DNA Decipher Journal | May 2018 | Volume 8 | Issue 1 | pp. 56-73 56

Pitkänen, M., On the Correspondence of Dark Nuclear Genetic Code & Ordinary Genetic Code

Exploration

On the Correspondence of Dark Nuclear Genetic Code & Ordinary
Genetic Code

Matti Pitkänen 1

Abstract

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. The energy quantum of ordinary Josephson radiation is below the thermal
energy for photons but the notion of generalized Josephson junction saves the situation. For massive
particles associated with flux tubes the thermal energy T/2 is below the potential energy defined
by action potential and that of metabolic energy quantum. 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.

Keywords: DNA, RNA, genetic code, dark, ordinary, prebiotic evolution.

1 Introduction

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 [24]. 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 [24]. What is new is that the dark codons do not reduce to ordered
products of letters.

1Correspondence: Matti Pitkänen http://tgdtheory.com/. Address: Rinnekatu 2-4 A8, 03620, Karkkila, Finland. Email:
matpitka6@gamail.com.

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Pitkänen, M., On the Correspondence of Dark Nuclear Genetic Code & Ordinary Genetic Code

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 [22]. By
octave equivalence the ordering of the notes is not needed.

1.1 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.

1.2 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 (see http://tinyurl.com/y9akkwok) 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 with single aromatic ring are are reported by NASA to be generated
under outer space conditions (see http://tinyurl.com/y7sh9zk4). Carell et al [3] (see http:

//tinyurl.com/z65kpyo) have identified a mechanism leading to the generation of purines A and
G, which besides pyrimidines A,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 [25] [8].

Basic amino-acids are generated in the Miller-Urey type experiments (see http://tinyurl.com/

4q2arv). Also nucleobases have been genererated in Miller-Urey type experiments [4].

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.

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http://tinyurl.com/y9akkwok
http://tinyurl.com/y7sh9zk4
http://tinyurl.com/z65kpyo
http://tinyurl.com/z65kpyo
http://tinyurl.com/4q2arv
http://tinyurl.com/4q2arv


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Pitkänen, M., On the Correspondence of Dark Nuclear Genetic Code & Ordinary Genetic Code

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

1.3 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 rather near to action potential .05 eV. 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. The
energy quantum of ordinary Josephson radiation is below the thermal energy for photons but the notion
of generalized Josephson junction saves the situation. For massive particles associated with flux tubes
the thermal energy T/2 is below the potential energy defined by action potential and that of metabolic
energy quantum.

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.

2 A model for dark nuclei as dark DNA

To make progress one must construct a concrete model for the dark nuclei. The basic idea [23] is that
cylindrical variants of EZs discovered by Pollack [2] give rise to the dark counterparts of DNA, RNA, and

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Pitkänen, M., On the Correspondence of Dark Nuclear Genetic Code & Ordinary Genetic Code

amino-acids as dark proton sequences. tRNAs would be analogs of tritium and 3He.

2.1 Option I

Consider first the option, which I christen as Option I.

1. The TGD based model leads to the proposal for a formation of this kind of dark nuclear strings
such that the distance between protons is rather precisely electron Compton length Le ' .4×10−12

meters explains ”cold fusion” in terms of dark nucleosynthesis which should have preceded ordinary
nucleosynthesis by heating the material to the temperature required by it [27] [19].

Dark nucleosynthesis would have produced part of heavier nuclei outside stars. The binding energy
scale for dark nuclear physics would be scaled down like 1/length and 2.6 MeV binding energy per
nucleon for 3He of the ordinary nuclei would be scaled down by a factor 2−11 to 1.3 keV. Note
however that it is excitation energies of order 1 MeV what matters and would scale down to .5 keV.
This level does not yet correspond to biology as we know it but could be one step in the evolutionary
hierarchy leading from nuclear physics also based on nuclear strings to biology involving increase
of Planck constant heff/h = n identifiably as the dimension of algebraic extension of rationals
characterizing the complexity of the dynamics.

2. These dark nuclei have heff/h = n = 211 (or near to it) and cannot be those responsible for the
dark variants of biomolecules since the distances of dark protons given by electron Compton length
are much smaller than the distance between DNA nucleotides about .34 nm, which is roughly 142
times the electron Compton length 2.4× 10−3 nm.

A scaling of n by 27 would give L(141) = .3 nm scale to be compared with .34 nm so that the
p-adic length scale Le(k) would correspond to p-adic length scale L(k) with k = 141. The value
heff/h = n = 218 predicts nearly correct distance between nucleotides. The excitation energy scale
about 1 MeV would scale down to .5 eV, which corresponds to the nominal value of the metabolic
energy quantum and the bond energy of hydrogen bond.

Remark: The p-adic length scale associated with a system is defined to be L(k) if the size of the
system is in the half open interval [L(k), L(k+1)). One can also consider the possibility that p-adic
length scale corresponds to the upper end of [L(k − 1), L(k)).

3. The negative charge of DNA and RNA assignable to one oxygen of phosphate combining with ribose
and DNA/RNA base could come from the tubular EZ formed in the formation of DNA. The negative
charge of phosphates and the positive charge of dark protons could guarantee the stability of pairs
of dark proton sequences and ordinary RNA and DNA.

(a) DNA strand has radius of R = 1 nm. Le(141) = .3 nm is considerably shorter than R. The
Debye length RD of DNA gives rough idea about the scale above which the negative charge
of DNA nucleotides associated with the phosphates screened. RD should be longer than R:
otherwise it is possible to speak about charge of DNA only atomic length scales. One should
have RD > R: otherwise it does not make sense to assign negative DNA charge except in
atomic length scales. Le(141) < R requires that the dark codons are pancake like structures.

Remark: The rough estimates depend on how one identifies p-adic length scale. For the
identification as L(k) =

√
5Le(k) motivated by the mass formula for electron, one would have

L(k) =
√

5Le(k) giving L(141) = 0.67 nm. With this interpretation the estimate for the
screening radius would be still shorter than R.

(b) Pancake structure suggests that the dark codons are separate horizontal units of dark quarks
having length about 3Le(141) = .9 nm, which is still slightly shorter than R. A possible
solution of the problem is that dark codons correspond to flux tube loops at the magnetic

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Pitkänen, M., On the Correspondence of Dark Nuclear Genetic Code & Ordinary Genetic Code

body of DNA codon carrying three quarks. In this case the transversal size scale of dark codon
could be much longer. This kind of flux loops are assigned also with the ordinary nuclei.

Remark: Scaled up hadron physics would be associated with flux tubes of the magnetic body of the
codon at which one would have nucleons as 3-quark color singlets. I have already earlier proposed
that scaled variants of hadron physics [9] appear in TGD inspired biology. One motivation comes
from honeybee dance [1]!

4. What could force the decomposition to 3 dark proton units in 1-1 correspondence with the codons?
Pancake model suggest that dark nucleus consisting in a well-defined sense of dark nuclei represented
as nuclear strings, which are 3-proton analogs of tritium and 3He and protons themselves contain
dark quarks at horizontal flux loops. Many-sheeted space-time allows to consider this possibility
and I have considered this already in the original nuclear string model for ordinary nuclei: in this
case 4He with very large binding energy could define one this kind of sub-units. Dark codons as
genuine dynamical units would make natural the correspondence with ordinary codons.

The pairing dark amino-acids with positive charge with ordinary amino-acids might lead to problems
since 16 amino-acids are neutral. The only charged amino-acid residues are Lys (+), Arg (+), Asp (-)
and Glu (-).

1. The formation mechanism for dark proton sequences gives for dark amino-acids a large positive
charge. Amino-acids are however not accompanied by negatively charged phosphate ions. Does
charge neutrality require that the dark bonds between dark proton has negative charge so that one
has effectively neutron?

Dark weak interactions correspond to large value of n [27] so that in DNA length scale their proceed
as fast as electromagnetic interactions (weak bosons would behave like massless particles below
scaled up weak scale). This could make possible β decays changing the charges of the bonds
between dark protons or dark neutrons [27] and lead to a stability by β emission.

2. Proteins in water environment have a charge due to protons or electrons attaching to them. This
charge depends on pH and becomes negative above certain critical pH. One might think that the
limit of very large pH (no protons) corresponds to the situation in which the electrons of EZ attach
to amino-acids.

Dark codons do not have decomposition to letters whereas ordinary codons have. In a well-defined
sense one could say that dark code is holistic whereas the ordinary code is reductionistic.

1. This brings in mind western written language in which words decompose to letters. In some east-
ern languages the symbols of written language correspond to entire words. Do these differences
correspond at deeper level to ordinary and dark genes. Could the analytic and holistic aspects of
cognition relate to the differences between ordinary and dark code.

2. One cannot exclude the entanglement between codons and evolution as emergence of entanglement
even suggests this. Could this kind of entanglement give rise to basic units of DNA, in particular
genes and introns. Could the decomposition of gene into coding regions and introns could correspond
to a decomposition to unentangled products of internally entangled pieces. This would increase
exponentially the degrees of freedom involved and explain why organisms with practically the same
code can be at so different evolutionary levels. In the splicing process when intronic portions are cut
out from DNA sequence. Do the remaining pieces of RNA get entangled or does the decomposition
of dark RNA to unentangled pieces have some meaning? Note that also ordinary RNA would be
entangled or entangled. Could introns provide the means for decomposing the coding RNA to
unentangled pieces.

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Pitkänen, M., On the Correspondence of Dark Nuclear Genetic Code & Ordinary Genetic Code

3. The most natural possibility is that entanglement contains superposition of codon sequences in which
each sequence codes for the same amino-acid. The chemical codons appearing in the superposition
have different masses and chemical properties but in zero energy ontology (ZEO) this is possible.
Situation would be like for a superconductor in which coherent state means superposition of states
with different numbers of Cooper pairs and thus different fermion number in standard ontology but
in ZEO this problem disappears.

2.2 Option II

Option I is not exact scaling up of nuclear physics since entangled 3-proton states are basic units: this is
not the case in ordinary nuclear physics. Also neutrons are absent.

Could one have direct correspondence of nucleon states with the letters A, T, C, G so that the letters
of the codon would not entangle? Their ordering would be however important.

For Option II this is possible: nucleon has two spin states and two isotopic spin states in one-one
correspondence with A, T, C, G in suitable order. This kind of correspondence between spin-isospin
states of quarks and A, T, C, G was actually the original proposal discussed in [7]. This would give rise
to a realization of genetic code at the level of letters.

1. Could dark nuclei be formed as a pile of unentangled dark nucleons with size scale of order L(141)
and with vertical distance equal to that between RNA bases. For DNA and RNA would have dark
proton sequences. For amino-acids, which are not always charged one would have also neutrons.
This does not conform with the idea that Pollack effect is involved.

2. Now roughly one half of the dark letters are neutral so that RNA and DNA would have negative
charge, which is one half of its charge in the scale Le(141). The TGD view about nuclear strings
could come in rescue here [12]. The bonds between nuclei correspond to flux tubes with charge 0,
+1, or -1. Ordinary nuclear physics do not predict them but TGD does. If the dark neutrons are
connected to the next nucleon by a flux tube with charge +1, charge neutrality is achieved without
losing the identity of nucleon as neutron.

3. The mechanism generating EZs favors dark proton sequences and the negative charge associated
with phosphates could stabilize these sequences: this favors Option I.

4. There is also now a difference to ordinary nuclear physics in that in ordinary nuclear physics the
order of letters formed by the spin states of p and n is not believed to matter. Now it matters and
would be essential for the genetic code: if the order does not matter, one has only four codons!
One can however ask whether the ordering of ordinary nuclear strings is actually matters but our
measurement technology is not able to distinguish between the different orderings of nucleons. For
instance, the energies of different nucleon orderings could be very nearly the same.

5. The correspondence of the letters of genetic code with dark nucleon states is natural for unentangled
code. If the dark nucleons of the codon are allowed to entangle as the idea about evolution as
generation of entanglement suggests, one obtains more complex structures than for dark protons.

For codons formed from dark protons only 8 codons are possible. Also it seems that if dark code
with unentangled letters existed, its evolution to a code with entangled letters is not plausible
since it would suggest that the generation of entanglement induced also the entangled of the letters
A,T,C,G of the ordinary code. This view is in conflict with the physical intuition. It would seem
that ordinary DNA codons must be just product states of their letters and entangle as a whole to
dark codons.

Some concluding remarks are in order.

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Pitkänen, M., On the Correspondence of Dark Nuclear Genetic Code & Ordinary Genetic Code

1. Option II predicts only genetic codons but not the difference between DNA, RNA, amino-acids and
tRNA like Option I. Neither does it predict genetic code as the mapping of codons to amino-acids.
Thus Option II does not look promising. The idea about the evolution of genetic code is however
too attractive to be given up.

Perhaps ordinary nuclear physics and n = 211 dark counterpart correspond to steps in the evolution
for which the codons had 1 and 2 letters, perhaps entangled for 2-letter code. The 4 letters could
have been spin states of nucleons for ordinary nuclear physics. At this level one cannot speak about
DNA, RNA, tRNA, and amino-acids. One can also imagine entanglement of the letters of 2-letter
codon: maybe this could emerge at n = 211 level. At this level one could have simple analogs of the
basic biomolecules. Codons would be dark proton analogs of deuterium.

2. The fact that DNA has forms a coil of thickness about Le(151) = 10 nm suggests that also higher p-
adic length scales and maybe even higher level dark nuclear physics are involved. Also the thickness
of neuronal membrane has upper bound Le(151) to be contrasted with the thickness of ordinary
cell membrane given by Le(149) = Le(151)/2.

3. Genetic code could have emerged from a simpler code [10]. If only dark protons are allowed, the
unentangled product states would have only two letters giving rise to 8 codons if 3 dark protons
serve as a unit. I have proposed that 2-letter and 1-letter codes preceded the 3-letter code and fused
to 3-letter code. 2-letter code would have had 4 unentangled codons and 1-letter code 2 unentangled
codons.

3 TGD view about the emergence of chemical life

Consider first the basic assumptions.

1. Dark DNA, RNA,... emerged before chemistry and serve as templates for ordinary DNA, RNA,...
The replication, transcription, and translation for ordinary DNA, RNA,... are induced by the
corresponding processes for their dark counterparts.

2. Dark proton sequences are associated with tubular EZs in water generated by Pollack effect.

3. The amount of entanglement measured by entanglement negentropy (having a well-defined meaning
in adelic physics [29]) is expected to increase gradually during evolution. Hence one expects gener-
ation of more and more entangled sequences of dark nucleons. At the bottom - perhaps ordinary
nuclear physics - one would have the product states of dark nucleons. Perhaps dark nuclear physics
with n = 211 came next. After that came n = 218 dark nuclear physics. But which came first: dark
variants amino-acids, tRNA, RNA, or DNA and their chemical counterparts? And could one see
even genes as entangled codon sequences coding for the same protein?

3.1 The quantum vision about the prebiotic evolution

The following vision about quantal prebiotic evolution beginning from amino-acids suggests itself. The
basic idea is that all processes took place at dark level and induced the processes for ordinary biomolecules
in water environment. Even the enzyme and ribozyme actions essential in recent biology would be replaced
with corresponding actions at dark level and biochemistry would reduce to shadow dynamics.

1. Amino-acids are easiest to produce (as Miller-Urey experiment demonstrated (see http://tinyurl.
com/4q2arv)) requiring no enzymatic action and there is just single chemical amino-acid per dark
RNAs coding for it. Therefore the pairs of amino-acids and their dark variants could have emerged
first. Note that proteins were not yet present.

Remark: Vivo-vitro difference could mean that dark partner of biomolecule is present in vivo and
missing in vitro.

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2. DNA requires cell membrane. This requires RNA emerged after amino-acids. This implies that dark
variants of dark tRNA, their pairing with tRNA and the pairing of dark RNA with RNA emerged
next?

This picture supports that the old TGD inspired idea about the role of tRNA during RNA era.
Dark tRNA would have made possible the replication of dark RNA sequences (rather than the
translation of RNA to amino-acid sequence) during this era. The dark amino-acid of dark tRNA
would have served as a catalyst inducing the addition of dark RNA codon to the growing RNA
sequence. No chemical transcription machinery nor DNA was needed at this stage. This would
solve one hen-or-egg problem.

3. After that a revolution would have occurred. For some reason dark amino-acids began to attach
to the growing sequence of amino-acids and dark RNA codon was left alone. What prevented dark
RNA codon to attach to the growing dark RNA sequence? Was it the emerging entanglement
between dark codons giving rise to genes as entangled pieces of DNA that made this impossible.

This means entanglement also between the ordinary codons, which makes sense only in ZEO. If
possible at all this entanglement should respect genetic code so that entangled superposition would
involve only codons coding for the same amino-acid so that the translation to a single amino-acid
sequence rather than their quantum superposition is possible. If more general superpositions are
allowed the translation process would be like state function reduction to amino-acid sequence.

4. At this step the replication of both dark and ordinary RNA was lost and it seems that dark DNA-
DNA pairs replicating dark DNA and transcribing it to dark RNA and inducing corresponding
process at the level of chemistry must have emerged at the same time.

The emergence of DNA requires also the emergence of cell membrane. Could the emergence of cell
membrane relate to the emergence of dark nuclei in the p-adic length scale L(k), k = 151 and could
the double layered structure of cell membrane serve as an analog for that of DNA double strand?
Could lipid layers correspond to 2-D analogs of DNA strand with lipids taking the role of codons?

5. Could the full genetic code emerged in step-wise manner as proposed earlier [7, 16]? Genetic code
can be seen in a good approximation as a fusion of 16-letter code and 4-letter code. This might
be understood if the entanglement of dark codons emerges first as entanglement of only two first
letters.

What gave rise to the correspondences between dark DNA, RNA, tRNA, amino-acids and their dark
variants? How the amino-acids and nucleotide bases were selected?

1. The basic principle would be the condition that metabolic energy can be transferred between chemi-
cal and dark levels. This is possible if there identical transition energies in the spectra of biomolecules
and their dark variants making possible resonance.

2. Metabolic energy quantum in the range .4-.5 eV could correspond to the energy scale of dark k=141
nuclear physics if 1 MeV is taken as the estimate for a typical nuclear binding energy. Hydrogen
bonds also corresponds to this energy scale but this might be just what is needed to give rise to
coherent metabolic activity.

To sum up: for DNA,RNA, and tRNA the emergence of entanglement would have created the chemical
counterparts of quantum superpositions: ZEO is necessary since in positive energy ontology superpositions
are highly implausible.

There are some questions to ponder.

1. Why the decomposition into triplets? Does resonance condition for the metabolic energy transfer
select triplets as basic units and also the RNA-amino-acid correspondence? Do also intronic regions
have triplets as basic units?

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One ends up to a prediction of vertebrate genetic code also from a model of music harmony [22]. In
fact, the model explains also its slight variation and the 2 additional amino-acids. Could this help
to understand why the triplet code is so unique.

2. Could one imagine that also quarks and antiquarks were involved? Could dark nucleon pair with
dark quark with same spin and isospin and color confinement forces dark proton triplets? Dark
quarks indeed define a representation for A,T,C, G. In the model of topological computation [7, 16].
I have actually speculated with the possibility that dark quarks and antiquarks are paired with
ordinary DNA codons.

3. Could dark conjugate protons or their triplets of parallel dark DNA strands form Cooper pairs or
does pairing of dark protons triplets (their conjugates) with dark quarks (anti-quarks) give rise to
bosonic states?

3.2 Unidentified Infrared Bands as a test for the proposal

Unidentified Infrared Bands (UIBs) are an ill-understood phenomenon associated with radiation coming
from interstellar space. There are also other analogous phenomena having no explanation in terms of
molecular transitions [5] and one can ask whether they could be seen as signatures of dark nuclear physics.

1. UIBs are observed around bands around IR energies E ∈ {.11, .20, .375} eV.

2. Poly-aromatic hydrocarbons (PAHs) (see http://tinyurl.com/atx4t9a) are known to generate
UIBs [5]. Therefore the UIBs from interstellar space could originate from PAHs.

3.2.1 TGD based models for UIBs

TGD suggests several explanations for UIBs involving new physics related to the p-adic length scale
hypothesis and heff/h = n hierarchy.

1. For years ago I discussed a model for UIBs based on p-adic length scale hypothesis [5]. The idea
was that protons ”drop” from atomic space-time sheet with k = 137 to a larger space-time sheet to
k1 > 137 space-time sheet and the difference of zero point kinetic energies is liberated as radiation
[5]. The proposal was that the zero point kinetic energies give rise to a hierarchy of metabolic energy
quanta.

Second possibility is phase transition in which the size of the k = 137 space-time sheet increases
to k1 > 137 and liberates the difference of zero point kinetic energy. For the third option energy
preserving phase transition increasing heff/h = n by a factor (k1 − k)/2 followed by a phase
transition reducing the value of heff back to the initial one but without change of the size of the
space-time sheet would liberate the difference of zero point kinetic energies.

2. Also dark nuclear transitions could explain UIBs. For k = 141 as the p-adic length scale of DNA
letters would give nuclear energy scale E = .5 eV equal to the metabolic energy quantum by scaling
1 MeV for the ordinary nuclei. This is too high an energy but there are of course also smaller
energies possible for the nuclear excitations possibly explaining the UIBs.

The challenge is to explain not only the presence of these separate bands but also the band structure.
Local wave functions for dark protons are localized in scale of .34 nm (DNA). Estimate for the energy
scale associated with local excitations is obtained from particle in box model. The scale of these
excitations is roughly (L(137)/L(141))2 = 2−4. These excitations could be generated thermally.

3. What about hydrogen bonds? The strength of hydrogen bond - essentially the bond energy - is in
the range .4-.5 eV -, which as such does not correspond to the average UIB energy, which come

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approximately as three lowest powers of two. The range of bond energies is .1 eV is smaller than
the smallest UIB energy .11 eV.

UIBs can be associated with hydrogen bonds if there are states of bond with higher bond energy.
They could correspond to higher values of n = heff/h for the de-localized dark proton associated
with the bond (analogous to de-localized valence electron). For instance, if the energy of the bond
corresponds to the cyclotron energy of proton in a magnetic field associated with the bond, it is
proportional to n.

The photon energies come approximately as powers of 2. If the favored values of n are in bands
around n = 2k favored by the p-adic length scale hypothesis, one has hopes of understanding the
band structure in terms of transitions reducing the value of k.

Membrane potential (see http://tinyurl.com/chylvs9) plays a key role in metabolism and one can
wonder whether UIBs might relate to the potential energies defining energies EJ = ZeV of Josephson
photons associated with membrane if it acts like Josephson junction like structures associated with the
prebiotic lifeforms.

1. Membrane potential energy varies in the range (.04, .08) eV (cell interior is negatively charged).
Excitable cells (able to generate action potentials) include neurons, muscle cells, endocrine cells,
and some plant cells. The average value for them is around .06 eV and further depolarization makes
these cell more excitable. This suggests that the instability is caused by thermal radiation with
nearly the same energy. The threshold for the generation of the action potential Eact is in the range
(.050, .055) eV. Interestingly, during ageing neurons become more hyperpolarized and therefore less
excitable. In photoreceptors the resting potential energy can be as low as .03 eV making them very
sensitive to light.

2. In TGD inspired quantum biology axonal membrane can be seen as a generalized Josephson junction
[13, 14, 15] decomposing nanoscopically to Josephson junctions defined by cell membrane proteins.
The protein as junction would correspond to a magnetic flux tube along which various charged
particles with heff = n × h flow possibly as supra currents. As a special case cell membrane acts
like an ordinary Josephson junction. In this case the increment of the electrostatic energy of the
Cooper pair over membrane given by EJ = 2eV defines the energy of the smallest quantum of
Josephson radiation.

The intensity of thermal radiation at temperature T as function of photon energy E has a peak at
E ' 3T , which for room temperature about T = .03 eV gives Emax = .09 eV. The energy ZeV of
Cooper pair should be larger than Emax. For critical action potential one has Eact = 0.1 eV, which
is slightly above Emax = .09 eV so that the action potential has minimal value and thus minimizes
metabolic energy costs and implies quantum criticality with temperature as a critical parameter.

Note however that for energies below Emax the intensity of thermal radiation decreases so that also
these energies might serve as Josephson energies: this and the fact that incoming photons have
intensity higher than termal background at this energy could explain why some photoreceptors can
have eV = .03 eV.

3. Could also Josephson radiation relate to UIBs? The Josephson energy of Cooper pair for the
membrane potential is around EJ = 0.1 eV, which corresponds to the lowest UIB band, which
could thus correspond to action potential .05 eV of excitable membrane. The higher bands would
correspond roughly to two octaves suggesting that the action potentials in these case are roughly
.1 eV and .2 eV. Quantum criticality would suggest that temperatures scale like the energies of the
bands slightly higher than Emax ' 3T .

Metabolic energy transfer between magnetic body and biological body (defined in very general sense for
any system) is possible if the spectra of transition energies share common transition energies. Therefore

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the spectrum of transition energies assignable to hydrogen bonds could have many transition energies
common with that assignable to dark nuclear transitions and second and third explanation could be
consistent with each other.

3.2.2 Model for hydrogen bond

The explanations of UIBs in terms of hydrogen bonds encourages to consider a concrete model for the
hydrogen bond as flux tube. This suggests a connection with metabolism at cellular level involving
transfer of protons through cell membrane against potential gradient assumed to take place as dark
protons carrying the metabolic energy and providing it to ADP-ATP process after their return.

1. The simplest model for the proton inside flux tube is as particle in 1-D flux tube with magnetic
field. Unless the magnetic field strength and/or n is very large, the kinetic energy in the direction of
flux tube dominates and phase transition would change the scale of kinetic energy proportional to
n2 for fixed flux tube length. For n = 2k this would give too strong dependence of photon energies
on k.

2. On the other hand, if the flux tubes are flux loops of the magnetic body of molecule their lengths
naturally scale as n and the longitudinal kinetic energy is not affected in the transition. The
cyclotron energy proportional to n would change and for n ∼ 2k one obtains qualitatively correct
behavior.

For proton in magnetic field of Bend = .2 Gauss the cyclotron frequency is 300 Hz and corresponds to
Ec(Bend) = 1.2× 10−12 eV. The identification of Ec(B) = .5 eVs would give Ec(B) = n(B/Bend)×
Ec(Bend) = Ec(B) = .5 eV. An estimate for B for the flux tube of hydrogen bond comes from flux
quantization: eBS = 1 holds true for unit quantum of flux and for flux tube radius of one Angstrom
this would give B/Bend ∼ 5 × 108. This gives the estimate n ∼ 108 ∼ 227. The rather large value
conforms with the general vision for the values of n for dark protons whereas dark electrons of
valence bonds would have much smaller values. The emergence of dark protons could be seen as the
transition from chemistry already involving n as characterizer of valence bonds [28] to bio-chemistry.

3. The identification of the metabolic energy quantum in terms of cyclotron energy could apply also
in the case of cellular metabolism. The model for the generation of ATP from ADP assumes that
protons are pumped by the energy coming from nutrient molecules against the membrane potential.

The membrane potential correspond to energy of .05 eV but metabolic energy quantum is 10 times
larger. This looks like an inconsistency, which in thermodynamical approach is resolved by intro-
ducing of chemical potentials. In genuine quantum approach the introduction of thermodynamics
quantities is not allowed.

The general vision about metabolic energy as a tool to increase heff/h = n defining kind of molecular
IQ suggests that the transformation to dark proton at magnetic flux tube along which proton can
travel through the membrane is responsible for the most of the energy needed for pumping. After
the dark proton has returned through cell membrane it transforms to ordinary proton and liberates
the metabolic energy and makes possible ADP-APT transformation.

The above model assumes that the lengths of hydrogen bonds as flux loops scale like n. This makes
possible the reconnection of flux loops coming from opposite sides of the membrane to pair of flux
tubes along which dark protons can flow. Similar picture applies also to other biologically important
ions.

The general view about superconductivity in TGD Universe [13, 14] suggests that reconnection can
give rise to a Cooper pairs of protons with members at separate flux tubes. Also Cooper pairs of
electrons and biologically important ions could form by the same mechanism.

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3.3 PAH world hypothesis from TGD point of view

The so called PAH world hypothesis (see http://tinyurl.com/ycxm9zes) has been proposed as a pre-
biotic era preceding RNA world. As a matter of fact, PAH world hypothesis inspired more a detailed
development of TGD based model for dark nuclei.

Let us first list some properties of poly-aromatic hydrocarbons (PAHs) (see http://tinyurl.com/

atx4t9a).

1. PAHS consist of aromatic rings glued together along sides. By definition aromatic rings have
delocalized electrons. In benzene, which is the classical and simplest example of PAH, the electronic
state is quantum superposition of states in which bonds and double bonds alternate along the ring
but are shifted by 60 degrees with respect to each other. Naphtalene has two aromatic rings and
anthracene and pnenanthtrene have 3 rings.

2. PAHs are very stable non-charged non-polar molecules and are very common in Earth. They are
found in coal and tar deposits and produced in an incomplete combustion of organic matter. PAHs
are poisonous. For instance, tobacco smoke contains PAHs with carcinogenic effects. The stability
of PAHs motivates the belief that a large fraction of carbon in the interstellar space consists of
PAHs.

3. Benzene in difficult to detect in in the interstellar space since the rotational symmetry does not allow
to detect rotational transitions. Recently however nitrobenzene was detected so that benzene and
more complex PAHs presumably exist in interstellar space (see http://tinyurl.com/yap9ksrg).

Benzene and more complex PAHs can give rise to more complex aromatic by hydrogenation, oxidation,
carboxylation, and nitrogenation and led also to the basic building bricks of DNA and amino-acids and
PAHs are proposed to have played important role in prebiotic life.

1. PAH world hypothesis states that the polymer like sequences of PAHs serve as scaffoldings for the
formation of RNA like polymers (see http://tinyurl.com/ycxm9zes). The key motivation is that
the distances between PAHs are same as between RNA and DNA bases: 3.4 nm. The proposal is
that during PAH era RNA nucleosides A, U, C, G were attached to PAHs by hydrogen bonds.

2. Second hypothesis is that formaldehyde molecules [(H2C)=O] formed valence bonds with RNA
bases and with each other giving rise to sequences analogous to the phosphate-ribose backbone of
RNA. The sequence of disjoint CO=:s was replaced with the sequence ..(C-R)-O-(C-R)-O-.. with
R denoting the RNA nucleoside. After this hydrogen bonds were split and the predecessor of RNA
was detached from the PAH scaffolding. Later the pre-RNA strands were folded to form double pre-
RNA strands similar to ribozymes. The problem is to understand how the formaldehyde backbone
was replaces with more stable phosphate-ribose backbone.

In TGD framework dark nuclei would serve as scaffolding, which however does not detach from the
corresponding biomolecules. The distances between dark variants of biomolecules would explain why the
two distances are the same. Very many molecules, including PAHs, can attach around dark RNA/DNA
and the periodic structure would be reflect the properties of dark nuclei. This could explain UIBs as
emission bands of both dark nuclei and hydrogen bonds essential for the pairing and the transfer of
metabolic energy between ordinary and dark biomolecules. Also in DNA double strand hydrogen bonds
could serve similar function. If thermal radiation excites higher energy states of nuclei, the emission of
UIBs depends on temperature. Perhaps this could be tested.

UIBs could therefore serve as a direct signature of dark nuclear physics. If dark nuclei are not
associated with PAHs in vitro or in an environment not containing water, UIBs would be absent.

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4 Some reckless speculation about higher level variants of dark
genetic code

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 so attractive idea that I cannot
avoid the temptation to speculate about it and I have done it already earlier [11].

4.1 Could cell membrane correspond to dark nuclear physics for k > 141?

Cell membrane consisting of two lipid layers (see http://tinyurl.com/h9a2hsq) is 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 should be seen as analog of RNA: the counterpart of RNA era
would prevail at these levels.

Could cell membranes correspond to a fourth level in the hierarchy of nuclear physics? Or could
there be entire hierarchy coming assignable to certain p-adic length scales? One 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 double membrane in mitochondria and
2.5 µm assignable to cell nucleus: so many Gaussian Mersenne in so short length scale range is a number
theoretical miracle.

Remark: 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) - for neuronal membranes. The double cell membrane associated with mitochondria has
thickness 22 nm and corresponds to Le(153): the thickness of the two membranes is about 7 nm. This
observation allows to understand in what sense neurons and mitochondria are above ordinary cells in the
evolutionary ladder.

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?

Remark: One can argue that cell membrane - in particular neuronal membrane - is highly dynami-
cal 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.

2. Cell membrane consists of lipid bilayer. The lipid layer has three parts (see http://tinyurl.com/

h9a2hsq).

The totally hydrated layer nearest to water is hydrophilic head group, which in the case of phos-
pholipids contains negatively charged phosphate. This phosphate layer has thickness .7− 1.0 nm.

Below it is a partially hydrated layer of thickness .3 nm, which corresponds to L(141): this of course
puts bells ringing!

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.

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

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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 > 141 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 correspond to RNA replication (proposed to be
catalyzed by tRNA at RNA era). Even the analogs of tRNA and amino-acids but not proteins
should 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?

5. Both sides of the lipid bilayer would contain cylindrical lattices of dark RNA codons. In the case
of axon one could have the analog of dark RNA 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 RNA codons and dark RNA codons would code for them: this predicts
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 so that the dark nuclear physics would correspond to
k = 143 and n = 220. The number N of parallel dark RNA strands is 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.

Remark: The flux tubes connecting the dark DNA sequences above lipid layer to those associated
with DNA could make possible to realize topological quantum computation [7, 16] 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 analog of central nervous system. 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.

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 tem-
peratures suggest that scaling factors λ larger than λ = 16 in n = heff/h for n = 218 associ-
ated with DNA and RNA cannot be allowed. Single lipid layer would correspond to Le(145) =
4Le(141) = 1.25 nm and λ = 4. Single lipid layer with hydrophilic layer included corresponds to
Le(147) = 8Le(141) = 1.25 nm and λ = 8.

2. The value of heff/h = n would be n = 222 ∼ 4×106 for k = 149 and scaling factor would be λ = 16.
The value of the metabolic energy quantum is now around .04 eV whereas the action potential is
around .05 eV. As explained, in TGD Universe the cell membrane can be seen as Josephson junction
decomposing in an improved resolution to membrane proteins acting as Josephson junctions [13, 14].
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. For k = 151 the metabolic energy quantum would be scaled down to .02 eV (as noticed earlier, the
membrane potential for some photoreceptor is .03 eV). The energy at which the intensity of thermal
radiation at temperature of 300 K is Emax = .09 eV. The potential energy gain over cell membrane
for a Cooper of charged particles would be EJ = .045 eV, which is roughly one half of of the energy
of thermal photon at the maximum Emax = 3T = .09 eV of the thermal distribution. The intensity
of the thermal radiation is reduced only by a factor .69 for E = Emax/2 so that there seems to be
a real problem.

4. As far metabolic energy quantum and Josephson radiation are considered, for k = 149 membrane
would be a quantum critical system. Quantum criticality would give rise to instability making

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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.

For k = 151 Josephson energy of Cooper pair is scaled down to EJ = .045 eV considerably below
Emax = .09 eV. Does this mean that Josephson radiation cannot carry information? Or could Nature
have found the means to overcome this problem? The notion of generalized Josephson junction central
in TGD inspired theory of EEG as communications from brain to MB [15, 6] could save the situation.

1. For the generalized Josephson junction the energy of quantum of Josephson radiation is E = EJ +
∆Ec, where ∆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 [21, 20] guarantees the spectrum of cyclotron energies is uni-
versal 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 [17, 18].

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 [26] active linear neuron groups re-
late 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 [10].

4.2 Microtubules as quantum critical systems

Also microtubules (see http://tinyurl.com/y8km9vve) 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.

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

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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 gradi-
ent 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 http://tinyurl.com/ybtjluaf) resp. GDP (see http://tinyurl.com/y8uok7kq). 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.

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I have proposed that flux tubes connecting tubulins to the lipids of the axonal lipid layer could give rise
to topological quantum computation [7, 7]. 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?

References

[1] Shipman B. The geometry of momentum mappings on generalized flag manifolds, connections with
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cornell.edu/~oliver/Shipman.gif, 1998.

[2] The Fourth Phase of Water : Dr. Gerald Pollack at TEDxGuelphU. Available at: https://www.

youtube.com/watch?v=i-T7tCMUDXU, 2014.

[3] Carell T et al. A high-yielding, strictly regioselective prebiotic purine nucleoside formation pathway.
Science. Available at:http://science.sciencemag.org/content/352/6287/833, 352(6287):833–
836, 2016.

[4] Ferus M et al. Formation of nucleobases in a millerurey reducing atmosphere. PNAS.Available at:
http://tinyurl.com/kxxc7db, 2017.

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[6] Pitkänen M. Dark Matter Hierarchy and Hierarchy of EEGs. In TGD and EEG. Online book.
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[7] Pitkänen M. DNA as Topological Quantum Computer. In Genes and Memes. Online book. Available
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[8] Pitkänen M. Evolution in Many-Sheeted Space-Time. In Genes and Memes. Online book. Available
at: http://tgdtheory.fi/public_html/genememe/genememe.html#prebio, 2006.

[9] Pitkänen M. General Theory of Qualia. In Bio-Systems as Conscious Holograms. Online book.
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[10] Pitkänen M. Genes and Memes. In Genes and Memes. Online book. Available at: http:

//tgdtheory.fi/public_html/genememe/genememe.html#genememec, 2006.

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[12] Pitkänen M. Nuclear String Hypothesis. In Hyper-finite Factors and Dark Matter Hierar-
chy. Online book. Available at: http://tgdtheory.fi/public_html/neuplanck/neuplanck.html#
nuclstring, 2006.

ISSN: 2159-046X DNA Decipher Journal www.www.dnadecipher.com

Published by QuantumDream, Inc.

http://math.cornell.edu/~oliver/Shipman.gif
http://math.cornell.edu/~oliver/Shipman.gif
https://www.youtube.com/watch?v=i-T7tCMUDXU
https://www.youtube.com/watch?v=i-T7tCMUDXU
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http://tgdtheory.fi/public_html/genememe/genememe.html#dnatqc
http://tgdtheory.fi/public_html/genememe/genememe.html#prebio
http://tgdtheory.fi/public_html/hologram/hologram.html#qualia
http://tgdtheory.fi/public_html/genememe/genememe.html#genememec
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http://tgdtheory.fi/public_html/neuplanck/neuplanck.html#nuclstring


DNA Decipher Journal | May 2018 | Volume 8 | Issue 1 | pp. 56-73 73

Pitkänen, M., On the Correspondence of Dark Nuclear Genetic Code & Ordinary Genetic Code

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[14] Pitkänen M. Quantum Model for Bio-Superconductivity: II. In TGD and EEG. Online book.
Available at: http://tgdtheory.fi/public_html/tgdeeg/tgdeeg.html#biosupercondII, 2006.

[15] Pitkänen M. Quantum Model for Nerve Pulse. In TGD and EEG. Online book. Available at:
http://tgdtheory.fi/public_html/tgdeeg/tgdeeg.html#pulse, 2006.

[16] Pitkänen M. Three new physics realizations of the genetic code and the role of dark matter in bio-
systems. In Genes and Memes. Online book. Available at: http://tgdtheory.fi/public_html/

genememe/genememe.html#dnatqccodes, 2006.

[17] Pitkänen M. Are dark photons behind biophotons. In TGD based view about living matter and remote
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tgdlian.html#biophotonslian, 2013.

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//tgdtheory.fi/public_html/tgdlian/tgdlian.html#persconsc, 2013.

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[22] Pitkänen M. Geometric theory of harmony. Available at: http://tgdtheory.fi/public_htm/

articles/harmonytheory.pdf, 2014.

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//tgdtheory.fi/public_htm/articles/PollackYoutube.pdf, 2014.

[24] Pitkänen M. About Physical Representations of Genetic Code in Terms of Dark Nuclear Strings.
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[25] Pitkänen M. One step further in the understanding the origins of life. Available at: http://

tgdtheory.fi/public_htm/articles/purineorigin.pdf, 2016.

[26] Pitkänen M. Artificial Intelligence, Natural Intelligence, and TGD. Available at: http://

tgdtheory.fi/public_htm/articles/AITGD.pdf, 2017.

[27] Pitkänen M. Cold fusion, low energy nuclear reactions, or dark nuclear synthesis? Available at:
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[28] Pitkänen M. Does valence bond theory relate to the hierarchy of Planck constants? Available at:
http://tgdtheory.fi/public_htm/articles/valenceheff.pdf, 2017.

[29] Pitkänen M. Philosophy of Adelic Physics. Available at: http://tgdtheory.fi/public_htm/

articles/adelephysics.pdf, 2017.

ISSN: 2159-046X DNA Decipher Journal www.www.dnadecipher.com

Published by QuantumDream, Inc.

http://tgdtheory.fi/public_html/tgdeeg/tgdeeg.html#biosupercondI
http://tgdtheory.fi/public_html/tgdeeg/tgdeeg.html#biosupercondII
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http://tgdtheory.fi/public_htm/articles/harmonytheory.pdf
http://tgdtheory.fi/public_htm/articles/PollackYoutube.pdf
http://tgdtheory.fi/public_htm/articles/PollackYoutube.pdf
http://tgdtheory.fi/public_htm/articles/genecodemodels.pdf
http://tgdtheory.fi/public_htm/articles/purineorigin.pdf
http://tgdtheory.fi/public_htm/articles/purineorigin.pdf
http://tgdtheory.fi/public_htm/articles/AITGD.pdf
http://tgdtheory.fi/public_htm/articles/AITGD.pdf
http://tgdtheory.fi/public_htm/articles/krivit.pdf
http://tgdtheory.fi/public_htm/articles/valenceheff.pdf
http://tgdtheory.fi/public_htm/articles/adelephysics.pdf
http://tgdtheory.fi/public_htm/articles/adelephysics.pdf

	Introduction
	Insights
	Conditions on the model
	Vision

	A model for dark nuclei as dark DNA
	Option I
	Option II

	TGD view about the emergence of chemical life
	The quantum vision about the prebiotic evolution
	Unidentified Infrared Bands as a test for the proposal
	TGD based models for UIBs
	Model for hydrogen bond

	PAH world hypothesis from TGD point of view

	Some reckless speculation about higher level variants of dark genetic code
	Could cell membrane correspond to dark nuclear physics for k>141?
	Microtubules as quantum critical systems