Connection between dark nucleon code and bioharmony

The model of genetic code based on bioharmony has evolved through many sidetracks (see this) but the the version discussed in many sidetracks (see this, this, and this) is roughly consistent with the original model and also gives a connection with the model of dark nuclear code.

Bioharmony and resonance mechanism for dark photon communications

The faces of icosahedron and tetrahedron (and also octahedron appearing in the model of genetic code as icosa-tetrahedral tessellation of hyperbolic space H³ (see this) are triangles. The proposal is that they somehow correspond to 3-chords made of dark photons, which in turn represent genetic codons.

Communications by dark 3-photons represent codons. 3N-photons represent in turn genes. The communications rely on cyclotron 3N-resonance so that the vertices of the faces of icosa-tetrahedron must contain charged particles coupling to a magnetic field. The magnetic field strengths at flux tubes associated with charged particles would determine the cyclotron frequencies.

Information is encoded to the frequency modulation of cyclotron frequencies. The chords serve as addresses much like in computer language LISP. If the modulations of 3N frequencies are identical and in synchrony, the outcome of the receiver consisting of 3N charged particles is a sequence of 3N-resonances giving rise to an 3N-pulse sequence. Nerve pulse patterns could emerge by this mechanism.

One can also consider 3N-signals for which only M<3N modulations are identical and in synchrony. In this manner communications to subsets of the receiver are possible. For instance, some subset of codons of dark gene or dark protein can be selected as a receiver, possibly controlled. This selection could de-entangled the receiver to de-entangled coherent pieces.

There is a direct connection with empiria. Biophotons, whose origin remains poorly understood, can be identified as ordinary photons resulting from the decay of dark 3N-photons to ordinary photons.

The realization in terms of dark nucleons looks more plausible if also DtRNA and DAAs are realized in terms of icosa-tetrahedral picture (the dark counterpart of information molecules X will be denoted by DX). This is because the amino acids are often neutral unlike DNA nucleotides which are negatively charged. The dark charge assignable to the icosa-tetrahedron can be controlled by pionic bonds with charges 0,+/- 1 so that it can be 3 units for DDNA and vanish for amino acids. A natural proposal is that the charge of icosa-tetrahedron compensates the charge of the amino acid and tRNA.

There are pairings of type DX-DY. The pairings DDNA-DRNA, DRNA- DtRNA and DtRNA-DAA induce the biochemical dynamics of transcription and translation. There are also pairings DX-X. DDNA-DNA and DRNA-RNA unique DtRNA-tRNA pairing is 1-to-many and relates to the wobble phenomenon. The pairings between dark nucleon variants of biomolecules and corresponding dark 3N-photons make possible biocommunications and control.

Details of the bioharmony model

Consider now a more detailed bioharmony model of the genetic code based on the geometries of icosahedron and tetrahedron.

1. Icosahedron has 12 vertices and 20 faces, which are triangles. The idea is that the 12 vertices correspond to the notes of 12-note scale. Tetrahedron has 4 vertices and 4 faces and is self-dual whereas the dual of icosahedron is dodecahedron having 20 faces and 12 faces.
2. 12-note scale can be represented as a Hamiltonian cycle at an icosahedron going once through all vertices. The frequencies at the neighboring points as edges of a face in cycle relate by a frequency scaling of 3/2: this gives rise to the Pythagorean variant of quint cycle.

Octave equivalence means the identification of frequencies differing by a multiple of octaves. Octave equivalence can be used to reduce all frequencies to a single octave. If the scaling is exactly 3/2 at all steps there is a slight-breaking of octave equivalence since (3/2)¹² does not quite correspond to an integer number (7) of octaves. Pythagoras was well aware of this.

Given cycle assigns to faces 3-chords defining a harmony with 20 chords assignable to the faces of the icosahedron. For dodecahedron there is only single harmony with 12 chords and 20-note scale which could correspond to Eastern scales. For the tetrahedron the Hamiltonian cycle is unique.

Some kind of symmetry breaking is present as in the case of dark nucleon code. 2 AA doublets must split to singlets. If (ile,ile,ile,met) coded by UAX could correspond to (ile,ile) and (met,met) such that (met,met) is split to (ile,met). In absence of symmetry breaking one would have 11 doublets as predicted.

There is (stop,stop) doublet (UAA, UAG) and (stop,trp) doublet (UGA,UGG). These doublets could correspond to the faces of the tetrahedron. Only one face would code for amino acid in the vertebrate code. Other faces would not have corresponding tRNA?

For bacterial codes, the situation can be different. Pyl and sec appear as exotic amino acids. Could (UAA,UAG) for code for (stop,pyl) and (UGA,UGG) for (sec,trp) instead of (stop,trp)? Orientation preserving rotations form a 12-element group having Z₂ and Z₃ as subgroups. For Z₂ the orbits consist of 2 vertices and for Z₃ of 3 vertices (face) and 1 vertex. Z₃ symmetry could correspond to trp as singlet and vertebrate stop codons as triplet. For bacterial pyl and sec Z₂ with symmetry breaking is suggestive. Bioharmony, dark nucleon code, and icosa-tetrahedral code as a tessellation of H³

Bioharmony model involves icosahedron and tetrahedron. This looks ugly unless there is some really deep reason for their emergence. One can also ask why not also octahedron having triangular faces.

Hyperbolic 3-space H³ has interpretations as a mass shell of Minkowski space M⁴ at the level of M⁸ and as light-cone proper-time constant surface at the level of H. The 4-surface X⁴ in M⁸ contains mass shells of M⁴ corresponding to the roots of the polynomial P defining X⁴. Hence one expects that H³ plays a key role in quantum TGD both discretized momentum as defining a cognitive representation with momenta, which are algebraic integers associated with extension of rationals defined by P. H³ has infinite discrete subgroups of the Lorentz group analogous to discrete groups of translations in E³ as isometries and H³ allows an infinite number of tessellations (lattices).

Perhaps the simplest tessellation is icosa-tetrahedral tessellation involving also octahedrons and thus all triangular Platonic solids. This tessellation could give rise to genetic code by induction of tesselation to 3-surfaces or lower-D objects such as linear biomolecules, and cell membranes (see this). I do not however understand the mathematical details well enough but the following discussion is general.

Consider first the model for DDNA and DRNA allowing us to understand the connection between dark nucleon and dark photon realization of the genetic code physically.

1. The realization of DDNA/DRNA/DtRNA/DAA could correspond to a sequence of icosahedron-tetrahedron pairs at H³ contained by the 4-surface X⁴⊂ M⁸ and its H images which is also H³.
2. Each icosa-tetrahedron would contain a dark codon realized both as a face and dark nucleon triplet associated with it. The dark photon chord associated with the face must be the same as the codon defined by dark nucleon triplet. The dark nucleon triplets correspond to cyclotron frequency triplets, which in turn correspond to dark photon 3-chords associated with the Hamiltonian cycles.
3. The cyclotron frequencies are determined by magnetic fields at flux tubes so that Hamilton cycles must correspond to flux tube patterns. The simplest hypothesis is that the Hamilton cycle is a closed flux tube connecting all vertices of the icosahedron. Dark codon triplet corresponds to a face with 3 flux tube edges.

The simplest option is that the flux tubes defining the edges define the cyclotron frequencies defining the dark codon in bioharmony. The variation of flux tube thickness implies frequency modulation crucial for communications.

The realization of the Hamilton cycle requires that the magnetic field strength along the cycle is scaled by factor 3/2 to give a quint cycle.

One of the DtRNAs could correspond to trp. The second one would correspond to a stop codon in the vertebrate code: either the DtRNA codon is not present at all or or it does not pair with tRNA. TAG and TGA can code for pyl and sec in some bacterial versions of the code and in this case the corresponding dark DRNA codon would be represented at the DtRNA tetrahedron.

Since DRNA-DtRNA correspondence is 2-1 although not codon-wise, the natural first guess is that Z₂ orbits of the faces define the DRNA codons at the DtRNA icosahedron so that it would contain 2 codons for most DtRNAs. At the DtRNA tetrahedron the only option is Z₁ so there is a symmetry breaking.

If Z₂ corresponds to a reflection, the orbit always contains 2 codons. If Z₂ corresponds to a rotation by π, it might happen that the face invariant under π rotation and the orbit would consist of a single point. Could this explain why one has (ile,ile,ile,met) instead of (ile,ile) and (met,met)? The rotation axis should go through the invariant face and since the face is a triangle, π rotations lead out of the icosahedron. Therefore the answer is negative. Ile-met problem deserves a separate discussion.

1. The pairing of Z₂ related DDRNA faces with two different DtRNAs coding for ile and met rather than two mets means Z₂ symmetry breaking at the level of bioharmony. Could the fact that AUG acts as a start codon relate to this? Could it be that both AUG and AUA cannot act as start codons? It is difficult to invent any raeson for this.
2. The symmetry breaking could occur in DtRNA-DAA pairing and replace Dmet with Dile. Is it possible that the 3-chords for coding for ile and second met are nearly identical so that the resonance mechanism selects ile instead of met? Could the situation be similar for the codons coding for (stop,stop) and (stop,trp) and cause the coding of pyl or sec in some situations? The scale for the quint cycle model with octave equivalence does not quite close. Could this have some role in the problem?
3. Since similar ambivalence occurs for stop codons assigned to the tetrahedral Hamiltonian cycle, one can look at the tetrahedral Hamiltonian cycle. In this case a given edge of the cycle corresponds to a scaling by (3/2)³ so that 4 steps gives (3/2)¹², which is slightly more than 7 octaves. For the quint scale in Pythagorean sense, one obtains 4 notes in the same octave.

Exact octave equivalence corresponding to equally tempered scale in which half-note corresponds to frequency scaling 2^1/12, implies that there is only one 3-chord CEG#: this would explain why there are 3 stop codons in the vertebrate code!

If bacterial codes correspond to Pythagorean scale, there would be two different 3-chords since CEG# and EG#C are not quite the same. The reason is that the frequency ratios of chords are powers of 3/2)¹². This situation is completely exceptional.

In the quint scale there are small differences between the 4 chords. Could this explain why only one of these 3-chords codes for AA (trp) in vertebrate code and pyl or sec is coded instead of stop in bacterial codes? Amusingly, the chord CEG# ends many finnish tangos and therefore acts like a stop codon!

Could bacteria have a perfect pitch and live in a Pythagorean world? Could the transition to multicellulars mean the emergence of an algebraic extension of rationals containing 2^1/12 &esim; 1.059(, which is considerably larger than to (3/2)¹²/2⁷&esim; 1.0136)! Could people with perfect pitch have in their dark genome parts using Pythagorean scale or can they tune the magnetic flux tube radii to realize Pythagorean scale?

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.