Molecular orbital calculations on the conformation of polypeptides and proteins IV. The conformation of the prolyl and hydroxyprolyl residues

Abstract

Quantum-mechanical calculations by the all-valence electrons PCILO method carried out previously for the glycyl, alanyl, phenylalanyl, tyrosyl, histidyl and tryptophanyl residues are now extended to the particular case (because of the limitations imposed by the rigidity of the pyrrolidine ring upon the rotational angle Φ) of the prolyl and hydroxyprolyl residues. Both the cis and trans forms have been explicitly considered. The calculations carried out with Φ = 122° predict the existence of two energy minima for the individual residue, centred around ψ = 140 to 150° and ψ = 330 to 340°. The results are in good agreement with empirical computations (probably because in this particular case the stable conformations are largely determined by the minimum in the repulsion energy) which they complete and extend and with the available data on the conformation of these residues in lysozyme and myoglobin. The calculations predict the energy difference between the most stable cis and trans conformers of proline to be of the order of 0·5 kcal/mole in favor of the latter. The search for the most advantageous pathway for the cis-trans interconversion indicates that it should occur for the rotation of ω between 180 and 0° for ψ around 150°, the calculated energy barrier being 16·2 kcal/mole. Calculations carried out for a model of the prolyl residue in its homopolymers indicate that in these compounds the stable conformations are limited, both for the cis and trans polymers, only to ψ centred around 330°. The trans form should be about 1·4 kcal/mole more stable than the cis one. The barrier for the cis-trans isomerisation is, in this case, of the order of 15 kcal/mole and the easiest path runs through ω = 180° → 90° → 0°.