Binding-rebinding dynamics of proteins interacting nonspecifically with a long DNA molecule

We investigate how nonspecific interactions and unbinding-rebinding events give rise to a length- and conformation-dependent enhancement of the "macroscopic" dissociation time of proteins from a DNA, or in general for the release of ligands initially bound to a long polymer. By numerically simulating the release of ligands from polymers of different conformations, we show that the total dissociation time increases logarithmically with polymer length for an extended conformation, and as a power law for self-avoiding and compact conformations. For the latter two cases, the presence of self-avoidance acting between the diffusing ligands affects the power-law exponents. Our results are important in relating kinetic measurements of protein on- and off-rates for large DNAs to equilibrium affinities for a single binding site.