Modelling networks of biochemical reactions

Author's declaration: aware of legal responsibility I hereby declare that I have written this dis-sertation myself and all the contents of the dissertation have been obtained by legal means. Abstract The process in which a mathematical model of a molecular biological system is formulated and refined helps to articulate hypotheses and thereby supports the design of experiments to validate these hypotheses and the model itself. Once the model is validated it is used to speculate about mechanisms underlying a cell function of interest. In this disser-tation we describe and apply methods valid in a general framework of spatially homogeneous models of biochemical reactions networks. However , our focus is set specifically on practical applications to models of intracellular signalling pathways. We start with selecting the most plausible variant of a JAK-STAT pathway activation mechanism. Solution of this model selection task is based solely on a deterministic mathematical framework, represented by the ordinary differential equations. Moreover, here we exert a concept of ro-bustness based on the sensitivity analysis. Next, we extend the range of mathematical models of biochemical reactions network to a spatially homogeneous stochastic variant, represented by the continuous-time Markov process. To that end, we apply the probabilistic model checking technique to a simple enzymatic reaction model, exploring an idea of a property-specific sensitivity analysis. On this occasion, we have developed a supporting open source software named Tav4SB, used for scientific cloud computing. Finally, we exploit both deterministic and stochastic methods in a case study based on the heat-shock response model. We investigate the thermotolerance phenomenon and the effect of a combined hyperther-mia and a drug therapy of cancer. In principle, our results demonstrate feasibility and practical potential of techniques such as the sensitivity analysis and probabilistic model checking, as well as potential of a standardised, easily-accessible software, in the context of analysis of kinetic models of biological systems.