Determining the minimum number of types necessary to represent the sizes of protein atoms

Motivation: Traditionally, for packing calculations people have collected atoms together into a number of distinct 'types'. These, in fact, often represent a heavy atom and its associated hydrogens (i.e. a united atom). Also, atom typing is usually done according to basic chemistry, giving rise to 20-30 protein atom types, such as carbonyl carbons, methyl groups, and hydroxyl groups. No one has yet investigated how similar in packing these chemically derived types are. Here we address this question in detail, using Voronoi volume calculations on a set of high-resolution crystal structures. Results: We perform a rigorous clustering analysis with cross-validation on tens of thousands of atom volumes and attempt to compile them into types based purely on packing. From our analysis, we are able to determine a 'minimal' set of 18 atom types that most efficiently represent the spectrum of packing in proteins. Furthermore, we are able to uncover a number of inconsistencies in traditional chemical typing schemes, where differently typed atoms have almost the same effective size. In particular, we find that tetrahedral carbons with two hydrogens are almost identical in size to many aromatic carbons with a single hydrogen.