Figure 1. Statistical thermodynamic models of gene expression.

(A) All possible molecular configurations of a CRM with two binding sites (purple), that may or may not be bound by a transcription factor (green circle = activator, red circle = repressor). The statistical weight W of each configuration is shown to its right. Each occupied site makes a contribution to W in a multiplicative fashion. (B) Cooperative DNA-binding is modeled by introducing a multiplicative factor (ω) to the statistical weight of a configuration. The same configuration is shown along with its statistical weight W under a model with no cooperativity (top) and a model with self-cooperative DNA-binding (bottom). (C) Statistical weight contributions from TF-DNA interactions (W) and from TF-BTM interactions (Q) for each configuration, in the Direct Interaction model (blue circle = BTM). Each bound activator or repressor molecule contributes to the TF-BTM interaction term (Q) in a multiplicative fashion. The statistical weight also receives a contribution from BTM binding at the promoter; this term is not shown here. (D) Same as (C), but for the short range repression model. A bound repressor (red circle) does not have a direct interaction with the BTM. Also, there is one additional configuration allowed here, as compared to Direct Interaction: one where repressor is bound and “effective” in shutting down its neighborhood for binding at activator sites (bottom). The statistical weight (W) of this configuration is scaled by a factor of β_R, reflecting the strength of the repressor to change the chromatin accessibility. (E) Two ways to model the action of multiple bound activators: “additive effect” (top 2 configurations) and “multiplicative effect” (bottom). The total statistical weight (W×Q) under each model is shown. In the former, only one bound activator may contact the BTM in any configuration, while the latter has no such restriction and leads to transcriptional synergy.