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A central challenge in computational modeling of dynamic biological systemsis parameter inference from experimental time course measurements. However, onewould not only like to infer kinetic parameters but also study theirvariability from cell to cell. Here we focus on the case where single-cellfluorescent protein imaging time series data are available for a population ofcells. Based on van Kampen's linear noise approximation, we derive a dynamicstate space model for molecular populations which is then extended to ahierarchical model. This model has potential to address the sources ofvariability relevant to single-cell data, namely, intrinsic noise due to thestochastic nature of the birth and death processes involved in reactions andextrinsic noise arising from the cell-to-cell variation of kinetic parameters.In order to infer such a model from experimental data, one must also quantifythe measurement process where one has to allow for nonmeasurable molecularspecies as well as measurement noise of unknown level and variance. Theavailability of multiple single-cell time series data here provides a uniquetestbed to fit such a model and quantify these different sources of variationfrom experimental data.

Quantifying intrinsic and extrinsic noise in gene transcription using the linear noise approximation: An application to single cell data