This paper presents a new version of a periodic table for genetic codes using a ‘Leibnitz Number’ as a codon number or anticodon number, which is a natural binary code number and hence outwardly similar to the Gray code binary number. In the obtained periodic table or in the reformed table (a cube-shaped periodic table), the proteinaceous amino acids not only have periodicity, but also occupy mirror-symmetrical positions with respect to the xy-plane. Moreover, the cube-shaped periodic table allows a partial explanation of non-standard genetic codes and some predictions about providing potential candidates for non-standard genetic codons to be discovered in the future. By making a new format of a two-dimensional periodic table for anticodons as the primary reference point, all of the anticodon pairing with multiple codons can be intimately related to a mirror-symmetrical arrangement of amino acids with relation to the yz-plane in the two-dimensional periodic table.
In the later section two new indexes, the Inversion Number and the Miracle Number, are introduced to show that the codon numbers and anticodon numbers play a fundamental role in the structure underlying the genetic code table. These characteristic features, such as periodicity and mirror symmetry of the indexes, hold true for not just the Watson–Crick base-pairs, but also for the non-Watson–Crick base-pairs.
Furthermore, in the mammalian mitochondrial genetic code, some basic rules identical/similar to the standard genetic code can be disclosed. These results, including symmetric quality of amino acids and Inversion Numbers, suggest the necessary conditions for the existence of life systems. Additionally, the proposed periodic table can successfully understand the previous studies, such as codon ring, mutation ring, and biosynthetic pathways.
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