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Title: Stochastic analysis and control methods for molecular cell biology
Author: Lakatos, Eszter
ISNI:       0000 0004 6422 9162
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2017
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Stochastic fluctuations in cellular processes often have a dominant role in evoking heterogeneous behaviour in otherwise identical cells. From a modelling point of view, stochastic systems require specialised techniques to analyse and provide predictions about the underlying processes. Here we approach this problem by presenting several methods for the analysis of stochastic networks in molecular biology. First, we address the problem of obtaining simulated trajectories of such systems. This task can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the burden. Here, we develop a set of multivariate moment closures that allow us to describe the stochastic dynamics of nonlinear systems. We use multivariate Gaussian, lognormal, and gamma closure to capture how correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. In addition to the approximation method we also introduce our Python-based package that provides numerous tools to help non-expert users in stochastic analysis. Next, we present an approach to quickly evaluate the levels of noise in both naturally evolved and engineered biological systems. Controlling the behaviour of cells by rationally guiding processes is an overarching aim of recent research, but stochasticity proves a formidable obstacle in obtaining reliable models and designs. Here, we compute the states reachable by a stochastic system under some biologically relevant control input in cases with uncertainty about parameter values. Our algorithm provides a set of bounds on molecular dynamics at the level of population statistics that can be used for evaluating competing models and control strategies. In the third part, we introduce a formalism to study cellular decision making influenced by noise. Understanding the heterogeneity of phenotypes within a cell population is a long-time challenge in modelling, and Waddington's notion of a developmental landscape has become a powerful conceptual framework for this problem. Here, we derive quantitative potential landscapes that allow us to explore the global dynamics of the system. Using this method we study how different sources of noise and modifications in experimental conditions can induce significant changes in the landscape and the assumed cell fates. Finally, we propose a framework for model selection taking into account the inherent stochasticity of biochemistry. One of the main objectives of mathematical biology is identifying the most appropriate models and parameter values to describe known experimental results and provide predictions. Here, we develop and apply a Bayesian computational framework to identify dominant mechanisms controlling the variation of protein abundance between cell types. Using single cell expression of p53 in two cell lines, we compare the effect of transcription and protein degradation on the steady state distribution.
Supervisor: Stumpf, Michael P. H. Sponsor: Imperial College London
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral