Quantum model of nerve pulse IV: Could microtubule-axon system perform topological quantum computation?

The proposed picture is consistent with the model of DNA as a topological quantum computer [7] and with the idea that also microtubuli could be involved with tqc. The model of DNA as tqc in its basic form assumes that DNA is connected to the nuclear membrane and cell membranes associated with the cell body by magnetic flux tubes such that each nucleotide is connected to single lipid. Tqc programs are coded to the temporal braiding patters of lipids. This requires that lipid layer is liquid crystal and thus below the critical temperature. The flux tube connecting DNA to inner lipid layer and that beginning from outer lipid layer can form single flux tube or be split. If they form single flux tube braiding and tqc are not possible. During tqc the braid strands going through cell membrane are split and the dance of lipids induced by water flow defining time like braiding (hydrophilic lipid ends are anchored to the cellular water) induces braiding of the magnetic flux tubes which write the tqc program to memory. Furthermore, the lifetimes of flux tubes in the connected state must be short enough to prevent the generation of a nerve pulse. This is the case if the temperature is sufficiently below the critical temperature. The ionic supra currents are identifiable as the observed quantal non-dissipative currents flowing through the cell membrane when tqc is not on.

Centrioles have their own genetic code realized in terms of RNA and they play key role during gene replication when DNA is out of the game. This encourages to think that microtubuli make possible an independent tqc like process. How microtubule-axon system could then perform tqc? One can consider two options and also their hybrid in the proposed model for nerve pulse.

1. Option I: Magnetic flux tubes connect microtubules to the space-time sheet of cell exterior. In the model of DNA as tqc these flux tubes continue back to the nucleus or another nucleus: the flux tubes must be split at cell membrane during tqc and this splitting induces the required isolation from the external world during tqc. During nerve pulse the situation would be different and the flow of lipids in liquid phase could induce braiding: the isolation would however fail now. Tqc would explain why the axon melts during nerve pulse.

   One can become critical and ask why also the magnetic flux tubes from DNA could not end to the space-time sheet of the cell exterior. The justification for 'No' (besides isolation) could be that also cell soma would possess standing soliton sequence like waves and standing nerve pulses.

   Could one then see this tqc as a special variant of DNA-membrane tqc? The idea about magnetic flux tubes emanating from DNA and flowing along microtubuli interiors and radiating to the axonal membrane looks ugly: in any case, this would not affect tqc and nerve pulse could be seen as a direct gene expression.

2. Option II: For some years ago I considered the possibility of a gel-sol-gel phase transition proceeding along the surface surface of the micro-tubuli, accompanying nerve pulse, perhaps inducing nerve pulse, and coding for long term sensory memories in terms of 13 13-bit sequences defined by the tubulin helices with bit represented as a conformation of microtubule. This hypothesis might be easily shown to be wrong on basis of the available experimental facts already now. Suppose however that this phase transition happens and that the braid strands do not continue from the microtubular surface to the cell nucleus. In this case the braiding could be induced by a gel-sol-gel transition accompanying and perhaps generating the nerve pulse at the microtubular level and inducing the disassembly of the tubulins followed by re-assembly inducing the braiding. Also this braiding would contribute to tqc like process or at least memory storage by braiding.

The following considerations do not depend on the option used.

1. What comes first in mind is that the braiding codes memories, with memories understood in TGD sense using the notion of 4-D brain: that is in terms of communications between brain geometrically now and brain in the geometric past. In standard neuroscience framework braiding of course cannot code for memories since it changes continually. Nerve pulse sequences would code for long term sensory memories in a time scale longer than millisecond and microtubular phase transition could have a fine structure coding for sensory data in time scales shorter than nerve pulse duration. The fact is that we are able to distinguish from each other stimuli whose temporal distance is much shorter than millisecond and this kind of coding could make this possible. Also the direct communication of the auditory (sensory) input using photons propagating along MEs parallel to axon could also explain this.

2. In the model of DNA as tqc nucleotides A,T,C,G are coded into a 4-color of braid strand represented in terms of quarks u,d and their antiquarks. An analogous coding could be present also now. The coding would result if DNA is connected to microtubuli but this option does not look attractive. If each aminoacid can be accompanied by 3-braid with colors of any of DNA codons coding each aminoacid of tubulin would be connected to 3 lipids. As a matter fact, 3-braids can be regarded as fundamental sub-modules of tqc programs since 3-braid is the smallest N-braid which can do non-trivial tqc. Tubulins could be seen as higher level modules consisting of order hundred 500 amino-acids. This corresponds to a DNA strand with length of about .5 μm corresponding to p-adic length scale L(163) which is one of the four magic p-adic length scales (k=151,157,163,167) which correspond to Gaussian Mersennes. This higher level language character of microtubular tqc programs would conform with the fact that only eukaryotes possess them.

3. Cellular cytoskeleton consists of microtubuli. Could microtubular tqc -in either of the proposed forms- take place also at the cell soma level? Could DNA-nuclear membrane system define the primordial tqc and microtubular cytoskeleton-cell membrane system a higher level tqc that emerged together with the advent of the multicellulars? Is only the latter tqc performed at the multicellular level? The notions of super- and hypergenome encourage to think that both tqcs are performed in all length scales. One can imagine that ordinary cell membrane decomposes into regions above and below the critical point (the value of the critical temperature can be controlled. Those below it would be connected to DNA by flux tube bundles flowing inside the microtubular cylinders. Microtubular surfaces would in turn be connected to the regions above the critical point. One should also understand the role of M₁₃=2¹³-1 12-bit higher level "genetic code" assignable naturally to microtubuli. For instance, could the bit of this code tell whether the module defined by the tubulin dimer strand bundle participates tqc or not?

For background see that chapter Quantum Model of Nerve Pulse of "TGD and EEG".

References

[1] Soliton model.

[2] T. Heimburg and A. D. Jackson (2005), On soliton propagation in biomembranes and nerves, PNAS vol. 102, no. 28, p.9790-9795.

[3] T. Heimburg and A. D. Jackson (2005), On the action potential as a propagating density pulse and the role of anesthetics, arXiv : physics/0610117 [physics.bio-ph].

[4] K. Graesboll (2006), Function of Nerves-Action of Anesthetics, Gamma 143, An elementary Introduction.

[5] Physicists challenge notion of electric nerve impulses; say sound more likely.

[6] Saltation.

[7] The chapter DNA as Topological Quantum Computer of "Genes and Memes".