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Open Access Publications from the University of California

Scholarly Works (6 results)

  • Thesis
  • Peer Reviewed
UC Riverside Electronic Theses and Dissertations (2020)

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.

    Cover page: Mathematical Models of Blood Clot Deformation and Post-Translational Regulation of Enzymes in Metabolic Networks
    • Article
    • Peer Reviewed
    UC Riverside Previously Published Works (2020)
    Experimental measurements or computational model predictions of the post-translational regulation of enzymes needed in a metabolic pathway is a difficult problem. Consequently, regulation is mostly known only for well-studied reactions of central metabolism in various model organisms. In this study, we use two approaches to predict enzyme regulation policies and investigate the hypothesis that regulation is driven by the need to maintain the solvent capacity in the cell. The first predictive method uses a statistical thermodynamics and metabolic control theory framework while the second method is performed using a hybrid optimization-reinforcement learning approach. Efficient regulation schemes were learned from experimental data that either agree with theoretical calculations or result in a higher cell fitness using maximum useful work as a metric. As previously hypothesized, regulation is herein shown to control the concentrations of both immediate and downstream product concentrations at physiological levels. Model predictions provide the following two novel general principles: (1) the regulation itself causes the reactions to be much further from equilibrium instead of the common assumption that highly non-equilibrium reactions are the targets for regulation; and (2) the minimal regulation needed to maintain metabolite levels at physiological concentrations maximizes the free energy dissipation rate instead of preserving a specific energy charge. The resulting energy dissipation rate is an emergent property of regulation which may be represented by a high value of the adenylate energy charge. In addition, the predictions demonstrate that the amount of regulation needed can be minimized if it is applied at the beginning or branch point of a pathway, in agreement with common notions. The approach is demonstrated for three pathways in the central metabolism of E. coli (gluconeogenesis, glycolysis-tricarboxylic acid (TCA) and pentose phosphate-TCA) that each require different regulation schemes. It is shown quantitatively that hexokinase, glucose 6-phosphate dehydrogenase and glyceraldehyde phosphate dehydrogenase, all branch points of pathways, play the largest roles in regulating central metabolism.
      Cover page: Enzyme activities predicted by metabolite concentrations and solvent capacity in the cell
      • Article
      • Peer Reviewed
      UC Riverside Previously Published Works (2020)
      Budding yeast, Saccharomyces cerevisiae, serves as a prime biological model to study mechanisms underlying asymmetric growth. Previous studies have shown that prior to bud emergence, polarization of a conserved small GTPase Cdc42 must be established on the cell membrane of a budding yeast. Additionally, such polarization contributes to the delivery of cell wall remodeling enzymes and hydrolase from cytosol through the membrane, to change the mechanical properties of the cell wall. This leads to the hypothesis that Cdc42 and its associated proteins at least indirectly regulate cell surface mechanical properties. However, how the surface mechanical properties in the emerging bud are changed and whether such change is important are not well understood. To test several hypothesised mechanisms, a novel three-dimensional coarse-grained particle-based model has been developed which describes inhomogeneous mechanical properties of the cell surface. Model simulations predict alternation of the levels of stretching and bending stiffness of the cell surface in the bud region by the polarized Cdc42 signals is essential for initiating bud formation. Model simulations also suggest that bud shape depends strongly on the distribution of the polarized signaling molecules while the neck width of the emerging bud is strongly impacted by the mechanical properties of the chitin and septin rings. Moreover, the temporal change of the bud mechanical properties is shown to affect the symmetry of the bud shape. The 3D model of asymmetric cell growth can also be used for studying viral budding and other vegetative reproduction processes performed via budding, as well as detailed studies of cell growth.
        Cover page: Role of combined cell membrane and wall mechanical properties regulated by polarity signals in cell budding
        • Article
        • Peer Reviewed
        UC Riverside Previously Published Works (2023)
        The exact mechanism controlling cell growth remains a grand challenge in developmental biology and regenerative medicine. The Drosophila wing disc tissue serves as an ideal biological model to study mechanisms involved in growth regulation. Most existing computational models for studying tissue growth focus specifically on either chemical signals or mechanical forces. Here we developed a multiscale chemical-mechanical model to investigate the growth regulation mechanism based on the dynamics of a morphogen gradient. By comparing the spatial distribution of dividing cells and the overall tissue shape obtained in model simulations with experimental data of the wing disc, it is shown that the size of the domain of the Dpp morphogen is critical in determining tissue size and shape. A larger tissue size with a faster growth rate and more symmetric shape can be achieved if the Dpp gradient spreads in a larger domain. Together with Dpp absorbance at the peripheral zone, the feedback regulation that downregulates Dpp receptors on the cell membrane allows for further spreading of the morphogen away from its source region, resulting in prolonged tissue growth at a more spatially homogeneous growth rate.
          Cover page: A multiscale chemical-mechanical model predicts impact of morphogen spreading on tissue growth
          • Article
          • Peer Reviewed
          UC Riverside Previously Published Works (2019)
          Fibrin is a viscoelastic proteinaceous polymer that determines the deformability and integrity of blood clots and fibrin-based biomaterials in response to biomechanical forces. Here, a previously unnoticed structural mechanism of fibrin clots' mechanical response to external tensile loads is tested using high-resolution confocal microscopy and recently developed three-dimensional computational model. This mechanism, underlying local strain-stiffening of individual fibers as well as global stiffening of the entire network, is based on previously neglected nascent cohesive pairwise interactions between individual fibers (crisscrossing) in fibrin networks formed under tensile load. Existence of fiber-fiber crisscrossings of reoriented fibers was confirmed using 3D imaging of experimentally obtained stretched fibrin clots. The computational model enabled us to study structural details and quantify mechanical effects of the fiber-fiber cohesive crisscrossing during stretching of fibrin gels at various spatial scales. The contribution of the fiber-fiber cohesive contacts to the elasticity of stretched fibrin networks was characterized by changes in individual fiber stiffness, the length, width, and alignment of fibers, as well as connectivity and density of the entire network. The results show that the nascent cohesive crisscrossing of fibers in stretched fibrin networks comprise an underappreciated important structural mechanism underlying the mechanical response of fibrin to (patho)physiological stresses that determine the course and outcomes of thrombotic and hemostatic disorders, such as heart attack and ischemic stroke. STATEMENT OF SIGNIFICANCE: Fibrin is a viscoelastic proteinaceous polymer that determines the deformability and integrity of blood clots and fibrin-based biomaterials in response to biomechanical forces. In this paper, a novel structural mechanism of fibrin clots' mechanical response to external tensile loads is tested using high-resolution confocal microscopy and newly developed computational model. This mechanism, underlying local strain-stiffening of individual fibers as well as global stiffening of the entire network, is based on previously neglected nascent cohesive pairwise interactions between individual fibers (crisscrossing) in fibrin networks formed under tensile load. Cohesive crisscrossing is an important structural mechanism that influences the mechanical response of blood clots and which can determine the outcomes of blood coagulation disorders, such as heart attacks and strokes.
            Cover page: Contribution of nascent cohesive fiber-fiber interactions to the non-linear elasticity of fibrin networks under tensile load
            • Article
            • Peer Reviewed
            UC Riverside Previously Published Works (2023)
            While blood clot formation has been relatively well studied, little is known about the mechanisms underlying the subsequent structural and mechanical clot remodeling called contraction or retraction. Impairment of the clot contraction process is associated with both life-threatening bleeding and thrombotic conditions, such as ischemic stroke, venous thromboembolism, and others. Recently, blood clot contraction was observed to be hindered in patients with COVID-19. A three-dimensional multiscale computational model is developed and used to quantify biomechanical mechanisms of the kinetics of clot contraction driven by platelet-fibrin pulling interactions. These results provide important biological insights into contraction of platelet filopodia, the mechanically active thin protrusions of the plasma membrane, described previously as performing mostly a sensory function. The biomechanical mechanisms and modeling approach described can potentially apply to studying other systems in which cells are embedded in a filamentous network and exert forces on the extracellular matrix modulated by the substrate stiffness.
              Cover page: Combined computational modeling and experimental study of the biomechanical mechanisms of platelet-driven contraction of fibrin clots
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