Analysis of ion concentration effects on the kinetics of protein-nucleic acid interactions. Application to lac repressor-operator interactions

The effects of monovalent and divalent cations on the bimolecular rate constant of the reaction of a positively charged ligand with a nucleic acid polyanion are analyzed for two possible reaction mechanisms. One mechanism postulates that the association reaction occurs without intermediates, and that ion effects on the rate constant result entirely from the screening of the charged reactants by ionic atmospheres of low molecular weight ions (a screening-controlled mechanism). This mechanism is analyzed by analogy with the Bronsted-Bjerrum theory for the kinetics of interaction of low molecular weight ions. The second mechanism to be considered here postulates the existence of a ligand-DNA intermediate which is in rapid equilibrium with the reactants (pre-equilibrium mechanism). Ion concentration effects on the association rate constants for the pre-equBibrium mechanism result mainly from the release of counterions from the DNA upon formation of the intermediate. Both of the above mechanisms predict that the logarithm of the association rate constant,_a, will be a linear function of the logarithm of the monovalent cation concentration, [M+] (in the absence of competition by divalent cations or anions). Knowledge of the salt dependences of K_a and of the observed equilibrium constant k_obs of the ligand-nucleic acid interaction should usually be sufficient to determine whether a screening-controlled mechanism or a pre-equilibrium mechanism is suitable to describe the process. If the association reaction can be described by a pre-equilibrium mechanism, the number of ionic interactions involved in the ligand-nucleic acid intermediate can be estimated. This analysis, extended to include the effects of divalent cations on screening or on the pre-equilibrium step, is applied to literature data on the salt dependence of the kinetics of the interaction of lac represser with lac operator DNA. When the operator is present on bacteriophage λ DNA, the observed reaction kinetics are consistent with the formation of an intermediate repressor-DNA complex in a pre-equilibrium step. On the other hand, the kinetics of association of toe represser with synthetic foe operator fragments may be an example of a screening-controlled reaction.