Phenomenological theory of gel electrophoresis of protein-nucleic acid complexes

A phenomenological theory of gel electrophoresis is elaborated for protein-DNA complexes involving one, two, or three binding sites on the DNA molecule. The computed electrophoretic patterns simulate experimental patterns shown by both prokaryotic and eukaryotic systems. The mechanism whereby the electrophoretic protein-DNA ladder is generated upon titration of the operator with repressor is embodied in theory of mass transport coupled to reversible interactions under chemical kinetic control. In contrast to strong interactions (association constant greater than 10(12) M-1), patterns observed with weak complexes (K less than 10(10) M-1) could be simulated only by applying the cage effect, a model of which is formulated. Theoretical underpinning is provided for the electrophoretic estimation of equilibrium association constants, and requisite chemical kinetic conditions are elucidated for direct estimation of the rate constant for dissociation of the protein-DNA complex from gel patterns. The theory thus affords an experimenter with a means for determining the conditions required to render the gel retardation method a valid procedure for evaluating equilibrium constants and/or kinetic parameters for the particular protein-nucleic acid system under investigation. These several considerations apply not only to interactions of proteins with nucleic acids (DNA or RNA) but also to a wide range of macromolecular interactions involving peptides, drugs, and other ligands as well as large assemblies such as multienzyme complexes.