Salt dependence of the kinetics of the lac repressor-operator interaction: role of nonoperator deoxyribonucleic acid in the association reaction.

The kinetics of binding of lac repressor protein and operator deoxyribonucleic acid (DNA) have been studied as a function of monovalent and divalent cation concentration. The salt dependence of the association and dissociation rate constants has been interpreted in light of recent theoretical analyses based on Manning's counterion condensation model. The bell-shaped dependence of the association rate constant on salt concentration evidences a role for nonoperator DNA binding in the repressor's search for the operator site on a large DNA molecule. At intermediate mono- or divalent cation concentrations, the association rate goes through a maximum. At lower cation concentrations, it decreases and becomes dependent on DNA concentration; the high affinity of repressor for nonoperator DNA confines the protein to the DNA. At higher cation concentrations, the association rate decreases and becomes dependent on the weak affinity of repressor for nonoperator DNA. The kinetic data are fit to the theory of Berg and Blomberg [Berg, O. G., & Blomberg, C. (1978) Biophys. Chem. 8, 271] for the salt dependence of association kinetics with coupled diffusion, using published values of the affinity for nonoperator DNA. From this fit, one-dimensional diffusion of repressor along the DNA chain is estimated to be about 4 times faster on MgDNA than on NaDNA. At higher cation concentrations, the salt dependence of the association and dissociation rate constants is consistent with a preequilibrium mechanism for the association reaction [Lohman, T. M., deHaseth, P. L., & Record, M. T., Jr. (1978) Biophys. Chem. 8, 281]. Agreement between literature values (corrected for the presence of Mg2+) and experimental values of the rate constants in the presence of monovalent salt is quite good.