3-10 and Pi-Helices: Stochastic Events on Sequence Space; Reasons and Implications of their Accidental Occurrences across Protein Universe
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2009
- DOI:
- 10.48550/arXiv.0911.4871
- arXiv:
- arXiv:0911.4871
- Bibcode:
- 2009arXiv0911.4871P
- Keywords:
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- Quantitative Biology - Biomolecules;
- Quantitative Biology - Quantitative Methods