Abstract
Stochastic gene expression in regulatory networks is conventionally modelled via the Chemical Master Equation (CME) (van Kampen 1981). As explicit solutions to the CME, in the form of so-called propagators, are not readily available, various approximations have been proposed (Zechner et al. 2013, Feigelman et al. 2016, Popović, Marr and Swain 2016). A recently developed analytical method (Veerman, Marr and Popović 2017) is based on a scale separation that assumes significant differences in the lifetimes of mRNA and protein in the network, allowing for the efficent approximation of propagators from asymptotic expansions for the corresponding generating functions. Here, we showcase the applicability of that method to a ‘telegraph’ model for gene expression that is extended with an autoregulatory mechanism. We demonstrate that the resulting approximate propagators can be successfully applied for Bayesian parameter inference in the non-regulated model with synthetic data; moreover, we show that in the extended autoregulated model, autoactivation or autorepression may be refuted under certain assumptions on the model parameters. Our results indicate that the method showcased here may allow for successful parameter inference and model identification from longitudinal single cell data.
Footnotes
↵* Joint corresponding authors.