Models for protein localization in bacteria and chromatin structure in eukaryotes

In the first part of this thesis, we focus on the problem of how proteins localize within the cytoplasm of bacteria. Experimentally, it is found that proteins that have attractive interactions are able to localize to one or both of the poles in cylindrical bacteria. We put forward a model that only relies on the aggregating tendency of proteins and the occlusion by the bacterial nucleoid. Monte-Carlo simulations enabled us to find the stable and metastable localization patterns, allowing us to explore the phase space of parameters in our model. Our findings explains the different patterns observed for PopZ localization in Escherichia coli and Caulobacter crescentus as well as misfolded proteins. We find the kinetics of expressing proteins has a crucial role: unipolar patterning is an energetically favorable state while other polar patterns can be achieved at higher rates of protein expression. Using sets of different GFP tagged aggregating proteins we are able to experimentally test this prediction and alter the localization from unipolar to bipolar simply by increasing the rate of expression. In the second part, we consider the structuring of the DNA within the eukaryotic nucleous and its associated proteins. A new high-throughput experimental technique, Hi-C, is able to measure the looping frequencies between all parts of the genome. We transform the measured data and are able to extract a distance independent free energy by subtracting out the background free energy of interactions due to the polymer nature of DNA. Our mean-field model quantities the interaction strengths between chromatin factors and loops along the chromosomes in a protein pairwise interaction matrix J. Since the Hi-C data carries dierent biases, using our approach we are able to assess the best sets of corrections that lead to the free energy having the most mutual information with the underlying chromatin profiles. Further to this, we use Principal Component Analysis (PCA) to identify the frequent modes of genome wide looping. Hence, we are able to correlate these with known domain structures such as boundaries between active and silent regions of the genome.