Cell Growth Model with Stochastic Gene Expression Helps Understand the Growth Advantage of Metabolic Exchange and Auxotrophy

Cooperative behaviors are highly prevalent in the wild, but their evolution is not understood. Metabolic flux models can demonstrate the viability of metabolic exchange as cooperative interactions, but steady-state growth models cannot explain why cooperators grow faster.

Stochastic Gene Expression Revisited

We investigate the model of gene expression in the form of Iterated Function System (IFS), where the probability of choice of any iterated map depends on the state of the phase space. Random jump times of the process mark activation periods of the gene when pre-mRNA molecules are produced before mRNA and protein processing phases occur. The main idea is inspired by the continuous-time piecewise deterministic Markov process describing stochastic gene expression. We show that for our system there exists a unique invariant limit measure. We provide full probabilistic description of the process with a comparison of our results to those obtained for the model with continuous time.

Challenges of analysing stochastic gene expression in bacteria using single-cell time-lapse experiments

Stochastic gene expression causes phenotypic heterogeneity in a population of genetically identical bacterial cells. Such non-genetic heterogeneity can have important consequences for the population fitness, and therefore cells implement regulation strategies to either suppress or exploit such heterogeneity to adapt to their circumstances. By employing time-lapse microscopy of single cells, the fluctuation dynamics of gene expression may be analysed, and their regulatory mechanisms thus deciphered. However, a careful consideration of the experimental design and data-analysis is needed to produce useful data for deriving meaningful insights from them. In the present paper, the individual steps and challenges involved in a time-lapse experiment are discussed, and a rigorous framework for designing, performing, and extracting single-cell gene expression dynamics data from such experiments is outlined.

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 time 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 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. These results indicate that our approach may allow for successful parameter inference and model identification from longitudinal single cell data.