An algorithm for the stochastic simulation of gene expression and cell population dynamics

Over the past few years, it has been increasingly recognized that stochastic mechanisms play a key role in the dynamics of biological systems. Genetic networks are one example where molecular-level fluctuations are of particular importance. Here stochasticity in the expression of gene products can result in genetically identical cells in the same environment displaying significant variation in biochemical or physical attributes. This variation can influence individual and population-level fitness. In this thesis we first explore the background required to obtain analytical solutions and perform simulations of stochastic models of gene expression. Then we develop an algorithm for the stochastic simulation of gene expression and heterogeneous cell population dynamics. The algorithm combines an exact method to simulate molecular-level fluctuations in single cells and a constant-number Monte Carlo approach to simulate the statistical characteristics of growing cell populations. This approach permits biologically realistic and computationally feasible simulations of environment and time-dependent cell population dynamics. The algorithm is benchmarked against steady-state and time-dependent analytical solutions of gene expression models, including scenarios when cell growth, division, and DNA replication are incorporated into the modelling framework. Furthermore, using the algorithm we obtain the steady-state cell size distribution of a large cell population, grown from a small initial cell population undergoing stochastic and asymmetric division, to the size distribution of a small representative sample of this population simulated to steady-state. These comparisons demonstrate that the algorithm provides an accurate and efficient approach to modelling the effects of complex biological features on gene expression dynamics. The algorithm is also employed to simulate expression dynamics within 'bet-hedging' cell populations during their adaption to environmental stress. These simulations indicate that the cell population dynamics algorithm provides a framework suitable for simulating and analyzing realistic models of heterogeneous population dynamics combining molecular-level stochastic reaction kinetics, relevant physiological details, and phenotypic variability and fitness