Theoretical assessment of the oligolysine model for ionic interactions in protein-DNA complexes

The observed salt dependence of charged ligand binding to polyelectrolytes, such as proteins to DNA or antithrombin to heparin, is often interpreted by means of the "oligolysine model." We review this model as derived entirely within the framework of the counterion condensation theory of polyelectrolytes with no introduction of outside assumptions. We update its comparison with experimental data on the structurally simple systems for which it was originally intended. We then compute the salt dependence of the binding free energy for a variety of protein-DNA complexes with nonlinear Poisson-Boltzmann (NLPB) simulation methods. The results of the NLPB calculations confirm the central prediction of the oligolysine model that the net charge density of DNA remains invariant to protein binding. Specifically, when a cationic protein residue penetrates the layer of counterions condensed on DNA, a counterion is released to bulk solution, and when an anionic protein residue penetrates the condensed counterion layer, an additional counterion is condensed from bulk solution. We also conclude, however, that the cumulative effect of charged protein residues distant from the binding interface makes a significant contribution to the salt dependence of binding, an observation not accommodated by the oligolysine model.