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Stochastic models of gene transcription with upstream drives: Exact solution and sample path characterisation

Presented by: 
Justine Dattani
Monday 13th June 2016 - 15:00 to 16:00
INI Seminar Room 2
Gene transcription is a highly stochastic, dynamic process. As a result, the mRNA copy number of a given gene is heterogeneous both between cells and across time. I will present a framework to model gene transcription in populations of cells with time-varying (stochastic or deterministic) transcription and degradation rates. Such rates can be understood as upstream cellular drives representing the effect of different aspects of the cellular environment, e.g. external signalling, circadian rhythms, or chromatin remodelling. I will show that the full solution of the generic master equation for gene transcription contains two components: a model-specific, upstream effective drive, which encapsulates the effect of the cellular drives (e.g., entrainment, periodicity or promoter randomness), and a downstream transcriptional Poissonian part, which is common to all models. This analytical framework allows us to treat cell-to-cell and dynamic variability consistently, unifying several approaches in the literature.   Our general solution confers to us two broad advantages. The first is pragmatic: the theory provides us with new approaches for solving non-stationary gene transcription models, analysing single-cell snapshot and time-course data, and reducing the computational cost of sampling solutions via stochastic simulation. The second advantage is conceptual: studying the solution of a broad class of models in generality provides us with physical intuition for the sources of noise and their characteristics, and the ability to deduce which models are analytically solvable (along with the form and structure of their solutions). I will demonstrate some such benefits by applying our solution to several biologically-relevant examples.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons