Understanding the physical basis of the salt dependence of the electrostatic binding free energy of mutated charged ligand-nucleic acid complexes

The predictions of the derivative of the electrostatic binding free energy of a biomolecular complex, ΔGel, with respect to the logarithm of the 1:1 salt concentration, d(ΔGel)/d(ln[NaCl]), SK, by the Poisson-Boltzmann equation, PBE, are very similar to those of the simpler Debye-Hückel equation, DHE, because the terms in the PBE's predictions of SK that depend on the details of the dielectric interface are small compared to the contributions from long-range electrostatic interactions. These facts allow one to obtain predictions of SK using a simplified charge model along with the DHE that are highly correlated with both the PBE and experimental binding data. The DHE-based model developed here, which was derived from the generalized Born model, explains the lack of correlation between SK and ΔGel in the presence of a dielectric discontinuity, which conflicts with the popular use of this supposed correlation to parse experimental binding free energies into electrostatic and nonelectrostatic components. Moreover, the DHE model also provides a clear justification for the correlations between SK and various empirical quantities, like the number of ion pairs, the ligand charge on the interface, the Coulomb binding free energy, and the product of the charges on the complex's components, but these correlations are weak, questioning their usefulness.

Research highlights► The Poisson-Boltzmann equation's ΔGel is not proportional to d(ΔGel)/d(ln[NaCl]). ► The generalized Born model explains this lack of proportionality cited above. ► d(ΔGel)/d(ln[NaCl]) does not depend on the details of the molecular interior. ► The Debye-Hückel equation can quickly predict d(ΔGel)/d(ln[NaCl]). ► This explains the proportionality between d(ΔGel)/d(ln[NaCl]) and simple quantities.