Table 1.

Different events in the stochastic gene expression model and the corresponding changes in population counts when events occur probabilistically

Model events	Reset in population count	Propensity function f(z1, z2, m, p)
Zj production	zj(t) → zj(t) + i	kjαji, i ∈ {0,1,…}
Zj degradation	zj(t) → zj(t) − 1	γjzj(t)
Transcription	m(t) → m(t) + i	kmαiz1(t), i ∈ {0,1,…}
mRNA degradation	m(t) → m(t) − 1	γmm(t)
Protein translation	p(t) → p(t) + 1	kpm(t)z2(t)
Protein degradation	p(t) → p(t) − 1	γpp(t)

Third column lists the event propensity function that determines how often an event fires. Random processes m(t) and p(t) denote the number of mRNA and protein molecules inside the cell at time t, respectively. The values z_j(t), j ∈ {1,2} represent levels of cellular factors z_j that affect transcription and translation rates.