The role that mechanistic mathematical modeling and systems biology will play in molecular medicine and clinical development remains uncertain. In this study, mathematical modeling and sensitivity analysis were used to explore the working hypothesis that mechanistic models of human cascades, despite model uncertainty, can be computationally screened for points of fragility, and that these sensitive mechanisms could serve as therapeutic targets. We tested our working hypothesis by screening a model of the well-studied coagulation cascade, developed and validated from literature. The predicted sensitive mechanisms were then compared with the treatment literature. The model, composed of 92 proteins and 148 protein–protein interactions, was validated using 21 published datasets generated from two different quiescent in vitro coagulation models. Simulated platelet activation and thrombin generation profiles in the presence and absence of natural anticoagulants were consistent with measured values, with a mean correlation of 0.87 across all trials. Overall state sensitivity coefficients, which measure the robustness or fragility of a given mechanism, were calculated using a Monte Carlo strategy. In the absence of anticoagulants, fluid and surface phase factor X/activated factor X (fX/FXa) activity and thrombin-mediated platelet activation were found to be fragile, while fIX/FIXa and fVIII/FVIIIa activation and activity were robust. Both anti-fX/FXa and direct thrombin inhibitors are important classes of anticoagulants; for example, anti-fX/FXa inhibitors have FDA approval for the prevention of venous thromboembolism following surgical intervention and as an initial treatment for deep venous thrombosis and pulmonary embolism. Both in vitro and in vivo experimental evidence is reviewed supporting the prediction that fIX/FIXa activity is robust. When taken together, these results support our working hypothesis that computationally derived points of fragility of human relevant cascades could be used as a rational basis for target selection despite model uncertainty.

Robustness, a long-recognized property of living systems, allows function in the face of uncertainty while fragility, i.e., extreme sensitivity, can potentially lead to catastrophic failure following seemingly innocuous perturbations. Carlson and Doyle hypothesized that highly-evolved networks, e.g., those involved in cell-cycle regulation, can be resistant to some perturbations while highly sensitive to others. The “robust yet fragile” duality of networks has been termed Highly Optimized Tolerance (HOT) and has been the basis of new lines of inquiry in computational and experimental biology. In this study, we tested the working hypothesis that cell-cycle control architectures obey the HOT paradigm. Three cell-cycle models were analyzed using monte-carlo sensitivity analysis. Overall state sensitivity coefficients, which quantify the robustness or fragility of a given mechanism, were calculated using a monte-carlo strategy with three different numerical techniques along with multiple parameter perturbation strategies to control for possible numerical and sampling artifacts. Approximately 65% of the mechanisms in the G1/S restriction point were responsible for 95% of the sensitivity, conversely, the G2-DNA damage checkpoint showed a much stronger dependence on a few mechanisms; ∼32% or 13 of 40 mechanisms accounted for 95% of the sensitivity. Our analysis predicted that CDC25 and cyclin E mechanisms were strongly implicated in G1/S malfunctions, while fragility in the G2/M checkpoint was predicted to be associated with the regulation of the cyclin B-CDK1 complex. Analysis of a third model containing both G1/S and G2/M checkpoint logic, predicted in addition to mechanisms already mentioned, that translation and programmed proteolysis were also key fragile subsystems. Comparison of the predicted fragile mechanisms with literature and current preclinical and clinical trials suggested a strong correlation between efficacy and fragility. Thus, when taken together, these results support the working hypothesis that cell-cycle control architectures are HOT networks and establish the mathematical estimation and subsequent therapeutic exploitation of fragile mechanisms as a novel strategy for anti-cancer lead generation.

The role of mechanistic modeling and systems biology in molecular medicine remains unclear. In this study, we explored whether uncertain models could be used to understand how a network responds to a therapeutic intervention. As a proof of concept, we modeled and analyzed the response of the human coagulation cascade to recombinant factor VIIa (rFVIIa) and prothrombin (fII) addition in normal and hemophilic plasma. An ensemble of parametrically uncertain human coagulation models was developed (N = 437). Each model described the time evolution of 193 proteins and protein complexes interconnected by 301 interactions under quiescent flow. The 467 unknown model parameters were estimated, using multiobjective optimization, from published in vitro coagulation studies. The model ensemble was validated using published in vitro thrombin measurements and thrombin measurements taken from coronary artery disease patients. Sensitivity analysis was then used to rank-order the importance of model parameters as a function of experimental or physiological conditions. A novel strategy for the systematic comparison of ranks identified a family of fX/FXa and fII/FIIa interactions that became more sensitive with decreasing fVIII/fIX. The fragility of these interactions was preserved following the addition of exogenous rFVIIa and fII. This suggested that exogenous rFVIIa did not alter the qualitative operation of the cascade. Rather, exogenous rFVIIa and fII took advantage of existing fluid and interfacial fX/FXa and fII/FIIa sensitivity to restore normal coagulation in low fVIII/fIX conditions. The proposed rFVIIa mechanism of action was consistent with experimental literature not used in model training. Thus, we demonstrated that an ensemble of uncertain models could unravel key facets of the mechanism of action of a focused intervention. Whereas the current study was limited to coagulation, perhaps the general strategy used could be extended to other molecular networks relevant to human health.

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