Approximation Models of Inexact Repeats in Spatial Conformations of Proteins

The problem of repeat recognition in tertiary structures of protein macromolecules, is considered. Recognition is based on the construction of a dot plot using a threshold decision rule and a spectral approach to estimating the distance between functions. Spatial conformations are considered based on the natural equation of the curve for the main protein chain (backbone) in three-dimensional space. When constructing a curve, the following constructive approximation methods are considered: trigonometric Fourier series, Fejer’s theorem, and Bernstein’s uniform approximation polynomials. It is shown that the approximative properties of Bernstein’s polynomials differ significantly from Fourier series and allow one to construct a protein molecule model that is most resistant to variations. Examples of comparison of structural motifs, and domain models are considered. Efficient computational implementation of the developed methods is based on the vectorization of computations.