Stereochemistry of polypeptide conformation in coarse grained analysis

The conformations available to polypeptides are determined by the interatomic forces acting on the peptide units, whereby backbone torsion angles are restricted as described by the Ramachandran plot. Although typical proteins are composed predominantly from {\alpha}-helices and {\beta}-sheets, they nevertheless adopt diverse tertiary structure, each folded as dictated by its unique amino-acid sequence. Despite such uniqueness, however, the functioning of many proteins involves changes between quite different conformations. The study of large-scale conformational changes, particularly in large systems, is facilitated by a coarse-grained representation such as provided by virtually bonded C{\alpha} atoms. We have developed a virtual atom molecular mechanics (VAMM) force field to describe conformational dynamics in proteins and a VAMM-based algorithm for computing conformational transition pathways. Here we describe the stereochemical analysis of proteins in this coarse-grained representation, comparing the relevant plots in coarse-grained conformational space to the corresponding Ramachandran plots, having contoured each at levels determined statistically from residues in a large database. The distributions shown for an all-{\alpha} protein, two all-{\beta} proteins and one {\alpha}+{\beta} protein serve to relate the coarse-grained distributions to the familiar Ramachandran plot.