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Implementation and analysis of mathematical models can serve as a powerful tool in understanding how intracellular processes in bacteria affect the bacterial phenotype. In this thesis I have implemented and analysed models of a number of different parts of the bacterium E. coli in order to understand these types of connections. I have also developed new tools for analysis of stochastic reaction-diffusion models.

Resistance mutations in the E. coli ribosomes make the bacteria less susceptible to treatment with the antibiotic drug erythromycin compared to bacteria carrying wildtype ribosomes. The effect is dependent on efficient drug efflux pumps. In the absence of pumps for erythromycin, there is no difference in growth between wildtype and drug target resistant bacteria. I present a model explaining this unexpected phenotype, and also give the conditions for its occurrence.

Stochastic fluctuations in gene expression in bacteria, such as E. coli, result in stochastic fluctuations in biosynthesis pathways. I have characterised the effect of stochastic fluctuations in the parallel biosynthesis pathways of amino acids. I show how the average protein synthesis rate decreases with an increasing number of fluctuating amino acid production pathways. I further show how the cell can remedy this problem by using sensitive feedback control of transcription, and by optimising its expression levels of amino acid biosynthetic enzymes.

The pole-to-pole oscillations of the Min-proteins in E. coli are required for accurate mid-cell division. The phenotype of the Min-oscillations is altered in three different mutants: filamentous cells, round cells and cells with changed membrane lipid composition. I have shown that the wildtype and mutant phenotypes can be explained using a stochastic reaction-diffusion model.

In E. coli, the transcription elongation rate on the ribosmal RNA operon increases with increasing transcription initiation rate. In addition, the polymerase density varies along the ribosomal RNA operons. I present a DNA sequence dependent model that explains the transcription elongation rate speed-up, and also the density variation along the ribosomal operons. Both phenomena are explained by the RNA polymerase backtracking on the DNA.