Relationship between Inter-Helical Angle and Sequential Distance

This paper presents a statistical analysis of helix-helix packing in 1290 high-resolution globular protein structures with less than 20 percent homology. Orientational preferences in helix packing are shown to be dominated by interactions between helices that are proximal in sequence. Such sequentially proximal interactions have a higher frequency of occurrence than sequentially distal interactions. This bias is described with a univariate probability density function that depends only on the sequential distance between interacting helices. We also compute bivariate probability densities that depend on both inter-helical orientation and sequential distance. The dominance of certain preferred orientations and sequential distance values in this bivariate distribution are observed. Angle preferences persist even when the bivariate distribution is normalized by the univariate distribution. This statistical analysis provides quantitative probability distributions from which statistical potentials for secondary structure assembly can be derived. Key-Words: Helix, inter-helical angle, sequential distance, helix packing, protein folding, statistical analysis