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Genes and Memes

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Year 2018



Increase of the dimension of extension of rationals as the emergence of a reflective level of consciousness?

in TGD framework the hierarchy of extensions of rationals defines a hierarchy of adeles and evolutionary hierarchy. What could the interpretation for the events in which the dimension of the extension of rationals increases? Galois extension is extensions of an extension with relative Galois group Gal(rel)= Gal(new)/Gal(old). Here Gal(old) is a normal subgroup of Gal(new). A highly attractive possibility is that evolutionary sequences quite generally (not only in biology) correspond to this kind of sequences of Galois extensions. The relative Galois groups in the sequence would be analogous to conserved genes, and genes could indeed correspond to Galois groups (see this). To my best understanding this corresponds to a situation in which the new polynomial Pm+n defining the new extension is a polynomial Pm having as argument the old polynomial Pn(x): Pm+n(x)=Pm(Pn(x)).

What about the interpretation at the level of conscious experience? A possible interpretation is that the quantum jump leading to an extension of an extension corresponds to an emergence of a reflective level of consciousness giving rise to a conscious experience about experience. The abstraction level of the system becomes higher as is natural since number theoretic evolution as an increase of algebraic complexity is in question.

This picture could have a counterpart also in terms of the hierarchy of inclusions of hyperfinite factors of type II1 (HFFs). The included factor M and including factor N would correspond to extensions of rationals labelled by Galois groups Gal(M) and Gal(N) having Gal(M)⊂ Gal(M) as normal subgroup so that the factor group Gal(N)/Gal(M) would be the relative Galois group for the larger extension as extension of the smaller extension. I have indeed proposed (see this) that the inclusions for which included and including factor consist of operators which are invariant under discrete subgroup of SU(2) generalizes so that all Galois groups are possible. One would have Galois confinement analogous to color confinement: the operators generating physical states could have Galois quantum numbers but the physical states would be Galois singlets.

See the chapter Could Genetic Code Be Understood Number Theoretically? or the article Does M8-H duality reduce classical TGD to octonionic algebraic geometry?.



Galois groups and genes

The question about possible variations of Geff (see this) led again to the old observation that sub-groups of Galois group could be analogous to conserved genes in that they could be conserved in number theoretic evolution. In small variations such as variation of Galois subgroup as analogs of genes would change G only a little bit. For instance, the dimension of Galois subgroup would change slightly. There are also big variations of G in which new sub-group can emerge.

The analogy between subgoups of Galois groups and genes goes also in other direction. I have proposed long time ago that genes (or maybe even DNA codons) could be labelled by heff/h=n . This would mean that genes (or even codons) are labelled by a Galois group of Galois extension (see this) of rationals with dimension n defining the number of sheets of space-time surface as covering space. This could give a concrete dynamical and geometric meaning for the notin of gene and it might be possible some day to understand why given gene correlates with particular function. This is of course one of the big problems of biology.

One should have some kind of procedure giving rise to hierarchies of Galois groups assignable to genes. One would also like to assign to letter, codon and gene and extension of rationals and its Galois group. The natural starting point would be a sequence of so called intermediate Galois extensions EH leading from rationals or some extension K of rationals to the final extension E. Galois extension has the property that if a polynomial with coefficients in K has single root in E, also other roots are in E meaning that the polynomial with coefficients K factorizes into a product of linear polynomials. For Galois extensions the defining polynomials are irreducible so that they do not reduce to a product of polynomials.

Any sub-group H⊂ Gal(E/K)) leaves the intermediate extension EH invariant in element-wise manner as a sub-field of E (see this). Any subgroup H⊂ Gal(E/K)) defines an intermediate extension EH and subgroup H1⊂ H2⊂... define a hierarchy of extensions EH1>EH2>EH3... with decreasing dimension. The subgroups H are normal - in other words Gal(E) leaves them invariant and Gal(E)/H is group. The order |H| is the dimension of E as an extension of EH. This is a highly non-trivial piece of information. The dimension of E factorizes to a product ∏i |Hi| of dimensions for a sequence of groups Hi.

Could a sequence of DNA letters/codons somehow define a sequence of extensions? Could one assign to a given letter/codon a definite group Hi so that a sequence of letters/codons would correspond a product of some kind for these groups or should one be satisfied only with the assignment of a standard kind of extension to a letter/codon?

Irreducible polynomials define Galois extensions and one should understand what happens to an irreducible polynomial of an extension EH in a further extension to E. The degree of EH increases by a factor, which is dimension of E/EH and also the dimension of H. Is there a standard manner to construct irreducible extensions of this kind?

  1. What comes into mathematically uneducated mind of physicist is the functional decomposition Pm+n(x)= Pm(Pn(x)) of polynomials assignable to sub-units (letters/codons/genes) with coefficients in K for a algebraic counterpart for the product of sub-units. Pm(Pn(x)) would be a polynomial of degree n+m in K and polynomial of degree m in EH and one could assign to a given gene a fixed polynomial obtained as an iterated function composition. Intuitively it seems clear that in the generic case Pm(Pn(x)) does not decompose to a product of lower order polynomials. One could use also polynomials assignable to codons or letters as basic units. Also polynomials of genes could be fused in the same manner.
  2. If this indeed gives a Galois extension, the dimension m of the intermediate extension should be same as the order of its Galois group. Composition would be non-commutative but associative as the physical picture demands. The longer the gene, the higher the algebraic complexity would be. Could functional decomposition define the rule for who extensions and Galois groups correspond to genes? Very naively, functional decomposition in mathematical sense would correspond to composition of functions in biological sense.
  3. This picture would conform with M8-M4× CP2 correspondence (see this) in which the construction of space-time surface at level of M8 reduces to the construction of zero loci of polynomials of octonions, with rational coefficients. DNA letters, codons, and genes would correspond to polynomials of this kind.
Could one say anything about the Galois groups of DNA letters?
  1. Since n=heff/h serves as a kind of quantum IQ, and since molecular structures consisting of large number of particles are very complex, one could argue that n for DNA or its dark variant realized as dark proton sequences can be rather large and depend on the evolutionary level of organism and even the type of cell (neuron viz. soma cell). On the other, hand one could argue that in some sense DNA, which is often thought as information processor, could be analogous to an integrable quantum field theory and be solvable in some sense. Notice also that one can start from a background defined by given extension K of rationals and consider polynomials with coefficients in K. Under some conditions situation could be like that for rationals.
  2. The simplest guess would be that the 4 DNA letters correspond to 4 non-trivial finite groups with smaller possible orders: the cyclic groups Z2,Z3 with orders 2 and 3 plus 2 finite groups of order 4 (see the table of finite groups in this). The groups of order 4 are cyclic group Z4=Z2× Z2 and Klein group Z2⊕ Z2 acting as a symmetry group of rectangle that is not square - its elements have square equal to unit element. All these 4 groups are Abelian.
  3. On the other hand, polynomial equations of degree not larger than 4 can be solved exactly in the sense that one can write their roots in terms of radicals. Could there exist some kind of connection between the number 4 of DNA letters and 4 polynomials of degree less than 5 for whose roots one can write closed expressions in terms of radicals as Galois found? Could the polynomials obtained by a a repeated functional composition of the polynomials of DNA letters also have this solvability property?

    This could be the case! Galois theory states that the roots of polynomial are solvable in terms of radicals if and only if the Galois group is solvable meaning that it can be constructed from abelian groups using Abelian extensions (see this).

    Solvability translates to a statement that the group allows so called sub-normal series 1<G0<G1 ...<Gk=G such that Gj-1 is normal subgroup of Gj and Gj/Gj-1 is an abelian group: it is essential that the series extends to G. An equivalent condition is that the derived series is G→ G(1) → G(2) → ...→ 1 in which j+1:th group is commutator group of Gj: the essential point is that the series ends to trivial group.

    If one constructs the iterated polynomials by using only the 4 polynomials with Abelian Galois groups, the intuition of physicist suggests that the solvability condition is guaranteed!

  4. Wikipedia article also informs that for finite groups solvable group is a group whose composition series has only factors which are cyclic groups of prime order. Abelian groups are trivially solvable, nilpotent groups are solvable, and p-groups (having order, which is power prime) are solvable and all finite p-groups are nilpotent. This might relate to the importance of primes and their powers in TGD.

    Every group with order less than 60 elements is solvable. Fourth order polynomials can have at most S4 with 24 elements as Galois groups and are thus solvable. Fifth order polynomial can have the smallest non-solvable group, which is alternating group A5 with 60 elements as Galois group and in this case is not solvable. Sn is not solvable for n>4 and by the finding that Sn as Galois group is favored by its special properties (see this). It would seem that solvable polynomials are exceptions.

    A5 acts as the group of icosahedral orientation preserving isometries (rotations). Icosahedron and tetrahedron glued to it along one triangular face play a key role in TGD inspired model of bio-harmony and of genetic code (see this and this). The gluing of tetrahedron increases the number of codons from 60 to 64. The gluing of tetrahedron to icosahedron also reduces the order of isometry group to the rotations leaving the common face fixed and makes it solvable: could this explain why the ugly looking gluing of tetrahedron to icosahedron is needed? Could the smallest solvable groups and smallest non-solvable group be crucial for understanding the number theory of the genetic code.

An interesting question inspired by M8-H-duality (see this) is whether the solvability could be posed on octonionic polynomials as a condition guaranteeing that TGD is integrable theory in number theoretical sense or perhaps following from the conditions posed on the octonionic polynomials. Space-time surfaces in M8 would correspond to zero loci of real/imaginary parts (in quaternionic sense) for octonionic polynomials obtained from rational polynomials by analytic continuation. Could solvability relate to the condition guaranteeing M8 duality boiling down to the condition that the tangent spaces of space-time surface are labelled by points of CP2. This requires that tangent or normal space is associative (quaternionic) and that it contains fixed complex sub-space of octonions or perhaps more generally, there exists an integrable distribution of complex subspaces of octonions defining an analog of string world sheet.

See the chapter Could Genetic Code Be Understood Number Theoretically? or the article Is the hierarchy of Planck constants behind the reported variation of Newton's constant?.



New support for the view about Cambrian explosion being caused by rapid increase of Earth radius

There was an interesting popular article in Quanta Magazine titled "Oxygen and Stem Cells May Have Reshaped Early Complex Animals".

The article dicusses the work of geobiologist Emma Hammarlund and tumor biologist Sven Påhlman: their interdisciplinary hypothesis is published as article in Nature with title "Refined control of cell stemness allowed animal evolution in the oxic realm".

Here is the abstract of their article.

Animal diversification on Earth has long been presumed to be associated with the increasing extent of oxic niches. Here, we challenge that view. We start with the fact that hypoxia (<1-3 per cent O2) maintains cellular immaturity (stemness), whereas adult stem cells continuously—and paradoxically—regenerate animal tissue in oxygenated settings. Novel insights from tumour biology illuminate how cell stemness nevertheless can be achieved through the action of oxygen-sensing transcription factors in oxygenated, regenerating tissue. We suggest that these hypoxia-inducible transcription factors provided animals with unprecedented control over cell stemness that allowed them to cope with fluctuating oxygen concentrations. Thus, a refinement of the cellular hypoxia-response machinery enabled cell stemness at oxic conditions and, then, animals to evolve into the oxic realm. This view on the onset of animal diversification is consistent with geological evidence and provides a new perspective on the challenges and evolution of multicellular life.

The proposal of Hammarlund and Påhlman

Cambrian explosion during which highly advanced lifeforms suddenly emerged - prolifiration and diversification of animal life are the terms used about this - is one of the mysteries of biology. For most of its 4.5-billion-year history, Earth has sustained life — but that life was largely limited to microbial organisms: bacteria, plankton, algae. For about 540 million years ago did larger, more complex species are assumed to dominate the oceans, but within just a few tens of millions of years (very short time on the evolutionary timescale), the planet had filled up with all kinds of animals. The fossil record from that period shows the beginnings of almost all modern animal lineages: animals with shells and animals with spines, animals that swam and animals that burrowed, animals that could hunt and animals that could defend themselves from predators. Also many lineages that disappeared were present as one learns from the book of Stephen Jay Gould describing in detail the Burgess Shale finding that revolutionized the picture about evolutionary biology and remains still a puzzle.

The belief is that the environment became considerable more oxic - that is contained oxygen - and lifeforms had to cope with this change. Before the change the animals in seas (believed to exist!) were anaerobic. The shifting to aerobic respiration was however an enormous metabolic advantange since the effectiveness of metabolic energy gain become roughly 20-fold. Increased metabolic feed in turn made possible the emergence of complexity during Cambrian period.

  1. The proposal of the authors is that the evolution of the capacity to maintain stem cells even in an oxic environment allowed the animals to keep stocks of stem cells needed for tissue growth and repair for that this required at gene level new genes coding for so called HIFs.
  2. Stem cells require low oxygen levels to preserve their stemness. Heightened oxygen levels cause them to differentiate abruptly. This explains why stems cells are often located in hypoxic regions of the body (say bone marrow) having low oxygen levels. There are however exceptions to this rule: stem cells can also survive in ocix regions such as skin or retina. Cancers also utilize stem cells to achieve growth.
  3. Hammarlund and Påhlman turned their attention to HIFs (hypoxia-inducible transcription factors), which are proteins, which for hypoxic enviroment shift the metabolism from aerobic to an-aerobic. For oxic environment they are not needed.

    HIF-2α remains however active also in oxic environment and make the cells behave as if the environment were hypoxic. This would allow the stem cells to survive. HIF-2α would however keep the stem cells in immature state also in the case of cancer. The hypothesis of Hammarlund and Påhlman was that HIF-2α functions similarly in normal animal tissues. They have seen some preliminary evidence for the hypothesis but further work is needed.

  4. HIFs could have helped the animals to survive in oxic environment. Consider an organism as a blob of cells. Before the oxygenation the stem cells would have been forced to the deep interior of the blob, where oxygen concentration was especially low. When oxygenation took place, and oxygen level varied, this trick did not work anymore and HIFs had to be invented.
  5. Hammarlund and Påhlman postulate what they call HIF-1, which would have helped stem cells to behave as if the environment were hypoxic. Later HIF-2α unique to vertebrates emerged and improved the situation further. Vertebrates are bigger and have longer time spans that invertebrates and they can live in oxygenated environments. Inveratebrates such as insects live most of their life as larvae under low-oxygen conditions and they cannot regenerate tissues as vertebrates can.
  6. Cancer would be the price paid for this evolutionary advance since cancer cells can proliferate because HIF-2 keeps the stem cells alive. OH present in oxygen rich environment is an oxidant causing cancer.
What caused the oxygenation? So called Great Oxygenation Event is believed to have occurred about about 2.25 billion years ago and thus preceded Cambrian explosion that occured about .5 billion years ago.The time lapse between these events is about 1.75 billion years and much longer than the duration of Cambrian period, which was only tens of millions years. Thus GOE was not the reason for the Cambrian explosion. What caused a further oxygenation or were the effects of GOE somehow postponed (wink-wink!)?

2. TGD view

My own proposal is that life evolved in underground oceans and entered to the surface of Earth in Cambrian explosion when oceans were formed at the surface of Eearth from cracks formed when Earth expanded rapidly in geological time scale. Before the explosion Earth did not have oceans and continents and was like Mars nowadays: even its radius was that of Mars. This picture follows from TGD based variant of Expanding Earth hypothesis. See this and this .

The habitat changed in the rapid expansion of Earth from hypoxic to oxic and the emergence of the hypothetical HIF-1 transcription factor would have been forced by this evolutionary pressure and made it possible for the lifeforms to adapt oxygen based metabolism. This would have led to a rapid evolution of animals and emergence of vertebrates. One can of course think that oxygenation developed already in the underground oceans as cracks caused in the crust by the expansion of Earth began to develop and provided oxygen. The alternative - not so plausible sounding - option is that the highly developed organisms developed underground slowly and only bursted to the surface of Earth in the explosion.

  1. Chemical markers (see this) indeed indicate dramatic change in the environment at the start of the Cambrian period. The markers are consistent with a massive warming due to the release of methane ice (clathrate hydrate, see this) trapped within the crystal structure of water. Methane clathrate is found deep under the sediments at the ocean floors. Methane hydrates are believed to form by migration of gas from deep along geological faults (the cracks produced by rapid expansion of Earth (see this).
  2. During the period before Cambrian explosion Earth would have been very much like in recent Mars. Even its radius would have been that of recent Mars! One can ask whether GOE forced the existing primitive lifeforms underground or saved only those already living underground. Situation would have been be very much like in the recent Mars, which also seems to possess undergound life.
The development of HIF proteins (hypoxia inducing factor) making possible for stem cells to survive in environments with varying and thus temporarily higher oxygen content would have been a natural reaction to the change of habitat.

What can one say about the emergence of animal life in TGD framework?

  1. The rapid evolution leading to the emergence of animals - if it was present - would relate to the quantum criticality associated with the increase of the effective Planck constant heff/h0=n by factor 2 increasing the size scale of Earth. The increase of heff/h0=n might have occurred at several levels of dark matter hierarchy, also at biological relevant scales and led to an increase of biological "IQ (note that evolution corresponds in TGD to gradual increase of number theoretical complexity and n characterizes the dimension of extension of rationals characterizing the complexity (see this).
  2. Animals use oxygen for breathing and are multicellular eukaryotes having cell membrane enclosing nucleus and other membrane bound organelles. The quantum critical period could have led to the emergence of a kind of symbiosis of various kind of organelles within cell membrane bounded volume. The p-adic length scale L(k) determined by the value of n assignable to the outer membrane of organelles could correspond to the prime k=163 (or 167). Inside plant cells having no cell membrane these organelles correspond to vacuoles (see this). The outer membrane that emerged in the transition increasing heff/h0 meant increase of the scale of quantum coherence to a longer p-adic length scale - say k=167 (or k=169=132 if doubling took place).
  3. Mitochondria would have emerged and made possible oxygen based respiration whereas plant like organisms preceding them utilized anaerobic respiration. Methanogenesis (see this) utilizing carbon instead of oxygen and producing carbon-dioxide and methane CH4(water in O2 based respiration) is the most natural option. The large methane storages underground would be due to methanogenesis.

    The recent findings (see this) indicate that there is life in Mars: methane emissions occurring periodically with a period of Martian year have been detected. This suggests that solar radiation is somehow able to enter to the interior of Mars or that it heats the underground Oceans. In TGD one can consider also the possibility that some part of solar photons transforms to dark photons and is able to propagate to the underground oceans through the Martian crust (see this).

  4. What was the primary source of metabolic energy? Direct solar radiation was absent in underground oceans. The immediate source of metabolic energy for the plant like organisms might have been dark nuclei consisting of dark proton sequences and liberating energy in the transitions reducing of heff/h0=n. Dark proton triplets give rise to dark variants of DNA, RNA, tRNA, and amino-acids (see this). These dark proton sequences could have formed by Pollack effect at the surface of Earth possibly containing some water and could have propagated along dark flux tubes to the interior: also in "cold fusion dark nuclei would be formed. Some fraction of them would transform to ordinary nuclei and liberate practically all the nuclear binding energy. Also transitions to dark nuclei with a smaller value of heff/h0 is possible and liberates energy usable as metabolic energy. Most dark nuclei could leak out along magnetic flux tubes (see this). The hen-egg problem - which came first, metabolism or genetic code - would trivialize in this framework.

    For p-adic length scale L(k=149)=5 nm - thickness of cell membrane - the typical dark nuclear excitation energy was about .5 eV, the nominal value of metabolic energy quantum. For L(151)=10 nm (thickness of neuronal membrane and DNA double strand its value is .25 eV. These estimates are based on the scaling of the typical nuclear excitation energy taken to be 1 MeV and are uncertain by a factor of 2 at least. One of course expects also higher excitation energies - even so high that they correspond to visible ordinary photons. Metabolic energy could have been liberated as dark photons in dark nuclear transitions transforming to ordinary photons and absorbed by the photosynthetic machinery.

    The (rough) estimate for the typical value of the dark photon energy is considerably lower than in ordinary photosynthesis. Pollack effect occurring in presence of gel phase bounding water volume suggests that for k=149 the transformation of dark proton sequences to ordinary ones: this mechanism would liberate energy per proton ∼ 1.5 eV (see this), which corresponds to infrared photon. The small value of the metabolic energy quantum need not be a problem: there is recent evidence that IR light with energy 1.76 eV can be used in photosynthesis (see this).

See the chapter Expanding Earth Model and Pre-Cambrian Evolution of Continents, Climate, and Life or the article with the same title.



Improved reckless speculation about higher level variants of dark genetic code

For some time ago I represented what I called reckless speculations about higher level variants of genetic code (see this for the updated version of the original article). The speculations turned out to be not only reckless but to contain besides an unrealistic working hypothesis for p-adic length scale of dark DNA also a numerical error in the estimate of dark nuclear excitation energy scale leading to a wrong track.

The wrong working hypothesis was the assumption that ordinary DNA, RNA, etc correspond to same p-adic length scale as their dark variants. Simple argument shows that the dark scales must result via radial scaling of the typically linear structures such as DNA, RNA, etc and also 2-D structures such as membranes and microtubules giving rise to 2-D lattice like realizations of genetic code generalizing the ordinary 1-D realizations.

Also new improved picture conforms with the vision that dark realizations of genetic code at various p-adic length scales serve as controllers of the ordinary biochemistry, which is kind of shadow dynamics. Replication, certainly one of the most mysterious feats of living matter, would reduce to the replication at the level of dark DNA in various p-adic length scales involved. This would be a huge simplification.

A hierarchy of dark nuclear physics with hierarchy of n= heff/h=n coming as certain powers of two so that the corresponding length scales correspond to p-adic length scales is an attractive idea. I have speculated with this idea already earlier.

1. Ideas

Consider first the general ideas.

  1. The assumption of prime values for k in L(k) would pose extremely tight constraints on the allowed p-adic length scales and values of heff/h0. One would have k∈{127,131,137,139,149}, k∈{151,157,163,167} and k∈{173,..} at least at the level of dark matter. So predictive an idea deserves to be killed, if not anything else.

    A further motivation for these speculations is that the Gaussian Mersenne primes MG,k=(1+i)k-1 for k∈{151,157,163,167} define p-adic length scale L(k)∝ 2k/2 between 10 nm assignable to the neuronal membrane and 2.5 μm assignable to cell nucleus: so many Gaussian Mersenne in so short length scale range is a number theoretical miracle.

  2. Cell membrane consisting of two lipid layers (see this) is a binary structure as also DNA double strand. DNAs replicate as would do also RNAs during RNA era. Also cells and therefore also cell membranes replicate so that the analogy might make sense. Since processes like translation and transcription do not occur, cell membrane might serve as 2-D as analog of RNA: the counterpart of RNA era might prevail at these levels. Neuronal membrane might correspond to 2-D analog of DNA.

    So: could various 2-D structures such as nuclear membrane, cell membrane, neuronal membrane, and microtubuli correspond to a new level in the hierarchy of dark codes for which genes and their dark variants would be 2-D rather than 1-D structures? One would have 2-D lattices of codons. Could there be entire hierarchy of them assignable to certain p-adic length scales? As 2-D realizations could be paired with their dark variants so that one could speak of dark variants of various membrane like structures. This applies also to microtubuli.

    The idea that dark variants of DNA, RNA, tRNA, and amino-acids are their radially scaled up variants generalizes also. The processes like replication of cell could be induced by a much simpler replication of 2-D dark DNA. This kind of pairing hierarchy could be behind miraculous looking replication of entire organisms. p-Adic fractality and hierarchy of dark DNAs could lurk behind the curtains.

  3. The structures of ordinary bio-matter and also their dark variants assumed to control them are characterized by p-adic length scales. How these p-adic length scales could relate? The natural idea inspired by scaling invariance is that the dark variants of 1-D linear structure and 2-D structures formed from ordinary bio-matter are obtained by radial scaling consistent with p-adic length scale hypothesis, and guaranteeing that the distances between building bricks are scaled to the size scales of dark variants of DNA and other basic molecules. This rule makes sense also for the 2-D structures. For instance, it would scale up the p-adic length scale L(143) characterizing lipid to L(149) assignable to single dark RNA strand or L(151) assignable to dark double DNA strand.
  4. One can argue that cell membrane - in particular neuronal membrane - is highly dynamical unlike RNA. In ZEO however dynamical evolutions of space-time surfaces as preferred extremals - correlates for behaviors - replace 3-D static patterns as basic entities so that the emergence of cell membrane might mean dark genetic code for dynamical patterns analogous to deterministic computer programs defining predetermined dynamical patterns. In central nervous system nerve pulse patterns coded by dark RNA could provide similar coding of behavioral patterns.
  5. I have claimed in earlier publications that the lipid double layer defining cell membrane has thickness Le(151)=10 nm: actually the thickness is Le(149)=5 nm for ordinary cells and 8-10 nm - roughly Le(151) - only for neuronal membranes. Therefore the emergence of neuronal membranes could be seen as an evolutionary step in p-adic and thus number theoretic sense. Needless to say, this little difference might be absolutely crucial for undestanding why neurons are at higher evolutionary level than ordinary cells. It would be nice if this difference could correspond to an increase of heff/h0=n and p-adic length scale of ordinary and dark membrane like structure by a factor 2.

    There is double cell membrane associated with mitochondria. The thickness of the two double membranes is about 7 nm so that they might correspond to k=149. The double membrane would have roughly the thickness 22 nm. If this structure is a functionally coherent structure it would corresponds to Le(153) and could be controlled by its dark counterpart.

  6. I have proposed that the flux tubes connecting the dark DNA sequences above lipid layer to those associated with DNA could make possible to realize topological quantum computation in terms of braiding induced by the 2-D liquid flow induced by nerve pulse patterns at nuclear membrane. Flux tubes might be associated with cytoskeleton and define an analog of central nervous system at the level of cell. A rough estimate for the numbers of codons for human DNA of length about 1 m and the number of codons allowed by the surface of the nuclear membrane are of order 109 so that the proposal might make sense.

    This proposal generalizes and has many alternative forms. For instance, microtubules inside axons could be connected by flux tubes to the surface of axons.

    One could also consider braidings between ordinary and dark levels, say braiding of flux tubes connecting lipid layers of neuronal membrane to 2-D analog of dark DNA. This braiding would code quantum computer programs and be part of coding of nerve pulse patterns inducing 2-D flow of lipids to memories represented as braidings. Quite generally, the braidings could be very naturally between ordinary and dark variants of structures considered.

2. Could cell membrane and neuronal membrane realize genetic codons as 2-D structures?

In the sequel I discuss in more quantitative level the idea that cell membrane and neuronal membrane realize analogs of genes as 2-D structures.

2.1 The p-adic length scales associated with the dark variants of 2-D structures?

Consider next the p-adic length scales associated with the structures considered.

  1. The thickness of ordinary cell membrane corresponds roughly to Le(149)=5 nm whereas the coiling associated with the cell membrane corresponds to Le(151). Also neurons correspond to Le(151). Could k=149 resp. k=151 define levels of ordinary cell resp. neuron in the hierarchy of dark nuclear physics?
  2. Cell membrane consists of lipid bilayer. The lipid layer has three parts (see this).
    1. The totally hydrated layer nearest to water is hydrophilic head group, which in the case of phospholipids contains negatively charged phosphate. This phosphate layer has thickness .7-1.0 nm.
    2. Below it is a partially hydrated layer of thickness .3 nm, which corresponds to L(141): this of course puts bells ringing!
    3. Hydrophobic lipid tail layer below it is dehydrated. The thickness of single lipid layer is 1.25-1.75 nm and would correspond to the p-adic length scale Le(145)= 1.2 nm. k=145 is not prime.
  3. The phosphate layer analogous to phosphate-ribose backbone and the thickness L(141) of partially hydrated layer suggests that it corresponds to EZ created in Pollack effect so that there would be parallel dark RNA sequence along axon (possibly helical as for microtubules). In the case of cell membrane would have lattice like system formed from dark protons, and maybe even dark neutrons (as an analog for the neutron halo in some nuclei).
  4. If the recent biology is the analog of RNA era for k=149 codes, their manifestations could be seen as analogs of RNAs and the number of different lipids associated with the cell membrane could give some idea about their number. Cell membrane could be seen as a 2-D analog of RNA polymer. Cell division implying membrane replication would be induced by dark RNA replication. Even the analogs of tRNA and amino-acids but not proteins might be present if one takes the analogy very seriously. Could one identify pairs of lipids and some molecules analogous to proteins appearing in cell division?
Both sides of the lipid bilayer of cell membrane would pair with 2-D lattice of dark RNA whose size scale would be obtained by radial scaling giving rise to what might be called dark cell membrane. In the case of neuronal membrane the dark lattice would consist of pairs of dark DNA codon and its conjugate. In the case of axon one could have the analog of dark DNA strand extended to a cylinder containing bundles of these strands at its surface. Lipid layers would be 2-D analogs of 1-D DNA strands in this case.

Lipids would be analogs of ordinary RNA codons and dark RNA codons would code for them: this would predict 64 different lipids in cell membrane. Single dark RNA would correspond to the size scale of single lipid given by L(143)=2L(141)=.625 nm. The dark nuclear physics would correspond to k=149. The number N of parallel dark RNA strands would be roughly the circumference of the axonal lipid layer divided by the size of single lipid about L(143)=.625 nm given by N∼ 2π × Le(167)/Le(143) = π × 224 ∼ 5× 106.

2.2. Thermodynamical constraints

Could this totally irresponsible speculation about p-adic hierarchy of dark nuclear physics and genetic codes survive thermodynamical constraints?

  1. The condition that metabolic energy quantum is not below thermal energy at physiological temperatures poses constrains on the model. I have considered several identifications of the the metabolic energy quantum. These identification need not be mutually exlusive.
    1. One interpretation is as 1-D zero point kinetic energy of proton at tubular space-time sheet of atomic size with transversal length scale L(137). This energy is invariant under scalings induce by increase of heff since heff2/L2 is not changed.
    2. Second identification of metabolic quanta would be as energies assignable to hydrogen bond and its dark variants.
    3. Third identification of the metabolic energy quantum would be as scaled variant of Eb(k)= 2(k-107)/2Eb of typical dark nuclear binding energy Eb=∼ 1 MeV. The value would be about .5 eV for k=149 and .25 eV for k=151.
  2. Note that the action potential assignable to k=151 neuronal membrane is around .05 eV (the membrane potential for some photoreceptors is .03 eV). In TGD Universe the cell membrane can be seen as Josephson junction decomposing in an improved resolution to membrane proteins acting as Josephson junctions. Josephson energy of Cooper pair is twice this - that is EJ=0.1 eV slightly above the maximum Emax=3T=.09 eV of the thermal distribution at physiological temperature.
  3. As far Josephson radiation are considered, for k=151 membrane would be a quantum critical system. Quantum criticality could give rise to instability making possible the generation of nerve pulses. During nerve pulse the dark protons at the dark space-time sheet would return to the neuronal membrane and destroy the ionic equilibrium. Also the temperature criticality of consciousness manifesting itself as the generation of hallucinations during fever could be understood. For k=151 the situation would be overcritical and will be discussed separately.
The Josephson energy of Cooper pair is scaled down to EJ=.1 eV near to Emax= .09 eV. This is slightly above the thermal energy but one could still argue that Josephson radiation cannot carry information. Or could Nature have found the means to overcome this potential problem? The notion of generalized Josephson junction central in TGD inspired theory of EEG as communications from brain to MB could save the situation.
  1. For the generalized Josephson junction the energy of quantum of Josephson radiation is E= EJ+Δ Ec, where Δ Ec is the difference of cyclotron energies at the two sides of the membrane. Ec is proportional to heff=n× h and large enough value of n guarantees that Ec is above Emax≈ 3T irrespective of the value of the membrane potential. The variations of the membrane potential modulate Josephson frequency, and are proposed to provide a coding of sensory data defined by nerve pulse patterns communicated to MB.
  2. heff=hgr= GMm/v0 hypothesis guarantees the spectrum of cyclotron energies is universal and does not depend on the mass m of the charged particle being in the range of visible and UV energies of photons (this allows to deduce information about the values of mass M and velocity parameter v0<c): bio-photons would be produced in energy conserving phase transitions transforming dark photons to ordinary ones.
  3. If MB itself (a structure which has size scale of Earth at EEG frequencies around 10 Hz) has low enough temperature, this would allow to overcome the limitations caused by the thermal masking of the ordinary Josephson radiation so that the frequency modulations by nerve pulse patterns could code for the sensory data. heff=hgr= GMm/v0 hypothesis indeed allows very large values of heff for which ordinary cyclotron energies proportional to heff would be ridiculously small for the ordinary value of h.
What about the situation for massive particles like proton? Now Maxwell-Boltzmann (Gaussian) distribution is a good approximation and for effectively D-dimensional system the value of distribution is reduced by 1/e at thermal energy Ecr= DT/2. One could argue that above this energy thermal masking can be avoided. For D=1 at magnetic flux tubes this would give Ecr=T/2=Emax/6. At Tphys=.03 eV one would have Ecr= 0.15 eV. Metabolic energy quantum would be above Ecr for k=151. Even k=153 possibly assignable to mitochondrial double membrane can be considered but represents an upper bound at physiological temperatures.

Remark: In TGD view about information processing in brain active linear neuron groups relate to verbal cognition and 2-D neuronal groups relate to the geometric cognition associated with the decomposition of perceptive field to objects. At cellular level DNA and cell membrane could perhaps be seen as counterparts for these structures. In TGD framework neuronal membrane is proposed to be a constructor of sensory representations communicated to the magnetic body (MB) using generalized Josephson radiation whereas motor control by MB has been assumed to take place via DNA.

3. Microtubules as quantum critical systems

Also microtubules (see this) are 2-D structures having a strong resemblance with the lipid layers of cell membrane. Could a higher level representation of genetic code similar to the one proposed for lipid layers make sense for them. Also now one can imagine that the microtubular surface is accompanied by its dark variant realizing 2-D genes with scaled up size. The p-adic prime should correspond to k>151 so that higher level realization of genetic code would be in question. In the case of axons a possible identification for the dark scale would be as the radius of the axonal membrane.

  1. Microtubules are hollow cylinders with outer resp. inner diameter equal to 24 resp. 12 nm (the scales differ by factor 2) so that their thickness is 12 nm is same as the inner radius and would correspond to L(151)=10 nm. They decompose to 13 parallel helical filaments consisting of 13 tubulin proteins having size scale of order Le(151).
  2. Tubulins are dimers of α and β tubulin and the pairs are oriented along the helical filament. One can estimate the size of α and β tubulin by diving the circumference of 24 nm of the microtubule with the number of filaments, which is 13. This gives for the size scale of tubulin the estimate Rtub∼ 12 nm not far from L(151). This supports the view that p-adic length scale L(151).

    The size scale of the transversal volume associated with lipid is roughly .62 nm that is L(143)=2L(141) so that they could correspond to k∈ {141,143}, presumably k=141. Therefore one could see microtubules as scaled up variants of cell membrane with scaling factor 2(151-141)/2= 25= 32. Similar scaling would take place for the value of n=heff/h giving n=223 so that microtubules would represent a higher level of evolution identified as increase of n. Microtubules have indeed emerged after cell membrane.

  3. It has been proposed that the α and β conformations of tubulin give rise to bit or even qubit. If this were the case, single helical filament rotating one full turn would have 213 states and carry 13 bits of information. 13 independent filaments would have 226≈ 64× 106 states and carry 26 bits of information. One could also think of codon as sequence of 13 filaments with the states of filaments representing 213 letters of the code.
  4. Microtubular surface has rather high charge density and is polarized: the almost stationary end has negative local charge density roughly equal to that of DNA whereas the growing end has lower surface charge density. One manner to control the charge of the tubulin dimer is in terms of the charge states of GDP and GTP by ionization of the phosphates. Maximal negative charge for tubulin dimer would be 5 units.

    Microtubules are highly dynamical objects with inherent instability and have varying length: one might say that microtubules are quantum critical objects. Quantum criticality and thus instability might relate to the fact that the metabolic energy quantum is very near to thermal energy at room temperature.

    The dynamics for the length of microtubule could be induced from the dynamics of EZ involving the flow of protons between microtubule and its magnetic body defined by dark DNA. The gradient in charge density would make possible positive net charge density at the growing end of the microtubule.

    In ZEO it looks reasonable to argue that the dynamical patters are coded by a generalization of genetic code just as computer programs code for deterministic dynamical patterns.

  5. What could the dark code behind the dynamics be? The α- and β tubulins of tubulin dimer involve GTP (see this) resp. GDP (see this). In the case of DNA one has XMP, X= A,T,C,G. The analogs of dark RNA sequences would contain mere G and the information coded by the tubulin would be determined by the conformation of the tubulin dimer giving 1-bit code. This looks somewhat disappointing.

    If the charge states of the phosphates of GDP and GTP can vary and all charge combinations for phosphates are possible, one has 23 charge states for GTP and 22 charge states for GDP. Together with the bit associated with the tubulin conformation this would give 26 states and realize 6 bits of the ordinary genetic code! One would have 2-D realization of the genetic code analogous to that proposed for the lipid layer with the state of tubulin analogous to RNA codon.

    This coding together with thermal criticality would make microtubule a dynamical object since the deviation of the tubulin charge from -1 units would spoil charge local charge neutrality of tubulin-dark RNA pair.

I have proposed that flux tubes connecting tubulins to the lipids of the axonal lipid layer could give rise to topological quantum computation. The size scale of lipid is about Le(141) and that of tubulin about Le(151)=32Le(141), and the the radius of axonal membrane is by two orders of magnitude larger than microtubular surface. Hence this proposal does not look realistic unless one assumes that sub-structures of cell membrane with size scale of order Le(167)/Le(151)=28 larger than tubulin size represented as space-time sheets with cell nucleus size L(167) have flux tube connections to tubulins.

This kind of map would give rise to a kind of abstraction about what happens at the level of axonal membrane integrating out un-necessary details. This abstraction is natural since microtubules would indeed correspond to a higher level of cognitive hierarchy. Roughly N=216 lipids would contribute to the information received by single tubulin. Could nerve pulse patterns can induce braiding of the flux tubes in this scale?

See the chapter About the Correspondence of Dark Nuclear Genetic Code and Ordinary Genetic Code or the article with the same title, or the shorter article About dark variants of DNA, RNA, and amino-acids .



About dark variants of DNA, RNA, and amino-acids

To make progress one must construct a concrete model for the dark nuclei. The recent picture relies strongly on various anomalies to which TGD provides a solution. The TGD inspired model for "cold fusion leads to the notion of dark nuclear physics - actually hierarchy of them labelle by the values of heff/h=n and corresponding p-adic length scales. Second basic idea is that cylindrical variants of EZs discovered by Pollack (see this) give rise to the dark counterparts of DNA, RNA, and amino-acids as dark proton sequences. tRNAs would be analogs of tritium and 3He. Pollack effect serves as a strong constraint for the model. Also the effects of ELF em fields on vertebrate brain combined with the rather recent finding about clustering of RNA II polymerase molecules exhibiting Comorosan effect provide valuable constraints on the model (see this) . The outcome of the arguments is that single strand of DNA, mRNA, tRNA and amino-acids most naturally correspond to k=149 and double stranded DNA to k=151.

Remark: The following argumentation is kind of Sherlock-Holmes-ing using all possible hints as constraints to select between imagined options rather than glorious march from axioms to theorems and thus not science in the usual sense.

1. Why one must have k=151 for dark DNA

Concerning the identification of the size scale of dark DNA one can consider several options. It however turns out that the p-adic length scale assignable to dark DNA is most naturally k=151 corresponding to the thickness 10 nm of DNA coil. The hypothesis that the integer k labelling p-adic length scale is prime is attractive working hypothesis leaving very few options under consideration. The options k=137 and k=149 are excluded since the pairing of dark DNA and ordinary DNA would not be possible without the coiling of ordinary RNA around dark DNA. This leaves only options for which k≥ 149 for prime values of k.

For prime values of k the options k<149 are not possible for dark DNA since ordinary DNA should coil around dark DNA. There is also second objection against k<149 from energetics inspiring the hypothesis DNA corresponds to k=151.

  1. The scaling of the dark nuclear binding energy Eb∼ 7 MeV per nucleon as L(107)/L(k) predicts very high binding energies for primes k<149. For instance, k=139 would correspond to the scaled binding energy Eb(139)=Eb L(107)/L(139), Ebsim 7 MeV, which is typical nuclear binding energy. This gives Eb(139)=Eb/2(139-107)/2=.14 keV.
  2. The TGD based explanation of Pollack effect provides a consistency test for the idea. In Pollack effect IR light (besides either kinds of energy feeds) induces the formation of negative charged exclusion zones (EZs) in water bounded by gel phase. In TGD based model this would correspond to the formation of dark proton sequences at magnetic flux tubes. The scale of dark nuclear binding energy would be most naturally in eV scale. The binding energy scale of hydrogen atoms in water molecules is about 5 eV which suggests that the binding energy scale for dark protons sequences is smaller since otherwise energy would be liberated. This would suggest k=149 as will be found.
  3. One can imagine that an external perturbation induces
    1. a transition in which the proton bound to water molecule transforms to its dark variant in higher energy state or
    2. that the proton goes over a potential wall, whose height is measured in eV:s.
    If the dark nuclear binding energy is higher than the binding energy of proton in water molecule, the process should liberate energy and could occur spontaneously unless high potential wall prevents it. Hence the first option seems the only realistic one. Note that one could consider the cancellation of dark nuclear binding energy and repulsive Coulomb energy which scale in the same manner as function of p-adic length scale so that still the net energy would scale increase in shorter p-adic length scales.
Pollack effect suggests that if k is prime, one must have k=149 for dark proton sequences formed in Pollack effect.
  1. For k=149 one has Eb(151)∼ Eb/2(149-107)/2=3.5 eV for Eb= 7 MeV, which is in UV range slightly above the visible range. The binding energy of hydrogen atom in water is about 5 eV which would require the incoming radiation to have energy 1.5 eV which is indeed in IR range. This option looks therefore realistic.
  2. For k=151 one would have Eb(151)∼ 7 MeV/2(151-107)/2=1.75 eV, which just above the IR energy range. Now the energy needed to transform ordinary protons to dark protons in Pollack effect would be in UV range so that this options seems to be excluded.
This argument suggests that dark proton sequences generated in Pollack effect are analogs of single DNA strand, which would naturally correspond to L(149)= L(151)/2. Also RNA would naturally correspond to this scale.
  1. L(151)≈ 10 nm is the thickness of coiled DNA double strand. The size scale of dark nucleons would be L(151) and the dark DNA strand should be horizontally scaled variant of ordinary DNA strand by a scaling factor λ ∼ L(151)/.33 nm = 30. DNA double strand would be obtained by a transversal scaling from the ordinary DNA double strand.
  2. The higher coilings of DNA could correspond to higher horizontally scaled variants of DNA corresponding to k=157,163, 167. k=167 would correspond to nuclear membrane length scale of 2.5 μm. The emergence of nuclear membrane in k=151 length scale would have been accompanied by the emergence of dark DNA in this scale. Cell membrane could correspond to k=173 and p-adic length scale 17.6 μm. Neurons have size varying from 4-100 micrometers (the definition of size depends on whether one includes axons) and might correspond to k=179,181 and length scales of .16 mm and perhaps even .32 mm.
The only justification for this speculative picture is that it is consistent with the other basic ideas about TGD inspired quantum biology.
  1. Cisse et al (see this found that RNA II polymerase molecules cluster during transcription and their dynamics involves multiples of the time scale τ=5 seconds. Comorosan reported long time ago that just these time scales are universal bio-catalysis The TGD inspired model (see this) for the findings of Cisse et al allows to sharpen the TGD based view about quantum biology considerably.
  2. The basic parameter of the model is the value of gravitational Planck constant hbargr= GMDm/v0 assigned to magnetic flux tubes mediating gravitational interactions. Already earlier work gives estimates for the value MD of dark mass and velocity parameter v0 and the model leads to the same estimates. The identification of the values of τ as Josephson periods assuming the potential difference V along flux tubes connecting reacting molecules is universal and same as over neuronal membrane fixed the value of hgr. The value of V along flux tube serving as Josephson junction would be universal and equal to membrane potential. Josephson radiation would have energies coming as multiples ot ZeV just above the thermal energy at physiological temperatures fixed by the membrane potential.
  3. The model forces the conclusion that the endogenous magnetic field Bend has at its upper bound Bend=.2 Gauss deduced from the findings of Blackman about effects of ELF em fields on vertebrate brain. The earlier ad hoc hypothesis was that Bend=.2 Gauss is minimum value of Bend. Furthermore, for the required value of hgr Bend=.2 Gauss corresponds to dark cyclotron energy of .12 keV, which is surprisingly large energy at the upper end of UV band: the earlier intuitive guess was that energy scale is in visible range.

    Also harmonics of cyclotron frequencies were found to have effects so that really large energy scales are involved with the interaction of ELF radiation and one can ask whether this picture really makes sense. This raises a question about the mechanism of the interaction of ELF em radiation with living matter. One also wonder why the ELF radiation has effects on both behavior and physiology.

    Assume

    1. that dark photons with energies coming as multiples of .12 keV are in question,
    2. that these dark photons excite dark cyclotron states in the cellular length scale deduced from flux quantization and
    3. that the dark cyclotron photons radiated as the excited cyclotron states return to the ground states perform some control action on ordinary DNA coil - this is in accordance with the basic vision about the role of magnetic body.
    X rays have energy range varying from 100 eV to 100 keV and wavelengths varying from 10 nm to .01 nm. The wavelength of an ordinary photon resulting from dark photon with energy of .12 keV would be of order 10 nm, the radius of DNA coil for k=151!

    Could this energy induce an analog of standing em wave in transversal degrees of freedom of DNA perhaps transformable to many phonon state with very large number of photos and thus classical acoustic wave? This would allow to understand how cyclotron harmonics can have non-trivial effects. The effects of ELF radiation on behavior and physiology could be understood as gene expression induced by the irradiation.

Both dark cyclotron radiation and radiation generated in dark nuclear transitions could have biological effects
  1. Can one relate energy scale of .12 keV associated with dark cyclotron radiation to atomic physics? The ionization energies behave as Z2eff/n2, where Zeff is nuclear charge minus the charge of the closed shells. Zeff is also reduced by electronic screening by other valence electrons. The binding energies of valence electrons decrease with the principal quantum number n so that only n=2 row of the periodic table might allow so high ionization energies for valence electrons.

    Oxygen is certainly the first candidate to consider. The ionization energy for oxygen is .12 eV from an estimate assuming that the effective nuclear charge is 6 (with the contribution of 2 valence electrons subtracted). The actual value is 68.9 eV: the reduction is due to electron screening. This value is smaller than the estimate estimate for Eb=.12 keV and since harmonics of this energy are involved, the interpretation in terms of ionization does not make sense.

  2. Not only oxygen but also heavier elements are ionized in living matter and at least to me this has remained more or less a mystery. Could dark photons emitted by dark nuclei of MB perform control by inducing the transitions and even ionization of oxygen and other biologically important atoms. The process could proceed also in opposite direction. The energy scale would correspond to that of nuclear excitations scaled down by the above ratio of p-adic length scales. If the energy scale of ordinary nuclear excitations is taken to be about 1 MeV, the dark energy scale for k=127 assignable to the dark nuclei created in "cold fusion" is keV. For k=131 the scale would be 250 eV and above the ionization energy scales for valence electrons. For k=137 the scale would be 17 keV. These dark nuclear transitions could generate dark photons inducing transitions of atoms and even ionizations.
2. What about dark variants of RNA, tRNA, and amino-acids?

Also RNA and amino-acids should have dark variants and one should understand their role. Suppose that the integer k characterizing the p-adic length scale is prime. The vision about RNA era preceding DNA era suggests that RNA accompanying dark RNA is at lower level in the evolution, and hence the value of heff is smaller for dark RNA than for dark DNA. Also the p-adic length scale for RNA would be shorter.

  1. The most natural option is that RNA corresponds to k=149 as also single DNA strand. This would conform with the above suggestion that the Pollack effect generates k=149 dark proton sequence (dark RNA?). DNA double strand would correspond to k=151.

    The emergence of k=151 level would mean the emergence of structures with scale characterized by L(151). This includes DNA double strand forming a coil with thickness L(151) and nuclear and cell membranes. During RNA era these structures would have been absent.Both DNA double strand and cell membrane have binary structures. Therefore single DNA strand and lipid layer could correspond to k=149. In transcription DNA opens and double strand becomes pair of strands having naturally k=149. Therefore mRNA should have also k=149.

  2. If amino-acids correspond to k=149 then also tRNA should correspond to k=149. On the other hand, tRNA does not form strands and should be more elementary structure than RNA. Could tRNA corresponds to k=139 or k=137? This would require that also the attached amino-acid would correspond to k=139 or k=137, which does not look plausible.

    Remark: TGD vision assumes tRNA was present already at RNA era and the role of amino-acid in tRNA was to catalyze RNA replication. In fact, RNA could have been just tRNA at very early stages.

What about amino-acids? The following arguments suggest that one has k=149 for both amino-acids and RNA.
  1. For dark amino-acids one can imagine p-adic evolutionary hierarchy analogous to that for DNA. In TGD inspired vision amino-acid sequences emerged together with DNA. Proteins can appear also as coils. Since mRNA pairs with single DNA strand and amino-acids with mRNA, it seems that amino-acids should correspond to k≥ 149?
  2. One could however argue that amino-acids are building bricks rather than information molecules and k could be rather small for dark amino-acids. Dark amino-acids should pair with proteins. Pairing without coiling is possible only if the length per letter is same as the length per amino-acid and thus same as for DNA letter, which is longer than the length taken by k=139 dark proton. Also this suggests k=149 for dark amino-acids and their coiling around the ordinary amino-acids.
See the chapter About the Correspondence of Dark Nuclear Genetic Code and Ordinary Genetic Code or the article with the same title.



About Comorosan effect in the clustering of RNA II polymerase proteins

The time scales τ equal 5, 10, and 20 seconds appear in the clustering of RNA II polymerase proteins and Mediator proteins (see this and the previous posting). What is intriguing that so called Comorosan effect involves time scale of 5 seconds and its multiples claimed by Comorosan long time ago to be universal time scales in biology. The origin of these time scales has remained more or less a mystery although I have considered several TGD inspired explanations for this time scale is based on the notion of gravitational Planck constant (see this).

One can consider several starting point ideas, which need not be mutually exclusive.

  1. The time scales τ associated with RNA II polymerase and perhaps more general bio-catalytic systems could correspond to the durations of processes ending with "big" state function reduction. In zero energy ontology (ZEO) there are two kinds of state function reductions. "Small" reductions - analogs of weak measurements - leave passive boundary of causal diamond (CD) unaffected and thus give rise to self as generalized Zeno effect. The states at the active boundary change by a sequence of unitary time evolutions followed by measurements inducing also time localization of the active boundary of CD. The size of CD increases and gives rise to flow of time defined as the temporal distance between the tips of CD. Large reductions change the roles of the passive and active boundaries and mean death of self. The process with duration of τ could correspond to a life-time of self assignable to CD.

    Remark: It is not quite clear whether CD can disappear and generated from vacuum. In principle this is possible and the generation of mental images as sub-selves and sub-CDs could correspond to this kind of process.

  2. I have proposed (see this) that Josephson junctions are formed between reacting molecules in bio-catalysis. These could correspond to the shortened flux tubes . The difference EJ=ZeV of Coulomb energy of Cooper pair over flux tube defining Josephson junction between molecules would correspond to Josephson frequency fJ= 2eV/heff. If this frequency corresponds to τJ= 5 seconds, heff should be rather large since EJ is expected to be above thermal energy at physiological temperatures.

    Could Josephson radiation serve as a kind of of synchronizing clock for the state function reductions so that its role would be analogous to that of EEG in case of brain? A more plausible option is that Josephson radiation is a reaction to the presence of cyclotron radiation generated at MB and performing control actions at the biological body (BB) defined in very general sense. In the case of brain dark cyclotron radiation would generate EEG rhythms responsible for control via genome and dark generalized Josephson radiation modulated by nerve pulse patterns would mediate sensory input to the MB at EEG frequencies.

    A good guess is that the energy in question corresponds to Josephson energy for protein through cell membrane acting as Josephson junction and giving to ionic channel or pump. This energy could be universal as therefore same also in the molecular reactions. The flux tubes themselves have universal properties.

  3. The hypothesis ℏeff= ℏgr= GMm/β0c of Nottale for the value of gravitational Planck constant gives large ℏ. Here v00c has dimensions of velocity. For dark cyclotron photons this gives large energy Ec∝ ℏgr and for dark Josephson photons small frequency fJ∝ 1/hgr. Josephson time scale τf would be proportional to the mass m of the charged particle and therefore to mass number of ion involved. Cyclotron time scale does not depend on the mass of the charged particle at all and now sub-harmonics of τc are natural.
The time scales assignable to CD or the lifetime-time of self in question could correspond to either cyclotron of Josephson time scale τ.
  1. If one requires that the multiplies of the time scale 5 seconds are possible, Josephson radiation is favoured since the Josephson time scale proportional to hgr ∝ m ∝ A, A mass number of ion.

    The problem is that the values A= 2,3,4,5 are not plausible for ordinary nuclei in living matter. Dark nuclei at magnetic flux tubes consisting of dark proton sequences could however have arbitrary number of dark protons and if dark nuclei appear at flux tubes defining Josephson junctions, one would have the desired hierarchy.

  2. Although cyclotron frequencies do not have sub-harmonics naturally, MB could adapt to the situation by changing the thickness of its flux tubes and by flux conservation the magnetic field strength to which fc is proportional to. This would allow MB to produce cyclotron radiation with the same frequency as Josephson radiation and MB and BB would be in resonant coupling.
Consider now the model quantitatively.
  1. For ℏeff= ℏgr one has

    r= ℏgr/ℏ= GMDm/cβ0= 4.5 × 1014× (m/mp) (y/β0) .

    Here y=MD/ME gives the ratio of dark mass MD to the Earth mass ME. One can consider 2 favoured values for m corresponding to proton mass mp and electron mass me.

  2. E= hefff gives the concrete relationship f =(E/eV) × 2.4 × 1014× (h/heff) Hz between frequencies and energies. This gives

    x=E/eV = 0.4× r × (f/1014 Hz) .

  3. If the cyclotron frequency fc=300 Hz of proton for Bend=.2 Gauss corresponds to bio-photon energy of x eV, one obtains the condition

    r=GMDmp/ ℏ β0≈ .83 × 1012x .

    Note that the cyclotron energy does not depend on the mass of the charged particle. One obtains for the relation between Josephson energy and Josephson frequency the condition

    x=EJ/eV = 0.4× .83 × 10-2× (m/mp)× (xfJ/Hz) , EJ= ZeV .

    One should not confuse eV in ZeV with unit of energy. Note also that the value of Josephson energy does not depend on heff so that there is no actual mass dependence involved.

For proton one would give a hierarchy of time scales as A-multiples ofτ(p) and is therefore more natural so that it is natural to consider this case first.
  1. For fJ=.2 Hz corresponding to the Comorosan time scale of τ= 5 seconds this would give ZeV= .66x meV. This is above thermal energy Eth= T=27.5 meV at T=25 Celsius for x> 42. For ordinary photon (heff= h) proton cyclotron frequency fc(p) would correspond for x>42 to EUV energy E>42 eV and to wavelength of λ<31 nm.

    The energy scale of Josephson junctions formed by proteins through cell membrane of thickness L(151)=10 nm is slightly above thermal energy, which suggests x≈ 120 allowing to identify L(151)=10 nm as the length scale of the flux tube portion connecting the reactants. This would give E≈ 120 eV - the upper bound of EUV range. For x=120 one would have GMEmp y/v0≈ 1014 requiring β0/y≈ 2.2. The earlier estimates (see this) give for the mass MD the estimate y∼ 2× 10-4 giving β0∼ 4.4× 10-4. This is rather near to β0= 2-11∼ me/mp obtained also in the model for the orbits of inner planets as Bohr orbits.

  2. For ion with mass number A this would predict τA= A× τp= A× 5 seconds so that also multiples of the 5 second time scale would appear. These multiples were indeed found by Comoran and appear also in the case of RNA II polymerase.
  3. For proton one would thus have 2 biological extremes - EUV energy scale associated with cyclotron radiation and thermal energy scale assignable to Josephson radiation. Both would be assignable to dark photons with heff=hgr with very long wavelength. Dark and ordinary photons of both kind would be able to transform to each other meaning a coupling between very long lengths scales assignable to MB and short wavelengths/time scales assignable to BB.

    The energy scale of dark Josephson photons would be that assignable with junctions of length 10 nm with long wavelengths and energies slightly above Eth at physiological temperature. The EUV energy scale would be 120 eV for dark cyclotron photons of highest energy.

    For lower cyclotron energies suggested by the presence of bio-photons in the range containing visible and UV and obtained for Bend below .2 Gauss, the Josephson photons would have energies ≤ Eth. That the possible values of Bend are below the nominal value Bend=.2 Gauss deduced from the experiments of Blackman does not conform with the earlier ad hoc assumption that Bend represents lower bound. This does not change the earlier conclusions.

    Could the 120 eV energy scale have some physical meaning in TGD framework? The corresponding wavelength for ordinary photons corresponds to the scale L(151)=10 nm which correspond to the thickness of DNA double strand. Dark DNA having dark proton triplets as codons could correspond to either k=149 or k=151. The energetics of Pollack effect suggests that k=149 is realized in water even during prebiotic period (see this).. In the effect discovered by Blackman the ELF photons would transform dark cyclotron photons having heff=hgr and energy about .12 keV. They would induce cyclotron transitions at flux tubes of Bend with thickness of order cell size scale. These states would decay back to previous states and the dark photons transformed to ordinary photons absorbed by ordinary DNA with coil structure with thickness of 10 nm. Kind of standing waves would be formed. These waves could transform to acoustic waves and induce the observed effects. Quite generally, dark cyclotron photons would control the dynamics of ordinary DNA by this mechanism.

    It is indeed natural to assume that Bend corresponds to upper bound since the values of magnetic field are expected to weaken farther from Earth's surface: weakening could correspond to thickening of flux tubes reducing the field intensity by flux conservation. The model for hearing (see this ) requires cyclotron frequencies considerably above proton's cyclotron frequency in Bend=.2 Gauss. This requires that audible frequencies are mapped to electron's cyclotron frequency having upper bound fc(e) = (mp/me) fc(p)≈ 6× 105 Hz. This frequency is indeed above the range of audible frequencies even for bats.

For electron one has hgr(e)= (me/mp)hgr(p) ≈ 5.3 × 10-4 hgr(p), ℏgr(p)=4.5× 1014/ (β0. Since Josephson energy remains invariant, the Josephson time scales up from τ(p)=5 seconds to τ(e)=(me/mP) τ(p)≈ 2.5 milliseconds, which is the time scale assignable to nerve pulses (see this).

To sum up, the model suggests that the idealization of flux tubes as kind of universal Josephson junctions. The model is consistent with bio-photon hypothesis. The constraints on hgr= GMDm/v0 are consistent with the earlier views and allows to assign Comorosan time scale 5 seconds to proton and nerve pulse time scale to electron as Josephson time scales. This inspires the question whether the dynamics of bio-catalysis and nerve pulse generation be seen as scaled variants of each other at quantum level? This would not be surprising if MB controls the dynamics. The earlier assumption that Bend=0.2 Gauss is minimal value for Bend must be replaced with the assumption that it is maximal value of Bend.

See the chapter About the Correspondence of Dark Nuclear Genetic Code and Ordinary Genetic Code or the article Clustering of RNA polymerase molecules and Comorosan effect.



Why do RNA polymerase molecules cluster?

I received a link to a highly interesting popular article telling about the work of Ibrahim Cisse at MIT and colleagues (see this): at this time about clustering of proteins in the transcription of RNA. Similar clustering has been observed already earlier and interpreted as a phase separation Similar clustering has been observed already earlier and interpreted as a phase separation (see this). Now this interpretation is not proposed by experiments but experimenters say that it is quite possible but they cannot prove it.

I have already earlier discussed the coalescence of proteins into droplets as this kind of process in TGD framework. The basic TGD based ideas is that proteins - and biomolecules in general - are connected by flux tubes characterized by the value of Planck constant heff=n× h0 for the dark particles at the flux tube. The higher the value of n is the larger the energy of given state. For instance, the binding energies of atoms decrease like 1/n2. Therefore the formation of the molecular cluster liberates energy usable as metabolic energy.

Remark: h0 is the minimal value of heff. The best guess is that ordinary Planck constant equals to h=6h0 (see this and this).

TGD view about the findings

Gene control switches - such as RNA II polymerases in the DNA transcription to RNA - are found to form clusters called super-enhancers. Also so called Mediator proteins form clusters. In both cases the number of members is in the range 200-400. The clusters are stable but individual molecules spend very brief time in them. Clusers have average lifetime of 5.1±.4 seconds.

Why the clustering should take place? Why large number of these proteins are present although single one would be enough in the standard picture. In TGD framework one can imagine several explanations. One can imagine at least following reasons.

  1. One explanation could relate to non-determinism of state function reduction. The transcription and its initiation should be a deterministic process at the level of single gene. Suppose that the initiation of transcription is one particular outcome of state function reduction. If there is only single RNA II polymerase, which can make only single trial, the changes to initiate the transcription are low. This would be the case if the molecule provides metabolic energy to initiate the process and becomes too "tired" to try again. In nerve pulse transmission there is analogous situation: after the passing of the nerve pulse generation the neuron has dead time period. As a matter of fact, it turns out that the analogy could be much deeper.

    How to achieve the initiation with certainty in this kind of situation? Suppose that the other outcomes do not affect the situation appreciabley. If one particular RNA polymerase fails to initiate it, the others can try. If the number of RNA transcriptase molecule is large enough, the transcription is bound to begin eventually! This is much like in fairy tales about princess and suitors trying to kill the dragon to get the hand of princess. Eventually the penniless swineherd enters the stage.

  2. If the initiation of transcription requires large amount of metabolic energy then only some minimal number of N of RNA II polymerase molecules might be able to provide it collectively. The collective formed by N molecules could correspond to a formation of magnetic body with a large value of heff=n×h. The molecules would be connected by magnetic flux tubes.
  3. If the rate for occurrence is determined by amplitude which is superposition of amplitudes assignable to individual proteins the the rate is proportional to N2, N the number of RNA transcriptase molecules.

    The process in the case of cluster is indeed reported to to be suprisingly fast as compared to the expectations - something like 20 seconds. The earlier studies have suggests that single RNA polymerase stays at the DNA for minutes to hours. This would be a possible mechanism allowing to speed up bio-catalysis besides the mechanism allowing to find molecules to find by a reduction of heff/h= n for the bonds connecting the reactants and the associated liberation of metabolic energy allowing to kick the reactants over the potential wall hindering the reaction.

Concerning the situation before clustering there are two alternative options both relying on the model of liquid phase explaining Maxwell's rule assuming the presence of flux tube bonds in liquid and of water explaining its numerous anomalies in terms of flux tubes which can be also dark (see this).
  1. Option I: Molecules could be in a phase analogous to vapour phase and there would be very few flux tube bonds between them. The phase transition would create liquid phase as flux tube loops assignable to molecules would reconnect form flux tube pairs connecting the molecules to a tensor network giving rise to quantum liquid phase. The larger then value of n, the longer the bonds between molecules would be.
  2. Option I: The molecules are in the initial state connected by flux tubes and form a kind of liquid phase and the clustering reduces the value of n and therefore the lengths of flux tubes. This would liberate dark energy as metabolic energy going to the initiation of the transcription. One could indeed argue that connectedness in the initial state with large enough value of n is necessary since the protein cluster must have high enough "IQ" to perform intelligent intentional actions.
Protein blobs are said to be drawn together by the "floppy" bits (pieces) of intrinsically disorder proteins. What could this mean in the proposed picture? Disorder suggests absence of correlations between building bricks of floppy parts of the proteins.
  1. Could floppiness correspond to low string tension assignable to long flux loops with large heff/h=n assignable to the building bricks of "floppy" pieces? Could reconnection for these loops give rise to pairs of flux tubes connecting the proteins in the transition to liquid phase? Floppiness could also make possible to scan the enviroment by flux loops for flux loops of other molecules and in case of hit (cyclotron resonance) induce reconnection.
  2. In spite of floppiness in this sense, one could have quantum correlations between the internal quantum numbers of the building bricks of the floppy pieces. This would also increase the value of n serving as molecular IQ and provide molecule with higher metabolic energy liberated in the catalysis.
What about the interpretation of the time scales 5, 10, and 20 seconds? What is intriguing that so called Comorosan effect involves time scale of 5 seconds and its multiplest claimed by Comorosan long time ago to be universal time scales in bio-catalysis.

See the chapter About the Correspondence of Dark Nuclear Genetic Code and Ordinary Genetic Code or the article Clustering of RNA polymerase molecules and Comorosan effect.



Expanding Earth hypothesis, Platonic solids, and plate tectonics as a symplectic flow

A FB discussion inspired by the recent findings of NASA suggesting the presence of life under the surface of Mars raised the question whether the TGD based Expanding Earth model is consistent with plate tectonics and with the motivating claim of Adams that the continents fit together nicely to cover the entire surface of Earth if its radius were one half of the recent radius. The outcome was what one might call Platonic plate tectonics.

  1. The expansion would have started from or generated decomposition of the Earth's crust to an icosahedral lattice with 20 faces, which contain analogs of what is known as cratons and having a total area equal to that of Earth before expansion. The prediction for the recent land area fraction is 25 per cent is 4.1 per cent too low. The simplest explanation is that expansion still continues but very slowly.
  2. The craton like objects (hereafter cratons) would move like 2-D rigid bodies and would fuse to form continents.
  3. The memory about the initial state should be preserved: otherwise there would exist no simple manner to reproduce the observation of Adams by simple motions of continents combined with downwards scaling. This might be achieved if cratons are connected by flux tubes to form a network. For maximal connectivity given triangular face is connected by flux tube to to all 3 nearest neighbour faces. Minimal connectivity corresponds to an essentially unique dodecahedral Hamiltonian cycle connecting cratons to single closed string. At least for maximal connectivity this memory would allow to understand the claim of Adams stating that the reduction of radius by factor 1/2 plus simple motions for the continents allow to transform the continents to single continent covering the entire surface of the scaled down Earth.
  4. The dynamics in scales longer than that of craton would be naturally a generalization of an incompressible liquid flow to area preserving dynamics defined by symplectic flow. The assumption that Hamilton satisfies Laplace equation and is thus a real or imaginary part of analytic function implies additional symmetry: the area preserving flow has dual.
For details see the chapter Expanding Earth hypothesis or the article Expanding Earth hypothesis, Platonic solids, and plate tectonics as a symplectic flow .



Did RNA replicate in codon-wise manner during RNA era?

There was a very interesting popular article in Spacedaily with title "Scientists crack how primordial life on Earth might have replicated itself" (see this). The research paper "Ribozyme-catalysed RNA synthesis using triplet building blocks" is here.

It is possible to replicate unfolded RNA strands in Lab by using enzymes known as ribozymes, which are RNA counterparts of enzymes, which are amino-adic sequences. In the presence of folding the replication is however impossible. Since ribozymes are in general folded, they cannot catalyze their own replication in this manner. The researchers however discovered that the replication using RNA triplets - genetic codons - as basic unit can be carried out in laboratory even for the folded RNA strands and with rather low error rate. Also the ribozyme involved can thus replicate. For units longer than 3 nucleotides the replication becomes prone to errors.

These findings are highly interesting in TGD framework. In TGD chemical realization of genetic code is not fundamental. Rather, dark matter level would provide the fundamental realizations of analogs of DNA, RNA, tRNA, and amino-acids as dark proton sequences giving rise to dark nuclei at magnetic flux tubes. Also ordinary nuclei correspond in TGD Universe to sequences of protons and neutrons forming string like entities assignable to magnetic flux tubes.

The basic unit representing DNA, RNA and tRNA codon and amino-acid would consist of 3 entangled dark protons. The essential aspect is that by entanglement the dark codons do not decompose to products of letters. This is like words of some languages, which do not allow decomposition to letters. This representation is holistic. As we learn to read and write, we learn the more analytic western view about words as letter sequences. Could the same hold true in evolution so that RNA triplets would have come first as entities pairing with dark RNA codons from from dark proton triplets as a whole? Later DNA codons would have emerged and paired with dark DNA codons. Now the coupling would have have been letter by letter in DNA replication and transcription to mRNA.

It is intriguing that tRNA consists of RNA triplets combined from amino-acids and analogs of mRNA triplets! The translation of mRNA to amino-acids having no 3-letter decomposition of course forces the holistic view but one can ask whether something deeper is involved. This might be the case. I have been wondering whether during RNA era RNA replicated using a prebiotic form of translational machinery, which replicated mRNA rather than translated RNA to protein formed from amino-acids (AAs).

  1. During RNA era amino-acids associated with pre-tRNA molecules would served as catalysts for replication of RNA codons. The linguistic mode would have been "holistic" during RNA er in accordance with the findings of the above experiments. RNA codon would have been the basic unit.
  2. This would have led to a smaller number of RNAs since RNA and RNA like molecules in tRNA are not in 1-1 correspondence. A more realistic option could have been replication of subset of RNA molecules appearing in tRNA in this manner.
  3. Then a great evolutionary leap leading from RNA era to DNA era would have occurred. AA catalyzed replication of RNA would have transformed to a translation of RNA to proteins and the roles of RNA and AA in tRNA would have changed. [Perhaps the increase of heff in some relevant structure as quantum criticality was reached led to the revolution?]
  4. At this step also (subset of) DNA and its transcription to (a subset of) mRNA corresponding to tRNA had to emerge to produce mRNA in transcription. In the recent biology DNA replicates and is transcribed nucleotide by nucleotide rather than using codon as a unit so that DNA and RNA polymerases catalyzing replication and transcription should have emerged at this step. An alternative option would involve the "tDNA" as the analog of "tRNA" and the emergence of polymerases later: this does not however look attractive if one accepts the idea about the transition from holistic to analytic mood.

    The ability of DNA to unwind is essential for the emergence of the "analytic linguistic mode" as an analog of written language (DNA) decomposing codons to triplets of letters. This must have been a crucial step in evolution comparable to the emergence of written language based on letters. Also the counterpart of RNA polymerase and separate RNA nucleotides for transcription should have emerged if not already present.

    The minimal picture would be emergence of a subset of DNA codons corresponding to RNAs associated with pre-tRNA and the emergence of the analogs of DNA and RNA polymerases as the roles of amino-acid and RNA codon in tRNA were changed.

  5. How DNA could have emerged from RNA? The chemical change would have been essentially the replacement of ribose with de-oxiribose to get DNA from RNA and U→ T. Single O-H in ribose was replaced with H. O forms hydrogen bonds with water and this had to change the hydrogen bonding characteristics of RNA.

    If the change of heff =n×h0 (one has h= 6× h0 in the most plausible scenario, see this and this) was involved, could it have led to stabilization of DNA. Did cell membrane emerge and allow to achieve this? I have proposed (see this) that the emergence of cell membrane meant the emergence of new representation of dark genetic code based on dark nuclei with larger value of heff.

The communication between dark and ordinary variants of biomolecules involves resonance mechanism and would also involve genetic code represented as 3-chords, music of light, and it is interesting to see whether this model provides additional insights.
  1. The proposal is that 3-chords assignable to nucleotides as music of light with allowed 64 chords defining what I have called bio-harmony is essential for the resonance (see this, this, and this). The 3 frequencies must be identical in the resonance: this is like turning 3 knobs in radio. This 3-fold resonance would correspond to the analytic mode. The second mode could be holistic in the sense that it would involve only the sum only the sum of the 3 frequencies modulo octave equivalence assigning a melody to a sequence of 3-chords.
  2. The proposal is that amino-acids having not triplet decomposition are holistic and couple to the sum of 3 frequencies assignable to tRNA and mRNA in this manner. Also the RNAs in tRNA could couple to mRNA in this manner. One could perhaps say that tRNA, mRNA and amino-acids codons sing whereas DNA provides the accompaniment proceeding as 3-chords. The couplings of DNA nucleotides to RNA nucleotides would realy on the frequencies assignable to nucleotides.
  3. If the sum of any 3 frequencies associated with mRNA codons is not the same except when the codons code for the same amino-acids, the representation of 3-chords with the sum of the notes is faithful. The frequencies to DNA and RNA nucleotides cannot be however independent of codons since the codons differing only by a permutation of letters would correspond to the same frequency and therefore code for the same amino-acid. Hence the information about the entire codon would be needed also in transcription and translation and could be provided either by dark DNA strand associated with DNA strand or by the interactions between the nucleotides of the DNA codon.
  4. The DNA codon itself would know that if is associated with dark codon and the frequencies assignable to nucleotides are determined by the dark DNA codon. It would be enough that the frequency of the letter depends on its position in the codon so that there would be 3 frequencies for every letter: 12 frequencies altogether.

    What puts bells ringing is that this the number of notes in 12-note scale for which the model of bio-harmony (see this and this) based on the fusion of icosahedral (12 vertices and 20 triangular faces) and tetrahedral geometries by gluing icosahedron and tetrahedron along one face, provides a model as Hamiltonian cycle and produces genetic code as a by-product. Different Hamiltonian cycles define different harmonies identified as correlates for molecular moods.

    Does each DNA nucleotide respond to 3 different frequencies coding for its position in the codon and do the 4 nucleotides give rise to the 12 notes of 12-note scale? There are many choices for the triplets but a good guess is that the intervals between the notes of triplet are same and that fourth note added to the triplet would be the first one to realize octave equivalence. This gives uniquely CEG #, C#FA,DF#/B b, and DG#B as the triplets assignable to the nucleotides. The emergence of 12-note scale in this manner would be a new element in the model of bio-harmony.

    There are 4!=24 options for the correspondence between {A, T, C, G} as the first letter and {C,C#,D,D#}. One can reduce this number by a simple argument.

    1. Letters and their conjugates form pyrimidine-purine pairs T, A and C,G. The square of conjugation is identity transformation. The replacement of note with note defining at distance of half-octave satisfies this condition (half-octave - tritonus - was a cursed interval in ancient music and the sound of ambulance realizes it). Conjugation could correspond to a transformation of 3-chords defined as

      CEG# ↔ DF#Bb , C#FA↔ D#GB .

    2. One could have

      {T, C} ↔ {CEG #, C#FA} , {A,G}↔ {DF#Bb,D#GB}

      or

      {T, C} ↔ {DF#Bb,D#GB} , {A,G}↔ {CEG#, C#FA} .

    3. One can permute T and C and A and G in these correspondences. This leaves 8 alternative options. Fixing the order of the image of (T, C) to say (C,C#) fixes the order of the image of (A, G) to (D,D#) by the half-octave conjugation. This leaves 4 choices. Given the bio-harmony and having chosen one of these 4 options one could therefore check what given DNA sequence sounds as a sequence of 3-chords (see this).

      Anyone willing to do this kind of experimentation obtains from me the program modules used the Garage band programs to produce a sequence of chords. A further interesting experiment would be check what kind of melodies come out if one assigns to a chord a note as the sum of frequencies of the chord reduced by octave equivalence to basic octave.

    That the position the frequency associated with the nucleotide depends on its position in the codon would also reflect the biochemistry of the codon and this kind of dependence would be natural. In particular, different frequencies associated with the first and third codon would reflect the parity breaking defining orientation for DNA.
See the chapter About the Correspondence of Dark Nuclear Genetic Code and Ordinary Genetic Code or the article with the same title.



Homonymy of the genetic code from TGD point of view

Peter Gariaev and colleagues have applied the linguistic notions of synonymy and homonymy to genetic code. Also the notion of syhomy fusing these concepts is introduced. Homonymy is visible in mRNa-tRNA pairing and induced by the 1-to-many pairing of the third mRNA nucleotide with tRNA nucleotide. The homonymy in mRNA-AA (AA for amino-acid) pairing is also present albeit rare.

The codons for the standard code can be divided to two classes. For 32 codons the first two letters fix AA completely. For the remaining 32 codons this is not the case. There is however almost unbroken symmetry in that U and C resp. A and G code for the same AA. The breaking of this symmetry is minimal appearing only for 3 4-columns of the code table and present for A-G only. The deviations from the standard code as a rule break A-G or T-C symmetry or re-establish it.

The notion of homonymy is highly interesting from TGD point of view. TGD leads to two basic proposals for non-chemical realization of genetic code predicting the numbers of DNA codons coding for amino-acid (AA) rather successfully. The first proposal relies on TGD based view about dark matter as heff/h=n phases of ordinary matter and identifies counterparts of DNA, RNA, tNRA, and AAs as entangled dark proton triplets.

Second proposal emerged from the model of music-harmony based on fusion of icosahedral and tetrahedral geometries. Codons are represented as photon triplets (dark or ordinary) defining the allowed 3-chords of given harmony defined by Hamilton cycle at icosahedron extended to Hamilton cycle to the fusion of icosahedron with tetrahedron along common face. Photon triplets give rise to resonant coupling giving rise to physical pairing of biomolecule and its dark counterpart. Remarkably, there are 3 different realizations of tRNA in terms of 3-chords. There is large number of bio-harmonies corresponding to Hamiltonian cycles. Since music expresses and creates emotions, the proposal is that a realization of emotions at molecular level adding additional degrees of freedom not visible at the level of chemistry is in question. This might give rise to a context dependence of the code.

The proposal is that genetic code at dark level extends to a sequence DDNA → DmRNA → DtRNA → DAA of horizontal pairings analogous to projections is fundamental one. Codon-codon pairings are realized via dark photon triplet resonance and mRNA-AA pairing by resonant coupling to the sum fXYZ=f1+f2+f3 of 3-chord frequencies: the codons coding same AA would have frequencies fXYZ differing only by a multiple of octave. One might perhaps say that AA sequence defines melody and mRNA sequence the accompaniment.

There is context dependence and homonymies already in DmRNA-DtRNA pairing and due the fact that DtRNA corresponds to a 2-harmony which is sub-harmony of 3-harmony and can be chosen in 3 different manners. The vertical pairings DDNA → DNA, DmRNA → mRNA, etc. also mediated by frequency couplings induce ordinary genetic code and horizontal pairings in DNA → mRNA → tRNA → AA. DAA → AA pairing dictates mRNA → AA pairing and mRNA → tRNA homonymy does not matter and actually makes the translation safer by increasing the number of tRNAs performing the same task.

The rather rare homonymies in DNA-AA pairing can be understood as accidental degeneracies. AA couples resonantly to the sum fXYZ=f1+f2+f2 of frequencies associated with codon XYZ and it can occur that the sum frequencies can be identical for two codons.

See the chapter Homonymy of the genetic code from TGD point of view or the article with the same title.



About the Correspondence of Dark Nuclear Genetic Code and Ordinary Genetic Code

The idea about the realization of genetic code in terms of dark proton sequences giving rise to dark nuclei is one of the key ideas of TGD inspired quantum biology (see this). This vision was inspired by the totally unexpected observation that the states of three dark protons (or quarks) can be classified to 4 classes in which the number of states are same as those of DNA, RNA, tRNA, and amino-acids. Even more, it is possible to identify genetic code as a natural correspondence between the dark counterparts of DNA/RNA codons and dark amino-acids and the numbers of DNAs/RNAs coding given amino-acid are same as in the vertebrate code. What is new is that the dark codons do not reduce to ordered products of letters.

During years I have considered several alternatives for the representations of genetic code. For instance, one can consider the possibility that the letters of the genetic code correspond to the four spin-isospin states of nucleon or quark or for spin states of electron pair. Ordering of the letters as states is required and this is problematic from the point of view of tensor product unless the ordering reflects spatial ordering for the positions of particles representing the letters. One representation in terms of 3-chords formed by 3-photon states formed from dark photons emerges from the model of music harmony (see this). By octave equivalence the ordering of the notes is not needed.

Insights

The above observations inspire several speculative insights.

  1. The emergence of dark nuclei identified as dark proton sequences would relate to Pollack's effect in which irradiation of water generates in presence of gel phase bounding the water what Pollack calls exclusion zones (EZs). EZs are negatively charged and water has effective stoichiometry H1.5O. EZs deserve their name: somehow they manage to get rid of various impurities: this might be very important if EZs serve as regions carrying biologically important information. The protons of water molecules must go somewhere and the proposal is that they go to the magnetic body of some system consisting of flux tubes. The flux tubes contain the dark protons as sequences identifiable as dark nuclei.
  2. Since nuclear physics precedes chemistry, one can argue that prebiotic life is based on these dark biomolecules serving as a template for ordinary biomolecules. To some degree biochemistry would be shadow dynamics and dark dynamics would be extremely simple as compared to the biochemistry induced by it. In particular, DNA replication, transcription, and translation would be induced by their dark variants. One can even extend this vision: perhaps also ordinary nuclear physics and its scaled up counterpart explaining "cold fusion" are parts of evolutionary hierarchy of nuclear physics in various scales.
  3. Nature could have a kind of R&D lab allowing to test various new candidates for genes by using transcription and translation at the level of dark counterparts of the ordinary basic biomolecules.
Conditions on the model

The model must satisfy stringent conditions.

  1. Both the basis A, T, C, G and A, U, C, G as basic chemical building bricks of RNA and DNA must have emerged without the help of enzymes and ribozymes. It is known that the biochemical pathway known as pentose-phosphate pathway generates both ribose and ribose-5-phosphate defining the basic building brick of RNA. In DNA ribose is replaced with de-oxiribose obtained by removing one oxygen.

    Pyrimidines U, T and C having single aromatic ring are are reported by NASA to be generated under outer space conditions (see this). Carell et al have identified a mechanism leading to the generation of purines A and G, which besides pyrimidines C,T (U) are the basic building bricks of DNA and RNA. The crucial step is to make the solution involved slightly acidic by adding protons. TGD inspired model for the mechanism involves dark protons (see this).

    Basic amino-acids are generated in the Miller-Urey type experiments. Also nucleobases have been genererated in Miller-Urey type experiments.

    Therefore the basic building bricks can emerge without help of enzymes and ribozymes so that the presence of dark nuclei could lead to the emergence of the basic biopolymers and tRNA.

  2. Genetic code as a correspondence between RNA and corresponding dark proton sequences must emerge. Same true for DNA and also amino-acids and their dark counterparts. The basic idea is that metabolic energy transfer between biomolecules and their dark variants must be possible. This requires transitions with same transition energies so that resonance becomes possible. This is also essential for the pairing of DNA and dark DNA and also for the pairing of say dark DNA and dark RNA. The resonance condition could explain why just the known basic biomolecules are selected from a huge variety of candidates possible in ordinary biochemistry and there would be no need to assume that life as we know it emerges as a random accident.
  3. Metabolic energy transfer between molecules and their dark variants must be possible by resonance condition. The dark nuclear energy scale associated with biomolecule could correspond to the metabolic energy scale of .5 eV. This condition fixes the model to a high extent but also other dark nuclear scales with their own metabolic energy quanta are possible.
Vision

The basic problem in the understanding of the prebiotic evolution is how DNA, RNA, amino-acids and tRNA and perhaps even cell membrane and microtubules . The individual nucleotides and amino-acids emerge without the help of enzymes or ribozymes but the mystery is how their polymers emerged. If the dark variants of these molecules served as templates for their generation one avoids this hen-and-egg problem. The problem how just the biomolecules were picked up from a huge variety of candidates allowed by chemistry could be solved by the resonance condition making possible metabolic energy transfer between biomolecules and dark nuclei.

Simple scaling argument shows that the assumption that ordinary genetic code corresponds to heff/h=n=218 and therefore to the p-adic length scale L(141)≈ .3 nm corresponding to the distance between DNA and RNA bases predicts that the scale of dark nuclear excitation energies is .5 eV, the nominal value of metabolic energy quantum. This extends and modifies the vision about how prebiotic evolution led via RNA era to the recent biology. Unidentified infrared bands (UIBs) from interstellar space identified in terms of transition energies of dark nuclear physics support this vision and one can compre it to PAH world hypothesis.

p-Adic length scale hypothesis and thermodynamical considerations lead to ask whether cell membrane and microtubules could correspond to 2-D analogs of RNA strands associated with dark RNA codons forming lattice like structures. Thermal constraints allow cell membrane of thickness about 5 nm as a realization of k=149 level with n= 222 in terms of lipids as analogs of RNA codons. Metabolic energy quantum is predicted to be .04 eV, which corresponds to membrane potential. The thickness of neuronal membrane in the range 8-10 nm and could correspond to k=151 and n=223 in accordance with the idea that it corresponds to higher level in the cellular evolution reflecting that of dark nuclear physics.

Also microtubules could correspond to k=151 realization for which metabolic energy quantum is .02 eV slightly below thermal energy at room temperature: this could relate to the inherent instability of microtubules. Also a proposal for how microtubules could realize genetic code with the 2 conformations of tubulin dimers and 32 charges associated with ATP and ADP accompanying the dimer thus realizing the analogs of 64 analogs of RNA codons is made.

See the chapter About the Correspondence of Dark Nuclear Genetic Code and Ordinary Genetic Code or the article with the same title.



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