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Storage and retrieval of the genetic information in cells is a dynamicprocess that requires the DNA to undergo dramatic structural rearrangements.DNA looping is a prominent example of such a structural rearrangement that isessential for transcriptional regulation in both prokaryotes and eukaryotes,and the speed of such regulations affects the fitness of individuals. Here, weexamine the in vitro looping dynamics of the classic Lac repressorgene-regulatory motif. We show that both loop association and loop dissociationat the DNA-repressor junctions depend on the elastic deformation of the DNA andprotein, and that both looping and unlooping rates approximately scale with thelooping J factor, which reflects the system's deformation free energy. Weexplain this observation by transition state theory and model the DNA-proteincomplex as an effective worm-like chain with twist. We introduce a finiteprotein-DNA binding interaction length, in competition with the characteristicDNA deformation length scale, as the physical origin of the previouslyunidentified loop dissociation dynamics observed here, and discuss therobustness of this behavior to perturbations in several polymer parameters.

Modulation of DNA loop lifetimes by the free energy of loop formation