Parametric Multispectral Mappings and Comparative Genomics

Abstract

This article describes new algorithms that allow for viewing genetic sequences in the form of their multispectral images. We presented examples of the construction of such mappings with a demonstration of the practical problems of comparative genomics. New DNA visualization tools seem promising, thanks to their informativeness and representativeness. The research illustrates how a novel sort of multispectral mapping, based on decomposition in several parametric spaces, can be created for comparative genetics. This appears to be a crucial step in the investigation of the genetic coding phenomenon and in practical activities, such as forensics, genetic testing, genealogical analysis, etc. The article gives examples of multispectral parametric sets for various types of coordinate systems. We build mappings using binary sub-alphabets of purine/pyrimidine and keto/amino. We presented 2D and 3D renderings in different characteristic spaces: structural, integral, cyclic, spherical, and third-order spherical. This research is based on the method previously developed by the author for visualizing genetic information based on new molecular genetic algorithms. One of the types of mappings, namely two-dimensional, is an object of discrete geometry, a symmetrical square matrix of high dimension. The fundamental properties of symmetry, which are traced on these mappings, allow us to speak about the close connection between the phenomenon of genetic coding and symmetry when using the developed mathematical apparatus for representing large volumes of complexly organized molecular genetic information.