Theory of delocalized ionic binding to polynucleotides: structural and excluded-volume effects

A previously developed theory for the delocalized binding of ions to polyelectrolytes was restricted to point ions and a structurally rigid polyelectrolyte. For the binding of substances like oligolysines and polyamines to DNA, the restriction to point ions would appear not to be realistic. For the binding of ions to flexible chains like single-stranded polynucleotides, the restriction to a rigid polyelectrolyte may not be realistic. In this article, we assess the effect of relaxation of these two restrictions. Excluded volume among bound ions is modeled by a hard-rod potential in the context of the theory of a one-dimensional fluid. The possibility that a flexible chain folds in some manner in the immediate vicinity of a bound ion is modeled by allowing the mean spacing between charged groups on the polymer to become smaller as the number of bound ions increases. We compare our results with recent data on the binding of a series of oligolysines to single-stranded polynucleotides, which conflict with the predictions of the original theory of delocalized binding of point ions to rigid polyelectrolytes. Inclusion of excluded volume among bound ions does not significantly improve agreement with the data. Substantial improvement in the level of agreement is obtained when the polyion chain is assumed to be flexible. One of our conclusions is that the excluded-site description of anticooperativity, which was designed for the binding of ligands to discrete sites on a polymer chain, and which does not include the effect of ionic forces, should not be used in cases of delocalized binding of ions.