3-10 and Pi-Helices: Stochastic Events on Sequence Space; Reasons and Implications of their Accidental Occurrences across Protein Universe

TL;DR

This study analyzes the probabilistic occurrence of 3-10 and Pi-helices in proteins, revealing their random, rare, and evolutionarily transient nature, supported by statistical modeling and a new sequence comparison algorithm.

Contribution

It provides a probabilistic framework for understanding 3-10 and Pi-helices, introduces a new algorithm for sequence differentiation, and explores their evolutionary implications.

Findings

Occurrences follow Poisson distribution, indicating randomness.

Sequence intervals fit gamma and exponential distributions.

Higher presence of these helices in disallowed Ramachandran regions.

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.