Sensitivity Analysis of Stochastic Discrete Biochemical Systems and Applications

The development and analysis of mathematical models of cellular processes are fundamental problems in Computational Biology. In many cases, these processes are represented as systems of biochemical reactions. This thesis studies a discrete stochastic model of homogeneous biochemically reacting systems, the Chemical Master Equation. Sensitivity analysis is a prominent tool for investigating the properties of a model, such as robustness with respect to variations in its parameters. We discuss a number of finite-difference sensitivity estimators for the Chemical Master Equation. In addition, we propose some new measures of practical parameter identifiability for this model, based on local sensitivity estimates. Also, we introduce a novel model reduction strategy of stochastic discrete biochemical networks, which utilizes sensitivity analysis and requires solving an optimization problem. The new methods are successfully tested on several critical models, arising in applications, including the epidermal growth factor receptor signalling pathway, the tumor suppressor protein and the Gemcitabine biochemical networks.