Frequencies of α-helix and β-strand are not equal

Our theoretical expected frequency assumes an equal frequency of 1/2 for both α-helices and β-strands. Note that as the members of S1, i.e. the α-helix and the β-strand, are indivisible, there is no associated observation-based expected frequency. However, the observed frequency is 43.5% for a helix and 56.5% for a β-strand. In terms of assembling larger folding units from stable smaller ones, perhaps the theoretical frequencies of the elements should rather reflect those of the simplest stable supersecondary structure units: the α-hairpin, β-hairpin, and βαβ unit. Remarkably, theoretical frequencies for the α-helix (3/7=42.9%) and β-strand (4/7=57.1%) calculated from these simple stable SSPs agree with those observed in the database with an error of just 0.6%.

When considering the observed frequency of elements within superfamilies, the results show an opposite trend of 55.8% for α-helix and 44.2% for β-strand. This trend might reflect the relative difficulty of classifying α-helical structures with respect to the other main classes. As opposed to structures containing β-strands, whose interactions are more rigidly dictated by backbone hydrogen bonds, α-helical interactions tend to vary by their contacts, tilt angles and packing arrangements. To accommodate these fine-grained structure features, SCOP splits all α-helical folds and contains more superfamilies in the all α class (507 superfamilies) than in the all β class (354 superfamilies). However, normalizing the α-helix and β-strand counts by the frequency of SCOP superfamilies among the main classes (all α, all β, α/β and α+β) only slightly alters the frequencies of α-helix (53.8%) and β-strand (46.2%). Thus, the abundance of superfamilies in the all α class alone does not explain the apparent overabundance of α-helices calculated at the superfamily level. The below table documents the ratio of α-helices and β-strands detected in superfamilies from each of the main SCOP classes. The ratios for α-helices present in the all α, α/β and α+β classes and for &beat;-strands found in the all β, α/β and α+β classes are all at or near identity (ranging from 0.99 to 1). The ratio of superfamilies belonging to the class all-α that contain β-strands is 0.13. In contrast, the ratio of superfamilies belonging to the class all-β that contain α-helices is significantly higher at 0.62, yielding an explanation for the observed superfamily frequencies of α-helix and β-strand. This might suggest that it is relatively easy to add α-helices to existing all-β structure cores as opposed to adding β-strands to existing all-α structure cores.