Variable ranges of interactions in polypeptide conformations with a method to complement molecular modeling

Formulations of conformational weights for helix-coil transitions can be extended to substantially more complex situations than are usually pursued. General rules for matrix multiplication that depend parametrically on the interaction ranges and numbers of rotamers of residues are presented. The orders of the matrices of statistical weights can be increased with chain length, so that an individual matrix element can represent any specified single conformation, as needed. By the appropriate choice of interaction ranges and numbers of available conformers, approximations can be introduced in which: (1) an average of the conformations of any chain segment is obtained, (2) specific residue-residue interactions are excluded, or (3) the conformation of a part of the chain is restricted or fixed. The method is appropriate for treating specific interactions in peptides and could be used together with available experimental information to develop models of conformational transitions. As such, the methods represent a class of calculations aimed at more rigorous calculations built around known features of a molecule. The aim is to facilitate calculations that bridge the gap between nonquantitative molecular model building and more rigorous but less directed molecular mechanics calculations. The method can directly include any desired longer range of interactions, if the interaction range is not too long to make impossible the manipulation of the requisite matrices. An outline is presented of an application to treat salt bridges in the C peptide of ribonuclease A.