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Paper No. 11-10

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DJ Woodcock, M Komorowski, BF Finkenstadt, CV Harper, JRE Davis, MRH White and DA Rand

A Bayesian hierarchical diffusion model for estimating kinetic parameters and cell-to-cell variability

Abstract: A central challenge in computational modelling of dynamic biological systems is parameter inferencefrom experimental time course measurements. One would like not only to measure mean parameter values but also estimate the uncertainty of single cell values and the variability from cell to cell. Here we focus on the case where single-cell uorescent protein imaging time series data is available for a population of cells. We present a two dimensional continuous-time Bayesian hierarchical diffusion model which has the potential to address the different sources of variability that are relevant to the stochastic modelling of transcriptional and translational processes at the molecular level, namely, intrinsic noise due to the stochastic nature of the birth and deaths processes involved in chemical reactions, extrinsic noise arising from the cell-to-cell variation of kinetic parameters associated with these processes and noise associated with the measurement process. The availability of multiple single cell data provides a unique opportunity to estimate such a model and explicitly quantify the sources of variation from experimental data. Inference is complicated by the fact that only the protein and rarely other molecular species are observed which typically leads to parameter identification problems. The Bayesian approach provides an extremely suitable framework as it o_ers the possibility to import posterior results from one experiment as prior information to another experiment in a statistically rigorous way. Furthermore, the use of the linear noise approximation makes estimation of this complex stochastic model computationally feasible. We provide a systematic derivation in matrix formulation of the resulting likelihood. Estimation results are obtained from a cohort of single cell uorescent protein imaging time series associated with the Prolactin gene.