Minimization of polypeptide energy. I. Preliminary structures of bovine pancreatic ribonuclease S-peptide.

Because the problem of computing protein structures from a knowledge of the amino acid sequence is so complex, we have approached it by making many simplifying assumptions and then removing these assumptions in stages until a computer program could ultimately be developed to yield the structure of a protein. Thus, using a hard-sphere potential, it was possible to compute the allowed coinformations of dipeptides and tripeptides,l of helical structures,2 ' of a cyclic octapeptide,4 and of the cyclic decapeptide gramicidin-S.5 Subsequently, the hardsphere potential was replaced by more complete energy expressions, and energy contours were computed for several dipeptides6' I and helical structures.' 8-10 Similar calculations have been reported by Ramachandran,1II 12 LiquoriI3' 14 and Flory.15, 16 In this paper, we make certain simplifying assumptions about the energies, and introduce the effect of the solvent (i.e., water). In addition, we report briefly on the exploration of several minimization techniques, and apply the most satisfactory one to the 20-residue N-terminus (S-peptide) of bovine pancreatic ribonuclease. Because of the problem of multiple apparent local minima, the structures reported here are to be regarded only as preliminary ones. In subsequent papers, we will report on energy minimization for some small polypeptides containing closed loops, and also on another minimization procedure which permits rapid minimization, starting with many arbitrary initial conformations. Calculation of the Energy.-Although we have shown that variations in bond lengths and bond angles affect the energy contours of dipeptides,7 we have not yet found it necessary to include this feature in calculations for small polypeptides; hence, the backbone and side-chain geometry were held fixed in the calculations reported in this paper. As before,9 a Lennard-Jones pairwise 6-12 potential function was used for the nonbonded interactions. However, in order to reduce the amount of computation, hydrogen atoms were not considered individually unless they can take part in a strong hydrogen bond. Instead, they were regarded as part of an extended "atom" such as a methylene group, etc. The coefficients of the attractive terms in the potentials were calculated by means of the Slater-Kirkwood equation,17 using the values of a and Neff given in Table 1. The coefficients of the repulsive terms were adjusted so as to minimize the pair-interaction energy when the interatomic distance was equal to the sum of the van der Waals radii as given in reference 15 or reference 20, plus 0.2 A (see ref. 16). This is equivalent to enlarging the van der Waals radii; the values of the enlarged radii are given in Table 1. Electrostatic interactions were computed by assigning partial charges to each atom and summing the contributions of all pairs, using Coulomb's law.9' 21 The partial charges were essentially those given elsewhere.21 Zero charge was assigned