Intrinsic and force-generated cooperativity in a theory of DNA-bending proteins

We study a statistical-mechanical model of the binding of DNA-bending proteins to the double helix including applied tension and binding cooperativity effects. Intrinsic cooperativity of binding sharpens force-extension curves and causes enhancement of fluctuation of extension and protein occupation. This model also allows us to estimate the intrinsic cooperativity in experiments by measuring the peak value of the slope of extension versus chemical-potential curves. This analysis suggests the presence of force-dependent cooperativity even in the absence of explicit intrinsic (energetic) cooperativity. To further understand this effect, we analyze a model with a pair of bends at variable spacing to obtain a spacing-dependent free energy of interaction between the two proteins. We find that the interaction is always attractive and has an exponential decay as a function of bend spacing. For forces greater than k _B T/A, where A is the persistence length, the interaction decay length is approximately [k_B TA/(4f)] 1/2 in accord with theoretical expectations. However, the force dependence of the strength of the interaction is more complex. For short interprotein separations, the interaction strength saturates at a level which varies roughly as f1/2, while at longer separations the amplitude of the exponential decay increases faster than linearly with force. Our results can be applied to single molecule experiments to measure the cooperativity between DNA-bending proteins or between other molecules which deform the semiflexible polymer with which they bind. Force-mediated interaction of DNA-bending proteins suggests a mechanism whereby tension in DNA in vivo could alter the distribution of proteins bound along DNA, causing chromosome refolding, or changes in gene expression.