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Mathematical Models of Blood Clot Deformation and Post-Translational Regulation of Enzymes in Metabolic Networks


Mathematical models are widely utilized to suggest and test physical and biological hypotheses for which no experimental validation is available at this time. This thesis contains three sections describing several different novel physics based mathematical models in which novel biological hypotheses are proposed and validated.

First, we develop a 3D mathematical model of a fibrin network, a material which determines the deformability and integrity of blood clots. The fiber network is simulated using Langevin dynamics, with each elastic fiber modelled using nonlinear springs. Computational implementation utilizes Nvidia GPUs. We use the model to test a novel structural mechanism of fibrin clots' response to external loads. This mechanism is based on neglected cohesive pairwise interactions between individual fibers in fibrin networks. The contribution of the fiber-fiber cohesion to the elasticity of fibrin networks is characterized in analysis of model simulations by evaluating changes in individual fiber stiffness, length, and alignment of fibers, as well as connectivity and density of the entire network.

Next, the model is extended to include a sub-model of filopodia of platelet cells which incorporates mechanical forces exerted by filopodia on individual fibrin fibers, and adherence of platelets to one another. Model simulations show how a hypothesized mechanism based on platelets sensing fiber stiffness and thereby adapting their behavior is fundamental for the formation of the distinct contraction phases observed in experiments. Moreover, we quantify how different levels of filopodia strength in response to different stiffness alters clot stability.

Last, a statistical thermodynamic and metabolic control theory framework using hybrid optimization-reinforcement learning (RL) is used to predict the post-translational regulation of enzymes in metabolic pathways. We utilize a non-linear least squares optimization approach to obtain a steady state. The problem of regulation is posed as a Markov decision process and the optimization routine is directly incorporated into a RL environment. The model is used to investigate the hypothesis that regulation is driven by the need to maintain the solvent capacity in the cell. Predictions suggest novel general principles: (1) regulation itself causes reactions to be much further from equilibrium instead of the assumption that non-equilibrium reactions are targets for regulation; (2) regulation is used to maintain concentrations of both immediate and downstream product concentrations rather than to maintain a specific energy charge; and (3) minimal regulation needed to maintain metabolite levels at physiological concentrations also results in a maximal obtainable energy production rate.

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