Helix-helix interactions and their impact on protein motifs and assemblies.

Protein secondary structure elements are arranged in distinct structural motifs such as four-alpha-helix bundle, 8alpha/8beta TIM-barrel, Rossmann dinucleotide binding fold, assembly of a helical rod. Each structural motif is characterized by a particular type of helix-helix interactions. A unique pattern of contacts is formed by interacting helices of the structural motif. In each type of fold, edges of the helix surface, which participate in the formation of helix-helix contacts with preceding and following helices, differ. This work shows that circular arrangements of the four, eight, and sixteen alpha-helices, which are found in the four-alpha-helical motif, TIM-barrel 8alpha/8beta fold, and helical rod of 16.3 helices per turn correspondingly, can be associated with the mutual positioning of the edges of the helix surfaces. Edges (i, i+1)-(i+1, i+2) of the helix surface are central for the interhelical contacts in a four-alpha-helix bundle. Edges (i, i+1)-(i+2, i+3) are involved in the assembly of four-alpha-helix subunits into helical rod of a tobacco mosaic virus and a three-helix fragment of a Rossmann fold. In 8alpha/8beta TIM-barrel fold, edges (i, i+1)-(i+5, i+6) are involved in the octagon arrangement. Approximation of a cross section of each motif with a polygon (n-gon, n=4, 8, 16) shows that a good correlation exists between polygon interior angles and angles formed by the edges of helix surfaces.