From Network Topology to Parameterization: An Optimized Model of Endothelial Mechanobiology

Abstract

Endothelial cells integrate biomechanical and biochemical cues to regulate vascular function, which can be modeled using cell signaling networks. Yet, the extent to which their signaling behavior is determined by network topology versus reaction-specific parameterization remains unclear. We developed a continuous logic-based ordinary differential equation model of vascular endothelial signaling containing 70 species and 123 regulatory reactions assembled from the literature. Model predictions were evaluated against 78 literature-defined directional responses to increased wall stress, wall shear stress, hypoxia, and TNF. We first tested whether a single global parameter triplet describing reaction weight (w), Hill coefficient (n), and half-maximal activation (EC50) could reproduce these observations. Investigator-selected global parameters reproduced 62 of 78 responses (79.49%). Monte Carlo sampling of 100,000 globally constant parameter sets improved agreement to 69 of 78 responses (88.46%), indicating that network topology alone captured most qualitative signaling behavior but remained sensitive to parameter choice. Allowing reaction-specific parameters increased the best agreement to 75 of 78 responses (96.15%). We then used a genetic algorithm to identify the smallest subset of reactions requiring reaction-specific specification while retaining a common constant-parameter spine for the remainder of the network. Complete agreement (100%) with all 78 literature-defined responses was achieved with reaction-specific parameterization of only 10 of 123 reactions. The optimized model was subsequently used to simulate continuous changes in wall shear stress, revealing pathway-dependent nonlinear responses, including monotonic increases in nitric oxide and pSmad1/5, nonmonotonic responses in endothelin-1 and NF-{kappa}B, and a biphasic pSmad2/3 response. These findings show that most observed endothelial signaling behavior can be reproduced by a fixed network topology with broadly shared reaction parameters with only a limited subset of interactions requiring quantitative specialization. This framework provides a compact endothelial signaling model for investigating mechanobiological regulation and for future integration with multiscale models of vascular adaptation and disease.