A Markovian arrival stream approach to stochastic gene expression in cells

We analyse a generalisation of the stochastic gene expression model studied recently in Fromion et al. (SIAM J Appl Math 73:195-211, 2013) and Robert (Probab Surv 16:277-332, 2019) that keeps track of the production of both mRNA and protein molecules, using techniques from the theory of point processes, as well as ideas from the theory of matrix-analytic methods. Here, both the activity of a gene and the creation of mRNA are modelled with an arbitrary Markovian Arrival Process governed by finitely many phases, and each mRNA molecule during its lifetime gives rise to protein molecules in accordance with a Poisson process. This modification is important, as Markovian Arrival Processes can be used to approximate many types of point processes on the nonnegative real line, meaning this framework allows us to further relax our assumptions on the overall process of transcription.

Automated summary

We analyze a generalization of the stochastic gene expression model that tracks the production of mRNA and protein molecules. This model uses techniques from point process theory and matrix-analytic methods. The gene activity and mRNA creation are modeled with a Markovian Arrival Process, and each mRNA molecule gives rise to protein molecules according to a Poisson process. This modification is important as it allows us to relax the assumptions on the transcription process.