There is little objective insight about various statistical aspects regarding the nature of occurrences of 3-10 and Pi-helices. Comprehensive set of reasons behind the existence of 3-10 and Pi-helices can only be obtained if the occurrence profile of these on the primary structure is unambiguously described from the perspectives of sequence, structure and evolution. Although studies about the compositional and energetic profile of 3-10 and Pi-helices aren't uncommon, merely that doesn't tell us why these (rather unstable) structures are found in the proteins at the first place. Considering all the non-redundant protein structures across all the major structural classes, the present study attempts to find the probabilistic distributions that describe several facets of the occurrence of these rare secondary structures in proteins. Structural causes for observing these statistical patterns are explained too. Probabilistic profiling of the occurrence of 3-10 and Pi-helices reveal their presence to follow Poisson flow on the sequence. With extensive analysis from varying standpoints we prove here that, such Poisson flows suggest the 3-10-helices and especially Pi-helices to be evidences of nature's mistakes on folding pathways. This hypothesis is further supported by results of critical evolutionary analysis on 20 major protein domain families, which reveal the definitive trend that proteins try to dispose these structures off during evolution, in favor of alpha-helices. Alongside these unexpected and significant results } , a new algorithm to differentiate between related sequences is proposed here that reliably studies evolutionary distance with respect to protein secondary structures.
Considering all available non-redundant protein structures across different structural classes, present study identified the probabilistic characteristics that describe several facets of the occurrence of 3(10) and Pi-helices in proteins. Occurrence profile of 3(10) and Pi-helices revealed that, their presence follows Poisson flow on the primary structure; implying that, their occurrence profile is rare, random and accidental. Structural class-specific statistical analyses of sequence intervals between consecutive occurrences of 3(10) and Pi-helices revealed that these could be best described by gamma and exponential distributions, across structural classes. Comparative study of normalized percentage of non-glycine and non-proline residues in 3(10), Pi and alpha-helices revealed a considerably higher proportion of 3(10) and Pi-helix residues in disallowed, generous and allowed regions of Ramachandran map. Probe into these findings in the light of evolution suggested clearly that 3(10) and Pi-helices should appropriately be viewed as evolutionary intermediates on long time scale, for not only the \alpha}-helical conformation but also for the 'turns', equiprobably. Hence, accidental and random nature of occurrences of 3(10) and Pi-helices, and their evolutionary non-conservation, could be described and explained from an invariant quantitative framework. Extent of correctness of two previously proposed hypotheses on 3(10) and Pi-helices, have been investigated too. Alongside these , a new algorithm to differentiate between related sequences is proposed , which reliably studies evolutionary distance with respect to protein secondary structures.
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to be evidences of nature's mistakes on folding pathways. This hypothesis is further supported by results of critical evolutionary analysis on 20 major protein domain families, which reveal the definitive trend that proteins try to dispose these structures off during evolution, in favor of alpha-helices. Alongside these unexpected and significant results
revealed that these could be best described by gamma and exponential distributions, across structural classes. Comparative study of normalized percentage of non-glycine and non-proline residues in 3(10), Pi and alpha-helices revealed a considerably higher proportion of 3(10) and Pi-helix residues in disallowed, generous and allowed regions of Ramachandran map. Probe into these findings in the light of evolution suggested clearly that 3(10) and Pi-helices should appropriately be viewed as evolutionary intermediates on long time scale, for not only the
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