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= h_eff/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 h_eff/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 M_G,k=(1+i)^k-1 for k∈{151,157,163,167} define p-adic length scale L(k)∝ 2^k/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 L_e(151)=10 nm: actually the thickness is L_e(149)=5 nm for ordinary cells and 8-10 nm - roughly L_e(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 h_eff/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 L_e(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 L_e(149)=5 nm whereas the coiling associated with the cell membrane corresponds to L_e(151). Also neurons correspond to L_e(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 L_e(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 × L_e(167)/L_e(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 h_eff since h_eff²/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 E_b(k)= 2^(k-107)/2E_b of typical dark nuclear binding energy E_b=∼ 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 E_J=0.1 eV slightly above the maximum E_max=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 E_J=.1 eV near to E_max= .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= E_J+Δ E_c, where Δ E_c is the difference of cyclotron energies at the two sides of the membrane. E_c is proportional to h_eff=n× h and large enough value of n guarantees that E_c is above E_max≈ 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. h_eff=h_gr= 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. h_eff=h_gr= GMm/v₀ hypothesis indeed allows very large values of h_eff for which ordinary cyclotron energies proportional to h_eff 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 E_cr= DT/2. One could argue that above this energy thermal masking can be avoided. For D=1 at magnetic flux tubes this would give E_cr=T/2=E_max/6. At T_phys=.03 eV one would have E_cr= 0.15 eV. Metabolic energy quantum would be above E_cr 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 L_e(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 R_tub∼ 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=h_eff/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 L_e(141) and that of tubulin about L_e(151)=32L_e(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 L_e(167)/L_e(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 updated original article About the Correspondence of Dark Nuclear Genetic Code and Ordinary Genetic Code or the shorter article About dark variants of DNA, RNA, and amino-acids .

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

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