Twist- and Tension-Mediated Elastic Coupling between DNA-Binding Proteins

We study the effective interaction between DNA-binding proteins that arises from elastic stresses in the DNA when tension is applied. Using the wormlike chain model, we calculate the free energy cost of introducing multiple nearby bends in the DNA. We find that the bend deformation energy promotes aggregation to straighten the linker DNA, while twist resistance of the linker leads to damped oscillations in the coupling free energy between two proteins. We calculate the mean first encounter time for proteins sliding along DNA, indicating, in some cases, an optimal applied tension for protein assembly. Our results highlight the need to consider DNA twist even when no torsion is applied and the DNA ends are free to rotate. The variable-range oscillatory coupling between DNA-binding proteins may provide a versatile mechanism for tension-mediated gene regulation.