PhD Comprehensive Exam | Monjur Morshed, Sensitivity Analysis For Stochastic Models of Biochemical Reaction Networks

Sensitivity Analysis For Stochastic Models of Biochemical Reaction Networks

Abstract

In the study of Systems Biology it is necessary to model and simulate the cellular processes and chemical reactions of a biochemical systems. This is achieved through a range of mathematical modelling approaches, typically relying on the Chemical Master Equation. Traditional methods employ deterministic models, but since many biological processes are inherently probabilistic, stochastic models must be used for a more accurate description of the system's dynamics. For instance, the stochastic fluctuations due to the presence of some low molecular populations may have a great impact on the biochemical system behavior. One particularly important tool in the study of biochemical systems is sensitivity analysis, which aims to quantify the dependence of a system's dynamics on model parameters. In order to construct, characterize, and validate the models, sensitivity analysis provides an important mathematical tool. We propose an adaptive tau-leaping algorithm for sensitivity analysis of stochastic biochemical systems, and provide analysis on known models. The new algorithm results in a lower computational cost compared to existing algorithms, for a negligible loss in accuracy.