CONFORMATIONAL ENERGY DERIVATIVES FOR POLYPEPTIDES WITH FLEXIBLE PROLINE RINGS

Abe and co-authors have recently proposed a method for rapid calculation of the first and second derivatives of conformational energy of polypeptides with respect to torsions. The method is based on the assumption that the molecule may be represented as a tree of rigid bodies without cyclic elements in it. Fixed proline rings seem to be an important limitation for the procedure. Since flexible pyrrolidine rings not only add cycles to the tree, but also result in variable valence angles, the following is done: (i) the structure of the tree and the summation procedure for recurrent equations are modified to adopt variable angles; (ii) a computational scheme is described which takes cyclic structures into account in evaluating the first and second derivatives of the energy; and (iii) the problem of ring closure is considered for a five-membered ring, and equations are derived for rapidly calculating the first and second derivatives of the dependent ring angles with respect to the independent variables. The approach proposed can also be applied to molecules with pentagonal and hexagonal sugar rings. © 1990.