Fig. 2
A two-state model of gene expression. a Each diploid cell has two genetic loci and the promoter (circle) of each gene can be in either an active (ρ 1) or an inactive (ρ 0) state. Each gene synthesizes mRNA molecules (m) with rate μ 1 or μ 0 if the promoter is active or inactive, respectively. Transitions between promoter states occur with a promoter activation rate k 1 and a promoter deactivation rate k 0. Each mRNA is degraded with rate δ. b Possible biochemical reactions and cell states of our model. A cell state x (grey box) is the number of active promoters ρ 1∈{0,1,2} and mRNA molecules m∈{0,1,2,…,M} in a cell, or x=[ρ 1,m]T. There are four possible biochemical reactions that change a cell from one state to another state: (1) promoter activation (blue arrow), which increases ρ 1 by 1; (2) promoter inactivation (purple arrow), which decreases ρ 1 by 1; (3) mRNA synthesis (orange arrow), which increases m by 1; and (4) mRNA degradation (gray arrow), which decreases m by 1. The propensity or probability per unit time (a k ) for a particular reaction (k) to occur is listed above the reaction arrows. The propensities depend on the model parameters θ={μ 0,μ 1,k 1,k 0}