Self-assembly is a fundamental process in cell biology and plays a crucial role in signal transduction, in cell movement, and in regulating the cytoskeleton. To understand the mechanisms behind this process, modeling and simulation methods are necessary because experimental techniques are only partially able to measure and analyze these phenomena in a living cell. One critical and challenging problem in accurately simulating assembly in the intracellular environment is the molecular crowding effect. In a living cell, the dense crowding of many different types of macromolecules can significantly enhance binding and assembly reactions. However, despite extensive studies of biochemistry in crowded media, it remains extremely difficult to predict how molecular crowding will quantitatively affect any given reaction system because of the many interrelated parameters in molecular crowding. In this thesis, I investigate the effect of individual parameters in a model dimerization system, and how these parameters, independently or in combination, influence binding chemistry in the model.

This thesis first develops an efficient two-dimensional computational model for simulating a dimerization reaction system in various crowded conditions, which is based on the Green's function reaction dynamics (GFRD) method. Second, this thesis investigates the model's parameter effects on the dimerization system, and describes interactions among several critical parameters: the total concentration of reactants and inert particles, the binding probability of a collision between two reactant monomers, the mean time of dissociation reactions, and the diffusion coefficient of the system. After showing the results of individual parameter effects, this thesis builds and validates a unified regression model of the equilibrium constant to accurately predict the simulation results for unknown parameter values. Third, this thesis examines the effects of three additional adjustable parameters in the binding process: the ratio of dimer area to monomer area, the ratio of inert particle area to reactant monomer area, and the threshold distance. In addition, in this thesis, the covariance of two different parameters in the model is examined. Finally, this thesis illustrates how to extend a two-dimensional model to a threedimensional model.

107 pages

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