Spectral Decomposition of Mappings of Molecular Genetic Information in the System Basis of Single Nucleotide Functions

Abstract

This paper presents and visualizes examples of large amounts of genetic information using a new class of cognitive computer graphics algorithms. These algorithms are related to the semiotics of perception and allow the interpretation of those properties of nucleotide sequences that are difficult to perceive by simple reading or by standard means of statistical analysis. This article summarizes previously presented algorithms for visualizing long nucleic acids based on the primary Hadamard–Walsh function system. The described methods allow us to produce one-dimensional mappings of nucleic acids by levels corresponding to their scale-integral physicochemical parameters and construct a spectral decomposition of the nucleotide composition. An example of the spectral decomposition of parametric representations of molecular genetic structures is given. In addition, a multiscale composition of genetic functional mappings visualizing the structural features of nucleic acids is discussed.

Parametric Multispectral Mappings and Comparative Genomics

“…Previously, in [3], we visualized the structural features of the RNA nucleotide composition of various coronaviruses. We also demonstrated the possibilities of visualizing the structure of the RNA nucleotide composition of different algorithms when visualizing in different metrics [1]. In all these cases, a single basic algorithm for multiscale visualization worked in parametric spaces, based on a system of orthogonal Walsh functions that reflected the features of the physicochemical structure of the four nucleotides [12].…”

“…However, the key difference is that we will show the spectral decomposition in these spaces. Previously, we showed the spectral decomposition in only one-dimensional space [1]. In this study, we implemented various discrete geometric algorithms to implement visualization by decomposition into multistructures (multispectral mapping).…”

“…The first stage represents the choice of the scaling parameter N, which specifies the number of nucleotides in each minimal structural element (visualization point or N-plet). The subsequent step is the division of the genetic sequence into three sequences under the binary sub-alphabets system described in [1][2][3]. These sub-alphabets are a trinity of traits: purine/pyrimidine, keto/amino, and two/three hydrogen bonds.…”

“…Previously, we described "structural, integral and frequency representations, in which the genetic sequence was displayed for each of the three sub-alphabets either by decimal values of the minimum fragments, or by the number of certain characters in the minimum sequence, or by frequencies, respectively." Additionally, in [1], it was demonstrated how one can implement spectral decomposition for one-dimensional mappings. In this article, we will take a look at this step with examples in comparing two different aligned human DNAs.…”

“…Thus, studies aimed at finding such unified algorithms of visualization of genetic data are relevant. This work is a development of the earlier stated concept of genometric analysis and visualization described in publications [1][2][3].…”