Hachimoji DNA from TGD perspective

The popular article " Freaky Eight-Letter DNA Could Be the Stuff Aliens Are Made Of" (see this) tells about very interesting discovery related to astrobiology, where the possible existence of variants of DNA and other bio-molecules are of considerable interest. The article "Hachimojii DNA and RNA: A genetic system with eight building blocks" (see this) published in Science tells about a discovery of a variant of DNA with 8 letters instead of 4 made by Hoshika et al (see this). By using an engineered T7 RNA polymerase this expanded DNA alphabet could be transcribed into Hachimoji variant of RNA. The double strand structure of hachimoji DNA is similar to that of ordinary DNA and it is thermodynamically stable.

No amino-acid counterparts assigned to the hachimoji RNA were engineered: this would require the existence of translation machinery. The possible existence of also additional amino-acids leads to the speculation is that both alien life forms utilizing this kind of extended code could have evolved. One can also ask whether mere synthetic hachimoji RNA could be enough for synthetic life.

The abstract of the article gives a more technical description about what has been achieved.

" We report DNA- and RNA-like systems built from eight nucleotide "letters" (hence the name "hachimoji") that form four orthogonal pairs. These synthetic systems meet the structural requirements needed to support Darwinian evolution, including a polyelectrolyte backbone, predictable thermodynamic stability, and stereoregular building blocks that fit a Schrödinger aperiodic crystal. Measured thermodynamic parameters predict the stability of hachimoji duplexes, allowing hachimoji DNA to increase the information density of natural terran DNA. Three crystal structures show that the synthetic building blocks do not perturb the aperiodic crystal seen in the DNA double helix. Hachimoji DNA was then transcribed to give hachimojii RNA in the form of a functioning fluorescent hachimoji aptamer. These results expand the scope of molecular structures that might support life, including life throughout the cosmos."

If the additional code letters for DNA (8 code letters instead of 4) really carry information, the number of codewords is extended by factor 2³=8 giving 2⁹=512 code words. What the number of amino-acids would be, can be only guessed: the simplest guess is that also now the number is scaled up by factor 8 but this is only a guess.

In the sequel I consider hachimoji code from TGD perspective. The natural guess is that the hachimoji code corresponds to 8 copies of the ordinary genetic code in some sense. TGD predicts two basic realizations of the genetic code corresponding to dark genetic code and bio-harmony.

1. In the case of the dark code it is possible to imagine an extension of the code based on the notion of dark nucleus and the number codons is multiplied by 8. In the case of bio-harmony fusion of 8 copies of bio-harmony allows to realize hachimoji code.
2. I have considered two basic realizations of bio-harmony giving also realization of the genetic code (see this). The first realization is as a fusion of 3 icosahedral harmonies and tetrahedral harmony. Second realization is as a fusion of 2 icosahedral harmonies and 1 toric harmony. These constructions do not however allow any elegant geometric interpretation since two different geometries are involved in both cases.

   During writing I was forced to reconsider this problem and realized that a fusion of 2 icosahedral harmonies with 20 chords and 2 dodecahedral harmonies with 12 chords produces genetic code with 20+20+12+12=64 codons. Icosahedral and docecadedral harmonies correspond to dual tesselations of sphere so that bio-harmony can be represented as a bundle over sphere with two notes represented as points of the fiber. Hachimoji harmony is obtained by replacing 2-point fiber with 8× 2-point fiber. The presence of the dual tesselations conforms with the fact that Eastern music uses micro-intervals, which rather naturally correspond to 20-note dodecahedral scale.

3. The reason why for the hachimoji code could the basic problem of the music scale realized in terms of rational frequency ratios. Already Pythagoras was aware of this problem. The construction of the scale as powers of quint (3/2-fold scalings of the basic frequency) using octave equivalence produces with 12 iterations 7 octaves but only approximately: the 12th iterate does not quite correspond to the basic note in the octave equivalence. Performing the 12-fold iteration 8 times gives therefore a refined scale with each note replaced with 8 almost copies identifiable as hachimoji scale.