Fig. 3: A mechanistic model of enhancer–promoter communication.
From: Nonlinear control of transcription through enhancer–promoter interactions
a, Stochastic promoter–enhancer interactions occur and disassemble with rates kclose and kfar. b, In the close state, the enhancer can trigger n reversible regulatory steps with forward and reverse rates kforward and kback. In the far state, regulatory steps can revert only at rate kback. c, The promoter operates in a basal two-state regime with a small on rate (\({k}_{{\rm{on}}}^{\mathrm{basal}}\)) unless all n regulatory steps have been completed, in which case it transiently enters an enhanced two-state regime with a higher on rate (\({k}_{{\rm{on}}}^{\mathrm{enh}}\)). d, Schematic of the parameter constraints under which the mechanistic model reduces to an apparent two-state model: kclose,far ≫ kforward,back ≫ \({k}_{{\rm{on}}}^{\mathrm{basal,enh}}\), koff, µ. e, Representative single-cell dynamics of enhancer–promoter interactions, promoter regulatory steps and promoter states predicted by the mechanistic model with n = 5 and rates satisfying the constraint on timescales described in d (time unit, 1/δ). f, Reduction of the mechanistic model to an apparent two-state model. The equation describes how the apparent on rate \({k}_{{\rm{on}}}^{\mathrm{app}}\) depends on contact probability (pc) and other parameters of the mechanistic model. g, Dependency of \({k}_{{\rm{on}}}^{\mathrm{app}}\) on contact probability, illustrated for the best fitting parameters shown in h and i. h, Best fit of the apparent two-state model to the experimental transcriptional response shown in Fig. 2b. i, Best fit of the apparent two-state model to the experimental mRNA distributions shown in Fig. 2c. Best-fit parameters are shown in Extended Data Fig. 4c.
