Diffusion-driven mechanisms of protein translocation on nucleic acids. 3. The Escherichia coli lac repressor--operator interaction: kinetic measurements and conclusions.

The association and dissociation kinetics of the Escherichia coli lac repressor--operator (RO) complex have been examined as a function of monovalent ion concentration and operator-containing DNA fragment length in order to investigate the mechanisms used by repressor in locating (and dissociating from) the operator site. Association rate constants (ka) measured with an 80- or a 203-base-pair lac operator containing DNA fragment are 3--5-fold smaller than those determined with a 6700-base-pair operator fragment or with intact lambda plac5 DNA (50000 base pairs) at all salt concentrations tested. At salt concentrations less than approximately 0.1 M KCl, association rate constants to all operator-containing DNA fragments (except lambda plac5 DNA) are insensitive to variations in salt concentration, but the limiting low salt value of ka appears to depend upon operator-containing DNA length. The value of ka for lambda plac5 DNA decreases significantly from the approximately 0.1 M KCl maximum at low salt. Above approximately 0.1 M KCl, repressor--operator association rate constants for all operator-containing DNA substrates tested show a similar decrease with increasing salt concentration, which does not appear to depend upon the length of the DNA molecule (except for the very small DNA fragments). In contrast to the association reaction, kd, the dissociation rate constant, decreases linearly (on a log kd vs. log [KCl] plot) with decreasing salt concentration over virtually the entire salt concentration range studied (0.05--0.2 M KCl). These results are consistent with the explanation of the unusually fast association kinetics for this system in terms of a two-step model in which repressor initially diffuses to a nonoperator DNA binding site (forming an RD complex) and then rapidly "scans" (in a locally correlated fashion) adjacent sites until the operator is located or the repressor dissociates from the chain. Dissociation of the RO complex follows the same two-step process in reverse. Quantitative comparisons are made between these results and the theoretical predictions of the two facilitating translocation mechanisms (one-dimensional "sliding" along the DNA double helix and direct transfer between DNA segments) developed in the first paper of this series [Berg, O. G., Winter, R. B., & von Hippel, P. H. (1981) Biochemistry (first paper of three in this issue)]. We conclude that the experimental data for the "faster-than-diffusion-controlled" interaction of repressor and operator can be quantitatively modeled by a two-step process in which sliding is the dominant transfer mechanism. Molecular models of the initial nonspecific binding event (including "hopping") as well as sliding and interchain transfer are discussed, and the possible roles of facilitated translocation mechanisms of the diffusion-driven type in this and other in vitro and in vivo protein--nucleic acid interaction processes are considered.