Tuesday, January 10, 2006

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 the previous posting "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-particles 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-particles, 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-particles 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-particles emerge.

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

The emergence of partitions of integers in the labelling of molecules by N-particles 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 particles 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-particles.

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-particles 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-particles labelling bio-molecules could be?

What the dark N-particles 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 of "Genes, Memes, Qualia,..."..

Matti Pitkanen

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