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The genetic code is a set of regulatory principles that control the translation of information encoded in messenger RNA (mRNA) into a sequence of amino acids. This study proposes a model starting from the relationships between its physicochemical properties of nucleobase in the codons. We employed a binary metric and the Kronecker product to represent the physicochemical properties of nucleobases in a vector space. This state space has a hierarchical order, with self-similarity and symmetry properties in the hydrogen bonds of triplets. The state space can be mapped under linear transformations to a toroidal geometry with allometric properties. Furthermore, this geometric representation highlights a charge symmetry that exists in amino acids and in the distribution of essential and non-essential amino acids. These results describe a state space between codon-anticodon interactions that can be interpreted as Bell states. This suggests that there is a quantum phenomenon involved in the mechanisms of information storage in DNA. In addition, toroidal geometry can be used to represent the sequences of codons of the mRNA that encode the sequence of amino acids of the proteins to find similarities or homologies between evolutionary related species. [ABSTRACT FROM AUTHOR]

The present study is devoted to describing the "logic" implicit in the standard genetic code. Bases are considered as physicochemical entities possessing two essential properties: molecular type and number of Hydrogen bonds involved (bases pairing) in the codon-anticodon specific interactions. It is proposed that the codon structure possesses a dual informative function: on the one hand, it determines its discriminating or non-discriminating character, and on the other hand, it determines a specific amino acid. These two aspects constitute the codon global information. Two different sets of rules are introduced to describe these different phenomena. It is established that, depending on the type of base occupying the second position, only two or three of the six codon properties located at defined positions determine the discriminating or non-discriminating behavior. With regard to the amino acid determining function of the codons for different sets of synonymous (singlets, doublets, triplets, quadruplets, or sextets), the number of informative properties integrating the codon and their typical positions characteristically change. Based on the rules presented here, it can be postulated that a codon can be defined as an asymmetric informative entity, whose global informative capacity results from the spatially organized combination of the six properties assigned by the three bases. [ABSTRACT FROM AUTHOR]