Free energies of amino acid side-chain rotamers in α-helices, β-sheets and α-helix N-caps

Abstract

Scales have previously been determined for the entropic cost of restricting amino acid side-chain rotations upon protein folding, giving the rule of thumb that the entropic cost of restricting a single side-chain bond is ≈0.5 kcal mol−1. However, this result does not consider the distinct preferences shown by amino acid side-chains for particular side-chain χ1 angles in the folded protein. For example, Glu in an α-helix has χ1 4% gauche− (g−), 39% trans (t) and 58% gauche+ (g+) showing that it is most favourable to restrict Glu χ1 as g+ in a helix while g− is least favoured. The change in side-chain conformational entropy is the same in both cases, but the free energy of each rotamer is different. Here, we determine the energies of every amino acid χ1 rotamer in α-helices, β-sheets and α-helix N-caps and each χ1χ2 rotamer pair in helices and sheets. The calculation uses observed rotamer distributions in secondary structure and the coil state, together with experimentally determined free energy changes for secondary structure formation. The results are sets of rotamer energies within a secondary structure that can be directly compared to each other. For example, we conclude that Tyr is the most stable residue in a β-sheet if only the trans rotamer is accessible; if only the gauche− conformation is available, Thr would be the most stabilising. Previously published scales of amino acid preferences for secondary structure are weighted averages of rotamer energies and therefore imply that Thr is the most stabilising substitution in a β-sheet in any side-chain conformation. Both side-chain conformational entropies and intrinsic secondary structure preferences are subsumed within our data; the results presented here should therefore be used in preference to both side-chain conformational entropies and intrinsic secondary structure preferences when the rotamer occupied in the folded state is known. The results may be useful in protein engineering, simulations of binding and folding, prediction of protein stability and peptide binding energies, and identification of incorrectly folded structures.