Application of the Ramanujan Fourier transform for the analysis of secondary structure content in amino acid sequences

Objective: A novel method is presented for the investigation of protein properties of sequences using Ramanuian Fourier Transform (RFT). Methods: The new methodology involves the preprocessing of protein sequence data by numerically encoding it and then applying the RFT. The RFT is based on projecting the obtained numerical series on a set of basis functions constituted by Ramanuian sums (RS). In RS components, periodicities of finite integer length, rather than frequency, (as in classical harmonic analysis) are considered. Results: The potential of the new approach is documented by a few examples in the analysis of hydrophobic profiles of proteins in two classes including abundance of alpha-helices (group A) or beta-strands (group B). Different patterns are provided as evidence. Conclusions: RFT can be used to characterize the structural properties of proteins and integrate complementary information provided by other signal processing transforms.