Cell as gel and the quantum 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 T_c 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 T_c 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 Ì M⁴ has interpretation as plane of non-physical polarizations and S² Ì 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 of TGD and EEG. References

[1] The chapter DNA as Topological Quantum Computer of Genes and Memes.
http://www.helsinki.fi/~matpitka/genememe/genememe.html#dnatqc.

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

[3] The chapter Quantum Model for Nerve Pulse of TGD and EEG.
http://www.helsinki.fi/~matpitka/tgdeeg/tgdeeg/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.