Interpretation of monovalent and divalent cation effects on the lac repressor-operator interaction.

We have investigated the effects of mixed Na+: Mg2+ ionic solutions on the stability of the nonspecific lac repressor-DNA complex. The effects of Mg2+ are simply interpreted in terms of its role as a competitor (with repressor) for DNA sites. From these studies, the binding constant of the Mg-DNA complex can be determined as a function of the concentration of Na+. We have used this information to interpret the data of Riggs and collaborators (Riggs, A.D., et al. (1970), J. Mol. Biol. 48, 67-83; 53, 401-417) on the ion dependence of the repressor-operator interaction. We find that there are approximately 70% as many ionic interactions in the repressor-operator complex as in the nonspecific complex. Our best estimate is that 8 +/- 1 ion pairs are formed. We calculate that the release of counterions in the formation of the specific complex contributes approximately 40% of the favorable free energy change in the association reaction under in vivo ionic conditions. Implications of these findings for the control of the lac operon and for the molecular relationship between the specific and nonspecific complexes are considered.