HIPERCUBOS BOOLEANOS APLICADOS NA CARACTERIZAÇÃO DE PROPRIEDADES DOS AMINOÁCIDOS ASSOCIADOS AO ROTULAMENTO A DO CÓDIGO GENÉTICO.

Abstract

Mathematical modeling of the genetic code enables, among other aspects, the analysis, interpretation and characterization of properties associated with amino acids and possible interferences in various situations, such as genetic mutations. Hasse diagrams, Gray codes and Boolean hypercubes represent some mathematical tools that can be used in this study. The genetic code consists of the association of triplets found in messenger RNA, formed by nitrogenous bases and amino acids found in proteins. By mapping the nitrogenous bases with the algebraic structure of the ring Z₄ = {0, 1, 2, 3}, it is possible to obtain 24 permutations, organized into three labels (A, B and C). Furthermore, the genetic code can be represented by a 6-dimensional Boolean hypercube, constructed from the Gray code table. The aim of this paper is to present a characterization of the genetic code through the Gray code and the Boolean hypercube, using the permutations 1203 and 3021 of the A labeling of the genetic code, in order to analyze physicochemical properties of amino acids. The methodology adopted in this work is based on a qualitative and quantitative nature, aiming at a descriptive study and an applied approach. The constructions performed allow a characterization of the properties associated with the amino acids of the genetic code, allowing a classification of the codons and possibilities of future applications in biological phenomena, such as genetic mutations. With this, it is possible to understand the existing connections between Biology, Algebra and Geometry, in addition to the analysis of the genetic code.

Keywords: Biology. Gray Codes. Hasse Diagrams.