AI Insight
This paper introduces a computationally efficient simulation method for gene regulatory networks that incorporates transcriptional bursting, a key source of variability between genetically identical cells. The authors develop an algorithm based on piecewise-deterministic Markov processes (PDMPs) that mimics the familiar structure of Gillespie's stochastic simulation algorithm (SSA) while significantly reducing computational cost, and they mathematically prove its exactness. Using a two-gene toggle switch as a case study, they demonstrate that bimodal gene expression distributions observed in real cells arise from differences in burst frequencies driven by gene-gene interactions, not from transcriptional bursting itself.
Why it matters
This method makes advanced stochastic modeling of gene networks more accessible to a broader scientific community, potentially accelerating research in cell biology, gene regulation, and the development of computational tools for analyzing single-cell RNA sequencing data.
arXiv:2507.01922v3 Announce Type: replace
Abstract: Single-cell data reveal the presence of biological stochasticity between cells of identical genome and environment, in particular highlighting the transcriptional bursting phenomenon. To account for this property, gene expression may be modeled as a continuous-time Markov chain where biochemical species are described in a discrete way, leading to Gillespie’s stochastic simulation algorithm (SSA) which turns out to be computationally expensive for realistic mRNA and protein copy numbers. Alternatively, hybrid models based on piecewise-deterministic Markov processes (PDMPs) offer an effective compromise for capturing cell-to-cell variability, but their simulation remains limited to specialized mathematical communities. With a view to making them more accessible, we present here a simple simulation method that is reminiscent of SSA, while allowing for much lower computational cost. We detail the algorithm for a bursty PDMP describing an arbitrary number of interacting genes, and prove that it simulates exact trajectories of the model. As an illustration, we use the algorithm to simulate a two-gene toggle switch: this example highlights the fact that bimodal distributions as observed in real data are not explained by transcriptional bursting per se, but rather by distinct burst frequencies that may emerge from interactions between genes.