Parameter inference with analytical propagators for stochastic models of autoregulated gene expression
Stochastic gene expression in regulatory networks is conventionally modelled via the Chemical Master Equation (CME). As explicit solutions to the CME, in the form of so-called propagators, are oftentimes not readily available, various approximations have been proposed. A recently developed analytical method is based on a separation of scales that assumes significant differences in the lifetimes of mRNA and protein in the network, allowing for the efficient approximation of propagators from asymptotic expansions for the corresponding generating functions. Here, we showcase the applicability of that method to simulated data from a telegraph model for gene expression that is extended with an autoregulatory mechanism. We demonstrate that the resulting approximate propagators can be applied successfully for Bayesian parameter inference in the non-regulated model; 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.