Thermodynamic extent of counterion release upon binding oligolysines to single-stranded nucleic acids

A major contribution to the binding free energy associated with most protein-nucleic acid complexes is the increase in entropy due to counterion release from the nucleic acid that results from electrostatic interactions. To examine this quantitatively, we have measured the thermodynamic extent of counterion release that results from the interaction between single-stranded homopolynucleotides and a series of oligolysines, possessing net charges z = 2-6, 8, and 10. This was accomplished by measuring the salt dependence of the intrinsic equilibrium binding constants--i.e., (delta log Kobs/delta log[K+])--over the range from 6 mM to 0.5 M potassium acetate. These data provide a rigorous test of linear polyelectrolyte theories that have been used to interpret the effects of changes in bulk salt concentration on protein-DNA binding equilibria, since single-stranded nucleic acids have a lower axial charge density than duplex DNA. Upon binding to poly(U), the thermodynamic extent of counterion release per oligolysine charge, z, is 0.71 +/- 0.03, which is significantly less than unity and less than that measured upon binding duplex DNA. These results are most simply interpreted using the limiting law predictions of counterion condensation and cylindrical Poisson-Boltzmann theories, even at the high salt concentrations used in our experiments. Accurate estimates of the thermodynamic extent of counterion binding and release for model systems such as these facilitate our understanding of the energetics of protein-nucleic acid interactions. These data indicate that for simple oligovalent cations, the number of ionic interactions formed in a complex with a linear nucleic acid can be accurately estimated from a measure of the salt dependence of the equilibrium binding constant, if the thermodynamic extent of ion release is known.