Friday, March 28, 2008

TGD based model for the evolution of genetic code: V

First some context. I have discussed the model for the evolution of genetic code and the ideas inspired by this model in previous postings (I, II, III, IV).

Biochemistry represents extremely complex and refined choreography. It is hard to believe that this reduces to a mere an unconscious and actually apparent fight for chemical survival. In TGD Universe consciousness would be involved even at the molecular level and magnetic body would be the choreographer whose dance would induce the molecular activities. This picture combined with the idea of standard plugs through and terminals at which flux tubes end, leads to a third trial to understand catalytic code.

The third trial differs from the second trial in that the letters X,Y,Z of the codon XYZ coding for the aminoacid do not correspond to COOH, residy R, and NH2 group. Rather, free aminoacid behaves like XY as in the first trial and X and Y correspond to flux tubes ending at OH and =O in COOH group. For the new option all - not only alpha helical and beta sheeted - aminoacids in the interior of the aminoacid sequence behave like the conjugate of letter Y for the codon XYZ coding for the aminoacid. The new model predicts that DNA, mRNA, tRNA, and aminoacids are in general connected by braid strands and provides a detailed picture about the role of braidings in transcription and translation. The topological dynamics of the magnetic body, its motor activities, would induce catalytic dynamics. Also a far reaching generalization of DNA as tqc paradigm emerges (see the postings I, II, III, IV, V, VI, VII, VIII, IX, X, XI, XII,XIII).

1. Flux tubes as a correlate for directed attention

Molecular survival is the standard candidate for the fundamental variational principle motivating the molecular intentional actions. There is entire hierarchy of selves and the survival at the higher level of hierarchy would force co-operation and altruistic behavior at the lower levels. One might hope that this hypothesis reduces to Negentropy Maximization Principle, which states the information contents of conscious experience is maximized. If this picture is accepted, the evolution of molecular system is analogous to the evolution of a society.

Directed attention is the basic aspect of consciousness and the natural guess would be that directed attention corresponds to the formation of magnetic flux tubes between subject and target. The directedness property requires some manner to order the subject and target.

  1. The ordering by the values of Planck constant is what first comes in mind. The larger space-time sheet characterized by a larger value of Planck constant and thus at a higher level of evolutionary hierarchy would direct its attention to the smaller one.
  2. Also the ordering by the value of p-adic prime characterizing the size scale of the space-time sheet could be considered but in this case directedness could be questioned.
  3. Attention can be directed also to thoughts. Could this mean that attention is directed from real space-time sheets to p-adic space-time sheets for various values of primes but not vice versa? Or could the the direction be just the opposite at least in the intentional action transforming p-adic space-time sheet to real space-time sheet. Perhaps directions are opposite for cognition and intention.

The generation of wormhole magnetic flux tubes could be the correlate for the directed attention, not only at molecular level, but quite generally. Metaphorically, the strands of braid would be the light rays from the eyes of the perceiver to the target and their braiding would code the motions of the target to a topological quantum computation like activity and form a memory representation at least. The additional aspect of directed attention would be the coloring of the braid strands, kind of coloring for the virtual light rays emerging from the eyes of the molecular observer. In the case of DNA this can induce a coloring of braid strands emerging from aminoacids and other molecules so that it would indeed become possible to assign to aminoacid the conjugate of the middle nucleotide of the codon XYZ coding for it.

Attention can be also redirected. For this process there is a very nice topological description as a reconnection of flux tubes. What happens is that flux tubes A→ B and C → D fuse for a moment and become flux tubes A→ D and C→ B. This process is possible only if the strands have same color so that the values of the quark charges associated with A and B are same.

This kind of process can modify tqc programs. For instance, in the case of the flux tubes coming from nucleotides X and Xc and ending to the lipid layer this process means that X and Xc and corresponding lipids become connected and genome builds memory representation about this process via similar link. If proteins are connected with mRNA connected to DNA in this manner, this process would allow the formation of flux tubes between aminoacids of two proteins in such a manner that protein would inherit from DNA codon the color of the middle nucleotide and its interactions effectively reduce to base pairing.

DNA would have memory representation about molecular processes via these changing braiding topologies, and one could say that these molecular processes reflect the bodily motions of the magnetic body. Entire molecular dynamics of the organism could represent an enormous tqc induced by the motor activities of the magnetic body. At the level of sensory experience similar idea has been discussed earlier: Out of Body Experiences and illusions such as train illusion could be understood in terms of motor action of magnetic body inducing virtual sensory percepts.

Attention can be also switched on and off. Here the structure of the lipid ends containing two nearby situated =O:s suggest the mechanism: the short flux tube connecting =O:s disappears. The minimization of Coulomb interaction energy at each end implies that re-appearance of the flux tubes creates a short flux tube with the original strand color.

2. Where do flux tubes begin from?

The view about magnetic body as a controller of biological body using genome as a control tool suggests that DNA is to a high degree responsible for directed attention and other molecules as targets so that flux tubes emanate from DNA nucleotides. The reason would be that the aromatic cycles of DNA correspond to larger value of Planck constant.

Some chemical or geometric property of DNA nucleotides or of DNA nucleotides of DNA strand could raise them to the role of subject. Aromatic cycle property correlates with the symmetries associated with large value of Planck constant and is the best candidate for this property. If this is accepted then also some aminoacid residues might act as subjects. Phe, His, Trp, Tyr contain aromatic cycle. The derivatives of Trp and Tyr act as neurotransmitters and His is extremely effective nucleophilic catalyst. This would make possible more specific catalytic mechanisms through the pairing of Phe, His, Trp, and Tyr with residues having flux tube terminals.

This raises the question about the physical interaction determining the color of the strand emerging from the aromatic cycle. The interaction energy of quark at the end of flux tube with the classical electromagnetic fields of nuclei and electrons of the ring should determine this. The wormhole contact containing quark/antiquark at the throat at space-time sheet containing nuclei and electrons could also delocalize inside the ring. One of the earliest hypothesis of TGD inspired model for living matter was that wormhole Bose-Einstein condensates could be crucial for understanding of the behavior of biomolecules. Wormhole throats with quark and antiquark at their throats appear also in the model of high Tc superconductivity. The only manner for the electronic space-time sheet to feed its electromagnetic gauge flux to larger space-time sheets using exactly two wormhole contacts is to use wormhole contacts with uc and d at their "upper" throat (T,G). For proton one would have dc and u at their "upper" throat (A,C). The presence of electron or proton at nucleotide space-time sheet near the end of flux tube might allow to understand the correlation. The transfer of electrons and protons between space-time sheets with different p-adic length scale is basic element of TGD based model of metabolism so that there might be some relation.

3. What aminoacids can act as plugs and terminals of flux tubes?

Standardization constraint suggests that flux tubes are attached to standard plugs and terminals. The explicit study of various biological molecules and the role of water in biology suggests that =O serves as a plug to which flux arrives and from which it continues. The intuitive reason for the proposal is that =O allows two hydrogen bonds. OH would in turn correspond to a terminal at which flux tube ends. One might be very naive and say that conscious biomolecules have learned the fundamental role of oxygen and water in the metabolism and become very attentive to the presence of =O and OH. =O appears in the residues of Asp, Glu, Asn, Gln. OH groups appear inside the residues of Asp,Glu and Ser, Thr.

It might not be very wise to restrict the molecular attention to only =O and OH and it is probably better to speak about probabilities for the flux tubes to attach to various kinds of terminals. Both SH and NH2 are chemically like OH both these them could act as terminals of flux tubes: NH2 (Asp,Gly,Glu,Arg) contain NH2 and Cys contains SH.

4. Directed attention generates memory representations and tqc like processes

Directed attention induces braiding if the target is moving and changing its shape. This gives rise to a memory representation of the behavior of the object of attention and also to a tqc like process. A considerable generalization of tqc paradigm suggests itself. Tqc could be induced by the braiding between DNA and lipids, DNA and proteins via folding processes, DNA RNA braiding and braiding between DNA and its conjugate, DNA and protein braiding. The outcome of tqc would be represented as the temporal patterns of biochemical concentrations and rates and there would be hierarchy of p-adic time scales and those associated with the dark matter hierarchy.

For instance, the protein content of lipid membranes is about 50 per cent and varies between 25 and 75 per cent so that protein folding and lipid flow could define tqc programs as self-organization patterns. The folding of protein is dynamical process: alpha helices are created and disappear in time scale of 10-7 seconds and the side chains of protein can rotate.

The details of the tqc like process depend on what one assumes. The minimal scenario is deduced from the transcription and translation processes and from the condition that magnetic body keeps control or at least keeps book about what happens using genome as a tool. The picture would be essentially what one might obtain by applying a rough model for web in terms of nodes and links.

  1. mRNA and mRNA and DNA must remain connected by flux tubes after transcription. The Yc of mRNA codon could be connected to =O plug in the aminoacid of tRNA molecule and this to Y in tRNA anticodon so that one would have DNA-aminoacid-tRNA link. Zc in mRNA would be connected to Z in tRNA anticodon giving mRNA-tRNA link. OH in aminoacid would be connected to X in tRNA dicodon XY giving aminoacid-tRNA link.

  2. When tRNA donates its aminoacid to the growing chain, the formation of the peptide bond separates one H2O and the X connection to OH becomes a connection to water molecule so that one obtains tRNA-H2O link. DNA-mRNA-aminoacid-tRNA link with color Y is preserved. Dn depolymerization of mRNA H2O molecule is used and the reverse change for linkings takes place.

  3. The recombination process for two conjugate DNA-mRNA-aminoacid-tRNA links can transform the flux tubes in such manner that one obtains aminoadic-aminoacid Y link between the =O:s of aminoacids A1 and A2 characterized by Y and Yc. As proposed, this mechanism could be central in the enzyme substrate interaction. The process would pair tRNAs corresponding to Y and Yc together to give DNA-mRNA-tRNA-tRNA-mRNA-DNA link providing a memory representation about aminoacid pairing A1-A2. One can say that magnetic body creates with the mediation of the genome dynamical tqc programs to which much of the biomolecular activity reduces. Not all however, since two aminoacid pairs A1-A2 and A3-A4 can recombine to A1-A4 and A3-A2 without DNA knowing anything about it. Magnetic body however knows.

  4. The constant part of the aminoacid inside aminoacid would behave like Yc if aminoacid is coded by XYZ whereas the ends and the protein would behave like dicodons XY (in second trial it would have behaved like YZ). If one assigns to the hydroxyl and amino groups of the residue the roles of object and subject also flux tubes connecting the residue groups become possible and protein does not behave like single nucleotide anymore although one can still say that everything reduces in a well-define sense to the genetic code.

4. Introns and DNA-protein attachment

An example is the situation in which protein acts as an enzyme attaching on DNA. Suppose that this process effectively reduces to a base pairing between aminoacid and DNA nucleotide. Protein can attach to any portion of DNA. Since nucleotide triplets and aminoacids in the first approximation correspond to same length in the respective chains, amino-acid is expected to correspond to nucleotide triplet. The simplest interaction is the attachment to the gene coding for the aminoacid itself but much more general enzymatic interactions are possible. This works if the gene does not contain introns or if the attachment is along single exon.

It is known that DNA can change its conformation from strand during enzyme-DNA action and the contraction of DNA strand might make possible to have enzyme-DNA interaction also in the case that attachment region corresponds to several exons. One can of course ask whether genes containing introns tend to code for proteins which are used for topological quantum computations. Introns, perhaps the repeating sequences with no obvious function, would have at least this useful function but very probably much more useful ones too (they are now known to be transcribed to RNA and TGD suggest that language corresponds to intronic gene expression). The emergence of introns might be somewhat like the emergence of information society.

The foldings of proteins tend to be conserved in the evolution whereas primary structure can change quite a lot apart from some aminoacids critical for enzymatic action. This confirms with the effective base pairing interaction between aminoacids and DNA and would mean that DNA-aminoacid tqc programs are rather robust against mutations.

5. Evolution and braidings

The evolution at the molecular level corresponds to the emergence of increasingly complex molecules using as basic building blocks aminoacid chains and non-translated residues attached to them in the post-translational processing of the aminoacid chains. Also increasingly complex reaction paths emerge. Molecular survival and the competition for the metabolic resources at molecular level could be seen as the basic driving force of this evolution.

Typically, in the original situation the enzymes would have received the substrate molecules from the environment but sooner or later this would have become difficult. The solution would have been a synthesis of the substrate from simpler ingredients by starting from some precursor.

If molecules (with magnetic bodies included) are conscious entities able to direct attention, one can imagine that magnetic body controlling them with the mediation of genome and able to actively modify it, could help through modifications of the genome to create to the catalyst a binding site able to bind the precursor. Immune system is doing this very intensively. If the enzyme binding the precursor already exists, a combination of genes coding for the enzyme and the enzyme having the metabolites as ligands could allow to achieve this. All this would reduce to the motor activities of magnetic body, in particular reconnection of flux tubes, kind of Shivas dance. Genome would not be anymore a sequence of DNA developing through random mutations under selection pressures.

Can one make any clear cut predictions about preferred mutations?

  1. Mutations are not expected to be always random point mutations but could be a result of a purposeful action of the magnetic body. Chemical similarity is expected to be conserved in good mutations. This is known to be the case. Allowed point mutations should conserve Y. Also bi-local mutations might occur and could be crucial for the coherence of the organisms. As found, the formation of flux tube between aminoacids A1 and A2 induces a flux tube between nucleotides Y and Yc at the corresponding genes. This flux tube could force the possibly intentional mutations to occur as simultaneous point mutations of the two genes conserving the conjugacy property and leaving thus braiding invariant.

  2. Folding is known to be more conserved than aminoacid sequence. Since folding is a collective property of gene, local chemistry might not be enough and the proposed non-local conservation laws might be needed. Bilocal mutations would also correlate the mutations of the binding sites of protein and ligand so that the crucial geometric conjugacy proposed to reduce to conjugation for Y would not be lost. The prediction would be conserved Y-Yc pairs in genes coding for protein and ligand and these pairs might allow to deduce the paired points. The paired nucleotides need not belong to the same strand since genes are evenly distributed between strand and its conjugate and characterized by A,G surplus. Strong form of conjugacy stating that paired genes belong to the strand and its conjugate sounds beautiful in the ears of mathematician at least and would be mirror image for the mutual avoidance of quark matter and antimatter at protein level. Some examples are in order. Ala/Ser, Ser/Thr, Ile/Val/Leu, Asp/Glu do not change Y. Lys/Arg (A/G)), Tyr/Phe (A/U), Gly/Ala (G/C),... are also prevalent and one might hope that they correspond to binary mutations in some important cases.

  3. If the flux tubes can connect also side chains the situation becomes more complex. There is a temptation to think that these flux tubes would connect only the nearby aminoacids and do not affect the large scale dynamics of folding. This would be the case if the value of Planck constant associated with these flux tubes is smaller than for the flux tubes connecting aminoacids as basic units. This kind of pairing would be consistent with Y-Yc rule since hydrophobic and hydrophilic residues would tend to be connected by a long flux tube. If flux tubes can begin from the aromatic side chains, the replacement of an aromatic side chain with an aromatic side chain is favored (also chemical similarity explains this). The most basic facts about folding do not provide obvious support the idea about flux tubes between residues.
    1. Hydrophobic residues tend to cluster in dense packing in protein interior (antimatter at quark level) and Val (T), Leu (T), Ile (T), Phe (T), Ala (C), and Gly (G) make 63 percent of the interior of protein: the special role of Gly (matter rather than antimatter) is due to the reduction of the side chain to hydrogen atom.
    2. Asp (A), Glu (A), Lys (A) and Arg (G) with ionized residues are mostly at the surface of protein and make 23 per cent of protein surface and 4 per cent of interior. As noticed earlier, matter and antimatter at quark level tend to be far from each other.
    3. Polar groups tend to be paired by hydrogen bonds and oppositely charged groups tend to be near each other. Acidic Cys residues tend to be in positions where they can form S-S bonds. This cannot be explained by Y-Yc pairing nor by the presence of bonds connecting residues in the proposed scenario. Aromatic residues tend to have favorable electrostatic interactions with each other and with S, O and amino groups.

In this framework aminoacids would have appeared before their precursors and possessed some function in RNA world, say the catalysis of join of RNA2 dinucleotides to the increasing chain as I have proposed. Competition might have led to the situation in which RNA2 learned to catalyze selectively generation of aminoacids from much simpler precursors (three of the proposed precursors contain only C,=O, and O-). The reduced genetic code would have been present at two levels: reader can decide whether this is a shortcoming of the model or a fundamental biochemical duality implying an exponential amplification of RNA and aminoacid populations.

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

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