Mathematical models of RNA and protein synthesis dynamics and their integration with gene expression data

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Gene expression is the ultimate example of a dynamic complex system that includes thousands of regulatory parts interacting at various time scales. Currently, we know much more about these parts than we know about their dynamics. For example, we don't know how DNA and RNA sequences specify RNA and proteins synthesis rates, which vary between genes over several orders of magnitude [1]. Without understanding these variations, we do not understand how natural sequences work, and we cannot engineer synthetic sequences that work reliably.In recent years, a growing number of experimental methods has been developed that can measure gene expression at the single-molecule and genome-wide level. Now that the data to understanding gene expression dynamics is available, mathematical models are needed to connect single-molecule dynamics to genome-wide data and to design new sequences with defined elongation dynamics and synthesis rate.In this project, the student will extend recently developed stochastic model reduction techniques [2] to solve models of transcription and translation dynamics that are based on the totally asymmetric simple exclusion process (TASEP) [3], a driven diffusive lattice gas model that forms a cornerstone of nonequilibrium physics. A primary goal is to analyse TASEP-based models of transcription and translation dynamics that account for non-uniform, sequence-dependent elongation rates, in accordance with recent experimental observations. A secondary goal is to use these models to infer transcription and translation elongation rates from genome-wide sequencing data [3]. A final goal is to cross-check these rates with known determinants of transcription and translation dynamics to better understand gene-specific variations of RNA and protein synthesis rates.The project will give the student a solid foundation in the basic molecular biology of transcription and translation, and its modelling using stochastic simulations. No previous background on these topics is assumed. A basic knowledge of probability theory and some experience in coding are necessary. The project is ideal for a student with a mathematics or physics degree who is interested in the quantitative modelling of living systems using stochastic models borrowed from nonequilibrium statistical physics. The student will be based in the C. H. Waddington building which houses the Centre for Synthetic and Systems Biology at the University of Edinburgh.