Lac repressor-operator interaction: DNA length dependence

The interaction of the E. coli lac operon repressor with its operator DNA has been directly examined as a function of the length of operator-containing DNA. The apparent bimolecular association rate constants were calculated as ka = (kd/KD), where the dissociation equilibrium constant, KD and the dissociation rate constant, kd, were measured by nitrocellulose filter adsorption assays. The values obtained for the overall association rate constants are compared with theoretical association rate curves for specific mechanisms. Association of the repressor with short operator containing DNA fragments (less than 70 base pairs) occurs at rates expected of three-dimensional diffusion. Our data also imply that at longer DNA lengths a combination of three-dimensional diffusion with one-dimensional sliding along with hopping and/or intersegment transfer must be involved to facilitate the repressor operator association.