Molecular orbital calculations on the conformation of polypeptides and proteins. II. Conformational energy maps and stereochemical rotational states of aromatic residues

Our previous quantum-mechanical calculations, by an all-valence-electrons method (PCILO) taking into account simultaneously the σ and π electrons of the system, on the conformation energy maps of the glycyl and alanyl residues are extended to the evaluation of these maps and of the stereochemical rotational states of the aromatic residues, phenylalanyl, tyrosyl, histidyl, and tryptophanyl in dipeptides. Calculations on model compounds are used for the predetermination of the side-chain rotational angles χ₁ and χ₂ which are then used as selected parameters for the evaluation of the conformational energy maps as function of the backbone rotational angles Φ and ψ. The theory predicts that the most stable conformation for these aromatic residues should occur in the same region, around Φ = 200, ψ = 140°, in which it was predicted to occur for the glycyl and alanyl residues and which was completely overlooked by most of the previous “empirical” computations. Recent experimental work by a group of Russian authors using NMR and infrared techniques seems to confirm the theoretical result for the alanyl and phenylalanyl residues. The paper indicates also the secondary local minima which appear for the different residues. The theoretically allowed general conformational area for the four aromatic residues, within the reasonable value of 5 kcal/mole above the deepest minimum, is somewhat larger than the similar area allowed by the “hard sphere” empirical calculations. Practically all available representative experimental points from the study of small molecules and of the proteins lysozyme and myoglobin fall within the allowed area, the agreement being better with the results of the quantum mechanical calculations than with those of the “hard sphere” approximation. The values of the side-chain rotational angles χ₁ and χ₂ and of their allowed combinations agree less satisfactorily with experiment, the experimentally observed combinations being more varied than the theoretically allowed ones. These last ones having, however, been predetermined on studies with model compounds, this situation is not astonishing. It is proposed to refine these results by a minimization with respect to the four parameters Φ, ψ, χ₁, and χ₂ involved.