Modelling bistable systems: a new model for meiosis initiation in Saccharomyces cerevisiae and an investigation of the bistable switch of meiotic-mitotic initiation

Abstract

Living cells process diverse information received from the environment and make important decisions to undergo cellular processes such as differentiation, cell growth, division and apoptosis. The complex information processing in cells is carried out by a network of biochemical switches and oscillators similar to those seen in complex electrical circuits. The main objective of systems biology is to acquire a thorough understanding of how the functions and behaviour emerge from the complex networks of interactions and components in biological systems. In this thesis, using the systems biology approaches of mathematical modelling, dynamical system analysis and computational simulations, we investigate one example of a gene regulatory system that exhibits bistable switching behaviour to gain deeper insight into its dynamic aspects. In the first section of this thesis, we develop a mathematical model for meiosis initiation of the budding yeast, Saccharomyces cerevisiae, incorporating the main mitosis initiator and its relationships to the meiosis initiation network. Using this mathematical model, we study meiosis and mitosis initiation dynamics under different extra-cellular nutrient levels. Our ultimate goal is to explore the experimentally-observed initial stage meiotic-mitotic switching behaviour in budding yeast under different nutrient conditions, which has not yet been explained at a gene expression level. We extend an available Boolean model of meiosis initiation, which is more biologically sound with stronger experimental validity than other models, and include all recent findings. We develop the model in an ODE framework that enables us to perform phase plane and bifurcation analyses to obtain deeper insights into the behaviour of the system. Our model accurately and qualitatively predicts the experimentally-revealed temporal variations in the related proteins under different nutrient conditions as well as diverse mutant studies related to meiosis and mitosis initiation. Further, the model explains the organism-level experimental outputs of mutation studies at the gene expression level. Using model simulations, we clarify the reasoning behind the conflicting experimental observations from two mutation studies carried out using different procedures.Experimental evidence shows that budding yeast cells can choose between meiosis and mitosis initiation alternatively depending on the available nutrient conditions at the early stage of these two cell division initiation processes. In the second section of this thesis, we use the constructed model to understand this initial phase meiotic-mitotic switching seen in budding yeast cells. In this section, we use dynamical system analysis tools such as phase space analysis, nullcline analysis and bifurcation analysis to explore the model's dynamics under varying nutrient conditions. Using these approaches, we show how meiosis and mitosis initiators form an all-or-none type of bistable switch in response to the available nutrient levels (mainly nitrogen). The transitions to and from the meiosis or mitosis states occur via saddle node bifurcations. This reversible switch helps the optimum usage of available nutrients and explains the mutually exclusive existence of the meiosis and mitosis pathways. Similarly as seen in experiments, temporal analysis of the switch shows that budding yeast cells can transit to mitosis from meiosis initiation throughout all the initial hours of meiosis initiation.Cellular systems behave robustly against external and internal perturbations. In the third section of this thesis, we investigate the robustness and probable effects on the meiotic-mitotic switch by perturbation of the parameters in the meiosis network. To identify the most sensitive set of parameters, we employ both local and global sensitivity analyses. Based on the global sensitivity analysis results, we find a common group of parameters sensitive in all the main states of the switch. After formulating a mathematical definition for robustness, we perturb this common sensitive group of parameters and study the robustness of meiosis and mitosis initiation against the perturbations at the gene expression level. To examine the effects on the meiotic-mitotic switch by perturbations of the parameters, we perturb the common parameter group and create parameter sets using Latin hypercube sampling. Using these sample parameter sets, we investigate the effects of the most sensitive parameters on the transition from meiosis to mitosis when the nutrient level is varied from a low value to a high value. The robustness analysis carried out at the gene expression level identifies that the state corresponding to the transitions between meiosis and mitosis is less robust against perturbations than the other states. We observe three different types of switches when the sensitive parameters are perturbed. We categorise them as normal bistable, memory-less and abnormal switches. The robustness of these switches is implied from the observation that the main function of the transition from meiosis to mitosis initiation, when nutrients are increased, is maintained despite perturbation of the most sensitive parameters in all three switch types.