Stochastic and delayed stochastic models of gene expression and regulation

Gene expression and gene regulatory networks dynamics are stochastic. The noise in the temporal amounts of proteins and RNA molecules in cells arises from the stochasticity of transcription initiation and elongation (e.g., due to RNA polymerase pausing), translation, and post-transcriptional regulation mechanisms, such as reversible phosphorylation and splicing. This is further enhanced by the fact that most RNA molecules and proteins exist in cells in very small amounts. Recently, the time needed for transcription and translation to be completed once initiated were shown to affect the stochasticity in gene networks. This observation stressed the need of either introducing explicit delays in models of transcription and translation or to model processes such as elongation at the single nucleotide level. Here we review stochastic and delayed stochastic models of gene expression and gene regulatory networks. We first present stochastic non-delayed and delayed models of transcription, followed by models at the single nucleotide level. Next, we present models of gene regulatory networks, describe the dynamics of specific stochastic gene networks and available simulators to implement these models.