Fig. 2.

A two-state stochastic model of the expression levels of one gene. a A diagram of the two-state gene expression model [76–78], where a gene stochastically switches from an inactive state to an active state at rate k_a and from an active state to an inactive state at rate k_i. The gene transcribes mRNA at rate s_m only when it is in the active state. The transcribed mRNA then degrades at rate δ. b Given s_m=200 and δ=1, the effects of k_a and k_i on the temporal dynamics of the gene’s mRNA copy number. Three example values of k_a and k_i are provided. Left: when both k_a and k_i are small, the mRNA copy number switches between small and large values. Middle: when k_a is much larger than k_i, the mRNA copy number remains large most of the time. Right: when k_a is much smaller than k_i, the mRNA copy number remains small most of the time. c Distributions of the gene’s mRNA copy number (across cells) corresponding to the three example settings in (b). Left: when the gene’s mRNA copy number switches between small and large values, the resulting distribution is bimodal with two modes at zero and around s_m/δ. Middle: when the gene’s mRNA copy number is large most of the time, the resulting distribution has a single mode around s_m/δ. Right: when the gene’s mRNA copy number is small most of the time, the resulting distribution has a single mode at zero. In summary, when k_a is small, the gene is expected to have biological zeros in cells with non-negligible probability