Sequence specificity in DNA binding is determined by association rather than dissociation

Sequence-specific binding of proteins to DNA is essential for accessing genetic information. Here, we derive a simple equation for target-site recognition, which uncovers a previously unrecognized coupling between the macroscopic association and dissociation rates of the searching protein. Importantly, this relationship makes it possible to recover the relevant microscopic rates from experimentally determined macroscopic ones. We directly test the equation by observing the binding and unbinding of individual lac repressor (LacI) molecules during target search. We find that LacI dissociates from different target sequences with essentially identical microscopic dissociation rates. Instead, sequence specificity is determined by the efficiency with which the protein recognizes different targets, effectively reducing its risk of being retained on a non-target sequence. Our theoretical framework also accounts for the coupling between off-target binding and unbinding of the catalytically inactive Cas9 (dCas9), showing that the binding pathway can be obtained from macroscopic data. One Sentence Summary Association and dissociation rates are anti-correlated for reactions that include a nonspecific probing step.