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

Histidine p K 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 (ΔG ij ) were obtained from the shifts in p K 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 ΔG ij when static structures were used and when the protein interior was treated empirically with a dielectric constant of 20. The ΔG ij when r ij ≤ 10 Å 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 ΔG 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 ) ≈5 Å interacted with ΔG ij ≈ 0.6 kcal/mole in 0.01 M KCl, but ΔG ij decayed to ≤0.10 kcal/mole when r ij = 20 Å. In 0.10 M KCl, ΔG ij ≈ 0.10 kcal/mole when r ij = 10 Å. In 1.5 M KCl, only short‐range interactions with r ij ≤ 5 Å persisted. Although at physiological ionic strengths the interactions between charges separated by more than 10 Å are extremely weak, in situations where charge imbalance exists many weak interactions can cumulatively produce substantial effects.