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Year 2006



Universal mechanism of catalytic action and stability of charged polymers

The idea that dark N-H-atoms could naturally serve as names of bio-molecules, and that molecules labelled by conjugate names could play the role of lock and key in catalytic action. This would mean that the emergence of symbolic representations and "molecular sex" between conjugate named molecules distinguishes bio-chemistry from the ordinary chemistry. Below some further remarks related to this idea.

1. Basic observations

The basic observations are following.

  1. Since fine structure constant for the interactions of dark electrons with proton (and any other charge) is scaled down by 1/hbar factor the effective charge of proton plus dark N-electron system is 1-N/λk and positive except for full shell of electrons with N=λk.

  2. The fusion of N-H-atom and its conjugate must liberate proton and decay of λk-atom requires that proton is feeded to the system.

2. A universal model for a catalytic action

The previous observations lead to a detailed model for bio-catalytic action.

  1. N-hydrogen atoms have effective charge 1-N/λk for N< λkso that the binding regions of catalysts and reacting molecules should carry effective fractional surface charge which is always positive: this is a testable prediction.

  2. Catalyst in general has several names: one for each reactant molecule. Catalytic action involving the formation of reactants-catalyst complex by fusion of N-H-atoms and their conjugates necessarily involves a temporary liberation of protons, one for each letter of each name of the catalyst.
  3. The generation of λk-H-atom in the fusion of letter and conjugate letter should correlate with the formation of hydrogen bonds between catalyst and substrate.
  4. The liberated protons could drop to a larger space-time sheet and liberate metabolic energy quanta kicking the complex formed by the reacting molecules over the potential wall separating it from the outcome of the reaction. In the transition to the final state the surplus energy would be liberated and kick a protons back to the original space-time sheet and λk-atom would decay to N-atom and its conjugate. Also metabolism could kick the dropped protons back to the system so that the catalyst would not be stuck to the product of the reaction.

3. How to understand the stability of charged bio-polymers?

The fact that the names of bio-molecules carry positive effective charge relates in an interesting manner to the problem of how charged bio-polymers can be stable (I am grateful for Dale Trenary for pointing me the problem and for interesting discussions). For instance, DNA carries a charge of -2 units per nucleotide due to the phosphate backbone. The models trying to explain the stability involve effective binding of counter ions to the polyelectrolyte so that the resulting system has a lower charge density.

The simulations of DNA condensation by Stevens however predict that counter ion charge should satisfy z> 2 in the case of DNA. The problem is of course that protons with z=1 are the natural counter ions. The positive surface charge defined by the dark N-H-atoms attached to the nucleotides of DNA strand could explain the stability. In the case of DNA double strand the combination of names and conjugate names liberates one proton per nucleotide and stability could be guaranteed by these, possibly dark, protons residing at a larger space-time sheet.

For more details see the chapter Crop circles and life at parallel space-time sheets: part I , where a brief overview about living systems as ordinary matter quantum controlled by dark matter is given. If you are too afraid that you neighbor spots you in the middle of act of reading something about crop circles, you might prefer the end of the chapter Many-Sheeted DNA.



A more precise definition of N-atom and dark matter as a matter in wrong place

Earlier I speculated with the notion of dark N-particle (-atom or -molecule) and the possible significance of N-p"../articles/ for the deeper understanding of lock and key mechanism of bio-catalysis and DNA replication.

Dark N-p"../articles/ associated with DNA, possibly hydrogen bonds, could serve as names for nucleotides so that the emergence of symbols would distinguish between molecules in vitro and vivo. Dark fermionic N-particle and λk-N, particle a would serve as names for DNA nucleotide and its conjugate and their composite would be λk-atom analogous to a full electronic shell and therefore highly stable. Quite generally, molecules with conjugate names would be like opposite sexes: sex, symbolic representations, and meaning would emerge already at the molecular level.

1. Objection

There is an obvious objection against dark N-hydrogen atoms as names of DNA nucleotides. λ is in general integer valued and λ ≈ 211 seems to be favored. This value of λ would however make the mass of N-hydrogen atom or its conjugate quite too high to be physically acceptable.

Somehow it seems that N-hydrogen atom involves only single ordinary proton. In this case however the total electronic charge of the system would be N units of dark electronic charge and one protonic charge, which seems strange. The resolution of the problem is that dark electron-electron Coulomb interaction energy is reduced by 1/λk by the scaling down of the dark fine structure constant (proportional to 1/hbar). Hence effectively electronic and protonic charges would compensate each other for λk atom whereas for N-atoms the charge would be effectively fractional and 1-N/λk units.

2. How to observe N-atoms?

The most elegant definition of dirt is as a matter in wrong place. It would seem that also dark matter is matter in wrong place, but only effectively.

The question is how to observe N-atoms and N-molecules. The key observation is that the transition energies of N-molecules are N times large than corresponding ordinary molecules. This makes them thermally stable under much higher temperatures. The transitions of these molecules give rise to dark N-photons, which can decay to N ordinary photons with same energies as emitted in the transitions of ordinary molecules.

The presence of spectral lines of transitions of atoms or molecules which are not be stable at the temperature of environment, would serve as a signature of dark N-p"../articles/. Interestingly, spectral analysis demonstrates the presence water inside sunspots, where the temperature varies in the range 3000-4500 K. The decay of N-photons to ordinary photons emitted by thermally stable N-water molecules with N> 10 would explain the finding. Also the quite recent evidence discovered by M. Moshina that Sun has a solid surface consisting mostly of calcium-ferrite is inconsistent with the fact that photosphere has temperature 5800 K. The explanation of the puzzle would be in terms of dark N-iron and other dark N-elements.

Without exaggerating one can say that the systematic search for the presence of molecules and condensed matter structures in places where it is thermally stable could revolutionize our world view.

3.Plasmoids as life forms?

There is evidence that plasmoids satisfy the basic criteria for primitive living systems (E. Lozneanu and M. Sanduloviciu (2003), Minimal-cell system created in laboratory by self-organization, Chaos, Solitons and Fractals, Volume 18, Issue 2, October, p. 335. See also Plasma blobs hint at new form of life, New Scientist vol. 179 issue 2413 - 20 September 2003, page 16.)

One of the basic ideas of TGD based quantum model of living systems is that plasmoids identified as rotating magnetic systems analogous to Searl device are primitive life forms and predecessors of the molecular life. Rotation generates radial electric field having non-vanishing divergence whose sign depends on the direction of rotation (difficult to understand in Maxwellian ED), which in turn generates radial ohmic current charging the system. The dropping of electrons of this current to larger space-time sheets at the boundaries of rotating system liberates zero point kinetic energy as a usable metabolic energy. This mechanism would define fundamental metabolic energy currencies also in ordinary living matter.

4. Is molecular high-T life possible?

Life based on dark N-molecules could in principle survive at high temperatures. I have already earlier considered half seriously the possibility that Earth interior (say mantle-core boundary) and even solar photosphere could serve as seats of high-T life developed from plasmoids and that the Earth interior would be like the womb of Mother Gaia, where life evolved from simple plasmoids. The basic inspiration came from the evidence that crop circles cannot be fraud. See the chapters Crop circles and life at parallel space-time sheets: part I and II, where a brief overview about living systems as ordinary matter quantum controlled by dark matter is given.



Are spontaneous decay and completion of dark N-hydrogen atoms behind DNA replication and lock and key mechanism?

The replication of DNA has remained for me a deep mystery and I dare to doubt that the reductionistic belief that this miraculous process is well-understood involves self deceptive elements. Of course the problem is much more general: DNA replication is only a single very representative example of the miracles of un-reasonable selectivity of the bio-catalysis. I take this fact as a justification for some free imagination inspired by the notion of dark N-atom discussed in What inherently dark atoms could be?.

1. Dark fermionic molecules can replicate via decay and spontaneous completion

Dark fermionic λk-molecule is ideally suited for replication. First of all, N=λk means that the analog of closed electronic shell is in question so that this (maximum) value of N is especially stable. The analogy with full Fermi electronic sphere and magic nuclei makes also sense.

Suppose that N=λk-molecule decays into N1-molecule and N2-molecule with N2k-N1. If λ is even it is possible to have N1= N2k/2 and the situation is especially symmetric. If fermionic N<λkk-sheeted) dark molecules are present, one can imagine that these molecules tend to be completed to full λk-molecules spontaneously. Thus spontaneous decay and completion would favor the spontaneous replication and dark molecules could be ideal replicators. Needless to say, the idea that the mechanisms of spontaneous decay and completion of dark N-p"../articles/ somehow lurk behind DNA replication and various high precision bio-catalytic processes is extremely attractive and would trivialize the deepest mystery of biology.

2. Reduction of lock and key mechanism to spontaneous completion

DNA replication and molecular recognition by the lock and key mechanism are the two mysterious processes of molecular biology. As a matter fact, DNA replication reduces to spontaneous opening of DNA double strand and to the lock and key mechanism so that it is enough to understand the opening of double strand in terms of spontaneous decay and lock and key mechanism in terms of spontaneous completion of N-particle ("particle" refers to atom or molecule in the sequel).

Consider bio-molecules which fit like a lock and key. Suppose that they are accompanied by dark N-p"../articles/, such that one has N1+N2k so that in the formation of bound state dark molecules combine to form λk-molecule analogous to a full fermionic shell or full Fermi sea. This is expected to enhance the stability of this particular molecular complex and prefer it amongst generic combinations.

For instance, this mechanism would make it possible for a nucleotide and its conjugate, DNA and mRNA molecule, and tRNA molecule and corresponding aminoacid to recognize each other. Spontaneous completion would allow to realize also the associations characterizing the genetic code as a map from RNAs to subset of RNAs and associations of this subset of RNAs with amino-acids (assuming that genetic code has evolved from RNA → RNA code as discussed here ).

As such this mechanism allows a rather limited number of different lock and key combinations unless λk is very large. There is however a simple generalization allowing to increase the representative power so that lock and key mechanism becomes analogous to a password used in computers. The molecule playing the role of lock resp. molecule would be characterized by a set of n letters represented by N-p"../articles/ with N in {N1,1,..N1,n} resp. {N2,1k-N1,1,..., N2,n= λk-N1,n}. The molecules with conjugate names would fit optimally together. N-molecules would be like letters of a text characterizing the name of the molecule.

The mechanism generalizes also to the case of n >2 reacting molecules. The molecular complex would be defined by a partition of n copies of integer λk to a sum of m integers Nk,i: ∑i Nk,ik.

This mechanism would provide a universal explanation for the miraculous selectivity of catalysts and this selectivity would have practically nothing to do with ordinary chemistry but would correspond to a new level of physics at which symbolic processes and representations based on dark N-p"../articles/ emerge.

3. Connection with the number theoretic model of genetic code?

The emergence of partitions of integers in the labelling of molecules by N-p"../articles/ suggests a connection with the number theoretical model of genetic code , where DNA triplets are characterized by integers n in {0,...,63} and aminoacids by integers 0,1 and 18 primes p< 64. For instance, one can imagine that the integer n means that DNA triplet is labelled by n-particle. λ=63 would be the obvious candidate for λ and conjugate DNA triplet would naturally have nc=63-n.

The model relies on number-theoretic thermodynamics for the partitions of n to a sum of integers and genetic code is fixed by the minimization of number theoretic variant of Shannon entropy which can be also negative and has thus interpretation as information. Perhaps these partitions could correspond to states resulting in some kind of decays of n-fermion to nk-fermions with ∑k=1r nk=n. The nk-fermions should not however correspond to separate p"../articles/ but something different. A possible interpretation is that partitions correspond to states in which n1 particle is topologically condensed at n2≥ n1 particle topologically condensed..at nr≥ nr-1-particle. This would also automatically define a preferred ordering of the integers ni in the partition.

An entire ensemble of labels defined by the partitions would be present and depending on the situation codon could be labelled not only by n-particle by any partition n=∑i=1r ni corresponding to the state resulting in the decay of n-particle to r N-p"../articles/.

4. Reduction of DNA replication to a spontaneous decay of λk-particle

DNA replication could be induced by a spontaneous decay of λk-particle inducing the instability of the double strand leading to a spontaneous completion of the component strands.

Strand and conjugate strand would be characterized by N1-particle and N2k-N1-particle, which combine to form λk-particle as the double strand is formed. The opening of the double strand is induced by the decay of λk-particle to N1- and N2-p"../articles/ accompanying strand and its conjugate. After this both strands would complete themselves to double strands by the completion to λk-particle.

It would be basically the stability of λk-particle which would make DNA double strand stable. Usually the formation of hydrogen bonds between strands and more generally, between the atoms of stable bio-molecule, is believed to explain the stability. Since the notion of hydrogen bond is somewhat phenomenological, one cannot exclude the possibility that these two mechanisms might be closely related to each other. I have already earlier considered the possibility that hydrogen bond might involve dark protons : this hypothesis was inspired by the finding that there seems to exist two kinds of hydrogen bonds (New Scientist 154 (2087):40�43, 21 June 1997).

The reader has probably already noticed that the participating N-molecules in the model of lock and key mechanism are like sexual partners, and since already molecules are conscious entities, one might perhaps see the formation of entangled bound states with positive number theoretic entanglement entropy accompanied by molecular experience of one-ness as molecular sex. Even more, the replication of DNA brings in also divorce and process of finding of new companions!

5. What the N-p"../articles/ labelling bio-molecules could be?

What the dark N-p"../articles/ defining the letters for the names of various bio-molecules could be? The obvious requirement is that the names of molecules cannot weigh too much. In the optimal situation there are just two options.

Dark N-hydrogen atoms are the lightest candidates for the names of bio-molecules. This mechanism would also conform with the belief that hydrogen bonds guarantee the stability of bio-molecules. At least, dark N-hydrogen atoms should be localizable in the vicinity of hydrogen bonds.

This idea is not a mere speculation. The first experimental support for the notion of dark matter came from the experimental finding that water looks in atto-second time scale from the point of view of neutron diffraction and electron scattering chemically like H1.5O: as if one fourth of hydrogen atoms would be dark (references can be found here). Attosecond time scale would presumably correspond to the first level of dark matter hierarchy and also higher level dark hydrogen could be present.

One can imagine also a second option. The model for homeopathy leads to a rather concrete integrated view about how magnetic body controls biological body and receives sensory input from it. The model relies on the idea that dark water molecule clusters and perhaps also dark exotically ionized super-nuclei formed as linear closed strings of dark protons perform this mimicry. Dark proton super-nuclei are ideal for mimicking the cyclotron frequencies of ordinary atoms condensed to dark magnetic flux quanta. Of course, also partially ionized hydrogen N-ions could perform the cyclotron mimicry of molecules with the same accuracy.

One can consider the possibility N-molecules/atoms correspond to exotic atoms formed by electrons bound to exotically ionized dark super-nuclei: the sizes of these nuclei are however above atomic size scale so that the dark electrons would move in a harmonic oscillator potential rather than Coulombic potential and form states analogous to atomic nuclei. The prediction would be the existence of magic electron numbers. Amazingly, there is experimental evidence for the existence of this kind of many-electron states. Even more, these states are able to mimic the chemistry of ordinary atoms.

For more detailed views see the chapter Many-Sheeted DNA.



What inherently dark atoms could be?

The basic implication of the dark matter hierarchy is that there is no need to assume that temperatures at various space-time sheets are widely different since the scaling of hbar can scale up the energies above the thermal threshold. This poses very strong constraints on TGD based view about quantum biology and increases its predictive power dramatically.

The original model for inherently dark atom relies on the scaling of hbar by λk at the kth level of the dark matter hierarchy. Here λ is integer and λ ≈ 211 defines a preferred value of λ. Also the harmonics and integer valued sub-harmonics of λ might be possible. In the case of hydrogen atom the model predicts that the energies of hydrogen atom proportional to 1/hbar2 are scaled down by 1/λ2k so that dark atoms would not be thermally stable at room temperature. In practice this would exclude dark atoms and molecules as biologically interesting inherently dark systems.

The topological condensation of ordinary atoms and molecules at λk-sheeted (now in the sense of "Riemann surfaces" over M4) dark magnetic flux quanta is however possible and means scaling up of the cyclotron energy by λk making possible cyclotron Bose-Einstein condensates at high temperatures identifiable as dark quantum plasmas. The same scaling occurs to the energy of dark plasma oscillations so that their energies can be above thermal threshold. Dark plasmoids and plasma oscillations are indeed fundamental in the TGD based model of quantum control in living matter.

This leads to a very restrictive model for living matter. This model is very successful but has some features which suggest that it is not the whole story. For instance, the conformal and rotational spectra of bio-molecules correspond to microwave frequencies and would be below thermal threshold and thus should be of minor importance in contrast with experimental facts. This would also reduce the importance of liquid crystals known to be of crucial for the functioning of living matter. There is also a feeling that the role of fermionic bio-ions such as Na+, K+, and Cl- should be more important than this picture allows.

In the sequel a modification of the notion of inherently dark atom in which the dark energy spectra are essentially the same as the ordinary ones, will be discussed.

1. Inherently dark atoms as radial anyons?

The model of inherently dark atoms as radial anyons predicts that the energy spectra of dark atoms and molecules are nearly the same as their ordinary counterparts.

  1. Dark atoms having ordinary size and ordinary energy spectrum could be possible if the principal quantum number n is fractionized to n→n/λk. The fractionization could make sense if the atomic space-time sheet is λk-folded and atoms become radial anyons. The corresponding Bohr orbits would close in the radial direction only after λk turns. The formation of dark atoms could be interpreted as a transition to chaos by period λk-folding in radial and angular degrees of freedom. This option would differ from the original model in that radial scaling in M4 by a factor λ2k is replaced by a radial λk-folding so that the M4 projection of dark atom has the same size as in the case of ordinary atom.

  2. Since dark atom would define a λk-fold covering of M4, one expects a degeneracy of states corresponding to the phase factors exp(ikn2π/λk), k=0,...,λk-1, where n labels the sheets of the λk-fold covering of M4. The nuclei and electrons of N≤ λk dark atom could form many-particle states separately and fermionic statistics becomes effectively para-statistics for the resulting N-atoms. Note that the N electrons and nuclei would be in identical states in ordinary sense of the word since Bohr orbits must be identical: kind of fermionic Bose-Einstein condensates become thus possible.

  3. The quantum transitions of N-atoms for N=λk would give rise to dark counterparts of the photons emitted in the ordinary atomic transitions. For N ≤ λk the energies of dark photons would be N times higher than the energies liberated in the ordinary transitions. The claims of Randell Mills about the scaling up of the binding energy of the hydrogen ground state by a square k2 of an integer in plasma state might be understood as being due to the formation of dark N=k2-atoms emitting dark photons with k2-fold energies de-cohering to ordinary photons. Also nore general states are however predicted now. A fraction of plasma phase in Mills experiments would be in dark plasma state. The chemistry of bio-molecules identified as N-molecules would definitely differ from the ordinary chemistry.

  4. The fractionization n→n/λk of the integer n labelling vibrational modes and cyclotron states would be unavoidable. Single particle cyclotron states having E= hbar (k)ω of the earlier picture would in this framework correspond to single particle states having n=λk or to N=λk-ion states. Fermionic N=λk-states are expected to have a special role since these configurations are analogous to noble gas atoms with full shells of electrons and to magic nuclei with full cells of nucleons. Most biologically important ions are fermions and N=λk states would give rise to what might be regarded as fermionic analogs of Bose-Einstein condensates. For bosonic ions there is no restriction to the occupation numbers of λk single particle states involved.

2. Connection with quantum groups?

The phase q= exp(i2π/λk) brings unavoidably in mind the phases defining quantum groups and playing also a key role in the model of topological quantum computation tqc}. Quantum groups indeed emerge from the spinor structure in the "world of classical worlds" realized as the space of 3-surfaces in M4× CP2 and being closely related to von Neumann algebras known as hyper-finite factors of type II1 . Unfortunately, the integer n characterizing the phase cannot be identified as λ. This allows to ask whether quantum groups could emerge in two different manners in TGD framework.

If so, living matter could perhaps be understood in terms of quantum deformations of the ordinary matter, which would be characterized by the quantum phases q= exp(i2π/λk). Hence quantum groups, which have for long time suspected to have significance in elementary particle physics, might explain the mystery of living matter and predict an entire hierarchy of new forms of matter.

3. Are both options for dark matter realized?

For N=λk molecules which dark photons emitted in the rotational and conformational transitions would be above thermal threshold. It is of course quite possible that both options are realized. The fact that also fermionic ions (such as Na+, K+, Cl-) are important for living system suggests that this is the case. This would also provide a justification for the hypothesis that microtubular conformations represent bits and allow protein conformational dynamics to serve as metabolic controller by providing microwave dark photons with energies above thermal threshold.

4. How to distinguish between N-molecules and ordinary molecules?

The unavoidable question is whether bio-molecules in vivo could be actually N-molecules or whether they could involve some component which is N-molecule. This raises a series of related questions.

  1. Could it be that we can observe only the decay products of dark N-fold molecules to ordinary molecules? Is matter in vivo dark matter and matter in vitro ordinary matter? Could just the act of observing the matter in vivo in the sense of existing science make it ordinary dead matter?

  2. How can one distinguish between N-fold and ordinary molecules? Electromagnetic interactions, and more generally gauge forces, do not allow to distinguish classically between these molecules since there are no direct quantum interactions between them. The gravitational forces generated by N-molecules are too weak to allow to distinguish from N molecules.

  3. The decay of N-molecule via decay to N ordinary molecules in principle allows to conclude that N-molecule was present. But could this process mean just the replacement of DNA in vivo with DNA in vitro?

  4. The emission of dark N-photons decaying via decay to N photons can serve as a signature of N-molecules. If the molecules are fermions this would in principle allow to exclude the interpretation in terms of coherent emission of photons from Bose-Einstein condensate of N ordinary molecules. Bio-photons indeed represent this kind of radiation having no obvious explanation in standard physics context.

These questions perhaps make it clear that it is not at all obvious that the living matter could not consist of dark N-molecules at least partially.

For more detailed views see the chapter Many-Sheeted DNA.



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