Woodcock, Dan J., Komorowski, Michal, Finkenstädt, Bärbel, Harper, Claire V., Davis, Julian R. E., White, Michael R. H. and Rand, D. A. (David A.) (2011) A Bayesian hierarchical diffusion model for estimating kinetic parameters and cell-to-cell variability. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. (Working papers, Vol.2011).

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Abstract

A central challenge in computational modelling of dynamic biological systems is parameter inference from 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 offers 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.

Item Type:	Working or Discussion Paper (Working Paper)
Subjects:	Q Science > QA Mathematics Q Science > QH Natural history > QH301 Biology
Divisions:	Faculty of Science > Statistics Faculty of Science > Centre for Systems Biology
Library of Congress Subject Headings (LCSH):	Biological systems -- Mathematical models, Cells -- Mathematical models, Time-series analysis
Series Name:	Working papers
Publisher:	University of Warwick. Centre for Research in Statistical Methodology
Place of Publication:	Coventry
Date:	2011
Volume:	Vol.2011
Number:	No.10
Number of Pages:	18
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access
Funder:	Engineering and Physical Sciences Research Council (EPSRC), Biotechnology and Biological Sciences Research Council (Great Britain) (BBSRC), Wellcome Trust (London, England), European Union (EU), University of Warwick. Dept. of Statistics, Manchester Academic Health Sciences Centre (MAHSC), Manchester Biomedical Research Centre, National Institute for Health Research (Great Britain) (NIHR)
Grant number:	67252 (WT), EP/C544587/1 (EPSRC), GR/S29256/01 (EPSRC), BB/F005938/1 (BBSRC), 005137 (EU), BBE0129651 (BBSRC)
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URI:	http://wrap.warwick.ac.uk/id/eprint/34880

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