Determining numbers of proteins bound to large DNAs is important for understanding their chromosomal functions. Protein numbers may be affected by physical factors such as mechanical forces generated in DNA, e.g. by transcription or replication. We performed single-DNA stretching experiments with bacterial nucleoid proteins HU and Fis, verifying that the force–extension measurements were in thermodynamic equilibrium. We, therefore, could use a thermodynamic Maxwell relation to deduce the change of protein number on a single DNA due to varied force. For the binding of both HU and Fis under conditions studied, numbers of bound proteins decreased as force was increased. Our experiments showed that most of the bound HU proteins were driven off the DNA at 6.3 pN for HU concentrations lower than 150 nM; our HU data were fit well by a statistical-mechanical model of protein-induced bending of DNA. In contrast, a significant amount of Fis proteins could not be forced off the DNA at forces up to 12 pN and Fis concentrations up to 20 nM. This thermodynamic approach may be applied to measure changes in numbers of a wide variety of molecules bound to DNA or other polymers. Force-dependent DNA binding by proteins suggests mechano-chemical mechanisms for gene regulation.

Single-DNA stretching and twisting experiments provide a sensitive means to detect binding of proteins, via detection of their modification of DNA mechanical properties. However, it is often difficult or impossible to determine the numbers of proteins bound in such experiments, especially when the proteins interact nonspecifically (bind stably at any sequence position) with DNA. Here we discuss how analogs of the Maxwell relations of classical thermodynamics may be defined and used to determine changes in numbers of bound proteins, from measurements of extension as a function of bulk protein concentration. We include DNA twisting in our analysis, which allows us to show how changes in torque along single DNA molecules may be determined from measurements of extension as a function of DNA linking number. We focus on relations relevant to common experimental situations (e.g., magnetic and optical tweezers with or without controlled torque or linking number). The relation of our results to Gibbs adsorption is discussed.

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.

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