Model for the irreversible dissociation kinetics of cooperatively bound protein–nucleic acid complexes

We present a quantitative model for the irreversible dissociation kinetics of cooperatively bound nonspecific protein–nucleic acid complexes. The model assumes that the major pathway of dissociation is via singly contiguously bound protein that “peels” off the ends of clusters of bound protein. It should therefore be most applicable for proteins that bind nucleic acids with high cooperativity (w > 10³). Furthermore, the model assumes that no redistribution of bound protein occurs during the time course of the dissociation. Solutions to the rate equations are presented for the entire time course of the dissociation. Under initial conditions such that the nucleic acid is less than fully saturated with protein, a single-exponential decay is predicted (if w is large). However, when the nucleic acid lattice is initially fully saturated, zero-order kinetics, corresponding to a constant rate of protein dissociation, is predicted. The experimental observation of zero-order dissociation kinetics in a cooperative protein–nucleic acid system is a good qualitative indicator for the dissociation mechanism discussed here. A discussion of the analysis of experimental data that enables one to extract molecular rate constants is presented. Furthermore, comparisons are made between the nonredistributing model presented here and Epstein's model Epstein, I. R. (1979) Biopolymers 18 , 2037–2050] in which protein can translocate infinitely quickly while bound to the nucleic acid, and hence protein clusters redistribute during dissociation and maintain an equilibrium distribution on the nucleic acid at all times.