Microtubules as Quantum Systems

Microtubules as Quantum Systems (Notes and considerations on R. Penrose and S. Hameroff's Orchestrated Objective Reduction Theory, Dr. Anirban Bandyopadhyay studies, Jürg Fröhlich Bose-Einstein condensation implications, Karthikeyan Marimuthu and Raj Chakrabarti on Dynamics and Control of DNA Sequence Amplification in TQC programs) Written and compiled by Giulio D’Agostino, Dublin - 2015 Did the observation by the group led by Dr. Anirban Bandyopadhyay about detection of quantum vibration in microtubule scale (up to 50 µm) can be replicated? Would this be a breakthrough in "quantum "consciousness"" studies? The results do not however prove Orchestrated Objective Reduction (Orch-OR), which involves poorly defined vision about quantum gravitational description of state function reduction, so that most predictions are just order of magnitude estimates relying on Heisenberg's Uncertainty Principle. The idea is that flux tubes form a 2-D coordinate grid consisting of parallel flux tubes in two different directions: the guess that they could consist of helical Fibonacci flux tubes and their mirror images is in my opinion not convincing. Crossing points would be associated with tubulins and the conformational state of tubulin could define a bit coding whether the braid strands defining coordinate lines are braided or not (swap or not). In this manner any bit pattern at microtubule defines a particular TQC program (as in “A proposal for microtubular memory code” studies). If also conformations are quantum superposed, one has ”quantum-quantum computation” (as in per the soliton hypothesis that claims to explain how action potentials are initiated and conducted along axons based on a thermodynamic theory of nerve pulse propagation). It however seems that conformation change is irreversible chemical reaction [J6] so that this option is not feasible. The increase of Planck constant could be associated with the phase transition to A-phase making possible high Tc dark super-conductivity for which evidence is observed … one can even estimate results for hef f /h = n if one requires that AC photons have energy above thermal threshold: n = heff / h = f visible / fAC would be the estimate. For biophoton energies one would obtain something like n ' 108 − 109, which pops up in different contexts in TGD (Topological Geometro Dynamics) framework. This picture generalizes in the fractal universe of TGD (Topological Geometro Dynamics) . One can form layers of 2-D coordinate grids and connect them by vertical flux tubes to obtain 3-D grid defining TQC. The brain is known to have grid-like architecture and neurons could by quantum computation produce bit/qubit defining swap or not/superposition of swap and not-swap for a larger scale TQC. Approximately two decades ago Penrose and Hameroff proposed a model that they called Orchestrated Objective Reduction (Orchestrated Objective Reduction (Orch-OR) ) [J17]. Besides the highly speculative quantum gravity related ideas, the model assumes that microtubules are quantum coherent systems essential for "consciousness". There are two basic challenges: one should formulate precisely what Orchestrated Objective Reduction (Orch-OR) really means and be able to identify the qubit: 1. The basic vision about quantum superposition of space- time geometries gives rise to “"consciousness"” as something analogous to quantum computation. State function reduction would thus reduce to a mechanism rather than being something irreducible. Most quantum physicists would disagree about this. The quantum superposed geometries would be protein conformations. Since there is no theory of quantum gravity, the proposal boils down to the ad hoc estimate for the time τ for Orchestrated Objective Reduction (Orch-OR) to take place claimed to be τ = ~/EG, where EG is the difference of gravitational energies for the superposed geometries. The estimates favor nuclear scale 5 fm and one needs a coupling between nano-scale physics of electrons and physics nuclei and London forces are suggested to be responsible for this coupling. It deserved to be mentioned that the gravitational energy for a blog of water with radius around 10−4 meters the size scale of large neuron - is about Planck mass so that gravitation and biology might relate. In my own proposal involving large gravitational Planck constant assigned to space-time sheets mediating gravitational interaction, Planck mass might serve as a threshold above which large values of Planck constant would emerge [K11, K9]. 2. Concerning the identification of qubit there is a long list of suggestions. The superposition of tubulin conformations was one of the first proposals. Jeffrey R. Reimers [J6], who has criticized heavily Orch-OR proposal, reports that irreversible chemical reaction is responsible for selecting conformation so that quantum superpositions would not make sense. Conformational switching could however be involved with classical computational aspects of biological information processing and Hameroff has proposed before Orchestrated Objective Reduction (Orch-OR) that microtubules could act as classical cellular automatons. Orchestrated Objective Reduction (Orch-OR) proposal involves several interesting ideas probably relevant for quantum "consciousness": 1. Aromatic rings have probably some deep role in quantum "consciousness". For instance, most psychoactive biomolecules and also DNA and three amino acids contain them. Hameroff and Penrose trace this role to London force between aromatic rings and quantum fluctuations making them qubits. I am unable to imagine what the exact proposal is. In any case, what is known is that electrons at aromatic rings are delocalized. Comment: My own humble proposal is that electrons could be further delocalized at magnetic flux tubes in longer scales and make cyclotron BE condensates of dark electrons (the physics of a rotating Bose-Einstein condensate is very reminiscent of that of a charged particle in a magnetic field; indeed the transverse force exerted on a single atom located in → r = (x, y) in the rotating frame is the sum of the trapping, centrifugal and Coriolis terms: F → = -mω2 ⊥ → r +mΩ2 → r +2mΩ → xν → . For Ω = ω⊥, we are left only with the Coriolis term 2mΩ → xν → , which is formally equivalent to the Lorentz force exerted by a uniform magnetic field on a charged particle with the cyclotron frequency being equal to 2ω⊥) or their Cooper pairs possible. They would make possible the coupling between receptor-information molecule complex and magnetic bodies at various levels of hierarchy. Hierarchy of Planck constants and negentropic entanglement suggests the existence of a new kind of state consisting of electrons (that is fermions) but analogous to Bose-Einstein condensate. 2. The idea about insulation provided by hydrophobic pockets of proteins against fluctuations destroying quantum coherence is nice and it would be natural to put aromatic rings into these pockets. 3. The needed long value of Orchestrated Objective Reduction (Orch-OR) decoherence time τ (originally assumed to correspond to 40 Hz thalamocortical resonance frequency) is one of the problems of Orc OR and the recent discovery of EEG like oscillations in kHz range [J9] is claimed to make the situation more tolerable. Comment: Fractal hierarchy of EEGs mediating communications between parts of biological body and corresponding magnetic body is basic prediction of TGD (Topological Geometro Dynamics) and the observation seems to provide evidence for this prediction. 4. Jeffrey R. Reimers et al challenges [J7] also Jürg Fröhlich Bose-Einstein condensation [J13] and claims that according to his own simulations the resulting state is extremely incoherent [J7]. There are however models which give Bose-Einstein condensation [J2] and the in [J3] the experimental findings about assembly of microtubules are interpreted as Jürg Fröhlich condensation. The frequency inducing the condensation would be however 3 orders of magnitude lower than predicted by Jürg Fröhlich. 5. The implications for experiments involving Quantum Brownian motion, quantum friction and decoherence in heavy quantum particle interacting with quantummechanical heat, Hamiltonian and quantum friction for particles interacting with light or moving trough a Bose_Einstein condensate and the decoherence for these systems. In the article ”Multi-level memory-switching properties of a single brain microtubule” [J12] it is reported that the hysteresis curve for current along MT as function of voltage is ideal square curve meaning that there is no dissipation involved with the change of the current direction. This would make MT as an ideal memory device. Whether Penrose/ Hameroff have in mind the use of current direction as qubit remains unclear. In a YouTube video talk Bandyopadhyay refers also to these results: 1. It is assumed that there are two kinds of hexagonal tubulin lattices labelled as A and B. As found there is strong evidence that A-type tubules do not exist stably. For both types the tubulin dimers defining dipoles are nearly axial and define candidates for conduction paths with winding periodicity of 13 tubulin dimers. For B type one has rows made of α or β type tubulins along with α and β have effective periodicity of five if one accepts discontinuity at after 2π rotation. One might think that this dictates the choice of the candidates for the conduction paths to consist of sequences of α − β dimers: for these sequences are along the microtubule. If hops occur between α and β this assumption is natural. The proposed pathways are however more general and - as it seems to me - based on rather ad hoc mathematical rule. 2. The notion of helical conduction pathway is the starting point. For B-type tubules this notion must be modified. Presumably the criterion for what it is to be a helical pathway is that they are straight-lines connecting nearest neighbors to each other- this is natural if conduction is identified as hopping between neighboring tubulin molecules. The position of each pathway represented by a value of discrete dynamical variable replacing spin as representation of qubit -essentially the angle φ = n × 2π/13 is in question. There are 13 different values for φ. For A-type conducting pathways the condition that one has α − β sequence very probably gives the the claimed pathways with periodicity 13. One can ask whether the pathways of type A are obtained by twisting the pathways of type B at the second end by 2π and whether living systems could be able to perform this twist to achieve phase transition between two states of the microtubule. 3. Instead of single pathway one considers groups of parallel pathways consisting of translates of a fixed pathway with a fixed gap ∆Φgap = ngap2π/13 along the circumference of microtubule. Is the idea is that the additional degree of freedom makes possible the analog of spin degree of freedom as angular position of the pathway? One could also consider the possibility that the translates of a pathway define a braid: this braid would be however trivial since the pathways are parallel. It might mean that topological qubits would be represented as quantum superpositions of helical conduction pathways with same gap ∆φ = ngap × 2π/13 between neighboring pathways. This is not what TGD (Topological Geometro Dynamics) suggests. 4. By n = 13 modulo arithmetics it can that the series of pathways with n = kngap mod 13, k = 1, 2, (…) generating additional gaps. One says that the decomposition occurs. The addition of translated parallel pathways can also lead to a pair of pathways with ngap = 0 or ngap = 1 in which case pathways overlap or touch. This is not allowed. What this means physically is unclear to me. One could also avoid touching simply by allowing only the translates to be such that kngap ≤ 13 holds true: even weaker condition can guarantee this. Dr. Anirban Bandyopadhyay emphasizes that A-type pathways are ideal for TQC whereas B-type pathways are ideal for communications. I did not understand the argument. Certainly this requires that a phase transition from B to A can take place. What one exactly means with topological quantum computation (TQC) is not at all obvious and one can consider several variants of it in TGD (Topological Geometro Dynamics) framework. 1. Zero energy ontology (ZEO) leads to the notion of unitary U-matrix having as its rows M matrices which are ”square roots” of density matrices which are products of hermitian matrix and unitary S-matrix. These matrices define time-like entanglement coefficients between the positive and negative energy states at the opposite boundaries of causal diamond (CD). For braid strands along light-like 3-surfaces defining string ends one obtains entanglement between fermions at the ends of strands. Since the entanglement matrix is unitary it defines density matrix which is sum over projection operator acting as identity matrices and state function reduction yields a negentropically entangled state carrying information. One can pose additional conditions on space-time like negentropic entanglement and ends up with a highly unique form of entanglement coefficients from the condition that any splitting of the system to two parts defines negentropic entanglement [K6]. 2. In absence of degeneracy giving rise to negentropic entanglement one would have ordinary entanglement and ordinary quantum measurement theory applies. The outcome of TQC would be statistically determined from state function reductions for large enough number of sub-CDs of given CD. It would be coded by quantum classical correspondence (QCC) to the parameters characterizing classical fields inside CD (frequencies, wave numbers,...). EEG patterns would be one particular representation of this kind. 3. Interaction free quantum measurement in principle allows to measure the quantum state without changing it (in the ideal situation, see Elitzur-Weizman bomb testing proposal): Bomb-testing problem as per Elitzur-Weizman bomb testing: A photon emitter, B - bomb to be tested, C,D - photon detectors. Mirrors in the lower left and upper right corners are half-silvered. One could therefore imagine a non-halting TQC and extraction of the information without halting it at all. Negentropic entanglement is stable under state function reduction by NMP (Negentropy Maximization Principle) [K6]: it can increase or it can be transferred but it cannot be reduced. Interaction free quantum measurement could make possible the reading the outcome of TQC without halting TQC. TQC would represent ”Akashic records” and by NMP (Negentropy Maximization Principle) Universe would be building increasing library of Akashic records. This might provide a general mechanism of term memory. 4. Also a generalization of ordinary 1-braid TQC to 2-braid TQC is suggestive. 1-D braid strands define braiding of orbits of point like particles in 3-D space space-time - say light-like 3-surface. In TGD (Topological Geometro Dynamics) framework the 1-D braid strands correspond to the boundaries of 2-D string world sheets and the evolution of string world sheets corresponds to 2-braid in space-time. One obtains a generalization of 1-braid TQC to 2-braid TQC in which knotting occurs for 2-D string world sheets of 4-D space-time rather than 1-D strings of 3-D space. Qubits at the ends of time-like braid strand are replaced with quantum states at space-like braid strands defining ends of string world sheet and TQC corresponds to a time evolution in which the 2-knotting of braid strands changes. The first basic operation is what Alexander the Great did for the knot - the breaking of 1-knot temporarily. What happens is following: if braid strand A goes over B before the moment of breaking, it goes below B after it. This is however not the only possible operation: also reconnection - basic operation for magnetic flux tubes - can take place: the braids strands AB and CD are replaced with AD and CB. These operations define standard vertices in closed string model. The sequence of these operations defines 2-braiding and one can assign to it a generalization of 1-braid TQC to 2-braid TQC. 2-braid TQC is not possible in super string models since strings are imbedding in spacetime having dimension higher than D = 4. The quantum states of braids strand would define qudits. In TGD (Topological Geometro Dynamics) qupits representable as superposition of pN states, p prime, are of special interest in TGD (Topological Geometro Dynamics) framework. The hierarchy of frequency scales kHz, MHz, and GHz could correspond to cyclotron frequencies for electron and perhaps also proton. In particular, the crucial role of water in making conductivity possible [J11] suggests that protonic cyclotron B-E condensate is important in the water core of MT at least but possibly also in longer length scales. 1. TGD (Topological Geometro Dynamics) allows magnetic monopole fluxes for flux tubes: in this case the cross section of the flux tube would be closed 2-D surface (sphere) rather than disk, and no current rotating around the tube would be needed to create the magnetic flux. This kind of flux tubes could explain the presence of magnetic fields in cosmic scales: in Maxwellian cosmology they are impossible in early cosmology because the needed currents are impossible. This kind of fluxes might be associated with super-conductors and even permanent magnets. The unit of magnetic flux Φ = R eBdS is h/2 for a disk cross section. For spherical cross section of monopole flux tube the flux is Φ = HeBdS and unit is 2h that is 4 times larger. This could serve as a test for whether one has monopole flux or standard flux. 2. If we consider the constant endogenous magnetic field Bend = .2 Gauss= .2 × 10−4 Tesla could explain the effects of ELF radiation to vertebrate brain [J4] as resulting from cyclotron transitions of large hef f B-E condensate? The cyclotron transitions could also be replaced with phase transitions scaling the value of p-adic prime and thus the value of the magnetic field: this option implies that all particles make the same transition simultaneously. The model yields essentially the same predictions as the earlier model. The phase transition scales down the radius of the flux tube characterized by p-adic length scale L(k) ' 2(k−151)/2 × L(151), L(151) ' 10nm by a power of two. The increase in cyclotron energy due to the reduction of flux tube radius is in good approximation ne(Bf −Bi)/m = neBf (1−2k) ' neBf where Bf is the field strength for the compressed magnetic flux tube. 3. For electron in endogenous magnetic field of .2 Gauss cyclotron frequency is fe ' .5 MHz: for proton one has fpweq 300 Hz (note that the ratio of cyclotron frequencies of electron and proton is given by the mass ratio mp/me ' 1843 ∼ 211) . The reported resonance frequency is f ' 8MHz, which is 24 times higher than fe. 4. This would mean that the p-adic length scale is reduced from L(k) to L(k−4). The possibility of this interpretation yields support for the p-adic length scale hypothesis. Purely number theoretic considerations predict that in biologically interesting length scale range ranging from 10 nm to 2.5 µm there are four p-adic length scales which correspond to Gaussian Mersenne primes: MG,n = (1 + i)n − 1, n = 151, 157, 163, 167. One could speak of a number theoretic miracle. It is easy to see that the transition induced by 8 MHz radiation could correspond to the transition k = 167 → 163 for electron. This gives strong support for the fundamental role of the miracle Mersenne scales. Bend corresponds to magnetic length of LB = p ~/eB = 5.7 µm not far from the p-adic length scale L(169) is L(169) ' 5.1 µm. LB would give flux quantum h/2. The problem is that this scale is by a factor 2 longer than the Mersenne scale L(167). Situation changes if the flux is monopole flux for flux tube with spherical rather than disk-like cross section. By previous argument the flux quantization would be obtained for a sphere with radius given by the p-adic length scale L(167). One would obtain Mersenne scale and the transition L(k) → L(k − 4) would correspond to k = 167 → k = 163 Proton cyclotron frequency would be scaled up in this transition to 4.8 kHz and it would be natural to identify frequencies in kHz frequencies as harmonics of fp. 5. The scaling k → k − 11 would transform fe = .5 MHz to fe = 1 GHz The p-adic scale would become k = 156. k = 157 would have been more attractive outcome. L(156) ' 57.6 nm looks too large to be radius for a magnetic flux tube assignable to the MT strand of thickness of order 4 nm. I would more naturally correspond to the length scale defined by a strand of 13 tubulins. 6. Microtubule strand corresponds to length scale 4 nm which suggests that p-adic length scale L(149) assignable to lipid layer of cell membrane characterizes the flux tubes defining the coordinate grid at MT surface. GHz frequency is assigned with the order water in the interior of MT L(145) ' 1.25 nm seems to be a good candidate for the corresponding p-adic length scale. fp = 1.35 GHz frequency is obtained if flux the transition is k = 167 → 145. Could DNA sequences code for TQC programs? (as implied in the publication “DNA as Topological Quantum Computer” by M. Pitkanen,, 2010) Microtubules are reported to have 8 resonance peaks for AC stimulation (kilohertz to 10 megahertz), which appear to correlate with various helical conductance pathways around the geometric microtubule lattice. The explanation is proposed in terms of current pathways which are identified topological qubits, still why not to speak about braid strands or specify what topological qubit means if one is speaking about TQC? References [J1] Discovery-of-quantum-vibrations-in-microtubulesinside-brain-neurons-corroboratescontroversial-20-year- old-theory-of-"consciousness"? http://www.kurzweilai.net/ discovery-of-quantum-vibrations-in-microtubules-insidebrain-neurons-corroborates-controversial-20-year-oldtheory-of-"consciousness"? [J2] Acousto-conformational transitions in cytoskeletal microtubules: implications for intracellular information processing. Nanobiology, 1:457–468, 1992. [J3] A. Bandyopadhyay. 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Evidence of massive global synchronization and the "consciousness": Comment on ”"consciousness" in the universe: A review of the ’Orchestrated Objective Reduction (Orch-OR) ’ theory” by Hameroff and Penrose. Biosens Bioelectron, 2013. [J15] S. Gupta and S. Hameroff. The Possibility of MAPs as Quantum Logic Gates in Neuronal Microtubules. https: // sbs. arizona. edu/ project/ "consciousness"/ report_ poster_ detail. php? abs= 1435 , 2013. [J16] S. Hameroff and R. Penrose. Reply to criticism of the Orchestrated Objective Reduction (Orch-OR) qubitOrchestrated Objective Reduction is scientifically justified. ScienceDirect. http: // www. sciencedirect. com , 2013. [J17] S. R. Hameroff and R. Penrose. Orchestrated reduction of quantum coherence in brain microtubules: A model for "consciousness". MIT Press, Cambridge, 1996. [K1] M. Pitk¨anen. Dark Matter Hierarchy and Hierarchy of EEGs. In TGD (Topological Geometro Dynamics) and EEG. Onlinebook. http://TGD (Topological Geometro Dynamics) theory.fi/public_html/TGD (Topological Geometro Dynamics) eeg/TGD (Topological Geometro Dynamics) eeg.html#eegdark, 2006. BOOKS RELATED TO TGD (Topological Geometro Dynamics) 18 [K2] M. Pitk¨anen. DNA as Topological Quantum Computer. In Genes and Memes. Onlinebook. http://TGD (Topological Geometro Dynamics) theory.fi/public_html/ genememe/genememe.html#dnatqc, 2006. [K3] M. Pitk¨anen. Genes and Memes. In Genes and Memes. Onlinebook. http://TGD (Topological Geometro Dynamics) theory.fi/public_html/genememe/ genememe.html#genememec, 2006. [K4] M. Pitk¨anen. Homeopathy in Many-Sheeted SpaceTime. In Bio-Systems as Conscious Holograms. Onlinebook. http://TGD (Topological Geometro Dynamics) theory.fi/public_html/hologram/hologram.html#homeoc, 2006. [K5] M. Pitk¨anen. Knots and TGD (Topological Geometro Dynamics) . In Quantum Physics as Infinite-Dimensional Geometry. 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Quantum Astrophysics. In Physics in Many-Sheeted Space-Time. Onlinebook. http://TGD (Topological Geometro Dynamics) theory.fi/public_html/ TGD (Topological Geometro Dynamics) class/TGD (Topological Geometro Dynamics) class.html#qastro, 2006. [K10] M. Pitk¨anen. Quantum Model for Nerve Pulse. In TGD (Topological Geometro Dynamics) and EEG. Onlinebook. http:// TGD (Topological Geometro Dynamics) theory.fi/public_html//TGD (Topological Geometro Dynamics) eeg/TGD (Topological Geometro Dynamics) eeg/TGD (Topological Geometro Dynamics) eeg.html#pulse, 2006. [K11] M. Pitk¨anen. TGD (Topological Geometro Dynamics) and Astrophysics. In Physics in Many-Sheeted Space-Time. Onlinebook. http://TGD (Topological Geometro Dynamics) theory.fi/public_html/TGD (Topological Geometro Dynamics) class/TGD (Topological Geometro Dynamics) class.html#astro, 2006. [K12] M. Pitk¨anen. Three new physics realizations of the genetic code and the role of dark matter in bio-systems. In Genes and Memes. Onlinebook. http://TGD (Topological Geometro Dynamics) theory.fi/public_html/genememe/ genememe.html#dnatqccodes, 2006. [K13] M. Pitk¨anen. Topological Quantum Computation in TGD (Topological Geometro Dynamics) Universe. In Genes and Memes. Onlinebook. http://TGD (Topological Geometro Dynamics) theory.fi/public_html/genememe/ genememe.html#tqc, 2006.