Competitive electrostatic binding of charged ligands to polyelectrolytes: Practical approach using the non-linear Poisson-Boltzmann equation

We have developed a practical analytical treatment of the non-linear Poisson-Boltzmann (P-B) equation to characterize the strong but non-specific binding of charged ligands to DNA and other highly charged macromolecules. These reactions are notable for their strong salt dependence and anti-cooperativity, features which the theory fully explains. We summarize analytical results for concentration profiles and ion binding in various regimes of surface curvature and ionic strength, and show how counterion size and charge distribution may influence competitive binding. We present several practical applications of the formalism, showing how to estimate the ligand concentration needed to effectively compete with a given buffer salt, and how to calculate the amounts of counterion species bound at various distances from the DNA surface under given bulk solution conditions. We cast our results into the form of a Scatchard binding isotherm, showing how the apparent binding constant K(obs) and S = -dlog K(obs)/dlog[M⁺] can be predicted from the basic theory. Anti-cooperativity arises naturally without steric repulsion, and binding curves can be fitted with K(obs) and effective charge as the only free parameters. We extend the analytical P-B analysis to an arbitrary number of counterion species, and apply the results to fit and predict three-ion competition data.