Characterization of the properties of amino acids using the Hasse diagram associated with the A labeling of the genetic code

Abstract

The application of mathematical structures in the modeling of the genetic code is something that several researchers have been carrying out, seeking to characterize mathematically what the biological world accomplishes. Of these structures, the Boolean lattices, Hasse diagrams and Hamming distance, have been used in the process of analyzing mutational phenomena, enabling a physical-chemical analysis of amino acids, in addition to allowing the algebraic characterization of the genetic code. The mathematician Claude E. Shannon was the forerunner of code theory and applied elements of engineering in biology. The constructions of this work will be through the mapping of the nitrogenous bases adenine, cytosine, guanine, thymine / uracil, {A, C, G, T/U} with the ring Z₄={0, 1, 2, 3}, where it is possible to obtain 24 permutations, which can be divided into 3 labels (A, B and C), according to geometric characteristics. The objective of this work is to present the construction of the Boolean lattices and primal and dual, whose permutations are, respectively 0132 and 2310 of the labeling A. An analysis of the differences and physicochemical similarities of the amino acids will be carried out on these constructions, through the biological characterization of the constructions and the calculation of the averages of the Hamming distances among the codons, which can be used in the analysing mutational phenomena process.