Association kinetics with coupled diffusional flows. Special application to the lac repressor--operator system

The time development of the association of the lac repressor to the operator is considered in a model where the repressor is allowed to bind unspecifically to DNA and move along the DNA chain in a one-dimensional diffusion. The coupling to the three-dimensional diffusion outside the chain is introduced by letting the repressor associate and dissociate from the chain until it is finally bound to the operator. All distance correlations along the chain are included. The mean time of association is calculated and through a comparison with experimental data the molecular parameters are determined. The one-dimensional diffusion constant is found to be of the order of 10(-9) cm(2)s(-1). The model is sufficiently general to be applicable to other similar systems.