Direct simulation of a stochastically driven multi-step birth-death process

The description of transcription as a stochastic process provides a framework for the analysis of intrinsic and extrinsic noise in cells. To better understand the behaviors and possible extensions of existing models, we design an exact stochastic simulation algorithm for a multimolecular transcriptional system with an Ornstein-Uhlenbeck birth rate that is implemented via a special function-based time-stepping algorithm. We demonstrate that its joint copy-number distributions reduce to analytically well-studied cases in several limiting regimes, and suggest avenues for generalizations.