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

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

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

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

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

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

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

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

1. States in the quark degrees of freedom

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

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

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

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

2. States in the flux tube degrees of freedom

Consider next the states in flux tube degrees of freedom.

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

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

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

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

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

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

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

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

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

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

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

4. Understanding the symmetries of the code

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

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

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

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

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

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

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

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

5. Some comments about the physics behind the code

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

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

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

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

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

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

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