Range of interaction between DNA-bending proteins is controlled by the second-longest correlation length for bending fluctuations.

When a DNA molecule is stretched, the zero-force correlation length for its bending fluctuations-the persistence length A-bifurcates into two different correlation lengths-the shorter "longitudinal" correlation length ξ_{∥}(f) and the longer "transverse" correlation length ξ_{⊥}(f). In the high-force limit, ξ_{∥}(f)=ξ_{⊥}(f)/2=sqrt[k_{B}TA/f]/2. When DNA-bending proteins bind to the DNA molecule, there is an effective interaction between the protein-generated bends mediated by DNA elasticity and bending fluctuations. Surprisingly, the range of this interaction is not the longest correlation length associated with transverse fluctuations of the tangent vector along the polymer, but instead is the second longest longitudinal correlation length ξ_{∥}(f,μ). The effect arises from the protein-bend contribution to the Hamiltonian having an axial rotational symmetry which eliminates its coupling to the transverse fluctuations.