Fourier Analysis of Conservation Patterns in Protein Secondary Structure

Residue conservation is a common observation in alignments of protein families, underscoring positions important in protein structure and function. Though many methods measure the level of conservation of particular residue positions, currently we do not have a way to study spatial oscillations occurring in protein conservation patterns. It is known that hydrophobicity shows spatial oscillations in proteins, which is characterized by computing the hydrophobic moment of the protein domains. Here, we advance the study of moments of conservation of protein families to know whether there might exist spatial asymmetry in the conservation patterns of regular secondary structures. Analogous to the hydrophobic moment, the conservation moment is defined as the modulus of the Fourier transform of the conservation function of an alignment of related protein, where the conservation function is the vector of conservation values at each column of the alignment. The profile of the conservation moment is useful in ascertaining any periodicity of conservation, which might correlate with the period of the secondary structure. To demonstrate the concept, conservation in the family of potassium ion channel proteins was analyzed using moments. It was shown that the pore helix of the potassium channel showed oscillations in the moment of conservation matching the period of the α-helix. This implied that one side of the pore helix was evolutionarily conserved in contrast to its opposite side. In addition, the method of conservation moments correctly identified the disposition of the voltage sensor of voltage-gated potassium channels to form a 3₁₀ helix in the membrane.