Figure 2.

π–π and cation–π interactions between His and Phe at different pH values. Binding energies (rainbow color bar) from QM calculations of His–Phe pairs in solution for pairwise interactions between (A) Phe and His⁰ (at high pH) and (B) Phe and His⁺ (at low pH) projected onto density contour gradients (white–brown color bar) created by counting the frequency of each His–Phe pair geometry as sampled from 6609 high-resolution PDB structures. The geometries of His–Phe are mapped in terms of angular parameters P and Tθ₂, these being two of the six geometric measures required to represent all pairwise interactions (see Figure 1). The density counts include all PDB pairs from both neutron diffraction and X-ray data sets. The quantum calculations were performed on selected pairs from those found in the sampled database. We note that each selected pair underwent energetic optimization and consequently its final geometry may deviate from its original starting structure. The pairwise interactions are categorized as stacked or CH–π based on distance and angle cutoffs (see Methods and Figure S4 for further details). All other geometries are classified as “other”. The size of the symbol represents the D geometric parameter (i.e., the distance, D, between the centroids of the Phe and His rings). The stacked geometries for His⁰–Phe and His⁺–Phe may refer to π–π and cation–π, respectively. The numbers overlaid onto the maps correspond to the geometries depicted in panel C. (C) Selected pairwise geometries and their corresponding binding energies for His⁰–Phe pairwise interactions (geometries 1–3; see also panel A) and His⁺–Phe pairwise interactions (geometries 4–6, see also panel B). Pairwise interactions 1 and 2 are minimal energy geometries His⁰–Phe characterized by CH–π or π–π interactions, respectively. Geometry 3 shows a pairwise His⁰–Phe interaction involving a perpendicular CH–π interaction in which His serves as the hydrogen acceptor. Geometries 4 and 5 show minimal energy conformations for CH–π and cation–π interactions, respectively, in His⁺–Phe pairs. Geometry 6 shows a His⁺–Phe pair engaged in a perpendicular CH–π interaction (with His serving as the hydrogen donor).