Extended Data Fig. 9: A two-state model with heterogeneous binding energies can successfully account for experimental observations.

a, Top: Binding energy landscape along λ-DNA as inferred from the position weight matrix (in vivo²⁶, Class A binding motif 1, Fig. 2g). Black line, coarse-grained binding energy landscape (\(\bar h_i\), 1 kb window moving average). Right, corresponding histogram of binding energies. Bottom: Inhomogeneous propensity for condensation for the model (\(h_i\), Eq. 17 and 18 Supplementary Note). Right, corresponding histogram of \(h_i\)s. b, Condensed fraction for Klf4-GFP at different concentrations (as in Fig. 2d). Blue line, fit to the model with homogeneous binding energies (parameter values: J = 3.37 kT, C₀ = 292 nM, 𝛼=0.0016 kT). c, Average steady-state spatial profiles of Klf4 condensation along λ-DNA. Blue line, steady-state profile (obtained after 200 iterations) for homogeneous binding energies (average over 100 individual kymographs). This average can vary from 0 to 1 (0 and 1 correspond to the -1 and +1 states in the model). Red line, average steady-state profile for heterogeneous binding energies. Black line, average pixel intensity of Klf-GFP along λ-DNA. d, Fraction bound of MBP-Klf4-GFP at different concentrations. Red line, fit to the model with heterogeneous binding energies (parameter values: J = 1.02 kT, C₀ = 64.95 nM, 𝛼=0.0016 kT). e, Solid lines, Pearson correlation coefficient between the spatial condensation profile obtained from the model and \(\bar h_i\) as a function of bulk protein concentration. Red and green lines, model predictions with heterogeneous binding energies for J = 3.16 kT and J = 0 kT. Black line, model prediction, for the model fitted to the data in d. Circles, experimental correlations between intensity and \(\bar h_i\) profiles (same as in Fig. 4e). f, Average kymograph (400 realizations) predicted from the model at a concentration of 250 nM. g, Representative kymograph realizations at 234 nM and 313 nM concentrations (see Supplementary Note). h, Experimental kymographs at the indicated concentrations (thresholded to display only the condensed state in white).