Fluctuations of an α‐helix

Fluctuations in backbone dihedral angles in the α‐helical conformation of homopolypeptides are studied based on an assumption that the conformational energy function of a polypeptide consisting of n amino‐acid residues can be approximated by a 2 n ‐dimensional parabola around the minimum point in the range of fluctuations. A formula is derived that relates 〈Δθ i Δθ j 〉, the mean value of the product of deviations of dihedral angles ϕ i and ψ i (collectively designated by θ i ) from their energy minimum values, with a matrix inverse to the second derivative matrix F , n of the conformational energy function at the minimum point. A method of calculating the inverse matrix F n −1 explicitly is given. The method is applied to calculating 〈Δθ i Δθ j 〉 for the α‐helices of poly( L ‐alanine) and polyglycine. The autocorrelations 〈(Δϕ i ) 2 〉 and 〈(Δψ i ) 2 〉 at 300°K are found to be about 66 deg 2 and 49 deg 2 , respectively, for poly( L ‐alanine), and 84 deg 2 and 116 deg 2 , respectively, for polyglycine. The length of correlations of fluctuations along the chain is found for both polypeptides to be about eight residues long.