Flexibility of $\alpha$-helices: Results of a statistical analysis of database protein structures

TL;DR

This study quantitatively analyzes the flexibility of alpha-helices in proteins using statistical methods, identifying key modes of deformation and their implications for protein structure and function.

Contribution

It introduces a principal-component analysis of alpha-helix flexibility across protein structures and models the modes of deformation with a simple spring model.

Findings

Identified three main modes of alpha-helix flexibility: two bend modes and one twist mode.

Flexibility modes follow Gaussian distributions and scale with helix length.

Simple spring model reproduces the dominant flexibility modes.

Abstract

$\alpha$-helices stand out as common and relatively invariant secondary structural elements of proteins. However, $\alpha$-helices are not rigid bodies and their deformations can be significant in protein function ({\it e.g.} coiled coils). To quantify the flexibility of $\alpha$-helices we have performed a structural principal-component analysis of helices of different lengths from a representative set of protein folds in the Protein Data Bank. We find three dominant modes of flexibility: two degenerate bend modes and one twist mode. The data are consistent with independent Gaussian distributions for each mode. The mode eigenvalues, which measure flexibility, follow simple scaling forms as a function of helix length. The dominant bend and twist modes and their harmonics are reproduced by a simple spring model, which incorporates hydrogen-bonding and excluded volume. As an application, we examine the amount of bend and twist in helices making up several coiled-coil proteins. Incorporation of $\alpha$-helix flexibility into structure refinement and design is discussed.