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Genes and Memes

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Year 2008

Crying and screaming cells and magnetic bodies expressing their emotions

By using nanotechnological methods James Gimzewski [3], his student Andrew Pelling and collaborators discovered that the cell walls of bacterium Saccharomyces cerevisiae perform periodic motion with amplitude about 3 nm in the frequency range .8-1.6 kHz (one octave) [2]. Or more concretely, bacteria produce sounds audible to humans with average frequency of 1 kHz in a range of one octave. The frequency has strong temperature dependence, which suggests a metabolic mechanism. From the temperature dependence one deduces the activation energy to be 58 kJ/mol, which is consistent with the cell's metabolism involving molecular motors such as kinesin, dynein, and myosin. The magnitude of the forces observed (10 nN) suggests concerted nanomechanical activity is operative in the cell.

From less formal popular "../articles/ [4] one can learn that it is difficult to avoid the impression that intelligent communication is in question. Dying cells produce a characteristic screaming sound. One can also distinguish between normal cells and cancel cells on basis of the sound they produces as well as between mammalian and bacterial cells.

What might be the explanation of these findings in TGD framework?

  1. It is known that the region of frequencies audible to human ear is from about 20 Hz to 2×104 Hz. This is more or less same as the range of frequency range of sferics, the em noise in atmosphere [5]. This suggests a strong coupling between electromagnetic oscillations and sound as also the fact that biological structures are piezo-electrets transforming em oscillations to sounds and vice versa.

  2. The activation energy per mole corresponds to .6 eV per molecule which is at the upper range for the variation range the energy associated with the fundamental metabolic energy quantum identified as the change of zero point kinetic as proton is transferred from atomic space-time sheet to much larger space-time sheet or vice versa.That metabolic energy is needed to produce the sounds supports the view that the sounds are produced intentionally.

  3. If one takes seriously the notion of magnetic body as intentional agent controlling biological body [1], one is led to ask which must sound a totally crazy question in reductionistic ears: could magnetic body express its emotions in terms of frequencies of cyclotron transitions transformed to sound via genetic expression using piezo-electric mechanism? Could it be that the photons involved are dark photons with large value of Planck constant so that their energy is above thermal energy. Could one ask a materialistic scientist to consider anything more irritating that singing and crying magnetic bodies!

  4. Suppose that the homeopathic mechanism is based on replication of pseudomolecules with same magnetic body as that of solvent molecules and that neutral dark nuclear strings realize analogs of DNA, RNA, and aminoacids and realizing genetic code exactly in its vertebrate nuclear form and appearing also in the TGD based model of cold fusion and biological transmutations. If so, then homeopathic mechanism (recognition of molecules) could involve also the transformation of cyclotron radiation to sound at the level of "biological bodies" of molecules.

  5. If this picture makes sense then also our speech as a self expression of the magnetic body might involve genetic code mapping sequences of DNA codons to temporal patterns of cyclotron radiation in turn transformed to speech by above mechanism. This would require a realization of genetic code at level of dark matter: could it be that dark nuclear code could define universal quantum level realization of language? The findings of Peter Gariaev and others and structural resemblance of intronic portion of genome with language and their report that DNA sequences are coded to temporal patterns of the rotation angle of the polarization of laser light (in turn inducing genetic expression).


[1] The chapter The Notion of Wave-Genome and DNA as Topological Quantum Computer of "Genes and Memes".

[2] Pelling et al (2004), Local Nanomechanical Motion of the Cell Wall of Saccharomyces cerevisiae, Science 20 August: Vol. 305. no. 5687, pp. 1147 - 1150.
[] [3] James Gimzewski.
[4] A. Goho (2004), Rattle and Hum: molecular machinery makes yeast cells purr. Science News, August 21.
M. Wheeler, (2004) Signal Dicovery?, Smithsonian Magazine. March issue.
M. Wertheim (2003), Bucky Balls and Screeming Cells:the amazing miniature world of UCLA chemist Jim Gimzewski, LAWeekly, April 4-10.
[5] A. Saleh (2001), Capturing the Earth's songs. ABC Science Online.

Fore more details the chapter The Notion of Wave-Genome and DNA as Topological Quantum Computer.

Dark nuclear strings as analogs of as analogs of DNA-, RNA- and amino-acid sequences and baryonic realization of genetic code

In the earlier posting I considered the possibility that the evolution of genome might not be random but be controlled by magnetic body and that various DNA sequences might be tested in the virtual world made possible by the virtual counterparts of bio-molecules realized in terms of the homeopathic mechanism as it is understood in TGD framework. The minimal option is that virtual DNA sequences have flux tube connections to the lipids of the cell membrane so that their quality as hardware of tqc can be tested but that there is no virtual variant of transcription and translation machinery. One can however ask whether also virtual amino-acids could be present and whether this could provide deeper insights to the genetic code.

The minimal option is that virtual DNA sequences have flux tube connections to the lipids of the cell membrane so that their quality as hardware of tqc can be tested but that there is no virtual variant of transcription and translation machinery. One can however ask whether also virtual amino-acids could be present and whether this could provide deeper insights to the genetic code.

  1. Water molecule clusters are not the only candidates for the representatives of linear molecules. An alternative candidate for the virtual variants of linear bio-molecules are dark nuclei consisting of strings of scaled up dark variants of neutral baryons bound together by color bonds having the size scale of atom, which I have introduced in the model of cold fusion and plasma electrolysis both taking place in water environment . Colored flux tubes defining braidings would generalize this picture by allowing transversal color magnetic flux tube connections between these strings.

  2. Baryons consist of 3 quarks just as DNA codons consist of three nucleotides. Hence an attractive idea is that codons correspond to baryons obtained as open strings with quarks connected by two color flux tubes. The minimal option is that the flux tubes are neutral. One can also argue that the minimization of Coulomb energy allows only neutral dark baryons. The question is whether the neutral dark baryons constructed as string of 3 quarks using neutral color flux tubes could realize 64 codons and whether 20 aminoacids could be identified as equivalence classes of some equivalence relation between 64 fundamental codons in a natural manner.

The following model indeed reproduces the genetic code directly from a model of dark neutral baryons as strings of 3 quarks connected by color flux tubes.

  1. Dark nuclear baryons are considered as a fundamental realization of DNA codons and constructed as open strings of 3 dark quarks connected by two colored flux tubes, which can be also charged. The analogs of DNA -, RNA -, and of amino-acid sequences would in turn correspond to sequences of dark baryons. It is assumed that the net charge of the dark baryons vanishes so that Coulomb repulsion is minimized.

  2. One can classify the states of the open 3-quark string by the total charges and spins associated with 3 quarks and to the two color bonds. Total em charges of quarks vary in the range ZB {2,1,0,-1} and total color bond charges in the range Zb {2,1,0,-1,-2}. Only neutral states are allowed. Total quark spin projection varies in the range JB=3/2,1/2,-1/2,-3/2 and the total flux tube spin projection in the range Jb = 2,1,-1,-2. If one takes for a given total charge assumed to be vanishing one representative from each class (JB,Jb), one obtains 4×5=20 states which is the number of amino-acids. Thus genetic code might be realized at the level of baryons by mapping the neutral states with a given spin projection to single representative state with the same spin projection. The problem is to find whether one can identify the analogs of DNA, RNA and aminoacids as baryon like states.

1. States in the quark degrees of freedom

Consider first the states of dark baryons in quark degrees of freedom. These states can be constructed as representations of rotation group and strong isospin group.

  1. The tensor product 222 is involved in both cases. Without any additional constraints this tensor product decomposes as 422: 8 states altogether. This is what one should have for DNA and RNA candidates. If one has only identical quarks uuu or ddd, one obtains only the 4-D representation corresponding to completely symmetric representation. These 4 states correspond to a candidate for amino-acids. Thus RNA and DNA should correspond to states of type uud and ddu and aminoacids to states of type uuu or ddd. What this means physically will be considered later.

  2. It is known that only representations with isospin 3/2 and spin 3/2 (D resonance) and isospin 1/2 and spin 1/2 (proton and neutron) are realized as free baryons. Now of course a dark -possibly p-adically scaled up - variant of QCD is considered so that more general baryonic states are possible. The spin statistics problem which forced to introduce quark color strongly suggests that the construction of the codons as sequences of 3 nucleons is not a good idea.

  3. Second nucleon like spin doublet - call it 2odd - has wrong parity in the sense that it would require L=1 ground state for two identical quarks (uu or dd pair). Dropping 2odd and using only 42 for the rotation group would give degeneracies (1,2,2,1) and 6 states only. All the representations in 422odd to get 8 states with a given quark charge and one should transform the wrong parity doublet to positive parity doublet somehow. Since open string geometry breaks rotational symmetry to a subgroup of rotations acting along the direction of the string, the attractive possibility is to add a stringy excitation with angular momentum projection Lz=-1 to the wrong parity doublet so that the parity comes out correctly. Lz=-1 orbital angular momentum for the relative motion of uu or dd quark pair in the open 3-quark string would be in question. The degeneracies for spin projection value Jz = 3/2,...,-3/2 are (1,2,3,2). Genetic code means spin projection mapping the states in 422odd to 4.

2. States in the flux tube degrees of freedom

Consider next the states in flux tube degrees of freedom.

  1. The situation is analogous to a construction of mesons from quarks and antiquarks and one obtains the analogs of p meson (pion) with spin 0 and r meson with spin 1. States of a given charge correspond to the tensor product 22=31 for the rotation group. Drop the singlet and take only the analog of neutral r meson. The physical meaning of this will be considered later.

  2. Without any further constraints the tensor product 33=531 gives 8+1 states. By dropping the scalar state this gives 8 states required by DNA and RNA analogs. Bosonic statistics allows only 5 unless the two color bonds have different charges. The degeneracies of the states for DNA/RNA type realization with a given spin projection for 53 are (1,2,2,2,1).

  3. For aminoacids only 5 completely symmetric under the exchange of flux tubes is required and is achieved if the two color bonds have identical charges. Genetic code means the projection of the states of 53 to those of 5 with the same spin projection and same total charge.

3. Analogs of DNA,RNA, aminoacids, and of translation and transcription mechanisms

Consider next the identification of analogs of DNA, RNA and aminoacids and the baryonic realization of the genetic code, translation and transcription.

  1. The analogs of DNA and RNA can be identified dark baryons with quark content uud and ddu and color bonds of different charges. There are 3 color bond pairs corresponding to charge pairs (q1,q2) = (-1,0), (-1,1), (0,1) (the order of charges does not matter). The condition that the total charge of dark baryon vanishes allows for uud only the bond pair (-1,0) and for udd only the pair (-1,1). These thus only single neutral dark baryon of type uud resp. udd: these would be the analogous of DNA and RNA codons. Amino-acids would correspond to either uuu or ddd with identical color bonds with charges (-1,-1), (0,0), or (1,1). uuu with color bond charges (-1,-1) is the only neutral state. Hence only the analogs of DNA, RNA, and aminoacids are obtained, which is rather remarkable result.

  2. The basic transcription and translation machinery could be realized as processes in which the analog of DNA can replicate, and can be transcribed to the analog of mRNA in turn translated to the analogs of amino-acids. In terms of flux tube connections the realization of genetic code, transcription, and translation, would mean that only dark baryons with same total quark spin and same total color bond spin can be connected by flux tubes. Charges are of course identical since they vanish.

  3. Genetic code maps of ( 422)(53) to the states of 4×5. The most natural map takes the states with given spin to a state with the same spin so that the code is unique. This would give the degeneracies D(k) as products of numbers DB {1,2,3,2} and Db {1,2,2,2,1}: D = DB×Db. Only the observed degeneracies D = 1,2,3,4,6 are predicted. The numbers N(k) of aminoacids coded by D codons would be

    [N(1),N(2),N(3),N(4),N(6)]=[2,7,2,6,3]\per .

    The correct numbers for vertebrate nuclear code are (N(1),N(2),N(3),N(4),N(6)) = (2,9,1,5,3). Some kind of symmetry breaking must take place and should relate to the emergence of stopping codons. If one codon in second 3-plet becomes stopping codon, the 3-plet becomes doublet. If 2 codons in 4-plet become stopping codons it also becomes doublet and one obtains the correct result (2,9,1,5,3)!

  4. Stopping codons would most naturally correspond to the codons, which involve the Lz=-1 relative rotational excitation of uu or dd type quark pair. For the 3-plet the two candidates for the stopping codon state are |1/2,-1/2{|2,k}, k = 2,-2. The total spins are Jz = 3/2 and Jz=-7/2. The three candidates for the 4-plet from which two states are thrown out are |1/2,-3/2{|2,k, |1,k}, k = 1,0,-1. The total spins are now Jz = -1/2,-3/2,-5/2. One guess is that the states with smallest value of Jz are dropped which would mean that Jz=-7/2 states in 3-plet and Jz = -5/2 states 4-plet become stopping codons.

4. Understanding the symmetries of the code

Quantum entanglement between quarks and color flux tubes would be essential for the baryonic realization of the genetic code whereas chemical realization could be said to be classical. Quantal aspect means that one cannot decompose to codon to letters anymore. This raises questions concerning the symmetries of the code.

  1. What is the counterpart for the conjugation ZYZ XcYcZc for the codons?

  2. The conjugation of the second nucleotide Y having chemical interpretation in terms of hydrophobia-hydrophily dichotomy in biology. In DNA as tqc model it corresponds to matter-antimatter conjugation for quarks associated with flux tubes connecting DNA nucleotides to the lipids of the cell membrane. What is the interpretation in now?

  3. The A-G, T-C symmetries with respect to the third nucleotide Z allow an interpretation as weak isospin symmetry in DNA as tqc model. Can one identify counterpart of this symmetry when the decomposition into individual nucleotides does not make sense?

Natural candidates for the building blocks of the analogs of these symmetries are the change of the sign of the spin direction for quarks and for flux tubes.

  1. For quarks the spin projections are always non-vanishing so that the map has no fixed points. For flux tube spin the states of spin Sz=0 are fixed points. The change of the sign of quark spin projection must therefore be present for both XYZ XcYcZc and Y Yc but also something else might be needed. Note that without the symmetry breaking (1,3,3,1) (1,2,3,2) the code table would be symmetric in the permutation of 2 first and 2 last columns of the code table induced by both full conjugation and conjugation of Y.

  2. The analogs of the approximate A-G and T-C symmetries cannot involve the change of spin direction in neither quark nor flux tube sector. These symmetries act inside the A-G and T-C sub-2-columns of the 4-columns defining the rows of the code table. Hence this symmetry must permute the states of same spin inside 5 and 3 for flux tubes and 4 and 2 for quarks but leave 2odd invariant. This guarantees that for the two non-degenerate codons coding for only single amino-acid and one of the codons inside triplet the action is trivial. Hence the baryonic analog of the approximate A-G and T-C symmetry would be exact symmetry and be due to the basic definition of the genetic code as a mapping states of same flux tube spin and quark spin to single representative state. The existence of full 4-columns coding for the same aminoacid would be due to the fact that states with same quark spin inside (2,3,2) code for the same amino-acid.

  3. A detailed comparison of the code table with the code table in spin representation should allow to fix their correspondence uniquely apart from permutations of n-plets and thus also the representation of the conjugations. What is clear that Y conjugation must involve the change of quark spin direction whereas Z conjugation which maps typically 2-plets to each other must involve the permutation of states with same Jz for the flux tubes. It is not quite clear what X conjugation correspond to.

5. Some comments about the physics behind the code

Consider next some particle physicist's objections against this picture.

  1. The realization of the code requires the dark scaled variants of spin 3/2 baryons known as D resonance and the analogs (and only the analogs) of spin 1 mesons known as r mesons. The lifetime of these states is very short in ordinary hadron physics. Now one has a scaled up variant of hadron physics: possibly in both dark and p-adic senses with latter allowing arbitrarily small overall mass scales. Hence the lifetimes of states can be scaled up.

  2. Both the absolute and relative mass differences between D and N resp. r and p are large in ordinary hadron physics and this makes the decays of D and r possible kinematically. This is due to color magnetic spin-spin splitting proportional to the color coupling strength as ~ .1, which is large. In the recent case as could be considerably smaller - say of the same order of magnitude as fine structure constant 1/137 - so that the mass splittings could be so small as to make decays impossible.

  3. Dark hadrons could have lower mass scale than the ordinary ones if scaled up variants of quarks in p-adic sense are in question. Note that the model for cold fusion that inspired the idea about genetic code requires that dark nuclear strings have the same mass scale as ordinary baryons. In any case, the most general option inspired by the vision about hierarchy of conscious entities extended to a hierarchy of life forms is that several dark and p-adic scaled up variants of baryons realizing genetic code are possible.

  4. The heaviest objection relates to the addition of Lz=-1 excitation to Sz=|1/2,1/2odd states which transforms the degeneracies of the quark spin states from (1,3,3,1) to (1,2,3,2). The only reasonable answer is that the breaking of the full rotation symmetry reduces SO(3) to SO(2). Also the fact that the states of massless p"../articles/ are labeled by the representation of SO(2) might be of some relevance. The deeper level explanation in TGD framework might be as follows. The generalized imbedding space is constructed by gluing almost copies of the 8-D imbedding space with different Planck constants together along a 4-D subspace like pages of book along a common back. The construction involves symmetry breaking in both rotational and color degrees of freedom to Cartan sub-group and the interpretation is as a geometric representation for the selection of the quantization axis. Quantum TGD is indeed meant to be a geometrization of the entire quantum physics as a physics of the classical spinor fields in the "world of classical worlds" so that also the choice of measurement axis must have a geometric description.

The conclusion is that genetic code can be understand as a map of stringy baryonic states induced by the projection of all states with same spin projection to a representative state with the same spin projection. Genetic code would be realized at the level of dark nuclear physics and perhaps also at the level of ordinary nuclear physics and that biochemical representation would be only one particular higher level representation of the code. A hierarchy of dark baryon realizations corresponding to p-adic and dark matter hierarchies can be considered. Translation and transcription machinery would be realized by flux tubes connecting only states with same quark spin and flux tube spin. Charge neutrality is essential for having only the analogs of DNA, RNA and aminoacids and would guarantee the em stability of the states.

For details see the chapter The Notion of Wave-Genome and DNA as Topological Quantum Computer.

Could virtual DNAs allow a controlled development of the genome?

In the previous postings I have discussed TGD based model of homeopathy and phantom DNA based on the possibility that water molecules receiving the magnetic bodies of biomolecules in homeopathic manifacture process can mimick those aspects of these molecules most relevant for the biological functions. By combining these ideas with DNA as topological quantum computer hypothesis, one ends up with the idea that the evolution of DNA is not just random mutations plus selection, but takes place in controlled manner like the development of computer hardware in the virtual mimicry of internal chemical milieu in turn providing an abstract representation for the external world.

The fundamental question in the evolution biology is the question about the interaction between genome (G), phenotype (P), and environment (E).

  1. The standard dogma is that the information transfer from G to P is unidirectional and that environment acts on G by inducing random mutations of G, from which E selects the lucky survivors as those with the best ability to reproduce. Lamarckism represents a deviation from standard dogma by assuming direct information transfer from E to G.

  2. Genetic expression is controlled by environment, at least by silencing , which is like selecting only few books to be read from a big library. Cell differentiation represents basic example of selective gene expression. DNA methylation and transposition are accepted to reflect information transfer from E to G, perhaps via P. These modifications are however believed to be short lasting and not transferred to the offspring since it is difficult to imagine a mechanism transferring the mutations to the germ cells.

  3. The question however remains whether the G P-E actually could complete to a closed loop G P-E-G so that genome could directly respond to the changing physical environment and could transfer the successful response to the next generation .

In TGD framework the sequence G P-E is replaced with a closed loop G-P-M-E to which E is attached at P by bidirectional arrow (organisms do also modify their environment actively). Magnetic body thus controls genome and receives information from cell membrane (P). The hierarchy of genomes (super-genome, hyper-genome,...) corresponding to the different levels of dark matter hierarchy allows this loop to be realized in different scales rather only at the level of single cell.

The question is whether the magnetic body of organism or higher level magnetic bodies could modify genomes, super-genomes, and hyper-genomes directly, perhaps by generating mutations of the genome in a short time scale; by monitoring how genetically modified organism survives in the environment; and -if the outcome of the experiment is successful - replacing the corresponding portion of DNA with the modified DNA both in ordinary germ cells. One can even ask whether the abstract model of the external environment provided by the internal chemical milieu might be mimicked by water magnetic bodies of water molecule clusters and provide a virtual world testing ground for a search of favorable mutations.

In DNA as a tqc vision essentially the development of a new computer hardware would be in question, and should take place in a controlled manner and involve an experimentation before going to the market rather than by random modifications taking place in computer CPUs. Second basic aspect of DNA as tqc paradigm is that water and bio-molecules live in symbiosis in the sense that self organization patterns of the cellular water flow define the tqc programs. The following first guess for how the development of computer hardware might be achieved is just a first guess but might have something to do with reality.

  1. What would be needed is a mechanism generating rapidly modifications of DNA. The mutations should be carried out using a kind of virtual DNA mimicking all the essential aspects of the symbolic dynamics associated with DNA. The magnetic bodies of DNA consisting of flux tubes connecting the nucleotides of DNA strands to cell membrane satisfy these conditions since A,T,G,C is coded to exotic light quarks u, d and anti-quarks `u, `d at the ends of flux tubes. DNA nucleotides could be replaced with clusters of water molecules but also other options can be imagined. Note that it does not matter when one speaks of mimicry of RNA or DNA molecules.

  2. If the proposed model of the phantom DNA and homeopathy is correct, this kind of virtual DNA exists and is generated in phantom DNA effect as magnetic bodies of DNA, including of course the magnetic flux tubes connecting the nucleotides to the cell membrane or conjugate strand of DNA.

  3. The crucial additional assumption would be that also the reversal of phantom DNA effect is possible and corresponds to the analog of DNA replication in which nucleotides attach to the virtual conjugate nucleotides of the virtual DNA strand or RNA strand in turn transformed to DNA strand be reverse transcription. The hypothesis would have rather strong implications for the genetic engineering since homeopathic remedies of genetically engineered DNA sequences could be transferred to cell nuclei just by drinking them.

  4. Phantom DNA sequences could form populations and - as far as their properties as a hardware of topological quantum computer are involved - evolve under selection pressures of the virtual world defined by the nuclear, cellular water, and intercellular water. A competition of components of tqc hardware developed by the higher level magnetic body to realize optimally tqc programs needed for survival would be in question. The simplest mutation of phantom DNA would replace the quark pairs at the ends the (wormhole-) magnetic flux tube with a new one and could occur in very short time scale. Also basic editing operations like cutting and pasting would be possible for these competing phantom DNA sequences. The winners in the competition would be transformed to actual DNA sequences by utilizing the reverse phantom DNA (or RNA -) effect and be inserted to genome. The genetic machinery performing cutting, gluing, and pasting of real DNA in a controlled manner exists. What is needed is the machinery monitoring who is the winner and making the decision to initiate the modification of the real DNA.

  5. The transfer of the mutations to germ cells could be achieved by allowing the population of the virtual DNA sequences to infect the water inside germ cells. The genetic program inducing the modification of DNA by using the winner of the tqc hardware competition should run automatically.

  6. One open question is whether the cellular or perhaps also extracellular water should represent the physical environment and - if answer is affirmative - how it achieves this. As a matter fact, considerable fraction of water inside cells is in gel phase and it might be that the intercellular water, which naturally defines a symbolic representation of environment, is where the virtual evolution takes place. Internal chemical milieu certainly reflects in an abstract manner the physical environment and the ability of the water molecule clusters to mimic bio-molecules would make the representation of the chemical environment possible. Also sudden changes of external milieu would be rapidly coded to the changes in internal milieu which might help to achieve genetic re-organization. The craziest dream is water based simulation of both genes, proteins, and molecules representing external world running at dark space-time sheets.

  • Water molecule clusters are not the only candidates for the representatives of linear molecules. An alternative candidate for the virtual variants of linear bio-molecules are dark nuclei consisting of strings of scaled up dark variants protons and neutrons bound together by color bonds having the size scale of atom, which I have introduced in the model of cold fusion and plasma electrolysis both taking place in water environment. Colored flux tubes defining braidings would generalize this picture by allowing color magnetic flux tube connections between these strings.

    For details see the chapter The Notion of Wave-Genome and DNA as Topological Quantum Computer.

  • A possible realization of water memory

    The Benveniste's discovery of water memory initiated quite dramatic sequence of events. The original experiment involved the homeopathic treatment of water by human antigene. This meant dilution of the water solution of antigene so that the concentration of antigene became extremely low. In accordance with homeopathic teachings human basophils reacted on this solution.

    The discovery was published in Nature and due to the strong polemic raised by the publication of the article, it was decided to test the experimental arrangement. The experimental results were reproduced under the original conditions. Then it was discovered that experimenters knew which bottles contained the treated water. The modified experiment in which experimenters did not possess this information failed to reproduce the results and the conclusion was regarded as obvious and Benveniste lost his laboratory among other things. Obviously any model of the effect taking it as a real effect rather than an astonishingly simplistic attempt of top scientists to cheat should explain also this finding.

    The model based on the notion of field body and general mechanism of long term memory allows to explain both the memory of water and why it failed under the conditions described.

    1. A model for the water memory and homeopathic effect

    1. Also molecules have magnetic field bodies acting as intentional agents controlling the molecules. Nano-motors do not only look co-operating living creatures but are such. The field body of the molecule contains besides the static magnetic and electric parts also dynamical parts characterized by frequencies and temporal patterns of fields. To be precise, one must speak both field and relative field bodies characterizing interactions of molecules. Right brain sings-left brain talks metaphor might generalize to all scales meaning that representations based on both frequencies and temporal pulse with single frequency could be utilized.

    2. The effects of complex bio-molecule to other bio-molecules (say antigene on basofil) in water could be characterized to some degree by the temporal patterns associated with the dynamical part of its field body and bio-molecules could recognize each other via these patterns. This would mean that symbolic level in interactions would be present already in the interactions of bio-molecules. Cyclotron frequencies are most natural candidates for the frequency signatures and the fact that frequencies in 10 kHz range are involved supports this view.

    3. The original idea was that water molecule clusters are able to mimic the bio-molecules themselves -say their vibrational and rotational spectra could coincide with those of molecules in reasonable approximation. A more natural idea is that they can mimic their field bodies. Homeopathy could rely on extremely simple effect: water molecule clusters would steal the magnetic bodies of the molecules used to manufacture the homeopathic remedy. The shaking of the bottle containing the solution would enhance the probability for bio-molecule to lose its magnetic body in this manner. For instance, water could produce fake copies of say antigenes recognized by basofils and reacting accordingly if the reaction is based on interaction with the magnetic body of the antigene.

    4. The basic objection against this picture is that it does not explain why the repeated dilution works. Rather, it seems that dilution of molecules reduces also the density of molecules. (I am grateful for Ulla Matfolk for questions which made me to realize this).

      1. The only way out seems to be that the magnetic bodies or water molecule clusters having these magnetic bodies can replicate. The shaking of the remedy could provide the needed metabolic energy so that the population of magnetic bodies grows to a limiting density determined by the metabolic energy feed. In principle it would be possible to infect unlimited amount of water by these pseudo-molecules. When in bottle the population would be in dormant state but in the body of the patient it would wake up and form a population of molecular actors and stimulate the immune system to develop immune response to the real molecule.

      2. Also magnetic bodies must replicate in cell replication and their role as intentional agents controlling bio-matter requires that this replication serves as a template for biochemical replication. On can indeed interpret the images about cell replication in terms of replication of dipole type magnetic field. This process is very simple and could have preceded biological replication. The question is therefore whether water is actually a living system in presence of a proper metabolic energy feed. Also the water's ability near critical point for freezing to form nice patterns correlating with sound stimuli might be due to the presence of the molecular actors.

      3. This picture fits nicely with the vision that evolution of water in this kind of life form might have happened separately and that pre-biotic chemical life forms have formed symbiosis with living water . In the model of DNA as topological quantum computer the asymptotic self organization patterns of water flow in the vicinity of lipid layers indeed define quantum computer programs by inducing the braiding of the magnetic flux tubes connecting DNA nucleotides to lipids so that this symbiosis would have brought in new kind of information processing tool.

      The magnetic body of the molecule could mimic the vibrational and rotational spectra using harmonics of cyclotron frequencies. Cyclotron transitions could produce dark photons with large Planck constant, whose ordinary counterparts resulting in de-coherence would have large energies due to the large value of hbar and could thus induce vibrational and rotational transitions. This would provide a mechanism by which molecular magnetic body could control the molecule. Note that also the antigenes possibly dropped to the larger space-time sheets could produce the effect on basofils. The transformation of large Planck constant photons to ordinary ones would reduce the frequency of photon by the factor hbar0/hbar: this kind of reduction represents basic finding about water memory. The so scaled scaling law states that favored scaling factor corresponds to hbar/hbar0∼ 2× 1010.

    5. There is a considerable experimental support for the Benveniste's discovery that bio-molecules in water environment are represented by frequency patterns, and several laboratories are replicating the experiments of Benveniste as I learned from the lecture of Yolene Thomas in the 7:th European SSE Meeting held in Röros . The scale of the frequencies involved is around 10 kHz and as such does not correspond to any natural molecular frequencies. Cyclotron frequencies associated with electrons or dark ions accompanying these macromolecules would be a natural identification if one accepts the notion of molecular magnetic body. For ions the magnetic fields involved would have a magnitude of order .03 Tesla if 10 kHz corresponds to scaled up alpha band. Also Josephson frequencies would be involved if one believes that EEG has fractally scaled up variants in molecular length scales.

    2. Why Benveniste's experiments could not be replicated?

    Consider now the argument explaining the failure to replicate the experiments of Benveniste.

    1. The magnetic bodies of water molecules need metabolic energy for communications with their "biological body" using the fractally scaled analog of EEG. There is no obvious source for this energy in water. The model for protein folding and DNA as topological quantum computer assumes that magnetic flux tubes connecting subject person and target of directed attention serve as correlates for directed attention at the molecular level . This should be true also in macroscopic scales so that the experimentalist and the bottle containing the treated water should be connected by magnetic flux tubes. If experimenter has directed his attention to the bottle of water, the resulting magnetic flux tubes could allow a transfer of metabolic energy as a radiation along massless extremals parallel to the flux tubes and defining TGD counterparts of Alfwen waves. Experimenter's strong motivation to replicate experiments would help to realize the transfer of the metabolic energy. Experimenters not knowing, which bottles were treated did not have these flux tube bridges to the bottles, and were not able to provide the needed metabolic energy, and the magnetic bodies of antigenes failed to generate the cyclotron radiation making them visible to the basofil.

    2. If this interpretation is correct, then Benveniste's experiment would demonstrate besides water memory also psychokinesis and direct action of desires of experimenters on physics at microscopic level. Furthermore, the mere fact that we know something about some object or direct attention to it would mean a concrete interaction of our magnetic body with the object.

    For details see the chapter The Notion of Wave-Genome and DNA as Topological Quantum Computer.

    Phantom DNA effect

    Phantom DNA is fourth anomalous effect in which the notion of magnetic body provides understanding (other three effects have been discussed in three previous postings). In phantom DNA effect [1] there is an elastic scattering of the coherent laser radiation from irradiated DNA. When one removes the DNA from the chamber containing it, and irradiates it by laser light, a weak pattern of scattered light is still produced: as if there were a kind of phantom DNA there. The pattern can last for months.

    For years ago I considered an explanation of the effect based on dropping of part of DNA to larger space-time sheets characterized by larger value of p-adic prime and remaining in the vessel as visible DNA is removed . A variant of this explanation inspired by the dark matter hierarchy is that the anomalous scattering takes place on dark DNA at wormhole flux tubes remaining in the vessel. The DNA strands would simply lose their magnetic bodies which could be stealed by clusters of water molecules so that they become able to mimic DNA molecules as far as their magnetic bodies are considered.

    The most science fictive possibility is that the flux tubes connect the vessel boundaries to the removed DNA by wormhole flux tubes which are very long and correspond to a large value of hbar. In this case the scattering would involve a phase transition increasing the value of Planck constant and a travel of photons to the removed DNA and back followed by a phase transition to ordinary photons.

    Similar explanation works also in the case of homeopathy and allows to understand why the classic experiments of Benveniste could not be replicated when experimenters did not know which bottles contained the treated water. In this case the molecules dissolved in water would lose their magnetic bodies as a consequence of the shaking of the homeopathic remedy and one can say that clusters of water molecules would steal their magnetic coats. This would allow them to mimic the behavior of molecules and their presence would allow the immune system would develop a resistance against real molecules. This of course works only if the cyclotron radiation from the magnetic body is responsible for the biological effects. It is known that em radiation at low frequencies is indeed responsible for the ability of molecules to recognize each other. The generation of cyclotron radiation requires metabolic energy and the magnetic flux tubes connecting the experimenter to the treated bottle of water (correlates for directed attention) could have served as bridges along which metabolic energy could be transferred by using topological light rays (MEs serving as TGD counterparts of Alfwen waves). Experimentalists certainly did have strong desire to have successful experiments and this helped to realize the transfer of the metabolic energy.

    If this is the correct explanation of phantom DNA effect and homeopathy, homeopathy and phantom DNA effect would provide fundamental research tools for studying the physics of the magnetic bodies of bio-molecules. Since dark matter characterized by large values of Planck constants is expected to reside at the magnetic bodies, also the study of dark matter would become possible using these methods.

    For details see the chapter The Notion of Wave-Genome and DNA as Topological Quantum Computer of "Genes and Memes".


    [1] P. P. Gariaev, V. I. Chudin, G. G. Komissarov, A. A. Berezin , A. A. Vasiliev (1991), Holographic Associative Memory of Biological Systems}, Proceedings SPIE - The International Society for Optical Engineering. Optical Memory and Neural Networks. v.1621, p. 280- 291. USA.

    Has dark matter at the magnetic flux tubes been photographed?

    I spent a very pleasant week in Hungary in second Unified Theories conference (thanks for organizers for creating extremely warm atmosphere) and had the opportunity to listen Peter Gariaev's lecture about the fascinating experimental discoveries made by his group about the interaction of laser light and also ordinary light with DNA. The lecture and the discussions with Peter led to an updating of eight-year old model for these effects and summarized the updated model in the article that I titled The Notion of Wave-Genome and DNA as Topological Quantum Computer. I glue below the introduction of the article.

    The Notion of Wave-Genome and DNA as Topological Quantum Computer

    For about eight years ago - inspired by a representation in CASYS2000 conference [1] - I developed a model (see this) for the fascinating effects of laser light on genome discovered by Peter Gariaev and his collaborators [1,2,3,4,5]. This model is somewhat obsolete since it does not involve the recent TGD inspired vision about quantum biology and DNA, and the discussions with Peter in the second Unified Theories conference 2008 in Budapest made clear the need to update this model containing also some misinterpretations.

    In this article the effects of laser light on living matter are discussed only briefly with a stronger emphasis on the photographs produced by the scattering of ordinary light on DNA reported in [5]. In TGD framework these photographs could be interpreted as photographs of wormhole magnetic flux tubes containing dark matter. This would realize the dream of making directly visible the basic new structure predicted by TGD inspired quantum biology.

    1  The findings of Peter Gariaev and collaborators

    These findings include the rotation of polarization plane of laser light by DNA [1], phantom DNA effect [4], the transformation of laser light to radiowave photons having biological effects [4], the coding of DNA sequences to the modulated polarization plane of laser light and the ability of this kind of light to induce gene expression in another organisms provided the modulated polarization pattern corresponds to an "address" characterizing the organism [1,4], and the formation of images of what is believed to be DNA sample itself and of the objects of environment by DNA sample in a cell irradiated by ordinary light in UV-IR range [5].

    Gariaev and collaborators have introduced the notion of wave genome [1] requiring the coding of DNA sequences to temporal patterns of coherent em fields forming a bio-hologram representing geometric information about the organism. Code could mean that nucleotide is represented by a characteristic rotation angle for the polarization plane of linearly polarized laser radiation scattering from it. This kind rotation is known to be induced by chromosomes by a mechanism which to my best knowledge is poorly understood. Other open questions concern the precise identification of the substrate of the bio-hologram, of the reference wave and of information carrying wave, and of the mechanism making possible (quantum) coherence in macroscopic length scales.

    The reading of the DNA sequence to a radiation pattern is assumed to rely on the propagation of an acoustic soliton along DNA [1]. Whatever this process is, one should also identify the reverse process inducing the activation of the genome as the target organism receives the radiation coding for the DNA provided the "address" is correct. One should also identify the mechanism transforming laser radiation to radio-waves at various frequencies as well as the mechanism creating what is believed to be the image of DNA sample and replicated images of some instruments used in experiment.

    2  The relevant aspects of TGD based view about living matter

    The called massless extremals (MEs or topological light rays) distinguish between TGD and Maxwell's electrodynamics: they represent classically signals propagating with light velocity in a precisely targeted and dispersion free manner, and are therefore excellent candidates for the communication and control tools in the TGD based model for a living system as a conscious hologram (see this) and this). The notion of magnetic/field body, which can have layers of even astrophysical size, is an essential element of the model. Magnetic body uses biological body as a sensory receptor and motor instrument and MEs mediate sensory input and control signals between the two kinds of bodies (see this). I have already earlier applied MEs and the notion of magnetic body in an attempt to understand Gariaev's findings (this).

    The new element is the model for DNA as topological quantum computer (tqc) (see this) based on time-like braidings of so called wormhole magnetic flux tubes connecting nucleotides to the lipids at lipid layers nuclear and cell membranes. The model leads to a wide variety of predictions about DNA itself (see this), to a universal model for a tissue memory in terms of space-like braidings of wormhole magnetic flux tubes (see this), to a more detailed model of nerve pulse explaining also the origin of EEG and its synchrony (this), to a model for the evolution of the genetic code (see this), to a model of catalyst action involving a phase transition reducing the value of Planck constant inducing the shortening of the flux tubes connecting the reacting molecules and thus forcing them to the vicinity of each other, and to a model of for protein folding (this) in which the presence of wormhole magnetic flux tubes connecting bio-molecules becomes almost a definition for what it is to be living. It is interesting to combine these new ideas with the earlier [1,2,2,4] and more recent [5] findings of Gariaev. Basically the challenge is to fuse the DNA as tqc model with the model of living systems as a conscious hologram (see this).

    3  The basic assumptions of model explaining findings of Gariaev

    The basic assumptions of the model to be discussed are following.

    1. The hierarchy of Planck constants requires a generalization of the notion of 8-D imbedding space H=M4×CP2 obtained by gluing together almost copies of H like pages of book along common back. The pages of the book carry matter with various values of Planck constant and the p"../articles/ at different pages of the book are dark relative to each other in the sense that they cannot appear in the same vertex of Feynman diagram. The p"../articles/ at different pages of the book can however interact via classical fields and via the exchange of (for instance) photons which suffer a phase transition changing Planck constant as they leak between different pages of the book. In principle it is therefore possible to photograph the magnetic flux tubes carrying dark matter, and the proposal is that this is what Gariaev and collaborators have actually achieved [5].

    2. Braid strands realized as wormhole magnetic tubes are correlates for a directed attention. DNA connected by strands to (say) experimental instrument directs its attention to the instrument. One could perhaps say that DNA "sees" the surrounding world. Also ordinary attention for vision and other senses could involve flux tubes connecting DNA to the object of perception. This explains the ability of DNA to generate images of objects of external world [5]. The hierarchy of Planck constants explains the transformation of laser light to radio waves [3] as a phase transition increasing Planck constant and thus also wavelength but keeping the energy of photons as such.

    3. Wormhole flux tubes carrying super-conducting matter in large hbar phase are characterized by anomalous em charges characterizing the nucleotides (see this), and thus define an excellent candidate for the substrate of bio-hologram. A coding of DNA nucleotides to the rotation of polarization plane results for photons traversing through these flux tubes if a large parity breaking making possible rotation of the polarization plane (Faraday effect) is assumed. This is made possible by large parity breaking of fractally scaled up variant of weak physics (see this) explaining also chiral selection.

    4. The model for the nerve pulse (see this) leads to the model of EEG waves in which EEG rhythms induce a complete analog of reference waves whereas nerve pulse induces the analog of information carrying wave. The model predicts a fractal hierarchy of EEGs (EXGs) and their counterparts associated with long ranged color and electro-weak gauge fields having MEs as classical correlates. EEG rhythms are associated with propagating soliton sequences and nerve pulse corresponds to a propagating perturbation associated with this soliton sequence rather than soliton. The model predicts automatically the synchrony and spatiotemporal coherence of neural firing. EEG photons correspond to a large value of Planck constant implying that their energies are above thermal energy at physiological temperatures so that their effects on living matter are not masked by thermal noise.

      This model generalizes essentially as such to the recent context: the counterparts of nerve pulses propagate along the complex formed by DNA connected to the nuclear or cell membrane or even to another cell nucleus by flux tubes. The prediction is that gene expression can be coherent in the scale of organ and even that of population. This conforms with the notion of super-genome stating that the sequences of DNA strands in different nuclei organize along magnetic flux sheet like text lines at the page of a book. The notion of hyper-genome means that these books from different organisms in turn organize to a pages of a book at higher level of fractal hierarchy and give rise to a gene expression at the level of population or even biosphere.


    [1] P. Gariaev et al (2000), The DNA-wave-biocomputer, CASYS'2000, Fourth International Conference on Computing Anticipatory Systems, Liege, 2000. Abstract Book, Ed. M. Dubois.
    [2] P. Gariaev, Brief introduction into WaveGenetics. Its scope and opporturnities., http://www.wavegenetics.jino-net.ru.
    [3] P. P. Gariaev et al(2002), The spectroscopy of bio-photons in non-local genetic regulation, Journal of Non-Locality and Remote Mental Interactions, Vol 1, Nr 3.
    http://www.emergentmind.org/gariaevI3.htm .
    [4] P. P. Gariaev, V. I. Chudin, G. G. Komissarov, A. A. Berezin , A. A. Vasiliev (1991), Holographic Associative Memory of Biological Systems, Proceedings SPIE - The International Society for Optical Engineering. Optical Memory and Neural Networks. v.1621, p. 280- 291. USA.
    [5]P. P. Gariaev, G. G. Tertishni, A. V. Tovmash (2007), Experimental investigation in vitro of holographic mapping and holographic transposition of DNA in conjuction with the information pool encircling DNA, New Medical Tehcnologies, #9, pp. 42-53. The article is in Russian but Peter Gariaev kindly provided a translation of the article to English.
    [6] F. A. Popp, B. Ruth, W. Bahr, J. B�hm, P. Grass (1981), G. Grolig, M. Rattemeyer, H. G. Schmidt and P. Wulle: Emission of Visible and Ultraviolet Radiation by Active Biological Systems. Collective Phenomena(Gordon and Breach), 3, 187-214.
    [7]Faraday effect, http://en.wikipedia.org/wiki/Faraday-effect.

    For more details see the chapter The Notion of Wave-Genome and DNA as Topological Quantum Computer. See also the article The Notion of Wave-Genome and DNA as Topological Quantum Computer.

    A Model for Protein Folding and Bio-catalysis

    The model for the evolution of genetic code leads to the idea that the folding of proteins obeys a folding code inherited from the genetic code. After some trials one ends up with a general conceptualization of the situation with the identification of wormhole magnetic flux tubes as correlates of attention at molecular level so that a direct connection with TGD inspired theory of consciousness emerges at quantitative level. This allows a far reaching generalization of the DNA as topological quantum computer paradigm and makes it much more detailed. By their asymmetric character hydrogen bonds are excellent candidates for magnetic flux tubes serving as correlates of attention at molecular level.

    The constant part of free amino-acid containing O-H, O=, and NH2 would correspond to the codon XYZ in the sense that the flux tubes would carry the "color" representing the four nucleotides in terms of quark pairs. Color inheritance by flux tube reconnection makes this possible. For the amino-adics inside protein O= and N-H would correspond to YZ. Also flux tubes connecting the acceptor atoms of hydrogen bonds are required by the model of DNA as topological quantum computer. The long flux tubes between O= atoms and their length reduction in a phase transition reducing Planck constant could be essential in protein-ligand interaction.

    The model predicts a code for protein folding: depending on whether also =O-O= flux tubes are allowed or not, Y=Z or Y=Zc condition is satisfied by the amino-acids having N-H-O= hydrogen bond. For =O-O= bonds Y-Yc pairing holds true. Y=Zc option predicts the average length of alpha bonds correctly. Y=Z rule is favored by the study of alpha helices for four enzymes: the possible average length of alpha helix is considerably longer than the average length of alpha helix if gene is the unique gene allowing to satisfy Y=Z rule. The explicit study of alpha helices for four enzymes demonstrates that the failure to satisfy the condition for the existence of hydrogen bond fails rarely and at most for two amino-acids (for 2 amino-acids in single case only). For beta sheets there ar no failures for Y=Z option.

    The information apparently lost in the many-to-one character of the codon-amino-acid correspondence would code for the folding of the protein and similar amino-acid sequences could give rise to different foldings. Also catalyst action would reduce to effective base pairing and one can speak about catalyst code. The DNA sequences associated with alpha helices and beta sheets are completely predictable unless one assumes a quantum counterpart of wobble base pairing meaning that N-H flux tubes are before hydrogen bonding in quantum superpositions of braid colors associated with the third nucleotides Z of codons XYZ coding for amino-acid. Only the latter option works. The outcome is very simple quantitative model for folding and catalyst action based on minimization of energy and predicting as its solutions alpha helices and beta sheets.

    I want to express my gratitude for Dale Trenary for interesting discussions, for suggesting proteins which could allow to test the model, as well as providing concrete help in loading data help from protein data bank. Also I want to thank Timo Immonen for loaning the excellent book "Proteins: Structures and Molecular Properties" of Creighton. Also Pekka Rapinoja for writing the program transforming protein data file to a form readable by MATLAB.

    For details see the new chapter A Model for Protein Folding and Bio-catalysis.

    TGD based model for the evolution of genetic code: VI

    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,V).

    The model for the evolution of genetic code leads to the idea that the folding of proteins obeys a code inherited from genetic code in the sense that aminoacid behaves like the conjugate Yc of the middle nucleotide of the codon XYZ coding for it and that flux tubes connecting aminoacids to each other connect conjugate aminoacids behaving like Y and Yc. Also catalyst action would reduce to effective base pairing in this picture. After some trials one ends up with a general conceptualization of the situation with the identification of wormhole magnetic flux tubes as correlates for attention at molecular level so that a direct connection with TGD inspired theory of consciousness emerges at quantitative level. This allows a far reaching generalization of the DNA as topological quantum computer paradigm and makes it much more detailed. Also earlier vision about function of neurotransmitters and other information molecules as carriers of links in the web formed by living body becomes very concrete. The final outcome is very simple quantitative model for folding and catalyst action based on minimization of energy and consistent with basic experimental facts as well as general ideas.

    Because the model represents a quantitative breakthrough in the evolution of the TGD based view about quantum biology and to save the time required by the painstaking manual tex-html translation, I decided to represent the material also as article entitled From Genetic Code to Code for Folding and Catalysis. The background making it easier to understand can be found in the chapter Evolution in Many-Sheeted Space-time containing also the article as a section.

    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 A Evolution in Many-Sheeted Space-time.

    TGD based model for the evolution of genetic code: IV

    I have discussed the model for the evolution of genetic code in previous postings (I,II,III). Thanks to the Ulla Mattfolk I learned about the idea of protein folding code - something which is expected to exist but is not understood. This led to a trial for the folding code discussed in posting III) and based on the assumption that aminoacid behaves like dinucleotide. This trial did not work but the learning of some basic facts about proteins and their interactions inspired second trial according to which aminoacid in the interior of aminoacid sequences behave like the conjugate of the nucleotide Y of the codon XYZ coding for it. This trial seems to work.

    There exists a wonderful book "Proteins: Structures and Molecular Properties" by Thomas E. Creighton and published 1993 by W. H Freeman Company. In the following I freely refer to the general facts discussed in this book rather than referring separately to every detail. While reading this book I learned that the first guess for the code of catalysis was wrong but is also became clear what was wrong. It became clear that free aminoacid should behave like the conjugate of the DNA codon XYZ -rather than only XY- but that an aminoacid inside aminoacid sequence effectively reduces to Y since the formation of the peptide bonds by the elimination of water molecule and formation of NH---O= hydrogen bonds effectively eliminates X and Z. The ends of aminoacid behave like dicodons which conforms with their special role in biocatalysis. Only aminoacids for which Y corresponds to quarks (not antiquarks) can form hydrogen bonds so that hydrophilic-hydrophobic dichotomy corresponds to a strong matter antimatter asymmetry at quark level.

    1. Matter antimatter asymmetry at the level of interactions of aminoacids

    The first thing that I learned was that second nucleotide Y in the codon XYZ coding for aminoacid is what matters. Only Y=A,G aminoacid residue can form hydrogen bonds and is hydrophilic and thus interacts strongly with water and DNA and RNA. In T,C case the formation of hydrogen bonds is impossible or rare (ser,thr). In their interactions with water these aminoacids are passive, or rather-avoid water- and tend to interact with each other. This division is fundamental for the understanding of the interactions of aminoacids. The division of aminoacids to hydrophobic resp. non-hydrophobic ones corresponds to the assignment of quarks to A and G and antiquarks to T and C so that strong matter antimatter asymmetry is in question. Similar asymmetry appears in cosmology: in TGD Universe antimatter resides inside cosmic strings in the interior of big voids containing matter as galaxies at their boundaries so that one can understand why antimatter is not visible.

    2. Flux tubes can connect with all electronegative atoms

    Also a plausible answer to the question which atoms can be connected by flux tubes emerges.

    1. The model for dinucleotide precursor code involves precursors for which 3 precursors contain only oxygen ions or double bonded oxygens. The only possible conclusion is that oxygen can connect to any DNA letter (quark or antiquark) and that first letter-precursor correlation is a selection of the most probable alternative. Also in water oxygen atoms should form flux tube contacts with each other and aminoacids and DNA. Also nitrogen atoms could form similar flux tube connections. Same would apply to sulphur appearing in met and tyr and to electronegative atoms in general.

    2. The guess that the presence of the flux tube would be a necessary prerequisite for the hydrogen bond formation is wrong. Hydrogen bonds are formed between polar groups of hydrophilic aminoacids so that this rule does not seem to hold true. Quite generally, biologically important ions are assumed to reside as dark variants at magnetic flux tubes in the model for EEG and nerve pulse. The di-sulphur associated with cys-cys pairs play a fundamental role in protein folding. This bond is not allowed by the generalized base pairing rule which suggest that only the hydrogen bond formation which can be assigned with flux tube contacts.

    3. Hydrophobic aminoacids could connect with the oxygen in water by flux tubes but they could not form hydrogen bonds. The phase transition increasing hbar would allow them to increase their distance from water molecules in a controlled manner. This would be essential for folding and make possible the formation of pockets connected by flux tubes of large hbar to water. In quantum models for evolution of consciousness these pockets are believed to play a prominent role.

    3. What can one learn from the formation of alpha helices and beta sheets?

    The formation of peptide bonds by the elimination of H2O= molecules and generation of hydrogen bonds between NH and O= is an essential step in the formation of alpha helices and beta sheets. Second observation is that aminoacids decompose naturally into three parts corresponding to O=COH, R, and NH2. This suggests that aminoacid actually corresponds to the entire DNA codon XYZ coding for it. OH could correspond to Z , R to Y, and NH2 to Z. In the formation of peptide bond the flux tube connecting to COH and thus to Z would be taken by the water molecule created in the formation of peptide bond leaving only XY. The first flux tube would connect HN and O= so that X would pair with Xc assignable to O. There are no problems with the formation of bond if O= can correspond to any code letter as in the case of water. Water would correspond to matter antimatter symmetric phase and an interesting question is what counterpart this phase could have in cosmology (bosonic matter?).

    The aminoacid inside protein would effectively behave like Yc in the effective base pairing. Depending on whether it corresponds to quark or antiquark, aminoacid would be hydrophilic or hydrophobic- or rather - able to form hydrogen bonds or not. Since hydrophobic aminoacids cannot form hydrogen bonds, the formation of these residue pairs would be inhibited. The hydrophilic and hydrophobic residues could tend to avoid each other and the phase transitions increasing Planck constant would make this possible. It must be emphasized that this brings in strong long range correlation between the dynamics of the aminoacid residues belonging to the first and third (second and fourth) column of the code table.

    Hydrophilic aminoacids would form hydrogen bonds which each other and with DNA and RNA. In catalytic biding sites this kind of hydrogen bonds are formed between polar groups: also hydrogen bonds with water are formed and they tend to neutralize possible static charges. Ser (UCZ) and thr (ACZ) are the only effectively hydrophobic aminoacids containing OH group (and thus strictly speaking amphiphilic). Perhaps it is not an accident thr the codon ACC coding for thr appears in the stem of tRNA containing aminoacid. Ser and thr are indeed able to form hydrogen bonds with hydrophilic aminoacids and the prediction is that these aminoacids have form XGZ belonging to the last column of the code table. There are however very few biochemical reactions of this kind useful for proteins. Ser is exceptional in that it is predicted to be able to form flux tubes connecting ser_1 coded by TCZ with ser2 coded by AGZ, Z=T,C. The OH group of ser can be seen as a correlate for this property.

    The aminoacids at the ends of the polymer behave effectively like dinucleotides. The aminoacid coded by XYZ would base pair like XcYc if in the beginning of polymer and to YcZc if at the end of polymer. These nucleotides should have very special selective role in DNA-aminoacid and RNA-aminoacid interactions. Remarkably, it is known that the cutting of COOH and NH2 away from the end of polymer in general makes protein folding impossible (also mutations can affect dramatically folding). The first nucleotide of protein is usually met containing sulphur and the conjugation associates met with stop and tyr codons. The association of met with stop is indeed natural for the free NH2 of met having no hydrogen bond in the beginning of the sequence.

    According to Creighton, the binding sites of catalyst and ligand in the reaction complex are conjugates both geometrically and physically. It would be nice to have a concrete representation of this conjugacy in terms of the genetic code. Geometric conjugacy is easy to understand in terms of the lock and key picture but I am not quite sure what physical conjugacy could mean. Standard physics intuition would suggests that hydrophilic aminoacids that behave as acids resp. bases attract each other. This option does not possess any obvious formulation in the proposed picture. Matter antimatter conjugation for the second nucleotide Y of XYZ looks however very natural so that the aminoacids in the first and third (second and fourth) row of the code table would tend to pair with each other. This mechanism might be flexible enough to allow to find a conjugate of a given binding site by trial and error. The interpretation would be that hydrophobia tends to create concave and hydrophily convex structures. The attraction between Y and Yc in the braided conjugate regions would due to the Coulomb interaction between quark and antiquark at the ends of the wormhole flux tube.

    The strong correlation between RNA dinucleotide and aminoacid in the case of tRNA conforms with this picture. The third flux tube associated with the aminoacid could connect with the third codon after the transition to RNA-aminoacid era. During RNA era tRNA2 would have connected the O=C-OH part of the aminoacid to water molecule.

    4. Interactions with DNA

    Also in the interactions with DNA and RNA the aminoacid in the interior of the sequence would base-pair" like Yc. The original idea about molecular sex would transform in the sense that the companion of the hydrophilic aminoacid would DNA nucleotide in general. Hydrophobic aminoacids would behave like hermits. The generic contacts with DNA would be contacts with single nucleotide and there would be 4 different basic contacts. Aminoacids are indeed known to form contacts with single nucleotide. Hydrophilic contacts would be favored and hydrophobic contacts avoided so that again Y=A,G aminoacids would play at the outer boundary of DNA would play the active role. The aminoacids inside a given column of the code table would interact in very much the same manner with DNA nucleotides as far as formation of hydrogen bonds is considered. The terminals of the protein polymer are predicted to behave like XcYc resp. YcZc if the corresponding codon is XYZ. Again only hydrophilic codons are expected to be able to form hydrogen bonds. N-terminal is usually met and met and should avoid DNA.

    5. Interactions of proteins with ions and electrons

    Proteins interact also with electrons and ions. Typical process are the addition or removal of proton, electron, ion such Ca++, or molecule such as O2. These interactions are not well understood. For instance, the interactions involve the transfer of electrons between ligand protein and protein inducing oxidation (electron is given), reduction (electron is received) or redox reaction (both reduction and oxidation take place). In metabolism redox process is central. These reactions are reversible and it is difficult to understand how electrons are able make their long journey from the interior of the ligand so fast and avoiding dissipative effects. The formation of cyclotron Bose-Einstein condensates and electronic Cooper pair condensates at the magnetic flux tubes connecting ligand and protein could be the solution of the mystery.

    6. How DNA nucleotides are connected with the hydrophilic ends of lipids?

    The starting point of all these developments was the model for DNA as topological quantum computer (tqc) described in the earlier postings I, II, III, IV, V, VI, VII, VIII, IX, X, XI, XII, XIII.

    It was assumed that braid strands defined by "wormhole magnetic" flux tubes join nucleotides to lipids and can continue through the nuclear or cell membrane but are split during tqc. The hydrophilic ends of lipids attach to water molecules and self-organization patterns for the water flow in gel phase induce a 2-D flow in the lipid layer which is liquid crystal defining tqc programs at the classical level as braidings. The flow indeed induces braiding if one assumes that during topological computation the connection through the cell membrane is split and reconnected after the halting of tqc.

    The challenge is to understand microscopically how the flux tube joins DNA nucleotide to the phospholipid. What is clear that the points at which the flux tubes attach should be completely standard plugs and the mechanism giving rise to polypeptids is an excellent guide line here. Recall that phospholipid, the dancer, has two hydrophobic legs and head. Each leg has at the hydrophilic end O=C-O-C part joining it to glyceride connected to monophosphate group in turn connected to the hydrophilic residue R. The most often appearing residues are serine, inositol, ethanolamine, and choline. Only three of these appear in large quantities and there is asymmetry between cell exterior and interior.

    Let us denote by =O1 and =O2 the two oxygens in question (analogs of right and left hemispheres!). The proposal is that DNA nucleotide and =O1 are connected by a flux tube: the asymmetry between right and left lipid legs should determine which of the legs is "left leg" and which O= is the "left brain hemisphere". =O2, the holistic "right brain hemisphere", connects in turn to the flux tube coming from the other symmetrically situated =O2 at the outer surface of the second lipid layer. During tqc this flux tube is split or disappears. The lipid residue R couples with the flow of the liquid in gel phase. Since =O is in question the quark or antiquark at the end can correspond to the DNA nucleotide in question. Also the necessary complete correlation between quarks and antiquark charges at the ends of flux tubes associated with =O1 and =O2 can be understood as being due to the minimization of Coulomb interaction energy.

    The phosphate groups associated with nucleotides of DNA strand contain also =O, which could act as a plug to which the flux tube from the nucleotide is attached. =O appears in biomolecules involved with varying functions such as signalling, control, and metabolism. =O might act as a universal plug to which flux tubes from electronegative atoms of information molecules can attach their flux tubes. This would also provide a concrete realization of the idea that information molecules (neurotransmitters, hormones) are analogous to links in Internet (see this): they would not represent the information but establish a communication channel. The magnetic flux tube associated with the information molecule would connect it to another cell and by the join to =O plug having flux tube to another cell, say to its nucleus, would create a communication or control channel.

    To repeat the earlier statement, 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 the chapter Evolution in Many-Sheeted Space-time.

    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 Xc Yc. One might also speak about molecular sex. The potential companions of the aminoacid associated with dicodon XY would be aminoacids associated with dicodon Xc Yc. 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 the chapter Evolution in Many-Sheeted Space-time.

    TGD based model for the evolution of genetic code: II

    The net is wonderful. Yesterday evening I decided to search for "../articles/ about the possible role of dinucleotides in prebiotic evolution. "Dinucleotide" as a search word gave something about NADH and the only thing I understood that this is not relevant. Then I decided to be very optimistic and use as search words "dinucleotide" "prebiotic" simultaneously. To my surprise I found two gems which guaranteed that I did not sleep too much during the last night!

    The first gem did not relate to dinucleotides in a direct manner but I learned that the attempts to synthesize RNA sequences from nucleotides lead to 2',5' form of RNA: recall that the production of 3',5' RNA sequences has not been successful, only single nucleotides have been produced (see the article Experimental Testing of Theories of an Early RNA World by A. D. Ellington). This fits completely with the cautious hypothesis that RNA1 indeed corresponds to 2',5' form of RNA consisting of A,G,U,I and that ordinary 3',5' RNA, which I call RNA2, emerged as dinucleotides, which can polymerize to longer sequences and that this process was catalyzed by aminoacids.

    Second gem was directly related to dinucleotides, prebiotics, and genetic code. Somewhat disappointingly, I am not the only person who has considered the idea of 2-code. The title of the paper by S.D. Copley. E. Smith and H. J. Morowitz was A mechanism for the association of aminoacids with their codons and the origin of the genetic code. To very briefly summarize the content of the paper (I am of course not chemist and I see the paper from by "biomolecules connected by magnetic flux tubes" perspective so that it is easy to ridicule me).

    1. The paper suggests that there was prebiotic code in which 2-codons formed by dinucleotides of RNA define the prebiotic code. The paper starts from facts well-known to biochemists (I wish I were a biochemist, really). The first nucleotide X of the dinucleotide XY assigns to XY one of the four simple precursors of aminoacids. The correspondence is

      C,A,U,G → α-keto glutarate (α-KG), oxaloacetate (OAA), pyruvate, α-keto acid.

      Ketone means a compound with a generic formula R1-(CO)-R2, where CO has double valence bond. For α-keto acid R1 is replaced with O-(CO) group.

      These letter sequences tell to the typical reader probably as little as they tell to me (I am doing the ridicule myself!). If prebiotic code would be like the usual code the code would map 16 dinucleotides to 4 precursors.

    2. It is the reaction pathway leading to the aminoacid rather than molecule, which is coded. This is new! We have move to a higher level of abstraction! The empirical observation is that second nucleotide Y of XY correlates very strongly with how hydrophobic the aminoacid is. Y= U corresponds to maximal hydrophobia and its conjugate Y=A to maximal hydrophily. Y= G and C are in between. At deeper level Y together with X determines which reaction pathway way leading from the precursor to the aminoacid is selected.

    3. Authors propose that this correspondence means that dinucleotides XY form covalent bonds with precursors and this bonding catalysis the reaction leading to the aminoacid. For obvious reasons I do not have strong opinions about this.

    Consider now the interpretation of the results in TGD framework.

    The coding of the reaction pathway would be in terms of braid strands. The two ("wormhole") magnetic flux tubes beginning from the X and Y would end up to the precursor. The quark u,d or antiquark uc, dc labeling X would tell which precursor the magnetic flux tube ends at. What is the rule involved? What property of nucleotide X and precursor fixes the correspondence characterizing reaction pathway? It certainly seems that the flux tube connects X to a catalytic "hot spot" since X and this hot spot must end up near to each other in the phase transition reducing Planck constant and thus length of the magnetic flux tube. The charges possibly assignable with the hot spots - what ever they are - is a good guess but there is more involved.

    It seems that the nucleotides of codon are like 4-digits with first digits having the highest significance. The division of dinucleotide XY to two nucleotides should correspond to a similar division UV of the precursor to two parts. U would change in the reaction in the same manner for all aminoacids resulting from a given precursor but the change should depend on X. One can identify at U as a portion at the right end of the precursor (see the article). The left end of precursor would in turn connect with Y.

    1. To get some idea one an start from the formation of flux tubes between DNA nucleotides and their conjugates and hope that something very similar happens as flux tubes are formed between RNA dinucleotides and precursor structures. The electromagnetic charge Qem(X) of the quark associated with nucleotide X should correlate with some property of the nucleotide, or rather the reaction pathway associated with the formation of the pair formed by nucleotide and its conjugate. Hydrogen bonds obviously characterize this pathway. Quark charge indeed correlates with the number of hydrogen bonds of the base pair: 3|Qem|+1= n(bonds). The sign of the quark charge in turn correlates with the direction of the hydrogen bonds.

    2. One might hope that also in the recent case the catalysis involves the formation of hydrogen bonds between dinucleotide and precursor structure. Authors suggest covalent bond and the appearance of double bonded oxygens in precursors does not leave much doubts. The reactions could however involve a co-catalyst forming hydrogen bonds with XY and covalent bonds with the precursor. Obviously also the co-catalyst should have UV type structure.

    3. One can ask whether the co-catalyst could behave effectively like the conjugate of the RNA dinucleotide for the reaction considered. If so, one could understand the selection of the reaction pathway, and the strategy would be to find simple bio-molecules which behave like RNA dinucleotides in this sense. The strongest and probably unrealistic assumption would be that NH2-N-O and O-NH-NH2 portions corresponding to A-T type hydrogen bonds and O-NH and NH2-N portions correspond to G-C type hydrogen bonds. Needless to say, neither the precursors nor aminoacids have this kind of portions: actually the precursors assigned to U,A,C contain only carbon and double-bonded O.

    4. There could be a close connection with hydrogen bonds and magnetic flux tubes defining braid strands. I have already earlier proposed that hydrogen bonds might involve new physics, in particular the fractionization of electron and proton charge. This led to the notion of N-atom with the idea being that the fractionization of em charge leads to the emergence of symbolic dynamics in the sense that molecules forming hydrogen bonds between each other correspond to fractional charges for electron or proton summing up to the standard charge. These conjugate charges would define name and "co-name" and these names would be more important for the dynamics than the details of the ordinary chemistry just as names are for the development (or non-development - as you wish) of theoretical physics;-). Half-hydrogen bond and its conjugate would also bring in "sex" at the molecular level. It remains a future challenge to see whether the notion of N-atom and braid concept can be fused together.

    An ideal experimentalist with infinite brilliance and funding resources and enjoying endless trust of decision makers might be interested in carrying out the following experiments.

    1. Test whether RNA dinucleotides catalyze the transformation of the precursors (or something more complex behaving like RNA dinucleotide as far hydrogen bonding is involved) to aminoacids. In particular, test whether it is RNA1 or RNA2, which catalyzes the transformation of precursors to aminoacids.

    2. Suppose that one has a prebiotic soup containing 4 precursors of aminoacids and some concentration of dinucleotides of RNA1 or RNA2. Suppose that this indeed leads to the formation of aminoacids. If these aminoacids still possess the braid connections with nucleotides, the aminoacids in turn could catalyze the formation of further dinucleotides as suggested in the previous posting and RNA era could begin. It might be worth of checking also this.

      1. It is known that Na-montmorillonate, which is a clay mineral appearing in volcanic ash, catalyses a mixture of both 2'5' and 3'5' RNA dinucleotides, which are also dominantly L-L or D-D (see this). This solution looks fairly reasonable.
      2. The generation of aminoacids from precursors would be most naturally catalyzed by RNA1 dinucleotides. Is it too much to hope that this process is not catalysis in the precise sense of the word but transforms RNA1 dinucleotides to RNA2 dinucleotides?! If so, primordial evolution could be initiated in laboratory! Check also this!
      3. Speaking more seriously, a process transforming RNA1 to RNA2 would be enough. 2',5' RNA appears in peach latent mosaic viroid DNA (see this), and there should exist a process transforming 3',5' RNA to 2',5' RNA and vice versa. One might hope that the mechanism is simple enough to be realized primordially.

    For details see the chapter Evolution in Many-Sheeted Space-time.

    TGD based model for the evolution of genetic code: I

    The notion of many-sheeted space-time could allow to understand many puzzles related to the pre-biotic evolution (the popular article The Origin of Life on Earth, by Leslie Orgel gives a good overall view about the situation). There are many constraints on the models for pre-biotic evolution. The models have also many difficulties.

    In TGD framework the situation looks much better.

    1. TGD replaces materialistic view about universe with a continual re-creation in which classical universe in 4-dimensional sense is replaced by a new one in each quantum jump.
    2. p-Adic length scale hypothesis allows to formulate the notion of evolution precisely as a generation of increasingly larger space-time sheets characterized by preferred p-adic primes. A second aspect is the emergence of new levels in dark matter hierarchy making possible macroscopic quantum coherence and inducing great leaps in evolution.
    3. Also a hierarchy of dark weak bosons and gluons becomes an essential part of the physics of living matter.
    4. The notion of field/magnetic body carrying dark matter is a further key element in the model and has become increasingly important during years, and the vision about DNA-cell membrane system as a topological quantum computer utilizing braids defined by magnetic flux tubes connecting nucleotides to lipids meant a breakthrough in the understanding of the real function of DNA in information processing. The magnetic flux tubes connecting biomolecuiles and the phase transitions changing the value of Planck constant associated with them and thus inducing shortening or lengthening of braid strands provide a completely new view about the miracles of bio-catalysis and this hypothesis has begun to show its power.

    A good manner to introduce the essentials of the TGD inspired model for the prebiotic evolution is by a sequence of questions and answers.

    Q: Is life as we know it result of an accident?


    A: Quantum TGD predicts a genuine cosmic evolution occurring by quantum jumps for which dynamics is characterized by Negentropy Maximization Principle. The generalization of the notion of space-time implies dark matter hierarchy with levels characterized by arbitrarily large values of Planck constant so that macroscopic quantum coherence is possible even in astrophysical length scales. Even astrophysical systems are analogous to atomic systems which implies a strong standardization of planetary system so that Earth like planets are abundant. There are also other good reasons for why the evolution of life would not have been accident in TGD Universe and life should appear everywhere in TGD Universe.

    Q: What were the most primitive living systems?

    A: The notion of magnetic body brings to biology several completely new elements. Magnetic flux quanta containing dark charged matter and quantum controlling ordinary matter in plasma phase is perhaps the simplest system which can develop characteristics of a living system. The braiding of magnetic flux tubes makes possible topological quantum computation and a fundamental representation of memories and its presence could be even taken as a definition for what it is to be living. Tqc programs correspond to asymptotic self organization patterns for liquid flows inducing braidings and are non-trivial in presence of external energy feed.

    Q: How metabolic machinery emerged?

    A: Many-sheeted space-time concept predicts a hierarchy of universal metabolic energy quanta as differences of zero point kinetic energies for space-time sheets characterized by different p-adic length scales. What remains is to understand how chemical energy storage and utilization mechanisms developed.

    Q: What is behind biocatalytic machinery?

    A: The magnetic flux tubes connecting bio-molecules imply long range correlations between molecules. The reduction of Planck constant for magnetic flux tubes implying their shortening provides a mechanism making possible for bio-molecules to "find" each other in a very selective manner, and explains also why molecules end up to precisely defined conformations necessary for a selective bio-catalysis. This picture leads to amazingly detailed understanding of existing results about emergence of biomolecules in experimental arrangements modelling "primordial soup".

    Q: How symbolic dynamics emerged?

    A: The notion of N-atom suggested by the fractionization of electron quantum numbers for dark matter hierarchy brings in a candidate for a symbolic dynamics assigning to molecules "names" which need not correlate very strongly with the chemical properties of the molecule but would dictate to a high degree its biochemical behavior. Molecular "sex" emerges in the sense that molecules labeled with "names" and "co-names" tend to pair. The model of DNA as tqc assumes a 4-coloring of braid strands realized by an assignment of DNA nucleotides to quarks and anti-quarks. Also this means symbolic dynamics since only molecules connected by colored braids have high probability to participate in same biochemical reaction and do it in a very specific manner. Since the quarks involved with braid strands can have fractional charges, molecular sex can be realized also in this manner.

    Q: What selected the bio-molecules during chemical evolution?

    A: The proposed symbolic dynamics based on the notions of colored braids and N-atom poses very strong constraints on the subsets of bio-molecules that can react with considerable rates. The assignment of quark to nucleotides via the correspondence A,T,G,C→ u,uc,d,dc allows to basic rules about distribution of nucleotides in DNA and genes (differing from each other) and in mRNA in terms of approximate matter antimatter symmetry, isospin symmetry and the breaking of these symmetries. Matter antimatter asymmetry is visible also in the experiments trying to mimic primordial life.

    Q: How biochemical pathways emerged?

    A: It is now possible to realize in practice sequences of arbitrarily complex self-catalyzing biochemical reactions utilizing DNA hairpins. The mechanism generalizes to more complex molecules. At a given step of the reaction sequence the structure formed during the previous steps acts as a key fitting to a lock represented by some hairpin in the solution, and opens it to a linear molecule and in this manner makes it a key. The braids between reactants make it possible for the key and lock to find each other.

    Q: How genetic code evolved?

    A: The following gives a summary about what might have happened.

    1. The symmetries of the third codon of the genetic code allow in DNA as tqc model an interpretation as isospin and matter antimatter symmetries for quarks and antiquarks assigned with DNA nucleotides and representing 4-color of braid strands. These symmetries together with the study of the detailed structure of tRNA lead to a model for the evolution of the genetic code as a fusion of a non-deterministic 1-code and one-to-one 2-code corresponding to the conjugation of mRNA molecules.
    2. During RNA era two kinds of RNAs, call them RNA1 and RNA2, were present and played the roles of mRNA and aminoacid sequences. 2-code resp. 1-code mediated the analog of replication resp. translation using hairpin like molecules tRNA1 and tRNA2 to bring in RNA nucleotides and RNA doublets to the growing RNAi sequence. Amino-acids attached to the stem of tRNA2 acted as catalysts.
    3. The transition to RNA-aminoacid(-sequence) era took place via a fusion of the tRNA1 and tRNA2 to the ordinary tRNA and instead of sequences of two kinds of RNAs were replaced by aminoacid sequences were formed. Without primordial RNA variant of ribosomes binding aminoacids together by peptide bonds the transition to RNA-protein dominated era would not have been possible. The active part of recent ribosomes is indeed RNA molecule.
    4. After a period of symbiosis involving all these three tRNAs a transition to DNA-RNA-aminoacid world took place as an aminoacid sequence acting like reverse transcriptase emerged.

    Q: Did RNA world precede the life as we know it?

    A: The model for the evolution of the genetic code forces to conclude that RNA world preceded the recent biology and allows also to deduce that the nucleotides involved with second form of RNA where A,T,U,I(nositol). The exotic RNA in question could have been 2',5' form of RNA rather than 3',5' RNA but this is not the only possibility.

    Genetic code was implicitly present already during RNA era in the sense that aminoacids and RNA di-nucleotides were paired by braid strands (given aminoacid was connected to a dinucleotide defining the first two nucleotides of codons coding aminoacid). Hence the strong form of RNA world hypothesis would be wrong: aminoacids would have played a key role although their sequences would have been absent. Some examples are in order.

    1. For instance, the aminoacids found from meteorites correspond to four dinucleotides GX, X= A,U,G,C. Second example: it has been possible to synthesize only A and G but not T and C in absence of enzymes. The interpretation is in terms of strong matter antimatter asymmetry at quark level. The proposal is that in the presence of aminoacids braided to dinucleotides it should be possible to produce dinucleotides XY for which some codons XYZ code for the aminoacid.
    2. One can also understand the strange finding that it possible to synthesize conjugate polymer from RNA template but the production of conjugate of conjugate is not possible. The braid strands connecting template and its conjugate explain the mysterious finding and the presence of aminoacids could provide a mechanism to overcome the difficulty.
    3. Polymers are formed only if the solution contains right handed nucleotides. Also primordial chirality selection could be understood in terms of braids: right handed nucleotides would be connected to left handed aminoacids and vice versa and these phases separate from each other. The difference in energy of these states is large as compared to that predicted by standard model since TGD predicts scaled up variants of weak interactions for which weak bosons are effectively massless in biologically relevant length scales.

    Q: Does the notion of protocell make sense?

    A: The model of DNA as tqc involves essentially the magnetic flux tubes connecting DNA nucleotides and cell membrane. Since topological quantum computation should have taken place also during the RNA era, some kind of cell membrane consisting of exotic RNA should have been present. It has been found that DNA indeed forms membrane like structures which are liquid crystals consisting of sequences of DNA nucleotides with length up to 20 nucleotides (See this) and same might be true in the case of exotic RNA.

    Q: How life could evolve in the harsh primordial environment? Does the notion of primordial ocean make sense?

    A: It seems plausible that primordial life came from interstellar space. Evolving life had however to cope with the grave difficulties due to the irradiation by UV light and meteoric bombardment. A simple solution of these problems is to evolve in the interior of Earth, say in underground lakes. This idea conforms nicely with the observation that continents would have formed a single super continent at time of Cambrian explosion provided the radius of Earth at that time was by a factor 1/2 smaller than now. TGD predicts that cosmic evolution does not occur continuously but by quantum jumps in which the Planck constant of appropriate space-time sheet increases. A phase transition of this kind increasing the radius of Earth during a relatively short time interval would have led to a burst of life from underground lakes to the surface of Earth. This would also explain the sudden emergence of a huge variety of highly developed life forms during Cambrian explosion.

    The answers to these questions give only a rough view about TGD based model of prebiotic evolution. A detailed picture (still developing) can be found from the completely rewritten chapter Evolution in Many-Sheeted Space-time. I have also re-organized the book completely to better reflect the progress due to the model of DNA as topological quantum computer.

    DNA as topological quantum computer: XIII

    In previous postings I, II, III, IV, V, VI, VII, VIII, IX, X, XI, XII I have discussed various aspects of the idea that DNA could acts as a topological quantum computer using fundamental braiding operation as a universal 2-gate.

    The model of DNA as topological quantum computer was originally motivated by the idea that quantum biology in TGD Universe might teach something about quantum computation like processes possibly taking place in living matter. It turned out that the model of DNA as topological quantum computer began to give lessons about quantum biology. In particular, one must assign 4-color to braid strands represented as flux tubes connecting DNA nucleotides A,T,C,G to lipids of nuclear or cellular membranes. In TGD Universe this color is naturally represented in terms 2 quarks u,d and their antiquarks (scaled up variants of ordinary quarks with large hbar and residing at flux tubes of "wormhole" magnetic fields defining the braid strands).

    This sounds definitely something very weird for anyone still inhabiting the simple standard model universe and not gone through 28 year lasting process of discovery starting from the basic idea of TGD and ending up with the recent highly refined picture about how TGD Universe differs from that of standard model. Recall however that the discovery of Barbara Shipman that the patterns of honeybee dance can be understood in terms of the mathematics of color group SU(3) of strong interactions, led her to suggest that quarks are directly involved with cognition and memory. This makes sense since DNA as tqc using 4-colored braids is expected to be closely involved with cognition and memory.

    The model led to the prediction that coding regions of DNA might be characterized by a breaking various symmetries at quark level, that is breaking of matter antimatter symmetry, isospin asymmetry, and asymmetry between uuc and ddc type matters (c refers to charge conjugation taking matter into antimatter) could take place at level of coding sequences. Three parameters should characterize this breaking.

    I made some sample calculations and found support for the breaking of matter antimatter and symmetry and the generation of anomalous em charge implied by this. Yesterday I learned (thanks go to Dale Trenary for crucial references) that simple basic facts about DNA which can be found from Wikipedia support the proposed vision about symmetry breaking although details were not quite correct.

    1. Chargaff's rules, which I already knew, imply an approximate but not complete matter antimatter symmetry at the level of the entire genome and one can find nice examples about the small breaking. Depending on the explicit corresponds of A,T,C,G with quarks. The breaking of matter antimatter symmetry is quite generally below per cent. The anomalous em charge per nucleon, which depends on scenario (2 options and their charge conjugates) is typically below .1 units per nucleotide. The following table gives representative examples about values of various parameters (anomalous em charge per nucleotide for two options, isospin per nucleotide, quark number per nucleotide, G+C/A+T ratio).

    2. The deviation of C+G/A+T from unity used to classify genomes characterizes the asymmetry between uuc and ddc type matters. C+G/A+T increases as the length of coding sequence increases.

    3. Szybalski's rules state that matter antimatter symmetry and isospin symmetry are broken for coding regions of DNA. The breaking pattern is however more intricate than I had expected. The coding part of the DNA decomposes in fifty-fifty manner into regions in which either matter or antimatter dominates and the directions of transcription and selection of template DNA are different for these regions so that mRNA breaks matter antimatter symmetry and always in the same manner. By the way, I had always thought that the template DNA is always the same. The structural matter antimatter asymmetry of mRNA is obviously translated to a functional asymmetry of DNA. A possible reason is that otherwise DNA would not be stable since it would generate too high anomalous em charge. One can wonder whether the matter antimatter asymmetry for mRNA is compensated by the opposite asymmetry for some other type of RNA inside cell nucleus.

    It thus seems that DNA as tqc and the coding of braid color by quarks allows to understand the poorly understood empirical rules about the distribution of codons in DNA. Many fascinating questions and working hypothesis can be considered besides those proposed already earlier.

    For details see the chapter DNA as Topological Quantum Computer. See also the brief article here.

    DNA as topological quantum computer and ageing

    The notion of anomalous em charge is one of the basic implications of the many-sheeted space-time concept. It can be assigned to wormhole contacts carrying fermion and antifermion quantum numbers at their throats. If the classical electromagnetic fields at the two space-time sheets are different, the wormhole contact couples to the difference of vector potentials and behaves like a particle with anomalous charge although the net charge is vanishing.

    In the model of DNA as topological quantum computer the braid strands (whose braiding defines tqc program) emanate from DNA nucleotides and end up to the lipids of the nuclear and cellular membranes. They are colored in the sense that one can tell whether the strand arrives from A,T,C or G. This is achieved by representing the braid strand as a wormhole magnetic flux tube with CP conjugate wormhole throats at its ends. To A,T,C,G one assigns a wormhole contact with quark u,d or its antiquark at the "upper" throat and its CP conjugate at the "lower" throat.

    There are also symmetries: A and T resp. G and C are mapped to quark and its antiquark so that DNA conjugation corresponds to CP conjugation. Chargaff's rules A≈ T and G≈ A for single DNA strand state that DNA as a whole is matter-antimatter symmetric. A and G are mapped to u,d or their antiquarks and correspond therefore to isospin doublet. This allows to interpret the almost exact A-G and T-C symmetries of the third nucleotide of codon in terms of strong isospin symmetry. Both symmetries can break down for short portions of DNA.

    The anomalous em charge of DNA is due to the fact that DNA is negatively charged (2 units of charge per nucleotide due to phosphate) and generates classical em field at the "upper" sheet of wormhole magnetic flux tube. The nearly vanishing Qa for DNA is interpreted as a stability condition for DNA. For long DNA strands Chargaff's rules A≈ T and G≈ A indeed guarantee the vanishing of Qa since A and T resp. C and G correspond to quark and its antiquark. There are four options concerning nucleotide quark correspondence and therefore also the identification of Qa: for one of them one has Qa= [2(A-T)-(G-C)]/3. Integer valuedness allows color singletness for the many quark-antiquark state assignable to DNA strand via the mapping of A,T,C,G to quarks and antiquarks.

    Telomeres are of special interests as far as anomalous em charge is considered. Chromosomes are not copied completely in cell replication, and one function of telomeres is to guarantee that the translated part of genome replicates completely for sufficiently many cell divisions. Telomeres consists of 3-20 kilobases long repetitions of TTAGGG, and there is a 100-300 kilobases long repeating sequence between telomere and the rest of the chromosome. Telomeres can form can also 4-stranded structures. Telemere end contains a hair-pin loop as a single stranded part, which prevents the action of DNA repair enzymes on the chromosome end.

    Telomerase is a reverse transcriptase enzyme involved with the synthesis of telomeres using RNA strand as a template but since its expression is repressed in many types of human cells, telomere length shortens in each cell replication. In the case of germ cells, stem cells and white blood cells telomerase is expressed and telomere length preserved. Telomere shortening is known to relate to ageing related diseases. On the other hand, overactive telomere expression seems to correlate with cancer.

    If telomeres possess braid strands, the compensation of Qa might provide an additional reason for their presence. If this the case and if telomeres are strict multiples of TTAGGG, the shortening of telomeres generates a non-vanishing Qa unless something happens for the active part of DNA too. Color singletness condition should however remain true: the disappearance of 3n multiples of TTAGGG in each replication is the simplest guess for what might happen. In any case, DNA strands would become unstable in cell replication. Qa could be reduced by a partial death of DNA in the sense that some portions of braiding disappear. Also this would induce ill functioning of tqc harware perhaps related to ageing related diseases. Perhaps evolution has purposefully developed this ageing mechanism since eternal life would stop evolution.

    For a more detailed exposition and background see the chapter DNA as Topological Quantum Computer.

    On direct testing of quantum consciousness

    Quantum entanglement and its reduction in "cognitive" quantum measurement could provide a direct test of quantum consciousness. Andrei Khrennikov [1] has proposed a mathematical formulation of "quantum like" behavior based on his proposal that so called context dependent probabilities could provide alternative description for quantum mechanical interference phenomenon. In quantum theory context would correspond to the choice of quantization axis. Khrennikov has also proposed a modification of Bell inequalities so that they apply on conditional probabilities: this would make it possible to avoid the task of preparing entangled state of brains. The hope is that one could forget completely the microscopic structure of quantum brain and test quantum like behavior by making simple experiments involving just questions to the subject persons and finding whether or not classical rules for conditional probabilities hold true or not.

    1. First experiment

    Bistable percepts induced by ambiguous figures are especially attractive from the point of view of experimentation. The question would be "Which of the two possible percepts?" and the outcome would be answer to this question. The first experiment reported in [2] was following.

    1. Consider a group S of subject persons. Divide it into two groups U and V containing equally many subject persons. Represent for members of U the question A (bistable percept A). From this one can deduce the probalities p(A=+) and p(A=-). Represent for members of V the question B and and immediately after than the question A (bistable percept A) for those who answered B=-. This experiment gives the conditional probabilities p(A=x/B=y).

    2. The quantity

      cos(θx) = [p(A=x)- p(B=+)p(A=x/B=+) -p(B=-)p(A=x/B=-)]/[2(p(B=+)p(B=-)p(A=x/B=+)p(A=x/B=-)1/2], x=+/-.

      measures the failure of the basic rule

      p(A=x)=p(B=+)p(A=x/B=+) +p(B=-)p(A=x/B=-)

      for classical conditional probability. Note that in quantum theory similar rules applies to transition amplitudes (conditional probability amplitudes) corresponding to the addition of a complete set of states in the inner product between two states (for instance, repeated application of this gives rise to path integral formulation).

    3. One can describe the situation in terms of "quantum like state"

      Ψ(A=x)= [p(B=+)p(A=x/B=+)]1/2 +e+/- [p(B=-)p(A=x/B=-)]1/2

      satisfying p(A=+x) =|Ψ(A=x)|2. If cos(θx) is non-vanishing one can say that that the situation is quantum like. Conte and collaborators conclude that this is indeed the case [2].

    2. Second experiment

    Second experimental test is more complex and involves generalization of Bell's inequality so that it involves conditional probabilities [1] Let A,B,C=+/- be arbitrary dichotomous random variables satisfying Kolmogorov axioms characterizing classical probability. Then the following analog of Bell inequality can be shown to hold true:

    P(A=+,B=+) + P(C=+,B=-)≥ P(A=+,C=+).

    In terms of conditional probabilities one has

    P(A=+/B=+)/P(B=+) + P(C=+/B=-)/P(C=+) ≥ P(A=+/C=+)/P(C=+).

    If the random variables are symmetrically distributed so that one has P(X=+/-)=1/2, for X=A,B,C one obtains

    P(A=+/B=+)+P(C=+/B=-)≥ P(A=+/C=+) .

    Note that this form of equality is by no means necessary. The symmetric distributions for the random variables would however correspond to maximal entanglement in spin system given best hopes for the violation of the Bell inequality.

    1. The test is following. Consider a group S of subject persons divided into subgroups U and V as above. Pose to the members of U question B and immediately after that question A for those who answered B=+ and question C for those who answered B=-1. For group V represent first the question C and for those who answer C=+ represent the question A. The failure of inequality could regarded as a direct proof for quantum like behavior. That failure does not occur does not of course mean that system is classical but only that the quantal effects are not large enough.

    2. The analogy with Bell's inequality suggest that the questions are analogous to posing the spins of spin pair in spin singlet state to an external magnetic fields determining the quantization axis. The inequality tend to fail when the directions of the magnetic fields for the two spins differ enough. Thus the failure is expected if the questions, in other words ambiguous figures producing bistable percepts differ enough.

    3. Criticism and possible improvement of the experiment

    In the case of spin pairs the tests of quantum behavior are carried out for the members of spin pair by putting them to magnetic fields having different directions. Now the pair of experiments is made for a single subject person. Hence there is no need to prepare quantum entangled pair of conscious entities.

    The use of ensemble is the problematic aspect of experiments. Human beings are extremely complex systems and one can argue that it is impossible to prepare an ensemble of identical systems in cognitive sense. A possible manner to avoid the problem would be the replacement of ensembles with a time series of experiments performed for a single subject person. In both experiments one could perform the two kinds of experiments many times to single subject person and deduce various probabilities and cos(θ) from the outcome of the experiments.

    4. Interpretation in terms of zero energy ontology and DNA as tqc

    The discussions with Elio Conte led to the realization that in zero energy ontology the experiments differ from the corresponding experiments for two-spin system only in that space-like entanglement is replaced with time like entanglement. The experiment would be essentially a measurement of probabilities defined by the matrix elements of M-matrix defining the generalization of S-matrix. Hence Bell's inequalities and their generalizations should apply in genuine quantum sense. By performing the experiments for a single subject person as time series one might be therefore able study whether quantum consciousness in the sense of TGD makes sense.

    Quantum consciousness approach however requires that bistable percepts have genuine microscopic quantum states as their physical correlates. This is not assumed in the approach of Khrennikov.

    1. If the vision about DNA as topological quantum computer makes sense, the question to the answer "Which of the two possible percepts?" can be regarded as a qubit which is some function of a large number of qubits and same function irrespective of the ambiguous figure used. This could hold quite generally, at least for a given sensory modality. The qubits appearing as arguments of this function are determined by the sensory input defined by the ambiguous figure. The ambiguous figure would take the role of magnetic field determining the directions of quantization axes for a large collection of qubits appearing as arguments of the Boolean function (one cannot exclude the possibility that neuronal synchrony forces all these axes to have same direction). Qubit could correspond to spin or some spin like variable. The quantization axes could correspond in this case to the direction of external magnetic field acting on 1-gate of tqc.

    2. Qubit could be replaced with an n-state system: this would require a generalization of the Bell inequalities. The model of DNA as tqc suggests that qubit might be replaced with qutrit defined by a quark triplet (third quark with vanishing color isospin would correspond to ill-defined truth value. The inability of subject persons to identify the percept always indeed encourages to consider this option. Color group SU(3) (SO(3) subset SU(3)) defines the set of possible quantization axes as points of the flag manifold F= SU(3)/U(1)× U(1) (SO(3)/SO(2)= S2). Quantization axes would be determined by the direction of color magnetic field in color Lie algebra and sensory input would define a sequence of 1-gates at the lipids ends of the braid strands, and realized as color rotations of the flux tube defining braid strand. This hypothesis would conform with the proposal of Barbara Shipman that honeybee dance that quarks are in some mysterious manner involved with cognition [3].

    For background see that chapter DNA as Topological Quantum Computer.


    [1] A. Khrennikov (2004), Bell's inequality for conditional probabilities as a test for quantum like behaviour of mind, arXiv:quant-ph/0402169.

    [2] E. Conte, O. Todarello, A. Federici, J. P. Zbilut (2008), Minds States Follow Quantum Mechanics During Perception and Cognition of Ambigious Figures: A Final Experimental Confirmation, arXiv:0802.1835v1 [physics.gen-ph].

    [3] B. Shipman (1998), The geometry of momentum mappings on generalized flag manifolds, connections with a dynamical system, quantum mechanics and the dance of honeybee.

    B. Shipman (1998), On the geometry of certain isospectral sets in the full Kostant-Toda lattice.

    B. Shipman (1998), A symmetry of order two in the full Kostant-Toda lattice.

    DNA as topological quantum computer: XII

    In previous postings I, II, III, IV, V, VI, VII, VIII, IX, X, XI I have discussed various aspects of the idea that DNA could acts as a topological quantum computer using fundamental braiding operation as a universal 2-gate.

    One of the challenges is the realization of single particle gates representing U(2) rotation of the qubit. The first thing to come mind was that U(2) corresponds to U(2) rotation induced by magnetic field and electric fields. Yesterday I realized much more elegant realization in terms of SU(3) rotation, where SU(3) is color group associated with strong interactions. Soon I remembered that there is direct evidence for the prediction that color SU(3) is associated with tqc and thus cognition: something that does not come first in mind! I have myself written text about the strange finding of topologist Barbara Shipman suggesting that quarks are in some mysterious manner involved with honeybee dance and proposed an interpretation.

    1. The realization of 1-gate in terms of ordinary rotations

    The realization of single particle gates as U(2) transformations leads naturally to the extension of the braid group by assigning to the strands sequences of group elements satisfying the group multiplication rules. The group elements associated with a nth strand commute with the generators of braid group which do not act on nth strand. G would be naturally subgroup of the covering group of rotation group acting in spin degrees of spin 1/2 object. Since U(1) transformations generate only an overall phase to the state, the presence of this factor might not be necessary. A possible candidate for U(1) factor is as a rotation induced by a time-like parallel translation defined by the electromagnetic scalar potential Φ=At.

    A possible realization for single particle gate- characterized by s subset SU(2)- would be as SU(2) rotation induced by a magnetic pulse. This transformation is fixed by the rotation axis and rotation angle around this axes. This kind of transformation would result by applying to the strand a magnetic pulse with magnetic field in the direction of rotation axes. The duration of the pulse determines the rotation angle. Pulse could be created by bringing a magnetic flux tube to the system, letting it act for the required time, and moving it away. U(1) phase factor could result from the electromagnetic gauge potential as a non-integrable phase factor exp(ie∫ Atdt/hbar) coming from the presence of scale potential Φ=At in the Hamiltonian.

    One can criticize this model. The introduction of magnetic pulses does not look an attractive idea and seems to require additional structures besides magnetic flux tubes (MEs?). It would be much nicer to assign the magnetic field with the flux tubes defining the braid strands. The rotation of magnetic field would however require changing the direction of braid strands. This does not look natural. Could one do without this rotation by identifying spin like degree of freedom in some other manner? This is indeed possible.

    2. The realization of 1-gate in terms of color rotations

    TGD predicts a hierarchy of copies of scaled up variants of both weak and color interactions and these play a key role in TGD inspired model of living matter. Both weak isospin and color isospin could be considered as alternatives for the ordinary spin as a realization of qubit in TGD framework. Below color isospin is discussed. Below color isospin is discussed but one could consider also a realization in terms of nuclei and their exotic counterparts differing only by the replacement of neutral color bond between nuclei of nuclear string with a charged one. Charge entanglement between nuclei would guarantee overall charge conservation.

    1. Each space-time sheet of braid strands contains quark and antiquark at its ends. Color isospin and hypercharge label their states. Two of the quarks of the color triplet form doublet with respect to color isospin and the third is singlet and has different hyper charge Y. Hence qubit could be realized in terms of color isospin I3 instead of ordinary spin but third quark would be inert in the Boolean sense. Qubit could be also replaced with qutrit and isospin singlet could be identified as a statement with ill-defined truth value. Trits are used also in ordinary computers. In TGD framework finite measurement resolution implies fuzzy qubits and the third state might relate to this fuzziness.

    2. Magnetic flux tubes are also color magnetic flux tubes carrying non-vanishing classical color gauge field in the case that they are non-vacuum extremals. The holonomy group of classical color field is an Abelian subgroup of the U(1)× U(1) Cartan subgroup of color group. Classical color magnetic field defines the choice of quantization axes for color quantum numbers. For instance, magnetic moment is replaced with color magnetic moment and this replacement is in key role in simple model for color magnetic spin spin splittings between spin 0 and 1 mesons as well as spin 1/2 and 3/2 baryons.

    3. There is a symmetry breaking of color symmetry to subgroup U(1)I3× U(1)Y and color singletness is in TGD framework replaced by a weaker condition stating that physical states have vanishing net color quantum numbers. This makes possible the measurement of color quantum numbers in the manner similar to that for spin. For instance, color singlet formed by quark and antiquark with opposite color quantum numbers can in the measurement of color quantum numbers of quark reduce to a state in which quark has definite color quantum numbers. This state is a superposition of states with vanishing Y and I3 in color singlet and color octet representations. Strong form of color confinement would not allow this kind of measurement.

    4. Color rotation in general changes the directions of quantization axis of I3 and Y and generates a new state basis. Since U(1)× U(1) leaves the state basis invariant, the space defined by the choices of quantization axes is 6-dimensional flag manifold F=SU(3)/U(1)×U(1). In contrast to standard model, color rotations in general do not leave classical electromagnetic field invariant since classical em field is a superposition of color invariant induced Kähler from and color non-invariant part proportional classical Z0 field. Hence, although the magnetic flux tube retains its direction and shape in M4 degrees of freedom, its electromagnetic properties are affected and this is visible at the level of classical electromagnetic interactions.

    5. If color isospin defines the qubit or qutrit in topological quantum computation, color quantum numbers and the flag manifold F should have direct relevance for cognition. Amazingly, there is a direct experimental support for this! Years ago topologist Barbara Shipman made the intriguing observation that honeybee dance can be understood in terms of a model involving the flag manifold F (see this, this, and this). This led her to propose that quarks are in some mysterious manner involved with the honeybee dance. My proposal was that color rotations of the space-time sheets associated with neurons represent geometric information: sensory input would be coded to color rotations defining the directions of quantization axes for I3 and Y. Subsequent state function reduction would provide conscious representations in terms of trits characterizing for instance sensory input symbolically.

    I introduced also the notions of geometric and sensory qualia corresponding to the two choices involved with the quantum measurement: the choice of quantization axes performed by the measurer and the "choice" of final state quantum numbers in state function reduction. In the case of honeybee dance geometric qualia could code information about the position of the food source. The changes of color quantum numbers in quantum jump were identified as visual colors. In state function reduction one cannot speak about change of quantum numbers but about their emergence. Therefore one must distinguish between color qualia and the conscious experience defined by the emergence of color quantum numbers: the latter would have interpretation as qutrit.

    To sum up, this picture suggests that 1-gates of DNA tqc (understood as "dance of lipids") are defined by color rotations of the ends of space-like braid strands and at lipids. The color rotations would be induced by sensory and other inputs to the system. Topological quantum computation would be directly related to conscious experience and sensory and other inputs would fix the directions of the color magnetic fields.

    For details see the chapter DNA as Topological Quantum Computer.

    Summary of possible symmetries of DNA suggested by the model of topological quantum computation

    The following gives a list of possible symmetries of DNA inspired by the identification of braid color.

    1. Color confinement in strong form

    The states of quarks and anti-quarks associated with DNA both wormhole wormhole throats of braided (living) DNA strand can be color singlets and have thus integer valued anomalous em charge. The resulting prediction depends on the assignment of quarks and antiquarks to A,T,C,G which in principle should be determined by the minimization of em interaction energy between quark and nucleotide. For instance 2(A-T)-(G-C) mod 3=0 for a piece of living DNA which could make possible color singletness. As a matter fact, color singletness conditions are equivalent for all possible for braid color assignments. This hypothesis might be weakened. For instance, it could hold true only for braided parts of DNA and this braiding are dynamical. It could also hold for entire braid with both ends included only: in this case it does not pose any conditions on DNA. Questions: Do all living DNA strands satisfy this rule? Are only the double stranded parts of DNA braided and satisfy the rule. What about loops of hairpins?

    2. Matter antimatter asymmetry at quark level

    A←→ T and G←→ C corresponds to charge conjugation at the level of quarks (quark ←→ antiquark). Chargaff's rules states A≈ T and C≈ G for long DNA strands and mean matter-antimatter symmetry in the scale of DNA strand. Double strand as a whole is matter anti-matter symmetric. Matter-antimatter asymmetry is realized functionally at the level of DNA double strand in the sense that only DNA strand is transcribed. The study of some examples shows that genes defined as transcribed parts of DNA do not satisfy Chargaff's rule. This inspires the hypothesis about the breaking of matter antimatter symmetry. Genes have non-vanishing net A-T and C-G and therefore also net Qa with sign opposite to that in control regions. Just as the Universe is matter-antimatter asymmetric, also genes would be matter-antimatter asymmetric.

    3. Isospin symmetry at quark level

    A←→ G and T←→ A correspond change of anomalous em charge by 1 unit and these operations respect color confinement condition. Local modifications of DNA inducing these changes should be preferred. The identification for the symmetries A←→ G and T←→ A for the third nucleotide of code is as isospin symmetries. For the vertebrate mitochondrial code the symmetry exact and for nuclear code slightly broken.

    4. Matter antimatter asymmetry and isospin symmetries for the first two nucleotides

    The first two nucleotides of the codon dictate to a high degree which amino-acid is coded. This inspires the idea that 3-code has emerged as fusion of 1- and 2-codes in some sense. There are two kinds of 2-codons. The codons of type A have fractional em charge and net quark number (consisting of either matter or antimatter at quark level) and are not able to form color singlets. The codons of type B have integer em charge and vanishing quark number (consisting of matter and antimatter) and are able to form color singlets. The 2-codons of type A (resp. B) are related by isospin rotations and there should be some property distinguishing between types A and B. There indeed is: if 2-codon is matter-antimatter asymmetric, 1-codon is not and vice versa.

    1. For almost all type A codons the amino-acid coded by the codon does not depend on the last nucleotide. There are two exceptions in the case of the nuclear code: (leu,leu,phe,phe) and (ile,ile,ile,met). For human mitochondrial code one has (ile,ile,ile,ile) and thus only one exception to the rule. The breaking of matter-antimatter symmetry for the third nucleotide is thus very small.

    2. For codons of type B the 4-columns code always for two doublets in the case of vertebrate mitochondrial code so that for codons with vanishing net quark number the breaking of matter-antimatter symmetry for the third nucleotide is always present.

    5. Em stability

    Anomalous em charge Qa vanishes for DNA and perhaps also mRNA strand containing also the G cap and poly-A tail which could compensate for the Qa of the transcribed region so that

    2(A-T)-(G-C)≈ 0

    or some variant of it holds true. Chargaff's rules for long DNA strands imply the smallness of Qa.

    6. Summary of testable working hypothesis

    Following gives a summary of testable working hypothesis related to the isospin symmetry and color singletness. The property of having integer valued/vanishing Qa is referred to as property P.


    1. Gene plus control region and also DNA repeats should have property P. Transcribed and control regions of gene have Qa with opposite signs.

    2. Transposons, repeating regions, the overhangs associated with the cut and paste of transposon, and the DNA strands resulting in cutting should have property P. This could explain why transposons can paste themselves to AT and GC (Qa=0) rich repeating regions of DNA. The points at which DNA can be cut should differ by a DNA section having property P. This gives precise predictions for the points at which transposons and pieces of viral DNA can join and could have implications for genetic engineering.

    3. If also mRNA is braided, it has property P. This can be only true if the poly-A tail compensates for the non-vanishing Qa associated with the translated region.

    4. Living hairpins should have property P. If only double helix parts of hairpins are braided, the prediction is trivially true by the palindrome property. tRNA or at least parts of it could be braided. Braids could end to the nuclear membrane or mRNA or to the amino-acid attachable to tRNA. For stem regions Qa is integer valued. The fact that the nucleotide of the anticodon corresponding to the third nucleotide of codon can base pair with several nucleotides of mRNA suggests that I(nositol) can have Qa opposite to that of A,T,C and U opposite to that of A,G. For 2-anticodon the pairing would be unique. This would give a lot of freedom to achieve property P in weak sense for tRNA. Braid structure for tRNA + amino-acid could be different that for tRNA alone and also in the translation the braid structure could change.

    5. Also aminoacids could be braided. Qa could vary and correspond to Qa for one of the codons coding for it. The aminoacid sequences of catalysts attaching to DNA strand should have opposite Qa for each codon-aminoacid pair so that aminoacid would attach only to the codons coding for it.

    For a more detailed exposition and background see the chapter DNA as Topological Quantum Computer.

    Transposons and anomalous em charge

    TGD based model of tqc relies on colored braids with the color of braid in one-one correspondence with nucleotides A,T,C,G and represented by 2 quarks and 2 anti-quarks. The basic prediction of the braid concept is anomalous em charge defined as the net quark charge assignable to DNA space-time sheets of DNA sequence. This notion makes sense also for more general molecules possessing braids. Transposons provide an especially simple manner to test the hypothesis that anomalous em charge is integer valued (quarks can form color singlet) or even vanishing (by stability).

    Transposons (see this and the article of D. F. Voytas (2008), Fighting fire with fire, Nature vol 451, January) are moving and copying genes. Moving genes cut from initial position and past to another position of double strand. Copying genes copy themselves first to RNA and them to a full DNA sequence which is then glued to the double strand by cut and paste procedure. They were earlier regarded as mere parasites but now it is known that their transcription is activated under stress situations so that they help DNA to evolve. In tqc picture their function would be to modify tqc hardware. For copying transposons the cutting of DNA strand occurs usually at different points for DNA and cDNA so that "sticky ends" result ("overhang" and its complement) (see ). Often the overhang has four nucleotides. The copied transposon have ends which are reversed conjugates of each other so that transposons are palindromes as are also DNA hairpins. This is suggestive of the origin of transposons./p>

    In order to avoid boring repetitions let us denote by "satisfy P" for having having integer valued (or even vanishing) Qa. The predictions are following:

    1. The double strand parts associated with the segments of DNA produced by cutting should satisfy P.
    2. The cutting of DNA should take place only at positions separated by segments satisfying P.
    3. The overhangs should satisfy P.
    4. Transposons should satisfy P.
    In the example mentioned here, the overhang is CTAG and has vanishing Qa.

    It is known that transposons - repeating regions itself - tend to attach to the repeating regions of DNA.

    1. There are several kinds of repeating regions. 6-10 base pair long sequences can be repeated in untranslated regions up to 105 times and whole genes can repeat themselves 50-104 times.
    2. Repeats are classified into tandems (say TTAGGG associated with telomeres), interspersed repetitive DNA (nuclear elements), and transposable repeat elements. Interspersed nuclear elements (INEs) are classified LINEs (long), SINEs (short), TLTRs (Transposable elements with Long Terminal Repeats), and DNA transposons themselves.
    3. LINEs contain AT rich regions. SINEs known as alus (about 280 bps) contain GC rich regions whereas mariner elements (about 80 bps) are flanked by TA pairs. LTRs have length 300-1000 bps. DNA transposons are flanked with two short inverted repeat sequences flanking the reading frame: "inverted" refers to the palindrome property already mentioned.

    AT and CG have vanishing Qa so that their presence in LINEs and SINEs would make the cutting and pasting easy allowing to understand why transposons favor these regions. Viruses are known to contain long repeating terminal sequences (LTR). One could also check whether DNA decomposes to regions satisfying P and surrounded by repeating sequences which satisfy P separately or as whole as in the case DNA transposons.

    For a more detailed exposition and background see the chapter DNA as Topological Quantum Computer.

    What selected the bio-molecules?

    The extremely low probabilities for the selection of bio-molecules from a super-astrophysical number of alternatives represents one of the bottleneck problems of biology relying on the prevailing view about biochemistry. The notion of braid could resolve this problem.

    Suppose that the presence of braids distinguishes between living and dead matter, that the four nucleotides are mapped to colored braid strands (that is to 2 quarks + 2 anti-quarks), and that a given amino-acid is mapped in a non-deterministic manner to one of the 3-braids associated with the DNA triplets coding for it. Braids could be associated besides DNA, amino-acids, and lipids also to other bio-molecules and define more general analogs of genetic codes as correspondences between bio-molecules able to react.

    The implication would be that the step of catalytic reactions bringing together the catalyst and reactants would occur by a temporary reduction of Planck constant only for subsets of bio-molecules connected by braid strands and the pattern of braid strands involved would define the geometro-dynamical pattern of the reaction. The outcome would be a selection of very restricted subsets of bio-molecules able to form reaction networks and of reaction pathways. This would imply Darwinian selection of subsets of bio-molecules able to co-exist and dramatically enhance the probability for the emergence of life as we know it.

    One challenge is to predict what kind of braids can begin from a given bio-molecule, say nucleotide or amino-acid. The physicist's guess would be that the (electromagnetic only?) interaction energy between bio-molecule and given pattern of wormhole contacts having quark and anti-quark at its throats should select the preferred braids as minima of the interaction energy. How closely the presence of hydrogen bonds (and of conjectured "half hydrogen bonds") relates to this is also an interesting question.

    For the model of DNA as topological quantum computer see the chapter DNA as Topological Quantum Computer.

    Structure and function of tRNA in braid picture

    The recent beautiful results (for a popular summary see [pwpop]) about programming of bio-molecular self assembly combined with the earlier model for the pre-biotic evolution inspire interesting insights about the role of braiding in translation. According to the TGD based model of pre-biotic evolution [prebio], 3-code should have resulted as a fusion of 1- and 2- codes to 3-code involving fusion of tRNA1 and tRNA2 to tRNA. Second hypothesis is that during RNA era the function of tRNA2 was to generate RNA2 double strand from single RNA strand and that amino-acids catalyzed this process. The considerations that follow strongly suggest that tRNA1 was involved with a non-deterministic generation of new RNA sequences essential for the evolution. After the establishment of 3-code these two process fused to a deterministic process generating amino-acid sequences. RNA era could still continue inside cell and play an important role in evolution.

    A. Structure of tRNA molecule

    The structure of tRNA- although more complex than that of hairpin- has much common with that of hairpins. Therefore it is interesting to look this structure from the point of view of TGD. For instance, one can find whether the notions of braiding, anomalous em charge and quark color could provide additional insights about the structure and function of tRNA. The shape of the tRNA molecule [tRNA] in 2-D representation is that of cruciform.

    1. tRNA molecule can be seen as single RNA strand just as hairpin. The five stems are double strands analogous to the necks of the hairpin. Strand begins at 5' end of the acceptor stem directed upwards. The second strand of acceptor stem continues as a toehold ending to 3' end of tRNA. The toehold has at its end ACC to which the amino-acid (rather than conjugate DNA) attaches.

    2. tRNA molecule contains three arms with hairpin structure. A arm containing the anticodon is directed downwards. D and T arms are horizontal and directed to left and right. Between T arm and A arm there is additional variable hairpin like structure but with highly degenerate loop is degenerate. It has emerged during evolution.

    3. The structure of tRNA minus anticodon depends on anti-codon which conforms with the fact T and D arms are related to the binding of amino-acid so that their nucleotide composition correlates with that of anticodon.

    B. Wobble base pairing

    The phenomenon of wobble base pairing [wobble] is very important. There are only about 40 tRNA molecules instead of 61 which means that one-to-one map between mRNA nucleotides and tRNA conjugate nucleotides is not possible. Crick suggests that so called wobble base pairing resolves the problem. What happens that the first nucleotide of anticodon is either A, G, U, or I(nosine) [inosine]. The base-pairings for third nucleotide are {A-U, G-C, U-{A,G}, I-{U,A,C}. The explanation for the non unique base pairing in the case of U is that its geometric configuration is quite not the same as in ordinary RNA strand. I is known to have 3-fold base pairing.

    Minimization of the number of tRNAs requiring that only three mRNA codons act as stopping signs predicts that the number of tRNAs is 40.

    1. It is convenient to classify the 4-columns of code table according to whether all four codons code for same amino-acid ((T,C,A,G)→ X), whether 4-column decomposes into two dublets: [(T,C),(A,G)]→ [X,Y], or whether it decomposes to triplet and singlet ([(T,C,A),G]→ [ile,met]). There are also the 4-columns containing stop codon: [(U,C),(A,G)]→ [(tyr,tyr),(stop,stop)] and [(U,C),A,G]→ [(cys,sys),stop,trp]. Mitochondrial code has full A-G and T-C symmetries whereas for vertebrate nuclear code 3 4-columns break this symmetry.

    2. Consider first 4-columns for which the doublet symmetry is broken. [tyr,tyr, top,stop] column must correspond to first tRNA nucleotide which is A or G (tyr). The absence of anti-codons containing U implies stop codon property. For [cys,sys,stop,trp] one must have A,G and C but U is not allowed. ile-met column can correspond to tRNAs with I and C as the first nucleotide.

    3. For 4-columns coding for two doublet amino-acids the minimal set of first tRNA codons is {A,G,U}. For completely symmetric 4-columns the minimal set of tRNA codons is {I,U}. Thus {A,G,U,I} would replace {A,G,U,C}.

    4. There are 9 completely symmetric 4-columns making 18 tRNAs, 5 doublet pairs making 15 tRNAs, ile-met giving 2 tRNAs, and the columns containing stopping codons giving 5 tRNAs. Altogether this gives 18+15+2+5= 40. Also the deviations from the standard code can be understood in terms of the properties of tRNA.

    C. Wobble base pairing in TGD framework

    Consider first the interpretation of wobble base pairing in TGD framework assuming the braiding picture and the mapping of nucleotides to quarks. The completely symmetric 4-columns correspond to unbroken isospin and matter-antimatter symmetries. 4-columns decomposing into doublets result from the breaking of matter-antimatter symmetry at quark level. ile-met column corresponds to the breaking of both symmetries. The base pairings of I obviously break both symmetries.

    The non-unique based pairing of U and I means that they cannot correspond to a unique quark or anti-quark in braiding U pairs with both A and G so that the braid strands starting from these RNA nucleotides must both be able to end to tRNA U. Hence tRNA U is not sensitive to the isospin of the quark. This non-uniqueness could relate to the assumed anomalous geometric character of the binding of U codon to tRNA sequence. The braid strands beginning from U, A, and C must be able to end up to I so that I can discriminate only between {U,C,A} and G.

    D. Anomalous em charge and color singletness hypothesis for tRNA

    One can test also whether the vanishing of anomalous em charge of tRNA leads to testable predictions. One can also try understand translation process in terms of the braiding dynamics. One must distinguish between the states of tRNA alone and tRNA + amino-acid for which braidings are expected to be different.

    Before continuing it must be made clear that braiding hypothesis is far from being precisely formulated. One question is whether the presence of the braiding could distinguish between matter in vivo and vitro. For instance, the condition that anomalous em charge is integer valued or vanishing for DNA hairpins in vivo gives strong condition on the loop of the hairpin but or hairpins in vitro there would be no such conditions. Second point is that amino-acids and I and U in tRNA1 could carry variable anomalous em charge allowing rather general compensation mechanism.

    D.1 tRNA without amino-acid

    1. The minimal assumption is that braiding hypothesis applies only to the stem regions of tRNA in this case. In this case the strands can indeed begin from strand and end up to conjugate strand. The possibility of color singletness and vanishing of total anomalous em charge are automatically satisfied for the stem regions as a whole in absence of non-standard base pairings. In general the acceptor stem contains however G*U base pair which is matter-antimatter symmetric but breaks isospin symmetry and gives unit anomalous charge for the acceptor stem. Also other stems can contain G*U , U*G pairings as also P*G and L*U pairings (P and L denote amino-acids Pro and Leu). The study of some concrete examples [tRNAseqs] shows that single G*U bond is possible so that anomalous em charge can be non-vanishing but integer valued for double strand part of tRNA. Suppose that a given amino-acid can have anomalous of any codon coding for it. If P in G*P pair has the anomalous em charge of the codon CCG, G*P pair has vanishing anomalous em charge. If L corresponds to CUA the value of anomalous em charge is integer.

    2. The anomalous em charge in general fails to vanish for the loops of hairpins. For the braids possibly associated with the loops of tRNA the strands can only end up to tRNA itself or nuclear membrane. If there are no braid strands associated with these regions, there is no color or anomalous em charge to be canceled so that the situation trivializes. On the other hand, in the case of tRNA I and U associated with the first nucleotide of the anticodon of tRNA can have a varying value of anomalous em charge. Therefore integer valued em charge and color singletness become possible for tRNA. tRNA can also contain aminoacids. If the aminoacids can carry a varying anomalous em charge with a spectrum corresponding to its values for DNA codons coding it, also they could help to stabilize tRNA by canceling the anomalous em charge.

    D.2 tRNA plus amino-acid

    1. Amino-acyl tRNA synthetase, which is the catalyst inducing the fusion of amino-acid with ACC stem [tRNA], could have braid strands to both amino-acid and tRNA and have regions with opposite anomalous em charges compensating separately that of amino-acid and of the active part of tRNA. The required correlation of amino-acid with anticodon would suggest that both D and T loops and A-loop are included. The simplest option is however that the anticodon is connected by braid to amino-acid so that braiding would define the genetic code at the fundamental level and the many-to-one character of genetic code would reflect the 1-to-many character of amino-acid-quark triplet correspondence. This hypothesis is easy to kill: for the portion of catalyst attaching to a given portion of DNA strand amino-acids and codons should have opposite anomalous em charges: Qa(amino)=-Qa(codon).

    2. After the catalysis involving reduction of hbar amino-acid and tRNA would form a system with a vanishing net anomalous em charge but with a braiding structure more complex than that before the fusion.

    3. In the translation process the braiding structure of tRNA- amino-acid system should re-organize: the braid strands connecting anticodon with amino-acid are transformed to braid strands connecting it to mRNA codon with a subsequent reduction of hbar of braid strands bringing tRNA into the vicinity of mRNA. In the transcription the anticodon-codon braiding would be replaced with amino-acid-mRNA braiding forcing formation of the amino-acid sequence. It will be later found that the simpler option without this step corresponds to the earlier hypothesis according to which amino-acids acted originally as catalysts for the formation of RNA double strand.

    4. tRNA is basically coded by genes which suggests that the general symmetries of the genetic code apply to to the variants of tRNA associated with same anticodon. Hence the variants should result from each other by isospin splits and modifications such as permutations of subsequent nucleotides and addition of AT and CG pairs not changing overall color and isospin properties. Also anomalous base pairs X*Y can be added provide their net anomalous em charge vanishes.

    5. tRNA has a complex tertiary (3-D) structure [tertiary] involving base pairing of distant nucleotides associated with the roots of the stem regions where tRNA twists sharply. This pairing could involve formation of braid strands connecting the nucleotides involved. The reduction of Planck constant for these strands could be an essential element of the formation of the tertiary structure.

    E. Triplet code as a fusion of singlet and doublet codes?

    In [prebio] I have discussed the hypothesis that the standard 3-code has emerged as a fusion of 1-codes with 4 1-codons and 2-code with 16 2-codons. It is interesting to see whether this model is consistent with the braid picture.

    E.1 tRNA as fusion of tRNA1 and tRNA1

    The earlier proposal was that the fusion of 1- and 2-code to 3-code meant (at least) the fusion of tRNA1 and tRNA2 to form a more complex tRNA of 3-code. This process would have involved fusion of 1- and 2-anticodons of tRNA. The visual inspection of tRNA shows that tRNA1 and tRNA2 could have been simple RNA hairpins during pre-biotic evolution. The variable loop associated with the T arm has indeed emerged during evolution and its function is believed to relate to the stability of tRNA [tRNA]. For instance, the anomalous em charge of the variable loop could compensate for the net em anomalous charge of amino-acid-tRNA system.

    tRNA1 is identifiable as a piece of tRNA extending from 5' end to the first nucleotide (wobble nucleotide) of the anticodon. tRNA2 would contain at its 5'-end 2-codon and plus T arm and second half of the acceptor stem. The simpler structure of D-arm (in particular, the stem involves only 3 codon pairs) conforms with this view.

    The emergence of tRNA anticodon as a fusion of 1-anticodon and 2-anti-codons could explain the wobble base pairing. The inverse assignment {U→ A, C→ G, {A,G}→ U, {U,A,C}→ I} deduced from the the number 40 of tRNAs and assigning unique 1-codon to only G could be interpreted as a non-deterministic correspondence generating new RNA sequences from existing ones.

    E.2 The change of the role of amino-acids in the transition from pre-biotic to biotic evolution

    In [prebio] it was proposed that during RNA era amino-acids catalyzed the replication of 2-RNA to its conjugate and that at some state the role of amino-acids and 2-anti-codons changed and instead of conjugate of 2-RNA strand amino-acid sequence was generated. In braiding picture this transition could be understood as a phase transition changing the dynamics of braiding.

    1. Before the transition the amino-acid-2-anticodon braid generated in the formation of tRNA2- amino-acid complex was replaced with 2-anticodon-RNA braid and amino-acid catalyzing the formation of RNA-conjugate strand pair.

    2. In the transition a new step emerged: amino-acid began to form a braid with RNA codon and amino-acid sequence instead of conjugate RNA strand was generated in the process. Note that the number of amino-acids could have been larger than 16 before the transition since several amino-acids could have catalyzed same pairing of 2-codon with its 2-anticodon.

    Contrary to the assumption of the original more complex model [prebio], tRNA1 and tRNA2 would have acted on same RNA sequences. Before the transition to 3-code tRNA2 and amino-acids would have been responsible for the formation of double strands of RNA (tqc at RNA level requires the presence of double strands). tRNA1 would have taken care of non-deterministic generation of new RNA sequences driving the evolution during RNA era. There is evidence that centrosomes have their RNA based code and this code might correspond to 2-codon code and involve also the non-deterministic 1-code.

    The objection is that the resulting RNA sequences contain A, G, U, and I and are analogous to conjugates of RNA sequences rather than being proper RNA sequences. A possible way out of the problem is to build a conjugate of this sequence using tRNA2. The problem is that if I base pairs with A,T, or C, ne obtains only the codons T,C,A. If U pairs with A and G as in the case of 1-code, also G is obtained. The presence of G*U pairs in tRNA2 suggests that these pairings were indeed present. The presence of I in the tRNA1 induced RNA sequences might prevent their interpretation as genuine RNA sequences, which would imply conjugation symmetry of RNA.

    The objection is that the resulting RNA sequences contain A, G, U, and I and are analogous to conjugates of RNA sequences rather than being proper RNA sequences. A possible way out of the problem is to build a conjugate of this sequence using tRNA1 again. Since I pairs with A,T, or C and U with A and G and G with G and A with U all nucleotides appear in the resulting sequence. The anomalous G*U base pairs in tRNA could be seen as remnants of RNA era. The presence of I in the tRNA1 induced RNA sequences might prevent their interpretation as genuine RNA sequences, which would imply conjugation symmetry of RNA.

    There is an additional argument supporting the idea that the coding of amino-acids emerges only after the formation of 3-code. If the 2-code would have coded for amino-acids before the fusion of the codes, the fusion should have involved also the fusion of corresponding RNA sequences in order to guarantee that the resulting 3-RNA sequence still codes for the amino-acids coded by 2-RNA sequences plus some new ones. This kind of fusion is not too plausible although I have considered this possibility in the earlier model [prebio].

    F. Was the counterpart of cell membrane present during RNA era?

    Topological quantum computation should have taken place already during RNA era. This suggest that the counterpart of the cell membrane was present already at that time. Quite recently it was reported that DNA duplexes of length 6 to 20 base pairs can join to longer cylinders which in turn form liquid crystals and that the liquid crystal phase separates from the phase formed by single DNA strands. Long strands had been already earlier known to form liquid crystals. This encourages to think that also RNA duplexes are able to self-organize in this manner so that the analog of cell nucleus containig RNA double helices as genetic material could have existed already during RNA era.

    The nuclear membranes could have consisted of either ordinary RNA or its variant consisting of A,T,G,I produced by tRNA1. The latter option would allow to distinguish between coding RNA and RNA used as building block of various structures. The sequences consisting of 30 RNA base pairs would correspond to the thickness of cell membrane and to the codon of M61 code. Lipid layer of thickness 5 nm would correspond to roughly 16 base pairs and to the codon assignable to M17.

    For a more detailed exposition and background see the chapter DNA as Topological Quantum Computer.

    Programming of bio-molecular self assembly pathways from TGD point of view

    There is an interesting work about programming bio-molecular self assembly pathways [Y. Peng Yin et al (2007), Programming biomolecular self-assembly pathways, Nature 451, 318-322 (17 January 2008)]. The catalytic self assembly of complexes of nuclei acids is carried out automatically by a program represented implicitly as a mixture of linear DNA strand acting as catalyst and so called hairpin DNAs containing three nucleation sites at, bt, ct - so called toeholds.

    A. Key ideas

    The basic idea is that a set of bio-molecular reactions can be programmed to occur in a desired order by using a generalization of lock and key mechanism. The simplest self assembly pathway can be specified by a collection of keys and locks. In the beginning there is only one key and the this key fits to only one door, which leads into a room with several doors. The lock eats the key but gives one or more keys. If the room contains several doors to which the keys fits, the reaction corresponds to addition of several branches to the already existing reaction product. By continuing in this manner one eventually ends up to the last room and at the last step the lock gives back the original key so that it can act as a catalyst.

    The translation of this idea to a program defining self assembly pathway is following.

    1. DNA hairpin [stemloop] defines key structural element of the self-assembly program. Hairpin is a single-stranded DNA strand in meta-stable configuration having form A+B+C such that B forms a loop and C is a palindrome [palindrome]. The formal expression for palindromy is C= At*: this means that C read backwards (Ct) is conjugate A* of A implying that A and C running in opposite direction can form a double strand (duplex) by hydrogen bonding. As catalytic a* acting as key forms a double strand with a, the hairpin molecule opens to a linear DNA molecule and energy is liberated. In this process original key is lost but the two other toe-holds bt and ct contained by the hairpin become available as keys. Each hairpin in the mixture of catalyst and hairpin molecules has its own lock and two keys.

    2. The process of opening new doors continues until all hairpin molecules are used. The key given by the last lock must be catalyst strand a*. The outcome is a molecule consisting of pieces of DNA strands and can possess a very complex topology. For instance, the formation trees and star like structures can be easily programmed.

    3. To run this program one needs only an optimal mixture of catalyst molecule and hairpin DNA molecules. In the applications discussed in hairpins have length of order 10 nm which corresponds to p-adic length scale L(151) defining also cell membrane thickness. That L(151) corresponds also to the length of 30-nucleotide sequence defining the codon of the code associated with Mersenne prime M61=261-1 might not be an accident. The simplest applications are autocatalytic formation of DNA duplex molecules and of branched junctions, nucleated dendritic growth, and autonomous locomotion of a bipedal walker.

    The basic idea in the realization of the autonomous motion of bipedal walker is to cheat the walker to follow a track marked by food. The walker literally eats the food and receives in this manner the metabolic energy needed to make the step to the next piece of food. The menu contains two kinds of hairpins as foods: hairpins A attached regularly along the desired path of the walker (second DNA strand) and hairpins B but not attached to the strand. The front leg l of the walker attaches to A and this catalyzes the formation of the duplex A*B as a waste and the liberated metabolic energy allows to make a step in which hind leg becomes the front leg.

    B. TGD view about the situation

    The possibility to program the self-assembly relies on the almost deterministic realization of the lock and key mechanism. The presence of braid strands could make this possible.

    1. Consider first the hypothesis about the cancelation of anomalous DNA charge. The palindromic character of A means that the neck of the hairpin has vanishing anomalous em charge and also vanishing color charge is possible. Hence palindromes are favored in TGD Universe. The circular piece B is not in general color singlet. It could have braid strands connecting it to it to some other DNA or nuclear membrane but this is not necessary. Same applies to the toehold at at the end of the other strand of neck.

    2. The attachment of the lock to key could be seen as a process in which a braid consisting of magnetic flux tubes connecting lock and key strands (DNA and its conjugate) is formed spontaneously and followed by a phase transition reducing hbar contracting the flux tubes and in this manner guiding the key to the lock.

    For a more detailed exposition and background see the chapter DNA as Topological Quantum Computer.

    DNA as topological quantum computer: XI

    In previous postings I, II, III, IV, V, VI, VII, VIII, IX, X I have discussed various aspects of the idea that DNA could acts as a topological quantum computer using fundamental braiding operation as a universal 2-gate.

    Since the representation in the book and in previous postings is bottom-up and not well-organized, it is perhaps worth of providing a summary about the model in both bottom-up (very briefly) and top-to-bottom manner.

    1. Bottom-up approach

    I ended up with the third model in bottom-up manner and this representation is followed also in the text. The model which looks the most plausible one relies on two specific ideas.

    1. Sharing of labor means conjugate DNA would do tqc and DNA would "print" the outcome of tqc in terms of RNA yielding aminoacids in the case of exons. RNA could result in the case of introns. The experience about computers and the general vision provided by TGD suggests that introns could express the outcome of tqc also electromagnetically in terms of standardized field patterns. Also speech would be a form of gene expression. The quantum states braid would entangle with characteristic gene expressions.

    2. The manipulation of braid strands transversal to DNA must take place at 2-D surface. The ends of the space-like braid are dancers whose dancing pattern defines the time-like braid, the running of classical tqc program. Space-like braid represents memory storage and tqc program is automatically written to memory during the tqc. The inner membrane of the nuclear envelope and cell membrane with entire endoplasmic reticulum included are good candidates for dancing halls. The 2-surfaces containing the ends of the hydrophobic ends of lipids could be the parquets and lipids the dancers. This picture seems to make sense.

    2. Top-down approach

    One ends up to the model also in top-down manner.

    1. Darwinian selection for which standard theory of self-organization provides a model, should apply also to tqc programs. Tqc programs should correspond to asymptotic self-organization patterns selected by dissipation in the presence of metabolic energy feed. The spatial and temporal pattern of the metabolic energy feed characterizes the tqc program - or equivalently - sub-program call.

    2. Since braiding characterizes the tqc program, the self-organization pattern should correspond to a hydrodynamical flow or a pattern of magnetic field inducing the braiding. Braid strands must correspond to magnetic flux tubes of the magnetic body of DNA. If each nucleotide is transversal magnetic dipole it gives rise to transversal flux tubes, which can also connect to the genome of another cell.

    3. The output of tqc sub-program is probability distribution for the outcomes of state function reduction so that the sub-program must be repeated very many times. It is represented as four-dimensional patterns for various rates (chemical rates, nerve pulse patterns, EEG power distributions,...) having also identification as temporal densities of zero energy states in various scales. By the fractality of TGD Universe there is a hierarchy of tqcs corresponding to p-adic and dark matter hierarchies. Programs (space-time sheets defining coherence regions) call programs in shorter scale. If the self-organizing system has a periodic behavior each tqc module defines a large number of almost copies of itself asymptotically. Generalized EEG could naturally define this periodic pattern and each period of EEG would correspond to an initiation and halting of tqc. This brings in mind the periodically occurring sol-gel phase transition inside cell near the cell membrane.

    4. Fluid flow must induce the braiding which requires that the ends of braid strands must be anchored to the fluid flow. Recalling that lipid mono-layers of the cell membrane are liquid crystals and lipids of interior mono-layer have hydrophilic ends pointing towards cell interior, it is easy to guess that DNA nucleotides are connected to lipids by magnetic flux tubes and hydrophilic lipid ends are stuck to the flow.

    5. The topology of the braid traversing cell membrane cannot not affected by the hydrodynamical flow. Hence braid strands must be split during tqc. This also induces the desired magnetic isolation from the environment. Halting of tqc reconnects them and make possible the communication of the outcome of tqc.

    6. There are several problems related to the details of the realization. How nucleotides A,T,C,G are coded to strand color and what this color corresponds to? The prediction that wormhole contacts carrying quark and anti-quark at their ends appear in all length scales in TGD Universe resolves the problem. How to split the braid strands in a controlled manner? High Tc super conductivity provides the mechanism: braid strand can be split only if the supra current flowing through it vanishes. A suitable voltage pulse induces the supra-current and its negative cancels it. The conformation of the lipid controls whether it it can follow the flow or not. How magnetic flux tubes can be cut without breaking the conservation of the magnetic flux? The notion of wormhole magnetic field saves the situation now: after the splitting the flux returns back along the second space-time sheet of wormhole magnetic field.

    To sum up, it seems that essentially all new physics involved with TGD based view about quantum biology enter to the model in crucial manner.

    For details see the chapter DNA as Topological Quantum Computer.

    About the arrow of psychological time and notion of self: once again!

    Quantum classical correspondence predicts that the arrow of subjective time is somehow mapped to that for the geometric time. The detailed mechanism for how the arrow of psychological time emerges has however remained open. Also the notion of self is problematic. I have proposed two alternative notions of self and have not been able to choose between them. A further question is what happens during sleep: do we lose consciousness or is it that we cannot remember anything about this period? The work with the model of topological quantum computation (see previous posting) has led to an overall view allowing to select the most plausible answer to these questions. But let us be cautious!

    A. Two earlier views about how the arrow of psychological time emerges

    The basic question how the arrow of subjective time is mapped to that of geometric time. The common assumption of all models is that quantum jump sequence corresponds to evolution and that by quantum classical correspondence this evolution must have a correlate at space-time level so that each quantum jump replaces typical space-time surface with a more evolved one.

    1. The earliest model assumes that the space-time sheet assignable to observer ("self") drifts along a larger space-time sheet towards geometric future quantum jump by quantum jump: this is like driving car in a landscape but in the direction of geometric time and seeing the changing landscape. There are several objections.

      1. Why this drifting?

      2. If one has a large number of space-time sheets (the number is actually infinite) as one has in the hierarchy the drifting velocity of the smallest space-time sheet with respect to the largest one can be arbitrarily large (infinite).

      3. It is alarming that the evolution of the background space-time sheet by quantum jumps, which must be the quintessence of quantum classical correspondence, is not needed at all in the model.

    2. Second model relies on the idea that intentional action -understood as p-adic-to-real phase transition for space-time sheets and generating zero energy states and corresponding real space-time sheets - proceeds as a kind of wave front towards geometric future quantum jump by quantum jump. Also sensory input would be concentrated on this kind of wave front. The difficult problem is to understand why the contents of sensory input and intentional action are localized so strongly to this wave front and rather than coming from entire life cycle.

    There are also other models but these two are the ones which come into my mind first.

    B. The third option

    The third explanation for the arrow of psychological time - which I have considered earlier but only half-seriously - began to look very elegant during last night. This option is actually favored by Occam's razor since it uses only the assumption that space-time sheets are replaced by more evolved ones in each quantum jump. Also the model of tqc favors it.

    1. The simplest assumption is that evolution in a reasonable approximation means shifting of the field patterns backwards in geometric time by some amount per quantum jump. This makes sense since the shift with respect to M4 time coordinate is an exact symmetry of extremals of Kähler action. It is also an excellent approximate symmetry for the preferred extremals of Kähler action and thus for maxima of Kähler function spoiled only by the presence of light-cone boundaries. This shift occurs for both the perceiver space-time sheet and perceived space-time sheet representing external world: both perceiver and percept change.

    2. Both the landscape and observer space-time sheet remain in the same position in imbedding space but both are modified by this shift in each quantum jump. The perceiver experiences this as a motion in 4-D landscape. Perceiver (Mohammed) would not drift to the geometric future (the mountain) but geometric future (the mountain) would effectively come to the perceiver (Mohammed)!

    3. There is an obvious analogy with Turing machine: what is however new is that the tape effectively comes from the geometric future and Turing machine can modify the entire incoming tape by intentional action. This analogy might be more than accidental and could provide a model for quantum Turing machine operating in TGD Universe. This Turing machine would be able to change its own program as a whole by using the outcomes of the computation already performed.

    4. The concentration of the sensory input and the effects of conscious motor action to a narrow interval of time (.1 seconds typically, secondary p-adic time scale associated with the largest Mersenne M127 defining p-adic length scale which is not completely super-atronomical) can be understood as a concentration of sensory/motor attention to an interval with this duration: the space-time sheet representing sensory "me" would have this temporal length and "me" definitely corresponds to a zero energy state.

    5. The fractal view about topological quantum computation strongly suggests an ensemble of almost copies of sensory "me" scattered along my entire life cycle and each of them experiencing my life as a separate almost copy. My childhood is still sensorily lived but has moved about 57 years backwards in geometric time and would live the year 1897 but enjoy all techno conveniences of the year 1950!

    6. The model of geometric and subjective memories would not be modified in an essential manner: memories would result when "me" is connected with my almost copy in the geometric past by braid strands or massless extremals (MEs) or their combinations (ME parallel to magnetic flux tube is the analog of Alfwen wave in TGD).

    C. Can one choose between the two variants for the notion of self?

    I have considered two different notions of "self" and it is interesting to see whether this picture might allow to choose between them.

    1. In the original variant of the theory "self" corresponds to a sequence of quantum jumps. "Self" would result through a binding of quantum jumps to single "string" in close analogy and actually in a concrete correspondence with the formation of bound states. Each quantum jump has a fractal structure: unitary process is followed by a sequence of state function reductions and preparations proceeding from long to short scales. Selves can have sub-selves and one has self hierarchy. The questionable assumption is that self remains conscious only as long as it is able to avoid entanglement with environment.

    2. According to the newer variant of theory, quantum jump has a fractal structure so that there are quantum jumps within quantum jumps: this hierarchy of quantum jumps within quantum jumps would correspond to the hierarchy of dark matters labelled by the values of Planck constant. Each fractal structure of this kind would have highest level (largest Planck constant) and this level would corresponds to the self. What might be called irreducible self would corresponds to a quantum jump without any sub-quantum jumps (no mental images). The quantum jump sequence for lower levels of dark matter hierarchy would create the experience of flow of subjective time.

      It would be nice to reduce the notion of self hierarchy to that of fractal quantum jump in the sense of dark matter hierarchy but there is an objection. Does this concept really make sense? Fractality is a geometric notion and subjective time does not reduce to the geometry. It is also not quite clear whether the reasonable looking idea about the role of entanglement can be kept.

    The older variant of self looks more attractive if one accepts the new model for the arrow of psychological time.

    1. Entire Universe performs the quantum jump and there is an infinite fractal hierarchy of scales associated with quantum jump and state function reduction/state preparation part of quantum jump proceeds as a sequence from long to short scales. One cannot assign any finite geometric duration to a given step in this sequence since the geometric duration assignable to the entire quantum jump would in this case be automatically infinite. In this framework our life cycle would most naturally correspond to a sequence of quantum jumps.

    2. The simplest guess for the interval of geometric time assignable to single quantum jump is as CP2 time. p-Adic time scales define alternative and perhaps more attractive identification. The larger the value of p-adic prime p, the faster the psychological time would flow and faster the experienced rate of evolution would be. Also the hierarchy of Planck constants suggests a hierarchy of these times and the concentration of attention to to dark matter levels would make the flow of psychological time much faster. The model of tqc suggests that each period of EEG rhythm corresponds to single quantum jump for corresponding "me" in un-entangled self-state.

    3. The ability to avoid entanglement with environment would be essential for the original notion of self. One can of however ask whether the assumption about the loss of consciousness in entanglement - that is during sleep - is really necessary. One could however argue that if consciousness is really lost during sleep, we could not have the deep conviction that we existed yesterday. Furthermore, during topological quantum computation entanglement is absent and thus this state should correspond to conscious experience. Night time is however the best time for tqc since sensory input and motor action do not take metabolic resources and we certainly do problem solving during sleep. Thus we should be conscious at some level during sleep and perform quite a long tqc. Perhaps we are!

      Could it be that we do not remember anything about the period of sleep because our attention is directed elsewhere and memory recall uses only copies of "me" assignable to brain manufacturing standardized mental images? Perhaps the communication link to the mental images during sleep experienced at dark levels of existence is lacking or sensory input and motor activities of busy westeners do not allow to use metabolic energy to build up this kind of communications. Hence one can seriously ask, whether self is actually eternal with respect to the subjective time and whether entangling with some system means only diving into the ocean of consciousness as someone has expressed it. We would be Gods as also quantum classical correspondence in the reverse direction requires (p-adic cognitive space-time sheets have literally infinite size in both temporal and spatial directions). This would be the most optimistic view that one can imagine.

    This arguments look nice but more arguments are needed to exclude the model of self as single quantum jump. D. What after biological death?

    Could the new option allow to speculate about the course of events at the moment of death? Certainly this particular sensory "me" would effectively meet the geometro-temporal boundary of the biological body: sensory input would cease and there would be no biological body to use anymore. "Me" might lose its consciousness (if it can!). "Me" has also other mental images than sensory ones and these could begin to dominate the consciousness and "me" could direct its attention to space-time sheets corresponding to much longer time scale, perhaps even to that of life cycle, giving a summary about the life.

    What after that? The Tibetan Book of Dead gives some inspiration. A western "me" might hope (and even try use its intentional powers to guarantee) that quantum Turing tape brings in a living organism, be it human or cat or dog or at least some little bug. If this "me" is lucky, it could direct its attention to it and become one of the very many sensory "me's" populating this particular 4-D biological body. There would be room for a newcomer unlike in the alternative models. A "me" with Eastern/New-Ageish traits could however direct its attention permanently to the dark space-time sheets and achieve what might she might call enlightment.

    For details see the chapter DNA as Topological Quantum Computer.

    DNA as topological quantum computer: X

    In previous postings I, II, III, IV, V, VI, VII, VIII, IX I have discussed various aspects of the idea that DNA could acts as a topological quantum computer using fundamental braiding operation as a universal 2-gate.

    Many problems of quantum computation in standard sense might relate to a wrong view about quantum theory. If TGD Universe is the physical universe, the situation would improve in many respects. There is the new fractal view about quantum jump and observer as "self"; there is p-adic length scale hierarchy and hierarchy of Planck constants as well as self hierarchy; there is a new view about entanglement and the possibility of irreducible entanglement carrying genuine information and making possible quantum superposition of fractal quantum computations and quantum parallel dissipation; there is zero energy ontology, the notion of M-matrix allowing to understand quantum theory as a square root of thermodynamics, the notion of measurement resolution allowing to identify M-matrix in terms of Connes tensor product; there is also the notion of magnetic body providing one promising realization for braids in tqc, etc... Taking the risk of boring the reader by repeating things that I have already said I will summarize these new aspects TGD below.

    There is also a second motivation. Quantum TGD and TGD inspired theory of consciousness involve quite a bundle of new ideas and the continual checking of internal consistency by writing it through again and again is of utmost importance. The following considerations can be also seen as this kind of checking. I can only represent apologies to the benevolent reader: this is a work in progress.

    A. Fractal hierarchies

    Fractal hierarchies are the essence of TGD. There is hierarchy of space-time sheets labelled by preferred p-adic primes. There is hierarchy of Planck constants reflecting a book like structure of the generalized imbedding space and identified in terms of a hierarchy of dark matters. These hierarchies correspond at the level of conscious experience to a hierarchy of conscious entities -selves: self experiences its sub-selves as mental images.

    Fractal hierarchies mean completely new element in the model for quantum computation. The decomposition of quantum computation to a fractal hierarchy of quantum computations is one implication of this hierarchy and means that each quantum computation proceeds from longer to shorter time scales Tn=2-nT0 as a cascade like process such that at each level there is a large number of quantum computations performed with various values of input parameters defined by the output at previous level. Under some additional assumptions to be discussed later this hierarchy involves at a given level a large number of replicas of a given sub-module of tqc so that the output of single fractal sub-module gives automatically probabilities for various outcomes as required.

    B. Irreducible entanglement and possibility of quantum parallel quantum computation

    The basic distinction from standard measurement theory is irreducible entanglement not reduced in quantum jump.

    B.1 NMP and the possibility of irreducible entanglement

    Negentropy Maximimization Principle states that entanglement entropy is minimized in quantum jump. For standard Shannon entropy this would lead to a final state which corresponds to a ray of state space. If entanglement probabilities are rational -or even algebraic - one can replace Shannon entropy with its number theoretic counterpart in which p-adic norm of probability replaces the probability in the argument of logarithm: log(pn)→ log(Np(pn). This entropy can have negative values. It is not quite clear whether prime p should be chosen to maximize the number theoretic negentropy or whether p is the p-adic prime characterizing the light-like partonic 3-surface in question.

    Obviously NMP favors generation of irreducible entanglement which however can be reduced in U process. Irreducible entanglement is something completely new and the proposed interpretation is in terms of experience of various kinds of conscious experiences with positive content such as understanding.

    Quantum superposition of unitarily evolving quantum states generalizes to a quantum superposition of quantum jump sequences defining dissipative time evolutions. Dissipating quarks inside quantum coherent hadrons would provide a basic example of this kind of situation.

    B.2 Quantum parallel quantum computations and conscious experience

    The combination of quantum parallel quantum jump sequences with the fractal hierarchies of scales implies the possibility of quantum parallel quantum computations. In ordinary quantum computation halting selects single computation but in the recent case arbitrarily large number of computations can be carried out simultaneously at various branches of entangled state. The probability distribution for the outcomes is obtained using only single computation.

    One would have quantum superposition of space-time sheets (assignable to the maxima of Kähler function) each representing classically the outcome of a particular computation. Each branch would correspond to its own conscious experience but the entire system would correspond to a self experiencing consciously the outcome of computation as intuitive and holistic understanding, abstraction. Emotions and emotional intellect could correspond to this kind of non-symbolic representation for the outcome of computation as analogs for collective parameters like temperature and pressure.

    B.3 Delicacies

    There are several delicacies involved.

    1. The above argument works for factors of type I. For HFFs of type II1 the finite measurement resolution characterized in terms of the inclusion Nsubset M mean is that state function reduction takes place to N-ray. There are good reasons to expect that the notion of number theoretic entanglement negentropy generalizes also to this case. Note that the entanglement associated with N is below measurement resolution.

    2. In TGD inspired theory of consciousness irreducible entanglement makes possible sharing and fusion of mental images. At space-time level the space-time sheets corresponding to selves are disjoint but the space-time sheets topologically condensed at them are joined typically by what I call join along boundaries bonds identifiable as braid strands (magnetic flux quanta). In topological computation with finite measurement resolution this kind of entanglement with environment would be below the natural resolution and would not be a problem.

    3. State function reduction means quantum jump to an eigen state of density matrix. Suppose that density matrix has rational elements. Number theoretic vision forces to ask whether the quantum jump to eigen state is possible if the eigenvalues of ρ do not belong to the algebraic extension of rationals and p-adic numbers used. If not, then one would have number theoretically irreducible entanglement depending on the algebraic extension used. If the eigenvalues actually define the extension there would be no restrictions: this option is definitely simpler.

    4. Fuzzy quantum logic (see this) brings also complications. What happens in the case of quantum spinors that spin ceases to be observable and one cannot reduce the state to spin up or spin down. Rather, one can measure only the eigenvalues for the probability operator for spin up (and thus for spin down) so that one has fuzzy quantum logic characterized by quantum phase. Inclusions of HFFs are characterized by quantum phases and a possible interpretation is that the quantum parallelism related to the finite measurement resolution could give rise to fuzzy qubits. Also the number theoretic quantum parallelism implied by number theoretic NMP could effectively make probabilities as operators. The probabilities for various outcomes would correspond to outcomes of quantum parallel state function reductions.

    C.Connes tensor product defines universal entanglement

    Both time-like entanglement between quantum states with opposite quantum numbers represented by M-matrix and space-like entanglement reduce to Connes tensor dictated highly uniquely by measurement resolution characterized by inclusion of HFFs of type II1

    C.1 Time-like and space-like entanglement in zero energy ontology

    If hyper-finite factors of II1 are all that is needed then Connes tensor product defines universal S-matrix and the most general situation corresponds to a direct sum of them. M-matrix for each summand is product of Hermitian square root of density matrix and unitary S-matrix multiplied by a square root of probability having interpretation as analog for Boltzmann weight or probability defined by density matrix (note that it is essential to have Tr(Id)=1 for factors of type II1. If factor of type I are present situation is more complex. This means that quantum computations are highly universal and M-matrices are characterized by the inclusion N subset M in each summand defining measurement resolution. Hermitian elements of N act as symmetries of M-matrix. The identification of the reducible entanglement characterized by Boltzmann weight like parameters in terms of thermal equilibrium would allow interpret quantum theory as square root of thermodynamics.

    If the entanglement probabilities defined by S-matrix and assignable to N rays do not belong to the algebraic extension used then a full state function reduction is prevented by NMP. Ff the generalized Boltzmann weights are also algebraic then also thermal entanglement is irreducible. In p-adic thermodynamics for Virasoro generator L0 and using some cutoff for conformal weights the Boltzmann weights are rational numbers expressible using powers of p-adic prime p.

    C.2 Effects of finite temperature

    Usually finite temperature is seen as a problem for quantum computation. In TGD framework the effect of finite temperature is to replace zero energy states formed as pairs of positive and negative energy states with a superposition in which energy varies.

    One has an ensemble of space-time sheets which should represent nearly replicas of the quantum computation. There are two cases to be considered.

    1. If the thermal entanglement is reducible then each space-time sheet gives outcome corresponding to a well defined energy and one must form average over these outcomes.

    2. If thermal entanglement is irreducible each space-time sheet corresponds to a quantum superposition of space-time sheets, and if the outcome is represented classically as rates and temporal field patterns, it should reflect thermal average of the outcomes as such.

    If the degrees of freedom assignable to topological quantum computation do not depend on the energy of the state, thermal width does not affect at all the relevant probabilities. The probabilities are actually affected even in the case of tqc since 1-gates are not purely topological and the effects of temperature in spin degrees of freedom are unavoidable. If T grows the probability distribution for outcomes flattens and it becomes difficult to select the desired outcome as that appearing with maximal probability.

    D. Possible problems related to quantum computation

    At least following problems are encountered in quantum computation.

    1. How to preserve quantum coherence for a sufficiently long time so that unitary evolution can be achieved?

    2. The outcome of calculation is always probability distribution: for instance, the output with maximum probability can correspond to the result of computation. The problem is how to replicate the computation with a sufficient accuracy. Or more precisely, how to produce replicas of the hardware of quantum computer defined in terms of classical physics?

    3. How to isolate the quantum computer from the external world during computation and despite this feed in the inputs and extract the outputs?

    D.1 The notion of coherence region in TGD framework

    In standard framework one can speak about coherence in two senses. At the level of Schrödinger amplitudes one speaks about coherence region inside which it makes sense to speak about Schrödinger time evolution. This notion is rather defined.

    In TGD framework coherence region is identifiable as inside which modified Dirac equation holds true. Strictly speaking, this region corresponds to a light-like partonic 3-surface whereas 4-D space-time sheet corresponds to coherence region for classical fields. p-Adic length scale hierarchy and hierarchy of Planck constants means that arbitrarily large coherence regions are possible.

    The precise definition for the notion of coherence region and the presence of scale hierarchies imply that the coherence in the case of single quantum computation is not a problem in TGD framework. De-coherence time or coherence time correspond to the temporal span of space-time sheet and a hierarchy coming in powers of two for a given value of Planck constant is predicted by basic quantum TGD. p-Adic length scale hypothesis and favored values of Planck constant would naturally reflect this fundamental fractal hierarchy.

    D.2 De-coherence of density matrix and replicas of tqc

    Second phenomenological description boils down to the assumption that non-diagonal elements of the density matrix in some preferred basis (involving spatial localization of p"../articles/) approach to zero. The existence of more or less faithful replicas of space-time sheet in given scale allows to identify the counterpart of this notion in TGD context. De-coherence would mean a loss of information in the averaging of M-matrix and density matrix associated with these space-time sheets.

    Topological computations are probabilistic. This means that one has a collection of space-time sheets such that each space-time sheet corresponds to more or less same tqc and therefore same M-matrix. If M is too random (in the limits allowed by Connes tensor product), the analog of generalized phase information represented by its "phase" - S-matrix - is useless.

    In order to avoid de-coherence in this sense, the space-time sheets must be approximate copies of each other. Almost copies are expected to result by dissipation leading to asymptotic self-organization patterns depending only weakly on initial conditions and having also space-time correlate. Obviously, the role of dissipation in eliminating effects of de-coherence in tqc would be something new. The enormous symmetries of M-matrix, the uniqueness of S-matrix for given resolution and parameters characterizing braiding, fractality, and generalized Bohr orbit property of space-time sheets, plus dissipation give good hopes that almost replicas can be obtained.

    D.3 Isolation and representations of the outcome of tqc

    The interaction with environment makes quantum computation difficult. In the case of topological quantum computation this interaction corresponds to the formation of braid strands connecting the computing space-time sheet with space-time sheets in environment. The environment is four-dimensional in TGD framework and an isolation in time direction might be required. The space-time sheets responsible for replicas of tqc should not be connected by light-like braids strands having time-like projections in M4.

    Length scale hierarchy coming in powers of two and finite measurement resolution might help considerably. Finite measurement resolution means that those strands which connect space-time sheets topologically condensed to the space-time sheets in question do not induce entanglement visible at this level and should not be affect tqc in the resolution used.

    Hence only the elimination of strands responsible for tqc at given level and connecting computing space-time sheet to space-time sheets at same level in environment is necessary and would require magnetic isolation. Note that super-conductivity might provide this kind of isolation. This kind of elimination could involve the same mechanism as the initiation of tqc which cuts the braid strands so the initiation and isolation might be more or less the same thing.

    Strands reconnect after the halting of tqc and would make possible the communication of the outcome of computation along strands by using say em currents in turn generating generalized EEG, nerve pulse patterns, gene expression, etc... halting and initiation could be more or less synonymous with isolation and communication of the outcome of tqc.

    D.4 How to express the outcome of quantum computation?

    The outcome of quantum computation is basically a representation of probabilities for the outcome of tqc. There are two representations for the outcome of tqc. Symbolic representation which quite generally is in terms of probability distributions represented in terms "classical space-time" physics. Rates for various processes having basically interpretation as geometro-temporal densities would represent the probabilities just as in case of particle physics experiment. For tqc in living matter this would correspond to gene expression, neural firing, EEG patterns,...

    A representation as a conscious experience is another (and actually the ultimate) representation of the outcome. It need not have any symbolic counterpart since it is felt. Intuition, emotions and emotional intelligence would naturally relate to this kind of representation made possible by irreducible entanglement. This representation would be based on fuzzy qubits and would mean that the outcome would be true or false only with certain probability. This unreliability would be felt consciously.

    In the proposed model of tqc the emergence of EEG rhythm (say theta rhythm) and correlated firing patterns would correspond to the isolation at the first half period of tqc and random firing at second half period to the sub-sequent tqc:s at shorter time scales coming as negative powers of 2. The fractal hierarchy of time scales would correspond to a hierarchy of frequency scales for generalized EEG and power spectra at these scales would give information about the outcome of tqc. Synchronization would be obviously an essential element in this picture and could be understood in terms of classical dynamics which defines space-time surface as a generalized Bohr orbit.

    Tqc would be analogous to the generation of a dynamical hologram or "conscious hologram" (see this). EEG rhythm would correspond to reference wave and the contributions of spikes to EEG would correspond to the incoming wave interfering with it. Two remarks are in order.

    D.5 How data is feeded into submodules of tqc?

    Scale hierarchy obviously gives tqc a fractal modular structure and the question is how data is feeded to submodules at shorter length scales. There are are certainly interactions between different levels of scale hierarchy. The general ideas about master-slave hierarchy assigned with self-organization support the hypothesis that these interactions are directed from longer to shorter scales and have interpretation as a specialization of input data to tqc sub-modules represented by smaller space-time sheets of hierarchy. The call of submodule would occur when the tqc of the calling module halts and the result of computation is expressed as a 4-D pattern. The lower level module would start only after the halting of tqc (with respect to subjective time) and the durations of resulting tqcs would come as Tn= 2-nT0 that geometric series of tqcs would become possible. There would be entire family of tqcs at lower level corresponding to different values of input parameters from calling module.

    D.6 The role of dissipation and energy feed

    Dissipation plays key role in the theory of self-organizing systems. Its role is to serve as a Darwinian selector. Without an external energy feed the outcome is a situation in which all organized motions disappear. In presence of energy feed highly unique self-organization patterns depending very weakly on initial conditions emerge.

    In case of tqc one function of dissipation would be to drive the braidings to static standard configurations, prevent over-braiding, and perhaps even effectively eliminate fluctuations in non-topological degrees of freedom. Note that magnetic fields are important for 1-gates. Magnetic flux conservation however saves magnetic fields from dissipation.

    External energy feed is needed in order to generate new braidings. For the proposed model of cellular tqc the flow of intracellular water induces the braiding and requires energy feed. Also now dissipation would drive this flow to standard patterns coding for tqc programs. Metabolic energy would be also needed in order to control whether lipids can move or not by generating cis type unsaturated bonds.

    For the model of DNA as topological quantum computer see the chapter DNA as Topological Quantum Computer.

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