UC San Diego

Random fluctuations play a fundamental role in all biological processes, from diffusion-reaction pathways to the stochasticity inherent to genetic variability. Determining how these random processes interact is critical to both understanding and eventually engineering biological systems. This dissertation deals with the dynamics of stochastic transport processes at the cell level. The first chapter presents a description of a novel microscope design to probe diffusive behavior in a cellular extract. The obtained data reveal both superdiffusive and subdiffusive behavior. This chapter also introduces several stochastic processes that capture the observed behavior. Differences in an ergodicity- breaking parameter between the experimental conditions support the use of these models. The second chapter describes a new algorithm for determining the anomalous scaling exponent of experimental data. The algorithm, which is based on a renormalization group operator, enables one to determine a distribution of anomalous diffusion exponents from single trajectories. When applied to the experimental data from the first chapter, the algorithm identified a rich distribution of anomalous exponents, signifying the nonstationary behavior indicative of transport process transitions. The implications of this result and its future applications are discussed. The third chapter describes a hard-sphere simulation algorithm for modeling reaction-diffusion systems in complex geometry. Details of the implementation and unresolved issues are outlined. The fourth section deals with the derivation of effective transport equations for cellular environments, which are highly crowded and characterized by complex geometry. A probabilistic formulation is proposed for solving a closure problem, which determines the effective diffusion coefficient. This chapter concludes with a computational example that serves both to demonstrate the efficacy and robustness of the proposed framework and to outline its possible applications