Transient Probability Distributions of Gene Regulatory Networks with Slow Promoter Kinetics

1. Introduction 1. Introduction 2. Transient Dynamics of... Example: The Self-Repressing... References In a previous work [1], we have shown that, under a suitable time-scale separation hypothesis, the stationary probability mass functions of gene regulatory networks can be written as mixtures of Poisson distribution.\n\nIn this work, we study the time-evolution of the probability mass function and show that it can be approximated via similar techniques.\n\nFirst, we review the relevant material from [1].\n\n1.1 The Reaction Network Structure In this paper, a GRN is formally defined as a set of nodes (genes) that are connected with each other through regulatory interactions via the proteins that the genes express. The regulatory proteins are called transcription factors(TFs). A ...