Flexibility of α-helices: Results of a statistical analysis of database protein structures

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α-helices stand out as common and relatively invariant secondary structural elements of proteins. However, α-helices are not rigid bodies and their deformations can be significant in protein function (e.g. coiled coils). To quantify the flexibility of α-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 α-helix flexibility into structure refinement and design is discussed.