Figure 6. Multiscale model of transcriptional bursting with additional features of the cell cycle.

In this model, the gene stochastically switches between three states: two active states, S₁₀ and S₁₁, and one inactive state S₀. Gene activation occurs in two steps, initially by the binding of transcription factors (at rate ${\lambda }_1$, reversible at rate ${\mu }_1$), and then as a secondary step by the binding and pause of the mRNA polymerase (at rate ${\lambda }_2$). Transitions from S₁₁ to S₀ also occur at rate ${\mu }_1$, due to detachment of both the transcriptional factors and polymerase. Transcription of nascent mRNA (at rate $K_N$) occurs only in state S₁₁ and results in immediate transition to state S₁₀. Nascent mRNA mature at rate $K_M$, and are subsequently translated into protein at rate $K_p$. Degradation of mRNA and protein occur with rates ${\delta }_m$ and ${\delta }_p$, respectively. We verify our pathway reporter method on three variations of the multiscale model. First, we assume all reactions are first-order Poisson processes (Case (2) in the main text). We then incorporate further details of the mRNA maturation process, where nascent mRNA occurs after a fixed amount of time (Case (3)). Finally, we incorporate features of the cell-cycle such as gene replication, dosage compensation, cell division, and cell-cycle length variability, as well as incorporating more realistic Erlang distributed maturation times (Case (4)).