Results from the LacI titration experiments.

The probability of looping as a function of Lac repressor concentration shown in fig. 4 was fitted to the two non-linear models from eqns. 1 and 2. Both models were fit independently as a ways to check the robustness of the least-squares methods with respect to data reparametrization. A subset of the data corresponding to concentrations of LacI 10 pM and higher is fitted to the linear model shown in eqn. 4 and its statistical mechanics counterpart. See section S4 in the Supporting Information S1 for a discussion of the different data fitting approaches. The literature values of the dissociation constants for and correspond to bulk binding assays performed in concentration ranges close to our TPM buffer conditions. The corresponding values for the binding energies of these operators are obtained from the dissociation constants using eqns. S5 and S11.