TGD diary: Homonymy of the genetic code from TGD point of view

The article behind the following considerations was motivated by the article of Peter Gariaev about the linguistic notions of synonymy and homonymy applied to genetic code. Homonymy is visible in mRNa-tRNA pairing and induced by the 1-to-many pairing of the third mRNA nucleotide with tRNA nucleotide. The homonymy in mRNA-AA (AA for amino-acid) pairing is also present albeit rare and might be explainable in terms of context dependence of this pairing.

The article summarizes much what is known about the theoretically poorly understood role of the third nucleotide of mRNA in the translation of mRNA to AAs. That many tRNAs correspond to same mRNA - synonymy - is not surprising since the number of tRNAs is smaller than that of mRNAs. There is however also homonymy present - the third nucleotide of mRNA can correspond to several tRNAs. If the AAs associated with homonymous tRNAs are same, the is no homonymy in mRNA-AA pairing. This is not quite always the case but the deviations are surprisingly small.

The article emphasizes the fact that the codons for the standard code can be divided to two classes. For 32 codons the first two letters fix AA completely. For the remaining 32 codons there is almost unbroken symmetry in that U and C resp. A and G code for the same AA. This symmetry is broken only for the the three 4-columns of the code table containing Stop codon or Start codon coding also for met: this symmetry breaking is unavoidable given that the number of both start and Stop codons is odd. This symmetry breaking is minimal and applies only to A-G whereas T-C symmetry is exact. For the deviations of the code from the standard code the deviation as a rule breaks A-G or T-C symmetry or re-establishes it.

The notion of homonymy is extremely interesting from TGD point of view. TGD leads to two basic proposals predicting the numbers of DNA codons coding for AA rather successfully.

The first proposal (see this) relies on TGD view about dark matter as h_eff/h=n phases of ordinary matter motivated by adelic physics extending physics to include also the correlates of cognition (see this) . The empirical motivation comes from several sources, in particular from the findings of Pollack discussed here. One can understand the formation of negatively charged regions - exclusion zones (EZs) - as being due to the transformation of part of protons to dark protons residing at magnetic flux tubes.

Dark genetic code would be realized in ters of dark proton sequences - to be denoted by DDNA, DmRNA, DtRNA, and DAA - would provide dark analogs of DNA, mRNA, tRNA, and AA. Biochemistry would emerge as a shadow of the much simpler dynamics of dark matter at flux tubes and genetic code would be induced by dark code code. The dark code would be sequence DDNA → DmRNA → DtRNA→ DAA of many-to-1 maps free of homonymies.
Second model of genetic code emerged accidentally from a geometric model of music harmony (see this) involving icosahedral (12 vertices-12-note scale and 20 faces-number of AAs) and tetrahedral geometries leading to the proposal that DNA codons and possibly also AAs correspond to 3-chords defining the harmony and obtained as unions of 20+20+20 3-chords associated with icosahedral 20-chord harmonies with symmetries Z₆,Z₃,Z₂ plus tetrahedral 4-chord harmony. There is large number of these harmonies bringing in additional degrees of freedom.

Remark: This model has obviously analogies with the notion of wave genome introduced by Peter Gariaev.

Since music both expresses and creates emotions the proposal is that these harmonies assigning additional hidden degrees of freedom to the magnetic bodies of DDNA, DRNA, etc... serve as correlates of emotions also at the molecular level. This emotional context could also give rise to context dependence of the code if several harmonies are realizable chemically. Taking seriously TGD inspired theory of consciousness (see this) and model of emotions (see this), one might say that the details of the code might depend slightly on the "emotional" state of DNA, RNA, and possibly other molecules.

In the sequel I will consider the following proposal for the various pairings of dark DNA and ordinary DNA visualizable as a 2× 4-matrix with two rows representing DDNA, DmRNA, DtRNA, DAA resp. DNA, mRNA, tRNA, AA.

The proposal is that genetic code at dark level extends to a sequence DDNA → DmRNA → DtRNA → DAA of horizontal pairings analogous to projections is the fundamental one, and realized via dark photon triplet resonance expect for the coupling to DAA for which coupling is based on the sum f_XYZ= f₁+f₂+f₃ of 3-chord frequencies. One might perhaps say that AA sequence defines melody and mRNA sequence the accompaniment. The frequencies f_XYZ for codons coding same AA would be same modulo octave multiple. There is context dependence and homonymies already in DmRNA-DtRNA pairing and due the fact that DtRNA corresponds to a 2-harmony as sub-harmony of 3-harmony and can be chosen in 3 different manners. Also this choice - perhaps by state function reduction - could correlate with emotional state.
There are also vertical mappings DDNA → DNA, DmRNA → mRNA, DtRNA → tRNA and DAA → AA. These pairings would induce the horizontal pairings DNA → mRNA → tRNA → AA at the chemical level. The homonymy at mRNA-tRNA level would have no effects on DNA-AA pairing.
Apart from mRNA-AA pairing all these pairings would be realized dynamically in terms of 3-chords (f₁,f₂,f₃) and giving rise to a resonant coupling between members of the pair connected by magnetic flux tubes to single dynamical unit carrying the dark photon triplets at the frequencies characterized by the 3-chord. The model for musical harmony (see this) leading also to a realization of genetic code suggests the existence of a large number of harmonies.

It is not however obvious whether these harmonies can be realized bio-chemically since the 3-chords must be resonance 3-chords for bio-molecules. For DNA-AA and mRNA-AA correspondence the constraints are the slightest ones since they couple to f_XYZ= f₁+f₂+f₃: AAs could have emerged in rather early stages of the prebiotic evolution. One cannot even exclude the possibility f_XYZ are same for different harmonies. Slight chemical modifications of DNA and mRNA and AA analogous to wobbling for tRNA might allow to realize the slightly different collections of 3-chords defining the harmonies.
The model leads to an explanation for the homonymy of mRNA → tRNA pairing as being induced by the mRNA-tRNA homonymy realized already at dark level. The rather rare homonymies in DNA-AA pairing can be understood as accidental degeneracies. AA couples resonantly to the sum f_XYZ=f₁+f₂+f₃ of frequencies associated with codon XYZ, and one can have f_X₁Y₁Z₁= f_X₂Y₂Z₂ modulo octave multiple for two codons. DAA coded by DDNA codes for AA and tRNA serves only in the role of transferring DAA-AA pairs and attaching them to DmRNA-mRNA pairs: the mRNA-AA pairing would be determined completely by dark molecules. It is actually advantageous to have tRNA homonymy since it can happen that the concentration of particular certain kind of tRNA is low.
What distinguishes between DNA and RNA and between codons and anti-codons is not obvious in the harmonic model. The most plausible identification for the map mapping codons to anti-codons is reflection symmetry of the icosahedron permuting opposite faces. An internal reflection changing the orientation of the scale could map DNA to RNA: this makes sense if the chords can be regarded as arpeggios.
The vision of biological evolution as chemical evolution in which dark variants of genetic code gradually find biological representations suggests a concrete model for RNA era. At that era AAs would have catalyzed mRNA replication possibly as non-faithful process. This era might have preceded tRNA era with mRNA replaced with tRNA analog corresponding to to the fusion of two 20-chord representations. The era before this could have been era with single 20-chord representation and corresponding tRNAs and amino-acids.