Abstract
If an infinitely long polymer has a primary structure characterized by an N-residue periodicity, a minimum energy conformation of the polymer under the constraint of the conformational N-residue periodicity corresponds to an equilibrium structure (energy minimal or unstable equilibrium structure) when this constraint is absent. Molecular mechanics calculations showed that with an infinitely long poly-(L,D)-alanine single-stranded beta 6.3-helix (which has a 2-residue periodicity with respect to the primary structure), its lowest energy conformation within the framework of the conformational 2-residue periodicity is also the lowest energy form of this beta 6.3-helix even when no conformational periodicity is assumed. In the course of this study, contour maps of helix parameters and conformation energies for beta structures of poly-(L,D)-alanine were examined. It was also found that beta 6.3-, beta 4.5-, alpha L,D-, and tau L,D-helices constitute the global minima in the whole conformational space of this polypeptide. In the present calculation, an improved formulation of the conformation energy was introduced to estimate the structure and conformation energy of an infinite periodic chain from results on a chain of finite length.