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 glob ular proteins. The standard model used nowadays to describe a coiled coil s tructure is derived from the mathematical description established more than 40 years ago by F.H.C. Crick (1953, Acta Crystallogr. 6, 685-689) from geo metrical arguments. In this paper, we apply stereochemical constraints to t he 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 measu red. In addition, the metrics equation method developed here ensures a mini mization of the distortions occurring during the coiling process relating t he original straight alpha-helix and the coiled coil minor helix. It leads to a modification of the widely used relation between the numbers of residu es per turn in the minor and alpha-helices, mathematically demonstrating a previously semiempirical result. This method can be extended to a wide rang e of coiled structures. (C) 1999 Academic Press.