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

Abstract

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 f(1/2), 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.

Mesoscopic models for DNA stretching under force: New results and comparison with experiments

“…(47) gives the two correct limits far from the transition Eqs. (45,46). In the fitting procedure, the parameter κ BS plays a similar role as the parameter J (see Eq.…”

“…The partition function is Z = (4π) N ±, (2 + 1)λ N ,± in case of periodic boundary conditions and by Z = (4π) N ,± V |0, ± 2 λ N ,± in case of free ends (where |V is the adequate free-end vector) [32]. Of course, boundary conditions are irrelevant at large N [45], and we have checked that finite size effects are negligible for the DNAs studied in the experiments considered in the following.…”

“…Eqs. (45,46) are a generalization of the result of Cizeau and Viovy [26] where the continuous Marko-Siggia interpolation, valid for range 1/κ F 4κ, was used.…”

“…A block thus corresponds to a given value of m. Eq. (22) has to be adapted to this case [33,[45][46][47] (Note that contrary to [33], we do not need to explicitly treat the two single strands in the B to S transition). In Dirac notations, we have:…”

A stochastic reaction-diffusion model for protein aggregation on DNA

“…In a later paper, Zhang and Marko considered a type of cooperativity that could potentially describe protein¯laments; however, their study focused on force-extension curves. 18 Speci¯cally, they reported that even moderate amounts of adjacent-site cooperative energy could strongly a®ect the force-extension pro¯les. Olson and co-workers took the modeling of HU-DNA complexes beyond the traditional statistical mechanics approach by considering realistic three-dimensional (3D) structural and mechanical features.…”