Modeling alpha-helical coiled coils: analytic relations between parameters.

This paper deals with the alpha-helical coiled coil secondary structure of proteins, which is found not only in many fibrous proteins but also in globular proteins. The standard model used nowadays to describe a coiled coil structure is derived from the mathematical description established more than 40 years ago by F. H. C. Crick (1953, Acta Crystallogr. 6, 685-689) from geometrical arguments. In this paper, we apply stereochemical constraints to the protein chains to refine this model. We present a model based on Crick's calculations with less restrictive hypotheses than the standard model and only requiring a set of initial parameters that can be experimentally measured. In addition, the metrics equation method developed here ensures a minimization of the distortions occurring during the coiling process relating the original straight alpha-helix and the coiled coil minor helix. It leads to a modification of the widely used relation between the numbers of residues per turn in the minor and alpha-helices, mathematically demonstrating a previously semiempirical result. This method can be extended to a wide range of coiled structures.