Modeling of nucleation-based stochastic processes in cellular systems

Molecular cell biology has been an intensively studied interdisciplinary field with the rapid development of experimental techniques and fast upgrade of computational hardware and numerical tools. Recent technological developments have led to single-cell experiments which allow us to probe the role of stochasticity in cellular processes. Stochastic modeling of the corresponding processes is thus an essential ingredient for the understanding and interpretation of cellular systems of interest. In this thesis, we explore several nucleation-based stochastic cellular processes, i.e. Min protein oscillation in Escherichia coli, pausing phenomena in DNA transcription, and single-molecule enzyme kinetics. We focus on the key experimental results and build up stochastic models accordingly to provide quantitative insights to the underlying physical mechanisms for the corresponding biological processes. We utilize specific mathematical methods and computational algorithms to gain a better understanding and make predictions for further experimental explorations in the relevant fields.