TGD based model for the evolution of genetic code: III

Ulla Mattfolk sent me again an interesting link, which happened to relate directly to what I have been doing during the last week, that is application of DNA as topological quantum computer hypothesis to the understanding of the evolution of the genetic code. The link was to an article about the idea of protein folding code - something which is expected to exist but is not understood. See also this. I realized that the prebiotic 2-code assigning to RNA dinucleotides aminoacids might define the folding code. This code would specify also what kind of catalytic reactions can occur between proteins and would dictate the catalytic stereo chemistry - or rather its changes - to a high degree.

1. The cautious working hypothesis is that living aminoacids are braided in the sense that from a given aminoacid there emanates two braid strands represented by "wormhole" magnetic flux tubes - let as call them simply threads. The threads are colored in the sense that they carry four different colors so that one has 16 color pairs: the color is specified in terms of quarks and antiquarks in a manner that I have explained earlier. The colors are in one-one correspondence with DNA nucleotides A,T,G,C: this hypothesis has led to a quite variety of predictions already shown to be correct. The colors of aminoacid threads are determined completely by the dinucleotide XY of DNA codon XYZ coding for the aminoacid.

2. In accordance with the explanation of the finding discussed in previous posting, X codes for the precursor of given aminoacid and would begin from the part of aminoacid common to all four aminoacids associated with the same dicodon XY. The thread corresponding to Y would begin from the variable part of these 4 aminoacids.

3. If the aminoacid is coded by more than 4 codons, it can have two different colored thread pairs. Ser, arg, and leu are this kind of aminoacids in case of the nuclear genetic code. One can say that aminoacid "remembers" which was the pair XY for the DNA codon coding it. The two variants of ser will be denoted by ser₁ and ser₂, same for leu and arg.

4. The thread pair can connect aminoacid to another aminoacid, DNA triplet or RNA dinucleotide or perhaps even more general braided biomolecule (say precursor of aminoacid). Given aminoacid is effectively equivalent to the dicodon XY appearing in the codons coding for it and the basic step of the biocatalytic reactions would be analogous to base pairing. Genes would not code only for the aminoacids but also for their stereochemistry. In a well-defined sense aminoacids and DNA and RNA dinucleotides would form a social network in which two members are friends if they correspond to dicodon XY and its conjugate X_c Y_c. One might also speak about molecular sex. The potential companions of the aminoacid associated with dicodon XY would be aminoacids associated with dicodon X_c Y_c. Also these DNA and RNA dicodons would be potential companions of the aminoacid. An open question is whether aminoacid can attach to any dicodon in DNA and RNA sequence or only to the dicodon part XY of codon XYZ: if so also DNA rather than only mRNA and tRNA could contain information about 3-codon decomposition of gene.

5. The phase transitions reducing Planck constant for the magnetic flux tubes defining the threads could bring aminoacid and its conjugate to the vicinity of each other. If the folding involves phase transitions reducing Planck constant, this makes possible to make a list about possible self contacts of protein once one knows the amino-acid sequence. In the case of catalytic reactions involving aminoacids, RNA, and DNA similar list about possible contact points between reactants can be given. That biocatalysis would reduce to symbolic dynamics based on gluing together of pieces of text and cotext would have extremely far reaching implications. For instance, aminoacid sequences attaching to DNA and catalyzing various kinds of processes should obey these rules and aminoacid sequence and its various conjugates could form analogs of DNA double strands.

6. In terms of the code table the rule would be that the companions of a given aminoacid are found by going in the code table two units up or down and two units right or left so that one remains inside the code table (the table representing the proposed folding code is here). A couple of examples about this bio-molecular social network are in order.
   1. The conjugates (companions) of Phe and Leu₁ are Asn and Lys and the conjugates of Leu₂ are Asp and Glu. Arg₁ and Ala conjugates as also Gly and Glu. The conjugates of Thr are Sys and Trp.
   2. The conjugates of Ser₁ are Ser₂ and Arg₂. Ser is its own conjugate and thus a completely exceptional aminoacid.
   3. Ile, met (which serves as starting aminoacid) and thr have the formal aminoacid associated with stop codons as a conjugate. Whether this has some physical meaning remains open.

Consider now objections against the proposal.

1. If the magnetic flux tubes connecting nucleotide and conjugate correlates strongly with base pairing, then also aminoacid sequence and its various conjugates could form analogs of DNA double strands such that the residues of the paired aminoacids are hydrogen bonded. In the case of α helix and β sheet this kind of mechanism is not involved since the hydrogen bonds are associated with the non-varying H₂N-(CH)-COOH part of the paired aminoacids and there are no selection rules telling which residues can be paired. One must carefully distinguish between ordinary chemistry and the dynamical selection rules coming from the proposal. It would be the possible changes of tertiary and quaternary structures of proteins about which the hypothesis can possibly say something.

2. Gly is an aminoacid for which one has R=H. The naive expectation that the magnetic flux tube pair should end up to hydrogen atom looks somewhat strange. The naive expectation that the magnetic flux tube pair should end up to hydrogen atom looks somewhat strange. One cannot avoid the question whether also water could be living in the sense that the hydrogen atoms of water molecules can be connected to biomolecules so that the phase transitions changing Planck constant could be an essential part of hydrophobic and hydrophilic quantum dynamics.

3. The presence of water is a key determinant in protein folding so that if the code is important for the folding, it must relate to the possibility that hydrophobic and hydrophilic interactions induce changes of the Planck constant for magnetic flux tubes. From the table of the side chain properties of aminoacids one finds that aminoacids with Y=A,G are hydrophilic and polar so that hydrophily would correspond to quark matter and hydrophobia for quark antimatter. Quark antimatter would tend to be at protein interior surface and quark matter at protein exterior surface. The same would hold true for protein and its conjugate and the formation of nearby contacts would not be frequent. Lengthening of the magnetic flux tubes and thus an increase rather than reduction of Planck constant would be favored.

There is a proposal that protein folding corresponds to a motion in a fractal spin glass energy landscape in presence of external perturbations due to the presence of water and leading to the bottom of some deep valley (see this). In TGD framework 3-D spin glass landscape is replaced by 4-D one (see this). The vacuum degeneracy of Kähler action implies 4-D spin glass energy landscape in the sense that quantum jump sequences lead to space-time sheets representing asymptotic self organization patterns depending only weakly on the initial conditions (with respect to subjective time measured as quantum jumps). Proteins would be like skilled musicians possessing a repertoire of motor activities represented by deep valleys in 4-D spin glass landscape. This picture generalizes to the functioning of living matter in various scales and the quantum dynamics of brain is a natural application giving also a connection with p-adicity since ultametric topology is naturally associated with the space of valley bottoms. In the case of catalytic reactions a quantum jump changing Planck constant for some magnetic flux tubes connecting some living biomolecules (DNA, RNA, aminoacids, water(?), ...) and changing the lengths of these flux tubes could be the basic mechanism leading from a given valley to a new one and dinucleotide genetic code would code this quantum jumps.

To sum up, this proposal for the folding code - or rather, the code of entire biocatalysis - is so beautiful that it deserves to be killed: this should be easy for a professional biochemist. If the hypothesis survives, it would provide a royal road to the understanding of the catalytic bio-chemistry.

For details see previous posting and the chapter Prebiotic Evolution in Many-Sheeted Space-time of "Genes and Memes".