Stochastic and physical modeling of fundamental biological processes

Modeling is a necessary tool to understand the large volumes of data generated from quantitative experiments on biological systems. It combines our knowledge of a phenomenon into a succinct mathematical or computational description. In this dissertation, we first describe briefly two applications of modeling in biophysics: loading of the replication clamp into the replisome in the archaeon Methanosarcina acetivorans and genome packing initiation during the self-assembly of the T4 bacteriophage. We then describe in detail two systems: an improved model of the lac genetic switch which includes DNA looping in its gene regulation mechanism, and a spatially resolved, whole-cell model of ribosome biogenesis in Escherichia coli, which we then extend to include cell growth and replication of its genome. For the first system, conditions and parameters affecting the range of bistability of the lac genetic switch in E. coli are examined for a model which includes DNA looping interactions with the lac repressor and a lactose analog. This stochastic gene-mRNA-protein model of the lac switch describes DNA looping using a third transcriptional state. We exploit the fast bursting dynamics of mRNA by combining a novel geometric burst approximation with the Finite State Projection method. This limits the number of protein/mRNA states, allowing for an accelerated search of the model's parameter space. We evaluate how the addition of the third transcriptional state changes the bistability properties of the model and find a critical region of parameter space where the phenotypic switching occurs in a range seen in single molecule fluorescence studies. Stochastic simulations show induction in the looping model is preceded by a rare complete dissociation of the loop followed by an immediate burst of mRNA rather than a slower build up of mRNA as in the two-state model. The overall effect of the looped state is to allow for faster switching times while at the same time further differentiating the uninduced and induced phenotypes. Furthermore, the kinetic parameters are consistent with free energies derived from thermodynamic studies suggesting that this minimal model of DNA looping could have a broader range of application. For the second system, we study the biogenesis of the ribosome. Central to all life is the assembly of the ribosome: a coordinated process involving the hierarchical association of ribosomal protein to the RNAs forming the small and large ribosomal subunits. The process is further complicated by effects arising from the intracellular heterogeneous environment and the location of ribosomal operons within the cell. We provide a simplified model of ribosome biogenesis in slow growing E. coli. Kinetic models of in vitro small subunit reconstitution at the level of individual ribosomal protein to ribosomal RNA interactions are developed for two temperature regimes. The model at low temperatures predicts the existence of a novel 5’-3’-central assembly pathway, which we investigate further using molecular dynamics. The high temperature assembly network is incorporated into a model of in vivo ribosome biogenesis in slow growing E. coli. The model, described in terms of reaction-diffusion master equations, contains 1336 reactions and 251 species that dynamically couple transcription and translation to ribosome assembly. We use the Lattice Microbes software package to simulate the stochastic production of mRNA, proteins, and ribosome intermediates over a full cell cycle of 120 minutes. The whole-cell model captures the correct growth rate of ribosomes, predicts the localization of early assembly intermediates to the nucleoid region, and reproduces the known assembly timescales for the small subunit with no modifications made to the embedded in vitro assembly network. Finally, we extend the spatially resolved whole-cell model of ribosome biogenesis to include the effects of growth, DNA replication, and cell division. All biological processes are described in terms of reaction-diffusion master equations and solved stochastically using Lattice Microbes. In order to determine the replication parameters, we construct and analyze a series of E. coli strains with fluorescently labeled genes distributed evenly throughout their chromosomes. By measuring these cells' lengths and number of gene copies at the single-cell level, we could fit a statistical model of the initiation and duration of chromosome replication. We found that for our slow-growing (120 minute doubling time) E. coli cells, replication was initiated 42 minutes into the cell cycle and completed after an additional 42 minutes. While simulations of the biogenesis model produce the correct ribosome and mRNA counts over the cell cycle, the kinetic parameters for transcription and degradation are lower than anticipated from a recent analytical time dependent model of in vivo mRNA production. Describing expression in terms of a simple chemical master equation, we show that the discrepancies are due to the lack of non-ribosomal genes in the extended biogenesis model which effects the competition of mRNA for ribosome binding, and suggest corrections to parameters to be used in the whole-cell model when modeling expression of the entire transcriptome