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TGD and EEG

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Year 2008



Cell as gel and the model of nerve pulse

The book Gels and Cells [4] of Pollack should be obligatory reading for anyone seriously interested about the real situation in biology. The book summarizes impressive amount of facts supporting the view that the prevailing view about cytoplasm as water containing molecules dis-solved into it it is badly wrong. These findings force to challenge the notions of channels and pumps and even the notion of continuous cell membrane must be questioned as well as basic view about the generation of action potentials. These findings have served as inspiration in the construction of TGD based view about quantum biology. The solution to various anomalies of living cell proposed by Pollack that cytosplasm is in gel phase [4] and that the phase transitions of gel phase are a universal building brick of various biological functions.

1. Cell as gel

Pollack describes in detail various aspects of cytoplasm as a gel phase and here only short summary can be given.

  1. Cytoplasm can be regarded as a network consisting of cross-linked negatively charged proteins. Water is condensed around the proteins to form structured water. If protein is hydrophilic, water self-organizes around it as a multilayered structure: the number of molecular layers can as high as 600 and the thickness of the layered structure is a considerable fraction of micrometer. If the protein is hydrophobic, water forms another structured phase known as clathrate water: in this case the number of hydrogen bonds between water atoms is large. These phases can be regarded as intermediate between ice and water. Also ordinary ions have this kind of layered structure around them. Chemical cross-links tend to be stable with heat, pH, and solvent composition whereas physical cross-links formed by intermolecular interactions are sensitive to environmental interactions and are of special interest from the point of view of phase transitions.

  2. Pollack proposes that the formation of polymers takes place in an environment containing layered water for the simple reason that monomers cannot diffuse to the layered water so that the probability of association with the end of the growing polymer increases.

  3. Cell interior is populated by micro-tubules, various filamentary structures, and the so called micro-trabecular matrix. Micro-trabecular network divides cell into a compartments in such a manner that the typical distance between two proteins in water is about 5 nm: this corresponds to the p-adic length scale L(149), the thickness of the lipid layer of cell membrane. This is probably not an accident and the micro-trabecular network might be closely involved with the highly folded network of intracellular membranes. There would be a layer of thickness of about 6 water molecules per given protein surface so that a dominating portion of intracellular water could be structured.

  4. The layered water has several tell-tale signatures that have been observed in gels. It freezes at much lower temperature than ordinary water; various relaxation times are shorter since the energy transfer to the water lattice occurs faster than to non-structure water; the diffusion rates of particles into the structured water are much slower than to ordinary water by entropy argument; a simple geometric argument tells that the larger the size of the hydrated ion the lower the diffusion rate; strong gradients of ionic concentrations can form in gel phase as has been observed.

The identification of the cytoplasm as a gel has profound implications for the standard views about cell.

  1. The original motivation for postulating semipermeable cell membrane, channels, and pumps was the need to hinder the diffusion of various ions between cell interior and exterior taking place if cytoplasm is ordinary water into which molecules are dissolved. If cytoplasm is in gel phase, cell membrane need not perform pumping and channeling anymore except perhaps in situations involving the formation of a local sol phase. This raises the question about the proper functions of the cell membrane.

  2. It is possible to drill to cell membrane holes with size of order 1 mm without an appreciable effect on the functioning of the cell and also show that these holes remain as such for long periods of time . It is also possible to splice cells into pieces continuing to function for days. That K+ flux through cell membrane does not change when lipids are partially removed. These findings force to ask whether the assumption about the continuity of the cell membrane might be too strong . Electron micrographs however demonstrate the presence of the bi-layered structure. What is intriguing that this structure is seen even in the absence of lipid layers. In TGD framework this paradoxical finding might be understood in terms of a presence of space-time sheets corresponding to p-adic length scales L(k), k=149,151 as vacuum structures predicted also by TGD inspired model of high Tc super-conductivity [2] .

  3. There is also the strange finding that water flux through cell membrane is much higher than the flux through isolate lipid bi-layer as if some unidentified channels were present. In TGD framework this might be seen as an evidence for the presence of (wormhole) magnetic flux tubes as carriers of water molecules.

  4. The fundamental assumptions about ionic equilibrium must be reconsidered, and the Hodkin-Huxley model for the generation of nerve pulse becomes more or less obsolete. Indeed, it has been found that action potentials can be generated even in absence of Na+ and K+ ions playing a key role in Hodkin-Huxley model. Rather remarkably, the high concentration of K+ ions and low concentration of Na+ ions in cytoplasm could be understood on basis of gel property only. Also new view about cell (note membrane-!) potential emerges. The standard paradigm states that the resting potential is over the cell membrane. Potentials of same order of magnitude have been however seen in de-membraned cells (50 mV in slight excess of action potential and critical potential), colloidal suspensions, and gels which suggest that larger part of cell than mere cell membrane is involved with the generation of the action potential and one should thus speak of cell potential instead of membrane potential.

  5. Pollack suggests that the phase transitions of the gel phase make possible to realize various functions at molecular and cellular level and represents empirical evidence for the phase transition like aspects assigned to these functions including sensitivity to various factors such as pH, temperature, chemical environment, electromagnetic fields, mechanical forces, etc... and the threshold behavior . Also the responses are typical for phase transitions in that they involve dramatic changes in volume, shape, di-electric constant, etc.. With these motivations Pollack discusses phase transition based models for contraction, motility, secretion, transport or molecules, organized flow of particles during cell division, cell locomotion, contraction of muscle, generation of action potentials, etc.. For instance, the transport of bio-molecules along micro-tubule could involve propagating gel-sol-gel phase transition meaning also propagating melting of the layered water around micro-tubule.

  6. Divalent ions, such as Mg++ and Ca++ can act as cross links between negatively charged proteins binding them to form networks. Monovalent ions cannot do this. Peripheral cytoskeleton is this kind of network consisting of micro-tubules and actin molecules cross-linked - according to Pollack- by Ca++ ions. On the other hand, it is known that Mg++ (Ca++) ions dominate in the cell interior (exterior) and that the presence of Ca++ ions in the cell exterior is crucial the for generation of nerve pulse. The influx of Na+ ions having higher affinity to proteins can induce a phase transition to sol-like phase. Pollack suggests a model of nerve pulse based on this mechanism of gel-sol phase transition for peripheral cytoskeleton: this model does not actually explain why Ca++ ions in the exterior of axon are necessary.

2. TGD based vision nerve pulse and its relation to Pollack's model

The vision about dark matter and the model of nerve pulse formulated in terms of Josephson currents brings an additional perspective to the role of pumps and channels and allows to avoid harmony with the standard views about their role.

  1. In long length scales visible matter forms roughly 5 per cent of the total amount of matter. In TGD Universe the dark matter would correspond to matter with large Planck constant including dark variants of ordinary elementary particles. In living matter situation could be the same and visible matter could form only a small part of the living matter. Dark matter would be however visible in the sense that it would interact with visible matter via classical electromagnetic fields and photon exchanges with photons suffering Planck constant changing phase transition. Hence one can consider the possibility that most of the biologically important ions and perhaps even molecules reside at the magnetic flux quanta in large hbar phase.

  2. Bosonic ions could form Bose-Einstein condensates at the flux tubes in which case supra currents flowing without any dissipation would be possible. The model for high Tc super-conductivity suggests that only electronic and protonic super-conductivity are possible at room temperature. If so, Cooper pairs of fermionic ions are excluded. New nuclear physics predicted by TGD could however come in rescue here. The TGD based model for atomic nucleus assumes that nuclei are strings of nucleons connected by color bonds having quark and antiquark at their ends. Also charged color bonds are possible and this means the existence of nuclei with anomalous charge. This makes possible bosonic variants of fermionic ions with different mass number and it would be interesting to check whether biological important ions like Na+,Cl-, and K+ might actually correspond to this kind of exotic ions.

This leads to the following TGD inspired vision about cell as a gel.

  1. DNA as tqc hypothesis and cell membrane as sensory receptor provide possible candidates for the actual functions of the cell membrane and ionic channels and pumps could act as kind of receptors. That standard physics is able to to describe gel phase is of course a mere belief and (wormhole) magnetic flux tubes connecting various molecules (DNA, RNA, aminoacids, biologically important ions) would be "new physics" cross-links could explain the strong correlations between distant molecules of the gel phase.

  2. Dark ionic currents are quantal currents. If the dark ions flow along magnetic or wormhole magnetic flux tubes connecting cell interior and exterior, their currents through cell membrane would be same as through an artificial membrane.

  3. Pumps and channels could serve the role of sensory receptors by allowing to take samples about chemical environment. One cannot exclude the possibility that proteins act as pumps and channels in sol phase if magnetic flux tubes are absent in this phase since also in TGD Universe homeostasis and its control at the level of visible matter in sol phase might requires them. The metabolic energy needed for this purpose would be however dramatically smaller and a reliable estimate for this would allow an estimate of the portion of dark matter in living systems.

  4. Quantum criticality suggests that the phase transitions for the gel phase are induced by quantum phase transitions changing the value of Planck constant for magnetic flux tubes and inducing the change of the length of the flux tube. Macroscopic quantum coherence would explain the observed co-operativity aspect of the phase transitions. Concerning locomotion and transport mountain climbing using pickaxe and rope inspires a guess for a general mechanism. For instance, a packet of molecules moving along actin molecule or a molecule carrying a cargo along micro-tubule could repeat a simple basic step in which a magnetic flux tube with large hbar is shot along the direction of the electric field along micro-tubule and stuck to a rachet followed by a phase transition reducing the value of hbar and shortening the flux tube and forcing the cargo to move forward. The metabolic energy might be provided by the micro-tubule rather than molecular motor.

  5. The reconnection of flux tubes would be a second phase transition of this kind. This phase transition could lead from a phase in phase proteins are unfolded with flux tubes connecting aminoacids to water molecules and thus possessing a large volume of layered water around them to a phase in which they become folded and flux tubes connect aminoacids to each other in the interior of protein. The phase transition could be associated with the contraction of connecting filaments of muscle cell. The phase transitions are also seen in "artificial protein" gels used for drug delivery applications, and are built from polymers arranged in alpha helices, beta sheets and common protein motifs . If wormhole magnetic flux are taken are taken as a basic prerequisite of life, one must ask whether these "rtificial proteins" represent artificial life.

  6. The fact that cytoskeleton rather than only cell membrane is involved with the generation of action potential conforms with the idea that nerve pulse propagating along axon involves also axonal micro-tubules and that Josephson currents between axon and micro-tubules are involved in the process.

  7. Di-valent ions (Ca++ ions according to Pollack) serve as cross links in the peripheral cytoskeleton. The influx of monovalent ions from the exterior of axon induces gel-sol phase transition replacing di-valent ions with monovalent ions. One can consider two models.

    i) The minimal assumption is that this phase transition is induced hbar increasing phase transition the flow of the monovalent ions like Na+ from the cell exterior along the magnetic flux tubes connecting axonal interior and interior. Suppose that in the original situation the flux tubes end to axonal membrane (this is not the only possibility, they could also end to Ca++ ions). The flux tubes extending to the axonal exterior could result by hbar increasing phase transition increasing the length of the flux tubes connecting peripheral cytoskeleton to the axonal membrane so that they extend to the exterior of axon. This option is rather elegant since gel-sol phase transition itself can be understood in terms of ßtandard chemistry". In this model the very slow diffusion rate of the ions to gel phase would have explanation in terms of new physics involving dark matter and (wormhole) magnetic flux tubes.

    ii) One can consider also an option in which divalent ions such as Ca++ or Mg++ are connected by two flux tubes to amino-acids of two negatively charged proteins whereas monovalent biological ions like Na+ would have single flux tube of this kind and could not act as cross links. In the phase transitions removing the cross links the replacement of divalent ion with two monovalent positively charged ions would take place. If one believes in standard chemistry, Na+ ions would flow in automatically. First the increase of Planck constant would induce the lengthening of the magnetic flux tubes and thus the expansion of the gel phase making possible the influx of monovalent ions. If Na+ ions are dark, flux tubes connecting peripheral cytoskeleton to the axonal exterior are required and the mechanism of option i) is also needed.

  8. The mechanisms i) and ii) could be fused to a single one. The hint comes from the presence of Ca++ ions in the exterior of axon is necessary for the generation of action potential. The simplest possibility is that the flux tubes connecting proteins to intracellular Ca++ cross links in gel phase connects them after the length increasing phase transition to extracellular Ca++ ions and Na+ ions flow along these flux tubes.

  9. The increase of the Planck constant would induce the expansion of the peripheral cytoskeleton making possible the inflow of Na+ ions, and divalent ions binding negatively charged actin molecules to a network would be replaced with inflowing Na+ ions. After this a reverse phase transition would occur. Both phase transitions could be induced by a quantal control signal (Josephson current) inducing quantum criticality and a change of Planck constant.

  10. A propagating Ca++ wave inducing the gel-sol-gel phase transition of peripheral cytoskeleton would accompany nerve pulse. Quite generally, Ca++ waves are known to play a fundamental role in living matter as kind of biological rhythms. Irrespective of whether one believes option i) or ii), this might relate to the cross-linking by flux tubes and gel-sol-gel phase transitions induce by phase transitions increasing Planck constant temporarily. The velocities and oscillation periods of Ca++ waves vary in an extremely wide range: this can be understood if the flux tubes involved correspond to a very wide spectrum of Planck constant.

To sum up, the strange discoveries about the behavior of cell membrane provide direct experimental evidence for the presence of dark matter in living systems, for the prediction that it interacts with ordinary matter via classical electromagnetic fields, and for the assumption that it does not dissipate appreciably and could therefore have large value of hbar and form macroscopic quantum phases.

In the model of Pollack for the action potential gel-sol-gel phase transition for the peripheral cytoskeleton accompanies the generation of the action potential. The model allows to understand reasonably well the behavior and the physical role of the ionic currents and explains various anomalies. I have discussed TGD based model of nerve pulse earlier in these blog postings. The Josephson junctions defined by (wormhole) magnetic flux tubes between microtubules and axonal membrane can be modeled as a coupled sequence of analogs of gravitational pendulums and in the continuum idealization Sine-Gordon equation is satisfied. EEG rhythms (actually a fractal hierarchy of EEGs are predicted ) are due to dark photon Josephson radiation associated with sequences of solitons. This corresponds to a situation in which the penduli rotate with a constant phase difference between neighbors. A kick to the rotating pendulum so that it starts to oscillate instead of rotating corresponds to a generation of nerve pulse. This kick would also induce a gel-sol-gel phase transition propagating along the peripheral cytoskeleton.

3. Gel-sol phase transition as quantum critical phase transition

The challenge is to understand how quantum criticality making possible the phase transition is induced.

  1. The primary Josephson currents from the micro-tubuli to the axonal membrane would reduce the magnitude of the cell potential below the critical value (slowing down of the pendulum rotation). This should somehow take the peripheral cytoskeleton near to quantum criticality and induce the increase of Planck constant for the flux tubes connecting peripheral cytoskeleton to the axonal membrane and increasing their length so that they would extend to axonal exterior. This would make possible the flow of monovalent dark ions (say Na+) from the axonal exterior replacing Ca++ acting as cross links between negatively charged proteins and in this manner induce gel-sol phase transition. The reverse phase transition would reduce Planck constant. If ionic currents are non-dissipative they flow back automatically much like oscillating Josephson currents.

  2. There are two forms of quantum criticality corresponding to critical sub-manifolds M2×CP2 and M4×S2, where M2 M4 has interpretation as plane of non-physical polarizations and S2 CP2 is a homologically trivial geodesic sphere of CP2 with vanishing induced Kähler form (see the Appendix of [1]). The latter kind of quantum criticality corresponds to very weak induced Kähler fields and thus to almost vacuum extremals. Given electromagnetic field can be imbedded as a 4-surface in many manners: as a vacuum extremal, as a surface maximizing Kähler electric energy, or something between them.

  3. Quantum criticality suggests that em fields in the cell interior corresponds to nearly vanishing induced Kähler fields and that in the resting state the em fields at cell membrane and peripheral cytoskeleton correspond to strong Kähler fields. The magnitude of the cell potential in the absence of the membrane is about .05 V and slightly below the magnitude of the critical potential . Hence the reduction of the magnitude of the em (-or more precisely- Kähler-) voltage between the inner boundary of the peripheral cytoskeleton and cell exterior to a small enough value could induce quantum criticality making hbar increasing phase transition for the magnetic flux tubes connecting peripheral cytoskeleton to the axonal membrane possible. This framework also allows to understand the paradoxical fact that a reduction of the magnitude of the cell potential induces the action potential rather than its increase as the naive idea about di-electric breakdown would suggest.

  4. The energy of the Josephson photon associated with cell membrane Josephson junction is about .05 eV at criticality for the generation of action potential. This is not too far from the value of the metabolic energy quantum liberated in the dropping of proton Cooper pair from k=139 atomic space-time sheet or of electron Cooper pair from k=151 cell membrane space-time sheet to a much larger space-time sheet. This leads to the idea that phase conjugate IR photons of Josephson radiation couple resonantly to the gel defined by the peripheral cytoskeleton and induce fast dropping of protons to larger space-time sheets and that this in turn induces the increase of Planck constant for magnetic flux tubes inducing gel-to-sol phase transition. This idea has been discussed already earlier and will reconsidered in the section where the relationship of the model with microtubular level is discussed.

  5. A comment relating this picture to DNA as tqc model is in order. The basic difference between TGD and standard model is that color rotations leave invariant the induced Kähler field but affect electro-weak gauge fields. In particular, color rotations change the intensity of em field by transforming em and Z0 fluxes to each other. In the recent case color rotation cannot obviously reduce the value of the electric field. The most elegant variant of the model of DNA as tqc replaces qubit with qutrit (true/false/undefined) presented as color triplet of quarks associated with the (wormhole) magnetic flux tubes connecting nucleotides with lipids . Hence the color rotations representing basic 1-gates would not affect induced Kähler fields and cannot induce phase transitions although they would affect cell potential. For 2-gate represented by the basic braiding operation permuting the ends of the neighboring strands the situation is different. Quantum criticality would make possible the generation of braiding by taking cell membrane to liquid state. The discussion about the effects of anesthetics in the sequel forces however to conclude that in the liquid crystal state action potentials are not possible. Propagating action potentials could however represent tqc programs as time-like braidings if it is microtubular surface that suffer gel-sol-gel transition during the nerve pulse.

4. A model for anesthetic action

The molecular mechanism of the anesthetic action is a fascinating unsolved problem of neurophysiology. Noble gases have very weak chemical interactions. Despite this many noble gas such as Xe, Kr, Ar but to my best knowledge not Ne and He, act as anaesthetics. Also chemically non-inert molecules have quite similar narcotic effect so that chemistry does not seem to matter as Hodgkin-Huxley model would predict.

It is known that the narcotic efficiency of anesthetics correlates with their solubility in lipids . Anesthetics also reduce the melting temperature of the lipid layer. Strong pressure increases the melting temperature and it is known that high pressure brings consciousness back. Thus anesthetic molecules dissolved into the lipid membrane should hinder the generation of the nerve pulse somehow and liquid state of the axonal membrane could be the reason for this. The explanation of the soliton model for the anesthetic action is that the metabolic energy needed to generate an acoustic soliton becomes too high when axon is too high above the critical temperature.

To get a useful perspective note that also the problem why ordinary cell and neuronal soma outside axonal hillock do not allow action potentials is poorly understood. The obvious idea is that anesthetized axonal membrane (or at least axonal hillock) is just like the ordinary cell membrane. The model for DNA-cell membrane system as a topological quantum computer requires the liquid-crystal property of the lipid layers of the ordinary cell membrane and neuronal membrane outside axonal hillock. If this is the case, then liquid phase for axonal membrane implied by the anesthetic action would indeed make it more or less equivalent with the ordinary cell membrane. Therefore the question is why the liquid-crystal property of the ordinary cell membrane prevents the generation of the action potential.

  1. Pollack's model suggests that anesthetics could hinder the occurrence of the gel-sol phase transition for the peripheral cytoskeleton. Suppose that (h/2p) increasing phase transition for the magnetic flux tubes connecting peripheral cytoskeleton to the axon extends them to the axonal exterior and makes possible the influx of monovalent ions inducing gel-sol phase transition.

  2. Suppose that the phase transition increasing (h/2p) is induced by the reduction of the voltage over the axonal membrane (assume to be much smaller than cell potential) inducing almost vacuum property and quantum criticality. Somehow the presence of anesthetics would prevent this. Either the voltage over the membrane is increased in magnitude so that the flow of dark ionic currents to the membrane is not enough to induce quantum criticality or the flow of dark currents is completely prevented. The first option is more economical and could be tested by finding whether the voltage over the axonal membrane (membrane in a solid state) is considerably smaller than that over the ordinary cell membrane (membrane in liquid-crystal state). The first option also predicts that during sleep the increase of cell potential (hyperpolarization) actually corresponds to the increase of the membrane potential.

For background see the chapter TGD Inspired Model for Nerve Pulse. References

[1] The chapter DNA as Topological Quantum Computer of Genes and Memes.
../genememe/genememe.html#dnatqc.

[2] The chapter Bio-Systems as Super-Conductors: Part I of Quantum Hardware of Living Matter.
../bioware/bioware.html#superc1.

[3] The chapter Quantum Model for Nerve Pulse of TGD and EEG.
tgdeeg.html#pulse.

[4]G. Pollack (2000), Cells, Gels and the Engines of Life, Ebner and Sons.
http://www.cellsandgels.com/.

[5] Sine-Gordon equation, http://en.wikipedia.org/wiki/Sine-Gordon.

[6]K. Graesboll (2006), Function of Nerves-Action of Anesthetics, Gamma 143, An elementary Introduction. http://www.gamma.nbi.dk.



Quantum model of nerve pulse VI: Deducing the presence and basic properties of dark matter from the strange behavior or cell membrane

The strange findings about the behavior of cell membrane [1,2,3,4,5,6] had strong impact on the evolution of TGD inspired model of biosystems. One would expect that when cell is posed to metabolic deprivation, it soon ceases to function since ionic pumps require a lot of metabolic energy. This did not happen. Second absolutely amazing finding was that ionic currents through cell membrane are obviously quantal and even more: remain essentially same when cell membrane is replaced with an artificial membrane.

TGD based model for nerve pulse in its recent form explains all these findings. One can however ask what is the role of ionic pumps and channels if oscillatory Josephson currents make pumps un-necessary. The vision about dark matter and the model of nerve pulse formulated in terms of Josephson currents brings an additional perspective to the role of pumps and channels and allows to achieve harmony with the standard views about their role.

  1. In long length scales visible matter forms roughly 5 per cent of the total amount of matter. In TGD Universe the dark matter would correspond to matter with large Planck constant including dark variants of ordinary elementary particles. In living matter situation could be the same and visible matter could form only a small part of the living matter. Dark matter would be however visible in the sense that it would interact with visible matter via classical electromagnetic fields. Hence one can consider the possibility that most of the biologically important ions and perhaps even molecules reside at the magnetic flux quanta in large hbar phase.

  2. The function of pumps and channels could be same as in standard model since also in TGD Universe homeostasis and its control at the level of visible matter requires them. The metabolic energy needed for this purpose would be however dramatically smaller and a reliable estimate for this would allow an estimate of the portion of dark matter in living systems. Pumps and channels could also serve the role of sensory receptors by allowing to take samples about chemical environment.

To sum up, the strange discoveries about the behavior of cell membrane provide direct experimental evidence for the presence of dark matter in living systems, for the prediction that it interacts with ordinary matter via classical electromagnetic fields, and for the assumption that it does not dissipate appreciably and could therefore have large value of hbar and form macroscopic quantum phases.

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

References

[1] G. Pollack (2001), Cells, Gels and the Engines of Life, Ebner and Sons.

[2] G. N. Ling (1962) A physical theory of the living state: the association-induction hypothesis; with considerations of the mechanics involved in ionic specificity. New York: Blaisdell Pub. Co.

Ibid(1978):Maintenance of low sodium and high potassium levels in resting muscle cells. Journal of Physiology (Cambridge), July: 105-23.

Ibid(1992): A revolution in the physiology of the living cell. Malabar, FL: Krieger Pub. Co.

Ibid, Three sets of independent disproofs against the membrane-pump theory.

G.N. Ling et al(1978): Experimental confirmation, from model studies, of a key prediction of the polarized multilayer theory of cell water. Physiological Chemistry and Physics, 10:1, 1978: 87-8.

[3] B. Sakmann and B. Neher (1983): Single-channel recording. Plenum Press, New York and London.

[4] W. K. Purves and G. H. Orians (1987): Life: The Science of Biology. Sunderland, Massachusetts: Sinauer.

[5] F. Sachs, F. Qin (1993), Gated, ion-selective channels observed with patch pipettes in the absence of membranes: novel properties of a gigaseal. Biophysical Journal, September: 1101-7.

[6] A. A. Lev et al (1993), Rapid switching of ion current in narrow pores: implications for biological ion channels. Proceedings of the Royal Society of London. Series B: Biological Sciences, June, 187-92.



Quantum model of nerve pulse V: Summary

Quite recently I learned [1,2,3,4,5] (thanks to Ulla Mattfolk) that nerve pulse propagation seems to be an adiabatic process and thus does not dissipate: the authors propose that 2-D acoustic soliton is in question. Adiabaticity is what one expects if the ionic currents are dark currents (large hbar and low dissipation) or even supra currents. Furthermore, Josephson currents are oscillatory so that no pumping is needed. Combining this input with the model of DNA as topological quantum computer (tqc) [8] leads to a rather precise model for the generation of nerve pulse. The following gives a brief summary of main points of the model in its recent form.

  1. The system would consist of two superconductors- microtubule space-time sheet and the space-time sheet in cell exterior- connected by Josephson junctions represented by magnetic flux tubes defining also braiding in the model of tqc. The phase difference between two super-conductors would obey Sine-Gordon equation allowing both standing and propagating solitonic solutions. A sequence of rotating gravitational penduli coupled to each other would be the mechanical analog for the system. Soliton sequences having as a mechanical analog penduli rotating with constant velocity but with a constant phase difference between them would generate moving kHz synchronous oscillation. Periodic boundary conditions at the ends of the axon rather than chemistry determine the propagation velocities of kHz waves and kHz synchrony is an automatic consequence since the times taken by the pulses to travel along the axon are multiples of same time unit. Also moving oscillations in EEG range can be considered and would require larger value of Planck constant in accordance with vision about evolution as gradual increase of Planck constant.

  2. During nerve pulse one pendulum would be kicked so that it would start to oscillate instead of rotating and this oscillation pattern would move with the velocity of kHz soliton sequence. The velocity of kHz wave and nerve pulse is fixed by periodic boundary conditions at the ends of the axon implying that the time spent by the nerve pulse in traveling along axon is always a multiple of the same unit: this implies kHz synchrony. The model predicts the value of Planck constant for the magnetic flux tubes associated with Josephson junctions and the predicted force caused by the ionic Josephson currents is of correct order of magnitude for reasonable values of the densities of ions. The model predicts kHz em radiation as Josephson radiation generated by moving soliton sequences. EEG would also correspond to Josephson radiation: it could be generated either by moving or standing soliton sequences (latter are naturally assignable to neuronal cell bodies for which hbar should be correspondingly larger): synchrony is predicted also now.

  3. The previous view about microtubules in nerve pulse conduction can be sharpened. Microtubular electric field (always in the same direction) could explain why kHz and EEG waves and nerve pulse propagate always in same direction and might also feed energy to system so that solitonic velocity could be interpreted as drift velocity. This also inspires a generalization of the model of DNA as topological quantum computer [7] since also microtubule-cell membrane systems are good candidates for performers of tqc. Cell replication during which DNA is out of game seems to require this and microtubule-cell membrane tqc would represent higher level tqc distinguishing between multi-cellulars and mono-cellulars.

  4. New physics would enter in several manners. Ions should form Bose-Einstein cyclotron condensates. The new nuclear physics predicted by TGD [8] predicts that ordinary fermionic ions (such as K+, Na+, Cl-) have bosonic chemical equivalents with slightly differing mass number. Anomalies of nuclear physics and cold fusion provide experimental support for the predicted new nuclear physics. Electronic supra current pulse from microtubules could induce the kick of pendulum inducing nerve pulse and induce a small heating and expansion of the axon. The return flux of ionic Josephson currents would induce convective cooling of the axonal membrane. A small transfer of small positive charge into the inner lipid layer could induce electronic supra current by attractive Coulomb interaction. The exchange of exotic W bosons which are scaled up variants of ordinary W+/- bosons is a natural manner to achieve this if new nuclear physics is indeed present. There are a lot of support for this new physics: cold fusion and nuclear transmutations in living matter [8] ( these I have discussed in previous postings).

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".

[8] The chapter Nuclear String Physics of "p-Adic Length Scale Hypothesis and Dark Matter Hierarchy".



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 microtubules 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 microtubules 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 microtubules 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 microtubules 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 microtubules. 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 microtubules. 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".



Quantum model of nerve pulse III: Relation to Hodgkin-Huxley model

Before the replacement of Hodgkin-Huxley model with a genuinely quantal model can be taken seriously, one must answer many difficult questions which also Hodgkin and Huxley must have faced as they developed their own model. In the following I will go through the basic questions and quantum answers to them.

1. Questions and answers

Q: In the resting state membrane potential is negative and cell has a negative net charge. What stabilizes the cell against the leakage of the negative charge if pumps and channels are not responsible for this?

A: The findings about the strange behavior of cell membrane inspire TGD based answer. Cell membrane space-time sheet is its own quantum world and the flow of ions occurs only in the presence of magnetic flux tubes connecting it to the external world. These currents a however oscillatory Josephson currents if dissipation is absent. Hence there is no need to cut completely the connections to the external world.

Q: How the resting state can result spontaneously if pumps are absent?

A: If ionic currents are Josephson currents, they are automatically oscillating and the return to the original state is guaranteed. The flux tubes carrying the ionic currents will be assumed to connect axonal microtubules to the space-time sheet of the cell interior. Consider first the most obvious objections.

  1. Dark ions could not transform to ordinary ones in the exterior of the cell membrane. This might indeed kill the model.

  2. If ionic currents are Josephson currents, they are automatically oscillating and the return to the original state is guaranteed. The objection is that all biologically important ions are not bosons and the model for high Tc super-conductor in its recent form allows only electronic and protonic Cooper pairs at room temperature [8]. TGD based nuclear physics however predicts the possibility of exotic nuclei for which one or more color bonds connecting nucleons to the nuclear string are charged. These exotic nuclei with electronic states identical to those of genuine ions could save the situation. The table below describes how cyclotron frequencies for B=.2 Gauss of the most important ions are modified in the simplest replacements with exotic ions. For instance, the notation Mg++- tells that there is double electronic ionization and electron shell of Argon as usual but that one color bond is negatively charged.

    23Na+19Ne+: 13.1 Hz → 15.7 Hz

    23Na+24→ Mg++-: 13.1 Hz→ 12.5 Hz

    39K+40→ A+: 7.7 Hz→ 7.5 Hz

    39K+40Ca++-: 7.7 Hz→ 7.5 Hz

    35Cl-40A-: 8.6 Hz →7.5 Hz

    fc(K+) and fc(Cl-) are replaced with the frequency 7.5 Hz and one can do only using the cyclotron frequencies fc(Ca++)/2=7.5 Hz, fc(Mg++)=12.5 Hz, and fc(Ca++)=15 Hz. The nominal values of the lowest Schumann frequencies are 7.8 Hz and 14.3 Hz. All ions with relevance for nerve pulse and EEG could be bosonic ions or bosonic pseudo-ions. I do not know how well the needed ionization mechanisms are understood in the standard framework.

For small oscillations the maximal charge transfer ΔQ generated by an oscillating ionic Josephson current during the cycle is proportional to hbar /fJ propto hbar2 and hbar /Ω propto hbar for solitonic situation. ΔQ is very small for the ordinary value of hbar : also the oscillation period is very small. For large values of hbar situation changes and large maximal ion transfers are possible.

An hbar increasing phase transition could be involved with the generation of the nerve pulse. Quantum criticality during nerve pulse generation indeed suggest the presence of flux tubes with varying values of hbar . The lifetimes of the connected flux tubes could be proportional to hbar at criticality. A fractal hierarchy of pulses and EEG like oscillations of the membrane potential corresponding to various values of hbar is suggestive.

Q: Can one make this more quantitative?

A: One can construct a model based on Sine-Gordon wave equation [7] for the phase different Φ between the superconductors connected by Josephson junction sequences defined by magnetic flux tubes and idealizable as a continuous Josephson junction.

  1. For a Josephson junction idealizable as a hollow cylinder with radius R and thickness d the expression of the Josephson current reads as

    J= J0sin(Ze∫ Vdt/hbar)

    J0 is in case of cell membrane given by

    J0= (Ze2π dR/Λ2) ×(hbar/m) ,

    where R and d would be now the radius and thickness of the axon, Λ is the magnetic peneration length, and m is the mass of the charge carrier. Although this expression does not hold true as such when Josephson junctions are replaced by magnetic flux tubes connecting microtubuli and axon, one can can safely make some qualitative conclusions. The amplitude of the Josephson current increases with hbar . For electron the value of the amplitude is by a factor x≈ Amp/me≈ 211A larger than for ion with a mass number A. This gives for electron Cooper pairs a unique role as an initiator of the nerve pulse. Note that the amplitudes of the Josephson currents of electron and ions are quite near to each other if one has hbar (ion)= 211A×hbar: this might explain why the powers of 211 for hbar seem to be favored.

  2. Electronic Josephson current dominates and makes it ideal for the generation of nerve pulse (kick to gravitational pendulum). This is possible if the net amount of electronic charge is so small that it flows out during the generation of flux tubes. For ions this need not occur even if ion densities are of same order of magnitude. Constant voltage V creates an oscillating current and no catastrophic leakage takes place and the resting state results automatically. The ionic Josephson currents assignable to the magnetic flux tubes connecting microtubules through the cell membrane to the external world could be responsible for the nerve pulse.

  3. The mechanical analog for Sine-Gordon system [8] assignable to Josephson junction is rotating pendulum but one must be cautious in applying this analogy. There are two options concerning the modeling of the situation.
    1. Membrane potential represents an external voltage V(t) and one has Φi= Zie∫ Vdt/hbar, where Φi is the phase difference between Bose-Einstein condensates.
    2. System is autonomous and membrane potential V(t)=hbar (dΦi/dt)/Zie is completely determined by the dynamics of any phase Φi. This option is highly predictive and discussed in the sequel.

  4. The analogy with gravitational pendulum allows to identify the phase angle Φ as the counterpart of angle Θ characterizing angular position of mathematical pendulum (note that this analogy can be misleading since it implicitly brings in 3-D thinking).
    1. In this picture rotating pendulum corresponds to a soliton sequence containing infinite number of solitons: both stationary and moving soliton sequences are obtained. The sign of Ω=dΦ/dt is fixed and approximately constant for large values of Ω. Resting potential could correspond to this kind of situation and Ω ≈ 2π kHz is suggested by kHz synchrony. A mechanism of this synchrony will be discussed below. For large values of hbar even values of Ω in EEG range could correspond to membrane potential. For large values of Ω one as V≈ hbarΩi/Zie. If also EEG rhythms correspond to Ω they must correspond to different values of hbar and f propto 1/hbar would hold true. Changes in the dominating EEG rhythm (40 Hz, 10 Hz, 5 Hz,..) could correspond to phase transitions changing hbar to given value for a large number of axons. The maximal charge transfer during single period is proportional to Δ Q propto 1/Ω.
    2. Hyperpolarization/polarization would mean fastening/slowing down of the pendulum rotation and slowing down would make the system unstable. Near criticality against the generation of nerve pulse would mean that pendulum is rotating rather slowly (Ω<< fJ ) so that a small kick can transform rotation to oscillation. The sign of V propto dΦ/dt would change and large amplitude oscillatory motion would result for single period only after which a kick in opposite direction would lead back to the resting state. Membrane potential varies between the resting potential V0=-75 V and V1=+40 V during nerve pulse: V1>|V0| would have killed the model. Note that V1=40 V is rather near to the critical potential about V1=50 V: ideally these potentials should be identical.
    3. The so called breathers -both stationary and moving- correspond to soliton-antisoliton bound state (see the visualization here). Breathers could be identified as large amplitude oscillations around Φ=0 ground state. Physical intuition suggests that breathers are possible also for a ground state corresponding to a rotating pendulum (representing moving or stationary waves). They would correspond to kicking of one pendulum in a sequence of penduli along z-axis rotating in phase at the initial moment. The kick could correspond to a genuine external perturbation generated by a pair electronic supra current pulses of opposite sign giving constant velocity increments ΔΩ initiating and halting the nerve pulse just like they would do in the case of tqc but in opposite time order. If the background corresponds to a propagating EEG wave, also nerve pulse is expected to propagate with same velocity. The propagation direction of EEG wave would also explain why nerve pulses propagate only in single direction.

  5. For the ordinary value of hbar , the frequency of the Josephson current corresponds to that assignable to energy .07 eV being around 1.6×1013 Hz and quite high. For x==hbar /hbar0=244 the frequency would be near to cyclotron frequency of about 1 Hz assignable to DNA strands. For x=3× 23× 13 the frequency would be near to the fundamental 10 Hz frequency which is secondary p-adic time scale associated with electron and correspond to the temporal duration of negative energy space-time sheet assignable to electron. For x=3× 23× 11 one would obtain a 640 Hz frequency which corresponds to the time scale of nerve pulse. It seems clear that the original hypothesis that only powers of 211 define the spectrum of Planck constant is too restrictive. The requirement that cyclotron frequencies and Josephson frequencies are proportional to each other for small oscillations would guarantee resonant behavior for common strength of the magnetic field would give hbar propto A. This would require that each ion species lives at its own flux tubes.

Q: What instabilizes the axon? Why the reduction rather than increase of the magnitude of the membrane potential induces the instability? Why the reduction of the resting potential below the critical value induces nerve pulse?

A: Large enough voltage pulse between microtubules and membrane could generate electronic DC supra current. The introduction of a small amount of positive charge to the inner lipid layer and staying there for some time would generate the voltage pulse between microtubules and lipid layer so that DC electronic supra current would be induced, and induce the reduction Δ V≈ .02 eV of the magnitude of the membrane potential. A similar introduction of negative charge would induce hyperpolarization and the direction of the current would be opposite if it is generated at all. The mechanism generating the small positive charge to the inner lipid layer could be based on the exchange of exotic W bosons between pairs of exotic nuclei at opposite sides of the cell membrane so that the negative charge of the inner lipid layer would be reduced.

Q: Can one understand the observed radial force, the increase of the radius of axons and the reduction of its thickness, and heating followed by cooling?

A: The observed outward force acting on a test system might be due to the ionic Josephson currents to which the test system responds. During the second half of the pulse the sign of the ionic force is predicted to change. The pressure caused by the electronic Josephson current pulse before the connection of flux tubes to single flux tube might relate to the increase of the radius of the axonal membrane and with the reduction of its thickness as well as the slight increase of its temperature as being due to the electrons which heat the lipid layer as they collide with it. The ions return at the second half of the pulse and could transfer the heat away by convection.

  1. This hypothesis gives the estimate for the force f per unit area as

    f2e(t)= (dn(lipid)/da) ×(J(t)/2e)× hbar k

    = (dn(lipid)/da) × U× (hbar2 k/2me)× sin(ωJ(2t)) ,

    U= (2π A/Λ2) .

    The parameter A corresponds to the parameter dR in the case that Josephson junctions have the thickness of axonal membrane, and is not relevant for order of magnitude estimate. R corresponds to the distance between microtubules and cell exterior space-time sheet to which flux tubes end. dn(lipid)/da is the 2-D density Josephson junctions equal to the density of lipids.

    k≈ 1/R is the wave vector of electron Cooper pair at the magnetic flux tube. The 3-momentum of electron is enormous for the proposed value of hbar , and the only possible interpretation is that the four-momentum of electron is virtual and space-like and corresponds to exchange of space-like virtual photon describing Coulomb interaction with lipid layer.

    Λ2 satisfies in the first approximation the formula

    Λ-2 = (4π e2ne/me)+ ∑I (4π e2nI/AmI)= αem16π2 ×hbar0[(ne/me)+ ∑I (nI/AImI)].

    Note that there is no real dependence on hbar . Above critical voltage electrons could dominate in the expression but during nerve pulse ions should give the dominating contributions. U cannot be too far from unity.

  2. From this one can integrate the total momentum of Cooper pairs transferred to the lipid layer before the flux tubes fuse together if one knows the value of time t when this happens. F propto hbar2/me2 proportionality implies that for the required large value of hbar /hbar0 ≈ 3× 233 the force is by a factor 6× 1020 stronger than for hbar0.

  3. The force caused by ionic Josephson currents on piston is given by

    f(t)= ∑I (2me/mI) (2/ZI) × f2e (τ)

    τ=(ZI/2)×(Ω/ωJ)× t .

  4. The comparison with the observed force gives estimate for the value of magnetic penetration length and thus density of electrons at the flux tube.

    According to [3] in one particular experiment the force on piston of area S= .01 cm2 at the maximum of voltage (t= 2π/Ω) is F= 2 nN. This gives a killer test for the model. One obtains an estimate for the parameter U=(Λ2/2π A) as

    U=Λ2/2πA= (dn(lipid)/da) × (hbar2 k/mpcF)× ∑I (2/AIZI) .

    The value of U should not deviate too much from unity. One can use the estimates

    hbar/hbar0=3×233 , k=2π/R.

    Note that the experimental arrangement forces to use this value of k. The actual value in normal situation would be smaller and depends on the distance of the boundary of the cell exterior space-time sheet on microtubules. Using the values d=10 nm and R=5 μm this gives

    U≈ ∑I (2/AIZI)× X ,

    X= 9× 266× (hbar02 2π/mpcFR)×(S/S(lipid)).

    The factor X=.9267 is of order unity! Taking into account that hbar/hbar0 is enormously large number it is difficult to believe that the result could be mere accident. Hence U does not deviate too much from unity and there are good hopes that the model works.

    For nI= xI/a3, a=10-10 m, and A= dR one obtains a direct estimate which combined with above estimate gives two conditions which should be consistent with each other:

    U= 76.1×∑I(xI/AI) ,

    U= .93×∑I(2/AIZI) .

    These estimates are consistent for xI≈ 10-2, which makes sense.

Q: Where the primary wave propagates: along axon or along microtubules?

A: This question need not make sense if microtubules and axon are connected by magnetic flux tubes to form single quantum coherent system. That axonal microtubules have constant electric field which is always in same direction could explain why the background soliton sequences and nerve pulses propagate always in the same direction and suggests that the primary wave propagates along microtubules. On the other hand, if W exchange between cell exterior and exterior reduces the negative charge of the inner lipid layer then axon could be seen as initiator. This could induce conformational or gel-sol phase transition propagating along microtubule and inducing the pair of voltage pulses in turn inducing the fusion of flux tubes at cell membrane which in turn would induce criticality of the axonal membrane. For this option axonal soliton would be a shadow of the microtubular soliton rather than completely independent dynamical process.

Q: How nerve pulse velocities are determined?

A: At first glance it seems v could be determined by boundary conditions guaranteing synchronization of neuronal activity rather than by dissipation as in Hodgkin-Huxley model. As a matter fact, dissipation turns out to affect also v just because it is determined by boundary conditions!

  1. Hodgkin-Huxley model would suggest that nerve pulse velocity v is dictated by frictional effects as an analog of a drift velocity. The rough order of magnitude estimates for the velocities of conformational waves along micro-tubuli are consistent with the velocities of nerve pulses. The proportionality v propto d of nerve pulse velocity to nerve axonal radius might be understood as resulting on the dependence on the length of flux tubes connecting axon and microtubules and mediating a frictional feedback interaction from axon. Feedback would be naturally reduced as d increases. Feedback interaction could explain also the sensitivity of the thermal parameters of the axonal membrane to the proteins in its vicinity. If the frictional feedback is due to the environmental noise at the axon amplified at quantum criticality this is what one expects. Quite generally, quantum criticality would explain the high sensitivity of the thermal parameters on noise. Saltation cannot be responsible for the higher conduction velocity in myelin sheathed portions of axon. The insulation would reduce the environmental noise at the level of axons and thus reduce the frictional feedback from axon to the microtubules.

  2. The introduction of friction is however problematic in the recent situation. In absence of boundary conditions Sine-Gordon equation predicts for the propagating soliton sequences a continuous velocity spectrum and friction should affect Ω and V but it is not clear whether it can affect v.

    1. In this framework the boundary boundary conditions at the ends of the axon or some subunit of axon would dictate the values of v: γΩ L/v=n2π corresponds to periodic boundary conditions (note that γ=(1-(v/c)2)1/2≈ 1 holds true). v=ΩL/n2π implies that friction indeed affects also v.

    2. This relationship states that the time taken by the nerve pulse propagate through the axon is always T= L/v =n2π/Ω: this would synchronize neurons and Ω≈ 2π kHz is suggested by the well-known 1 kHz synchrony difficult to understand in the standard framework where v would be determined by chemistry rather than geometry. Myelin shielding could in this picture guarantee that coherent wave propagation is possible over the entire axon so that boundary conditions can be applied.

    3. This would give v≈ ΩL/n2π≤ ΩL/2π. Ω= 2π kHz and n=1 would give for L in the range 1 cm -10 cm v in the range 10 m/s-100 m/s corresponding roughly to the observed range of values. For short axons velocity would be lower: for L=10 μm one would have v= .01 m/s. For longer axons the value of n could be higher or the axon would decompose into structural units for which periodic boundary conditions are satisfied. The sections between Ranvier nodes have length measured in millimeters as are also the lengths of axonal microtubules and 1 mm would correspond to a velocity of 1 m/s. The actual velocity for the myelinated sections varies between 18-100 m/s so that basic structural units should be longer.

    4. The proportionality of v to the radius of axon would follow from the proportionality of the length of the axon or its basic sub-unit (not longer than ≈ 10 cm) to its radius: the simplest geometric explanation for this would be in terms of scaling invariance of the axonal geometry consistent with fractality of TGD Universe. In the standard framework this proportionality would be explained by the minimization of dissipative losses in the case of long axons: one cannot exclude some variant of this explanation also now since friction indeed reduces v.
    5. There is an electric field associated with microtubules (always in same direction). Could this electric field play the role of external force feeding energy and momentum to the moving soliton sequence to compensate dissipation so that v would have interpretation as a drift velocity?

Q: Can one understand EEG in this framework?

A: Just like kHz waves also EEG generating waves could correspond to propagating soliton sequences. Since V is not affected, the value of hbar must be much larger and one must have hbar propto f, where f defines the EEG rhythm. It is known that EEG amplitudes associated with EEG rhythms behave roughly like 1/f. This can be understood. By Maxwell's equation the divergence of electromagnetic field tensor is proportional to 4-current implying the amplitude of EEG identified as Josephson radiation is proportional J0/Ω and therefore to hbar. The propagation velocity v= ΩL/2πn of EEG generating waves is rather slow as compared to kHz waves: for f=10 Hz one would have 10 cm long axon v=1 m /s. Synchronization results automatically from periodic boundary conditions at the ends of the axons.

Nerve pulses during EEG rhythms would have much slower velocity of propagation and the duration of nerve pulse would be much longer. The maximal charge transfer would be proportional to 1/hbar. It would thus seem that EEG and nerve pulse activity should exclude each other for a given axon. Ω is however smaller so that the generation of nerve pulse is easier unless also ion densities are lower so that J0 (analogous to gravitational acceleration g in pendulum analogy) is reduced. Perhaps this takes place. The consistency with the propagation velocity of microtubular conformational (or even gel-sol-gel) waves might pose additional constraints on v and thus on frequencies Ω for which nerve pulses are possible. That ordinary EEG is not associated with ordinary cells might be due to the fact that hbar is much smaller: the fractal analog of EEG generating waves could be present but these EEG waves would correspond to faster oscillations in accordance with the view about evolution as an increase of hbar.

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] Sine-Gordon

[8] The chapter Bio-Systems as Super-Conductors: part I of "The Quantum Hardware of Living Matter".



Quantum model of nerve pulse II: Basic inputs of TGD based model of nerve pulse

The model of nerve pulse whose inputs are summarized below can be motivated by the observed adiabaticity of the nerve pulse and by the strange findings about ionic currents associated with the cell membrane and by the model of Danish researchers for the nerve pulse [1,2,3,4]. The model involves also a fusion of various ideas of earlier models. In particular, Josephson currents and solitons are in a key role in the model but with the necessary flexibility brought in by the hierarchy of Planck constants.

The basic inputs of the model are following.

  1. The presence of acoustic soliton or density pulse proposed by Danish researchers [3] looks plausible but a a more fundamental quantum control mechanism inducing the acoustic soliton cannot be excluded. Among other things this should explain why acoustic solitons propagate always in the same direction. In particular, one can consider a soliton like excitation (say breather for Sine-Gordon equation) associated with the electronic or ionic Josephson currents running along magnetic flux tubes. The strange effects associated with the ionic currents through the cell membrane suggest quite generally that at least weak ionic currents through normal cell membrane are non-dissipative quantal currents. The adiabaticity of the nerve pulse suggests that also strong ionic currents are quantal.

  2. Strong ionic currents generating nerve pulse through axonal membrane are absent in the resting state. The naive explanation is simple: the life time of the magnetic flux tubes connecting the axonal interior to the exterior is short or the flux tubes are altogether absent. The observation that Josephson currents in constant voltage are automatically periodic suggests a less naive explanation allowing the flux tubes to be present all the time. The presence of ionic Josephson currents predicts a small amplitude oscillation of membrane potential for which 1 kHz synchronous oscillation is a natural identification. Josephson oscillation correspond naturally to propagating soliton sequences for Sine-Gordon equation [7]. The dynamics of the simplest modes is equivalent to the rotational motion of gravitational pendulum: the oscillation of membrane potential corresponds to the variation of dΦ/dt propto V. Note that if axon is above the melting temperature, the lipid layer is in gel phase and fluid motion is impossible. The surface density of lipids is dramatically reduced at criticality so that lipid layers behave like fluids [3]. This means that tqc is not possible by the braiding of lipids.

  3. Nerve pulse is generated when the magnitude of the negative membrane potential is reduced below the critical value. Generation of the nerve pulse is like a kick to a rotating gravitational pendulum changing the sign of Ω= dΦ/dt so that rotational motion is transformed to oscillatory motion lasting for about the period of rotation. An opposite but slightly stronger kick must reduce the situation to the original one but with a slightly higher value of Ω. These kicks could correspond to voltage pulse between microtubules and inner lipid layer of cell membrane induced by the addition of small positive (negative) charge on lipid layer. This pulse would induce electronic DC Josephson current inducing the kick and thus reducing V. The exchange of scaled variants of W bosons (assignable to W MEs) could mediate the transfer of charge through the cell membrane and reduce the membrane potential below the critical value but one can consider also other mechanisms.

  4. The conservative option would be that ordinary ionic currents take care of the rest and Hogkin-Huxley model applies. This was assumed in the earliest model in which soliton sequence for Josephson current was assumed to induce nerve pulse sequence: in the recent model this assumption does not make sense. The findings of Danish researchers do not however support the conservative option [3]. Nerve pulse could be due to dark ionic (possibly supra -) currents with large hbar with a low dissipation rate. Their flow would be made possible by the presence of magnetic flux tubes connecting cell interior and exterior.

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] Sine-Gordon

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



Quantum model of nerve pulse I: Soliton model of nerve pulse

In the first part of series I will briefly summarize soliton model of nerve pulse proposed by Danish researchers [1,2,3,4].

  1. The temperature of the axon is slightly above the critical temperature Tc for the phase transition leading from crystal like state of the lipid layers to a liquid crystal state. Near criticality the elastic constants and heat capacity of the membrane vary strongly and have maxima at criticality so that also sound velocity varies strongly near criticality. Also the relaxation times are long. There is also dispersion present meaning that the frequency of sound wave depends nonlinearly on wave vector. Non-linearity and dispersion are prerequisites for the presence of solitons which by definition do not dissipate energy.

  2. Variations of temperature, volume, area, and thickness and also other mechanical effects are known to accompany nerve pulse propagation. It is also known that the heat density and temperature of the cell membrane increases slightly first and is then reduced. This suggests adiabaticity in average sense. These findings motivate the assumption that nerve pulse actually corresponds to acoustic soliton [2,3].

  3. Soliton model reproduces correctly the velocity of nerve pulse inside myelin sheaths but it is not clear to me how well the much lower conduction velocity in non-myelin sheathed regions is reproduced. It is not clear how the lower values of the conduction velocity and its proportionality to the axonal radius in non-myelinated regions can be understood. Intuitively it however seems clear that the lower velocity is due to the feedback from the interaction of ions with the region exterior to cell membrane. In the case of myelin sheaths the conduction of nerve pulse is usually believed to take place via saltation [6]: the depolarization induced at Ranvier node is believed to be enough to take the membrane potential below critical value in the next node so that nerve pulse hops between the nodes. Insulation would improve the insulation and make this process possible. The reversible heat transfer process is however known to be present also in the myelinated portions of axon so that there must be a pulse propagating also in these regions [3]. It is not clear how the myelin sheet can increase the velocity in the soliton model but the reduction of the feedback inducing friction suggests itself.

  4. Soliton property predicts adiabaticity. Ordinary ionic currents however dissipate so that adiabaticity assumption is questionable in standard physics context. The model does not predict the growth of entropy followed by its reduction. This behavior is consistent with adiabaticity in a time resolution of order millisecond.

  5. The estimate for the capacitor energy density during the nerve pulse is considerably smaller than the energy density is many times magnitude smaller than that of the acoustic wave. This might allow to demonstrate that Hodgkin-Huxley model is not a complete description of the situation.

  6. Authors notice [2,3] that the shapes curves representing solitonic energy density and the capacitor energy density as a function of time are essentially identical. Same applies to the experimentally deduced heat change release curve and capacitor energy density for garfish axon. Also heat release and the deviation of the membrane potential from its resting value are in exact phase. These similarities could reflect a control signal responsible for the nerve pulse originating somewhere else, perhaps at microtubules. This could explain why secondary nerve pulse is not generated immediately after the first one although the temperature is slightly lower after the pulse than before it. This could of course be also due to the exhaustion of the metabolic resources.

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.



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