Association kinetics of site‐specific protein‐DNA interactions: Roles of nonspecific DNA sites and of the molecular location of the specific site

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Abstract
We have applied the formalism developed previously for the kinetics of domain‐localized reaction [S. Mazur and M. T. Record, Jr. (1986) Biopolymers 25, 985–1008] to describe complex mechanisms of association of a protein with a specific site on a large DNA molecule also containing many nonspecific binding sites. These nonspecific sites participate in the mechanism of formation of the specific complex through competitive binding and the facilitating mechanisms of sliding and transfer. The effects of localizing the sites in a domain are represented by a simple algebraic expression, and the sequence of interactions within the domain are described by equations closely related to a conventional, homogeneous solution mechanism. We apply this formalism to examine the interplay between sliding and direct transfer in domain‐localized interactions in general and in the lac repressor‐lac operator interaction in particular. Experimental investigation of the effect of the molecular location of the specific site (e.g., end vs middle of the polymer chain) on the kinetics of association may allow the contributions of sliding and direct transfer to be resolved.