STOCHASTIC MODELLING OF BIOLOGICAL REACTION NETWORKS WITH FEEDBACK STRUCTURES

Complex networks of chemical reactions mediate many processes in cellular biology, such as gene expression, chemotaxis, cell to cell signalling and circadian rhythm. Some reactions in cells involve low numbers of molecules and should therefore be viewed as intrinsically stochastic (i.e. discrete and probabilistic) events. Under these circumstances, the ordinary differential equation (ODE) approach conventionally used in chemical engineering should be substituted for a stochastic model based on Poisson processes. In this thesis, we analyze a series of nonlinear biological reaction networks. These networks involve positive or negative feedback structures, in which the regulated molecular species also acts as the feedback signal. These networks and their perturbations were systematically analyzed using both the stochastic as well as the deterministic (ODE) modelling approach. In the end we draw generalizable conclusions about the role of feedback and stochasticity in such networks. We conclude that stochastic models are indispensable in analyzing many nonlinear systems with few (less than 100) molecules. First, the deterministic model gives no indication about the variability of individual outcomes, which may be significant when the number of molecules is small. We found severa