Distance dependence and salt sensitivity of pairwise, coulombic interactions in a protein

Histidine pK(a) values were measured in charge-reversal (K78E, K97E, K127E, and K97E/K127E) and charge-neutralization (E10A, E101A, and R35A) mutants of staphylococcal nuclease (SNase) by (1)H-NMR spectroscopy. Energies of interaction between pairs of charges (DeltaG(ij)) were obtained from the shifts in pK(a) values relative to wild-type values. The data describe the distance dependence and salt sensitivity of pairwise coulombic interactions. Calculations with a continuum electrostatics method captured the experimental DeltaG(ij) when static structures were used and when the protein interior was treated empirically with a dielectric constant of 20. The DeltaG(ij) when r(ij) < or = 10 A were exaggerated slightly in the calculations. Coulomb's law with a dielectric constant near 80 and a Debye-Hückel term to account for screening by the ionic strength reproduced the salt sensitivity and distance dependence of DeltaG(ij) as well as the structure-based method. In their interactions with each other, surface charges behave as if immersed in water; the Debye length describes realistically the distance where interactions become negligible at a given ionic strength. On average, charges separated by distances (r(ij)) approximately 5 A interacted with DeltaG(ij) approximately 0.6 kcal/mole in 0.01 M KCl, but DeltaG(ij) decayed to < or =0.10 kcal/mole when r(ij) = 20 A. In 0.10 M KCl, DeltaG(ij) approximately 0.10 kcal/mole when r(ij) = 10 A. In 1.5 M KCl, only short-range interactions with r(ij) < or = 5 A persisted. Although at physiological ionic strengths the interactions between charges separated by more than 10 A are extremely weak, in situations where charge imbalance exists many weak interactions can cumulatively produce substantial effects.