Association kinetics with coupled diffusion III. Ionic-strength dependence of the lac repressor-operator association

The repressor-operator association is treated in a model where the repressor molecule can find its specific binding site, the operator, on a large DNA chain by performing a one-dimensional diffusion along the chain. The ionic-strength dependence is calculated by introducing a screened electrostatic potential around the DNA chain and coupling the free diffusion of the repressor in this potential to the proposed one-dimensional diffusion along the chain. The main influence on the association rate comes from the competitive binding of ions to the unspecific DNA sites. It is also demonstrated that during the time that the repressor is bound in a global sense, the diffusion along the chain will be made up of a strictly one-dimensional motion over fairly short distances, interspersed with many local dissociations during which the repressor in essence is free in solution.