Fig. 6: Effect of salt (0 M, 1.5 M, 3 M NaCl) on the potential of mean force (PMF) between selected amino acid pairs in explicit solvent and NaCl ions as a function of the center-of-mass (COM) distance.

a Cation–anion (with π–π contributions), b cation–anion (without π–π contributions), c hydrophobic–hydrophobic, d non-polar–non-polar, e polar–polar, f π–π, g hybrid cation–π/π–π (Arg–Tyr, solid lines) and cation–π (Lys–Phe, dashed lines) (+pol denotes refitted Tyr/Phe parameters were employed; as described in the text and Supplementary Information), h Cation–cation (with π–π contribution). The second well in (b) emerges from the interaction of Asp with an additional H atom in the Lys sidechain, which is displaced by ~1.7 Å from the two H atoms that contribute to the first well. To evaluate (g), a model for the polarized cation–π systems was developed (see “Methods”). The gray arrows in each panel highlight the general shift direction of the PMF minimum as salt concentration is raised. Upward arrows show the weakening of cation–anion interactions upon increasing salt. Downward arrows show strengthening of nonionic interactions and of hybrid cation–π/π–π and cation–cation interactions when both amino acids in the pair have π–orbitals. Statistical errors, mean ± s.d., are shown as bands; obtained by bootstrapping the results from n = 3 independent simulations. i Variation in the free-energy minimum (obtained from the profiles in a–h, mean ± s.d.) with salt. One-letter amino acid codes are used to identify each pair interaction. Source data are provided as a Source Data file.