting issue often cited has been model uncertainty. Development and validation of detailed network models requires a significant investment of time and material resources. Alternatively, development of tools using toy models often fails to demonstrate relevance to biologists or physicians. What is needed is a model system, that is simultaneously tractable and directly applicable to the study of disease. Human blood is perhaps such an ideal model system. Blood is a complex mixture of proteins and cells which collectively carry out many functions. However, one well studied facet of blood, which could serve as a valuable model system, is the coagulation cascade.

Fig. 1: Schematic of the extrinsic and intrinsic coagulation cascade. Upstream coagulation factors are activated by materials exposed following vessel injury chief among these Tissue Factor (TF). TF and activated factor VIIa (FVIIa) form a complex that activates factor X (fX) and IX (fIX). FXa activates downstream factors including factor VIII (fVIII) and fIX. Factor V (fV) is primarily activated by thrombin (FIIa). In addition, we included a secondary fV activation route involving FXa. FXa and FVa form a complex (prothrombinase) on activated platelets that converts prothrombin (fII) to FIIa. FIXa and FVIIIa can also form a complex (tenase) on activated platelets which that catalyzes FXa formation. Localized platelets are activated by external signals such as adenosine diphosphate (ADP) and thromboxane A2 (TXA2) or thrombin through protease-activated receptors (PARs). Thrombin also activates upstream coagulation factors, forming a strong positive feedback ensuring rapid activation. Tissue Factor Pathway Inhibitor (TFPI) downregulates FXa formation and activity by sequestering free FXa and TF-FVIIa in a FXa dependent manner. Antithrombin III (ATIII) neutralizes all proteases, making it perhaps the most powerful control element in the cascade. Thrombin itself plays an inadvertent role in its own inhibition by binding the surface protein thrombomodulin (TM), expressed on normal vasculature. The IIa-TM complex catalyzes the conversion of protein C (PC) to activated protein C (APC). APC attenuates the coagulation response by the proteolytic cleavage of fV/FVa and fVIII/FVIIIa.

In this study, we constructed a mechanistic model of coagulation in normal and hemophilic blood. We used this model to understand how physiological coagulation was altered by exogenous rFVIIa and prothrombin under different conditions. The current model described 193 proteins and protein complexes and 301 interactions (Fig. 1). Deterministic model equations were formulated as a system of non-linear Ordinary Differential Equations (ODEs). We assumed spatial homogeneity. However, we differentiated between fluid phase, endothelial and platelet localized species and processes. We used mass-action kinetics to describe the rate of each molecular interaction. The model had 467 unknown parameters (301 kinetic parameters and 166 initial conditions). The 301 kinetic parameters were either association, dissociation or catalytic rate constants. Model parameters were taken from literature or estimated using cell-based in-vitro studies. To compensate for parameter uncertainty, we estimated an ensemble of parameters consistent with the thrombin mea- surements. We validated the model ensemble using multiple independent test data sets. First, we compared model simulations with in-vitro measurements taken from Butenas et al. Second, we compared simulated thrombin trajectories with thrombin generation in plasma taken from patients with coronary artery diseases (this study). We analyzed the model ensemble using sensitivity analysis under different conditions to understand which architectural features were important in normal versus hemophilic coagulation. We found that the sensitivity of fluid phase fX/FXa interactions was indirectly proportional to fVIII/fIX level. The addition of rFVIIa and prothrombin did not alter the qualitative properties of the coagulation architecture. Rather, rFVIIa treatment restored normal thrombin formation by taking advantage of enhanced fX/FXa sensitivity induced by low fVIII/fIX levels. 

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