Intracellular Flows and Fluctuations

Mathematical models are now gaining in importance for descriptions of biological processes. In this thesis, such models have been used to identify and analyze principles that govern bacterial protein synthesis under amino acid limitation. New techniques, that are generally applicable for analysis of intrinsic fluctuations in systems of chemical reactions, are also presented. It is shown how multi-substrate reactions, such as protein synthesis, may display zero order kinetics below saturation, because an increase in one substrate pool is compensated by a decrease in another, so that the overall flow is unchanged. Under those conditions, metabolite pools display hyper sensitivity and large fluctuations, unless metabolite synthesis is carefully regulated. It is demonstrated that flow coupling in protein synthesis has consequences for transcriptional control of amino acid biosynthetic operons, accuracy of mRNA translation and the stringent response. Flow coupling also determines the choices of synonymous codons in a number of cases. The reason is that tRNA isoacceptors, cognate to the same amino acid, often read different codons and become deacylated to very different degrees when their amino acid is limiting for protein synthesis. This was demonstrated theoretically and used to successfully predict the choices of control codons in ribosome mediated transcriptional attenuation and codon bias in stress response genes. New tools for the analysis of internal fluctuations have been forged, most importantly, an efficient Monte Carlo algorithm for simulation of the Markov-process corresponding to the reaction-diffusion master equation. The algorithm makes it feasible to analyze stochastic kinetics in spatially extended systems. It was used to demonstrate that bi-stable chemical systems can display spontaneous domain separation also in three spatial dimensions. This analysis reveals geometrical constraints on biochemical memory circuits built from bistable systems. Further, biochemical applications of the Fokker-Planck equation and the Linear Noise Approximation have been explored