The Quantum Workings of the Rotating 64-Grid Genetic Code

A Tetrahedral Representation of the Genetic Code Emphasizing Aspects of Symmetry

The genetic code is a mapping of 64 codons to 22 actions, including polypeptide chain initiation, termination, and incorporation of the twenty amino acids. The standard tabular representation is useful for looking up which amino acid is encoded by a particular codon, but says little about functional relationships in the code. The possibility of making sense of the code rather than simply enumerating its codon-to-action pairings therefore is appealing, and many have attempted to find geometric representations of the code that illuminate its functional organization. Here, I show that a regular tetrahedron with each of its four faces divided into sixteen equilateral triangles (for a total of 64 triangular 'cells') is a particularly apt geometry for representing the code. I apply five principles of symmetry and balance in order to assign codons to the triangular cells of the tetrahedral faces. These principles draw on various aspects of the genetic code and the twenty amino acids, making the final construct a positional balance of the amino acids and their functions rather than a re-analysis of them. The potential significance of this exercise, and others like it, is that this way of organizing the biological facts may provide new insights into them.

Defragged Binary I Ching Genetic Code Chromosomes Compared to Nirenberg's and Transformed into Rotating 2D Circles and Squares and into a 3D 100% Symmetrical Tetrahedron Coupled to a Functional One to Discern Start From Non-Start Methionines through a Stella Octangula

BACKGROUND: Three binary representations of the genetic code according to the ancient I Ching of Fu-Xi will be presented, depending on their defragging capabilities by pairing based on three biochemical properties of the nucleic acids: H-bonds, Purine/Pyrimidine rings, and the Keto-enol/Amino-imino tautomerism, yielding the last pair a 32/32 single-strand self-annealed genetic code and I Ching tables. METHODS: Our working tool is the ancient binary I Ching's resulting genetic code chromosomes defragged by vertical and by horizontal pairing, reverse engineered into non-binaries of 2D rotating 4×4×4 circles and 8×8 squares and into one 3D 100% symmetrical 16×4 tetrahedron coupled to a functional tetrahedron with apical signaling and central hydrophobicity (codon formula: 4[1(1)+1(3)+1(4)+4(2)]; 5:5, 6:6 in man) forming a stella octangula, and compared to Nirenberg's 16×4 codon table (1965) pairing the first two nucleotides of the 64 codons in axis y. RESULTS: One horizontal and one vertical defragging had the start Met at the center. Two, both horizontal and vertical pairings produced two pairs of 2×8×4 genetic code chromosomes naturally arranged (M and I), rearranged by semi-introversion of central purines or pyrimidines (M' and I') and by clustering hydrophobic amino acids; their quasi-identity was disrupted by amino acids with odd codons (Met and Tyr pairing to Ile and TGA Stop); in all instances, the 64-grid 90° rotational ability was restored. CONCLUSIONS: We defragged three I Ching representations of the genetic code while emphasizing Nirenberg's historical finding. The synthetic genetic code chromosomes obtained reflect the protective strategy of enzymes with a similar function, having both humans and mammals a biased G-C dominance of three H-bonds in the third nucleotide of their most used codons per amino acid, as seen in one chromosome of the i, M and M' genetic codes, while a two H-bond A-T dominance was found in their complementary chromosome, as seen in invertebrates and plants. The reverse engineering of chromosome I' into 2D rotating circles and squares was undertaken, yielding a 100% symmetrical 3D geometry which was coupled to a previously obtained genetic code tetrahedron in order to differentiate the start methionine from the methionine that is acting as a codifying non-start codon.

Most Used Codons per Amino Acid and per Genome in the Code of Man Compared to Other Organisms According to the Rotating Circular Genetic Code

My previous theoretical research shows that the rotating circular genetic code is a viable tool to make easier to distinguish the rules of variation applied to the amino acid exchange; it presents a precise and positional bio-mathematical balance of codons, according to the amino acids they codify. Here, I demonstrate that when using the conventional or classic circular genetic code, a clearer pattern for the human codon usage per amino acid and per genome emerges. The most used human codons per amino acid were the ones ending with the three hydrogen bond nucleotides: C for 12 amino acids and G for the remaining 8, plus one codon for arginine ending in A that was used approximately with the same frequency than the one ending in G for this same amino acid (plus *). The most used codons in man fall almost all the time at the rightmost position, clockwise, ending either in C or in G within the circular genetic code. The human codon usage per genome is compared to other organisms such as fruit flies (Drosophila melanogaster), squid (Loligo pealei), and many others. The biosemiotic codon usage of each genomic population or 'Theme' is equated to a 'molecular language'. The C/U choice or difference, and the G/A difference in the third nucleotide of the most used codons per amino acid are illustrated by comparing the most used codons per genome in humans and squids. The human distribution in the third position of most used codons is a 12-8-2, C-G-A, nucleotide ending signature, while the squid distribution in the third position of most used codons was an odd, or uneven, distribution in the third position of its most used codons: 13-6-3, U-A-G, as its nucleotide ending signature. These findings may help to design computational tools to compare human genomes, to determine the exchangeability between compatible codons and amino acids, and for the early detection of incompatible changes leading to hereditary diseases.