ScienceDirect - Biosystems_ Conduction Pathways in Microtubules, Biological Quantum Computation, And Consciousness

8/12/2019 ScienceDirect - Biosystems_ Conduction Pathways in Microtubules, Biological Quantum Computation, And Consciou

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enceDirect - Biosystems: Conduction pathways in microtubules, biological quantum computation, and consciousness

://www.quantumconsciousness.org/biosystemselsevier.htm[03/06/2014 23:42:59]

BiosystemsVolume 64, Issues 1-3, January 2002, Pages 149-168

DOI:10.1016/S0303-2647(01)00183-6PII: S0303-2647(01)00183-6Copyright 2002 Elsevier Science Ireland Ltd. All rights reserved.

Conduction pathways in microtubules, biological quantum computation, and

consciousnessStuart Hameroff, Alex Nip, Mitchell Porter and Jack Tuszynski

Department of Anesthesiology and Psychology, Center for Consciousness Studies, University of Arizona, Tucson, AZ 85721,USA

Received 18 May 2001; accepted 20 September 2001. Available online 18 December 2001.

Abstract

Technological computation is entering the quantum realm, focusing attention on biomolecular information processing systemssuch as proteins, as presaged by the work of Michael Conrad. Protein conformational dynamics and pharmacological evidencesuggest that protein conformational statesfundamental information units (`bits') in biological systemsare governed byquantum events, and are thus perhaps akin to quantum bits (`qubits') as utilized in quantum computation. `Real time' dynamicactivities within cells are regulated by the cell cytoskeleton, particularly microtubules (MTs) which are cylindrical latticepolymers of the protein tubulin. Recent evidence shows signaling, communication and conductivity in MTs, and theoreticalmodels have predicted both classical and quantum information processing in MTs. In this paper we show conduction pathwaysfor electron mobility and possible quantum tunneling and superconductivity among aromatic amino acids in tubulins. Thepathways within tubulin match helical patterns in the microtubule lattice structure, which lend themselves to topological quantumeffects resistant to decoherence. The PenroseHameroff `Orch OR' model of consciousness is reviewed as an example of thepossible utility of quantum computation in MTs.

Author Keywords: Microtubules; Quantum computation; Consciousness; Protein conformation; Biolomolecular computation

Article Outline

1. Introduction: proteins, anesthesia and quantum computation1.1. Moore's law and quantum biology1.2. Protein conformational dynamics1.3. Quantum effects in proteins1.4. Quantum neuropharmacology: anesthesia and psychedelia2. Information processing in microtubules2.1. Microtubules and the cytoskeleton2.2. Tryptophan and histidine locations in tubulin2.3. Conduction pathways within tubulin2.4. Inter-tubulin conduction pathways in microtubules3. Quantum computation in microtubules3.1. PenroseHameroff `Orch OR' model3.2. Quantum states in the brain? Decoherence and biological feasibility3.3. Spatio-temporal spread of quantum states in the brain4. ConclusionAcknowledgementsReferences

1. Introduction: proteins, anesthesia and quantum computation1.1. Moore's law and quantum biology

Technology is approaching the limit of classical computing through the operation of Moore's Law, which states that the number
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3. Induced dipoleinduced dipole.

Type 3 induced dipoleinduced dipole interactions are the weakest but most purely non-polar. They are known as Londondispersion forces and they ensue from the fact that atoms and molecules which are electrically neutral and sphericallysymmetrical nevertheless have instantaneous electric dipoles due to asymmetry in their electron distribution (`electron cloud').The electric field from each fluctuating dipole in an electron cloud couples to others in electron clouds of adjacent non-polaramino acid side groups. The couplings are quite delicate (40 times weaker than hydrogen bonds) but are numerous andinfluential. The London force attraction between any two atoms is usually less than a few kiloJoules, however, thousands occur ineach protein. Electron clouds in aromatic ring structures (i.e. tryptophan, tyrosine, phenylalanine, histidine) are larger and morecomplex, and may give rise to cooperatively organized London forces particularly suited to governing protein conformational

states. Due to inherent uncertainty in electron localization, London forces are quantum effects which may couple to `zero pointfluctuations' of the quantum vacuum (Londonand Milloni).

1.4. Quantum neuropharmacology: anesthesia and psychedelia

Quantum dipole oscillations within hydrophobic pockets were first proposed by Frhlich (1968)to regulate protein conformationand engage in macroscopic coherence. In a series of proposals Conrad (e.g. 1994) showed how electron superpositions couldinfluence nuclear movement (conformation), and suggested that quantum superposition of various possible protein conformationsoccurs before one is selected. Roitberg et al. (1995)showed functional protein vibrations which depend on quantum effectscentered in two hydrophobic phenylalanine residues, and Tejada et al. (1996)have evidence to suggest quantum coherent statesexist in the protein ferritin. And recently Matsuno (2001)has claimed to observe magnetic quantum coherence in actin, a maincomponent of the contractile apparatus in muscle cells, and of the cytoskeleton in all cells.

Close examination of effects of general anesthetics (which erase consciousness) and hallucinogens (which are said to expandconsciousness) reveal that both act in opposite ways on delicate quantum effects.

The mechanism of general anesthesia supports a role for quantum London forces in the phenomenon of consciousness. A centuryago Meyer and Overton (working independently in Germany and England, respectively) showed a remarkable correlationbetween anesthetic potency and solubility in a particular lipid-like environment. Although these results were originally taken toimply that the anesthetics acted in lipids within the cell membrane, studies in the past decades (e.g. Wulf; Franks; Franks;Franks; Franksand Halseyand others) conclude that anesthetic gas molecules act in hydrophobic (lipid-like, water-excluding)regions within critical target proteins. The solubility/binding occurs by weak van der Waals London forces between the anestheticand non-polar amino acid groups (the same type of endogenous interactions occurring between non-polar amino acid groups inthe absence of anesthetics). Critical brain proteins affected by anesthetics include receptors for neurotransmitters such as gamma

amino butyric acid (GABA), acetylcholine, serotonin and glycine, as well as certain second messenger proteins, enzymes andtubulin which comprise microtubules (MTs) ( DeBrabander; Deland Dermietzel). What do anesthetics do at their site of action?

Franks and Lieb (1994)suggested that anesthetics act simply by following the MeyerOverton correlation: their mere presence inhydrophobic pockets prevents conformational switching. However, a variety of molecules, which follow the MeyerOvertoncorrelation and occupy the same pockets are nonanesthetic, or even convulsant ( Fang et al., 1996). The mere presence ofmolecules in hydrophobic pockets may be insufficient to explain anesthesia.

Another view is that anesthetics somehow disrupt van der Waals London force interactions normally occurring in the criticalhydrophobic pockets. Quantum superposition requires electron mobilityelectron pairs must be relatively free to roam amongallowed orbitals. Evidence shows that anesthetics retard electron mobilitythe movement of free electrons in a corona dischargeis inhibited by anesthetics (Hameroff and Watt, 1983). By forming their own London force attractions in hydrophobic pockets,anesthetics may inhibit electron mobility required for protein dynamics, quantum superposition and consciousness.

Nonanesthetics may be understood as occupying hydrophobic pockets without altering electron mobility, and convulsants asforming cooperative van der Waals interactions, which promote excessive electron mobility and protein dynamics in excitatoryproteins.

Another class of drugs, the hallucinogenic (`psychedelic') tryptamine, ergoline and phenylethylamine derivatives bind and act inhydrophobic pockets within serotonin receptors and elsewhere. For example the hallucinogens LSD (an ergoline) and DMT (atryptamine) are based on indole rings, exactly like that in tryptophan.Nichols et al. (1977)showed that these psychedelic drugsbind in hydrophobic pockets of less than 0.6 nm (6 ) length. Kangand Snydermeasured the capacity of a series of psychedelicdrug molecules to donate electron orbital resonance energy. In both studies, the drug's electron resonance donation is correlatedwith psychedelic potency.

Taken together with dependence of protein conformational regulation on quantum van der Waals forces, the anesthetic and

psychedelic studies suggest that (1) consciousness depends on quantum processes in hydrophobic pockets; (2) these quantumprocesses are inhibited by anesthetics which impair electron mobility in van der Waals London forces. The same processes areenhanced (hallucinations, but also enlightenment) in the presence of psychedelic drugs, e.g. those with indole rings donatingelectron resonance energy to indole rings in tryptophan within the hydrophobic pocket, forming a collective quantum state.Consciousness depends on quantum states of electrons within hydrophobic pockets in a class of brain proteins.


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With conformational states controlled by a quantum process, proteins may thus be viewed as quantum bits, or `qubits'. Forquantum computation, qubits can be arranged in a geometrical lattice (Lloyd, 1993). In biological systems the protein tubulin isarranged in a particular geometrical lattice in MTs whose functions appear to include organization, communication andinformation processing. Are MTs quantum computers?

2. Information processing in microtubules

2.1. Microtubules and the cytoskeleton

Interiors of living cells are functionally organized by webs of protein polymers known as the cytoskeleton (Fig. 2). Majorcomponents of the cytoskeleton are MTs, self-assembling hollow crystalline cylinders whose walls are hexagonal lattices ofsubunit proteins known as tubulin ( Fig. 3). Other major cytoskeletal components include actin, intermediate filaments, andcentrioles, MT-based organelles, which orient the cell and guide cell movement and division.

MTs are essential for a variety of biological functions including cell movement, cell division (mitosis) and establishment andmaintenance of cell form and function. In neurons (which lack centrioles), MTs self-assemble to extend axons and dendrites andform synaptic connections. Microtubule-associated proteins (MAPs) interconnect MTs to form MT-MAP networks, which definecell architecture and function. Once established, MT-MAP networks maintain and regulate synaptic strengths responsible forlearning and cognitive functions. MTs interact with membrane structures and activities (e.g. in actin-based dendritic spines) bylinking proteins (e.g. fodrin, ankyrin) and `second messenger' chemical signals. Woolf (1997)has shown that activation ofneuronal acetylcholine receptors causes changes in MT-MAP connections. (For a more complete description of the role of MTs

and other cytoskeletal structures in cognitive functions see Dayhoff; Hameroffand Hameroff). MTs have traditionally beenconsidered as purely structural components, however, recent evidence has demonstrated MT mechanical signaling andcommunication functions (see Table 1and Table 2).

Table 1. Experimental evidence for signaling in microtubules

Table 2. Theoretical models of microtubule information processing


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How might MTs signal and process information? Tubulin can undergo several types of conformational changes (e.g.Engelborghsand Cianci). In one example of tubulin conformational change observed in single protofilament chains, onemonomer can shift 27 from the dimer's vertical axis ( Melki et al., 1989). Whether that degree of mechanical deformation occursin tubulin within intact MTs is unknown; neighbor tubulins in the MT lattice might be expected to constrain movement.However, cooperativity among MT subunit tubulins bound `loosely' in the MT lattice by hydrophobic forces could coordinate

conformational changes, and support propagation of wave-like vibrational signals. MTs are also ferroelectric with electron andproton conduction, which may couple by phonons to conformational vibrations. The crystal-like MT structure makes themattractive candidates for quantum coherent excitations, e.g. in the gigaHz range by a mechanism suggested by Frhlich (`pumpedphonons' Fr; Fr; Frand Frcf. Penrose and Onsager, 1956).

One particular model of MT information processing potential utilizes Frhlich excitations of tubulin subunits within MTs tosupport computation and information processing (e.g. Rasmussen et al., 1990). The coherent excitations are proposed to `clock'computational transitions occurring among neighboring tubulins acting as `cells' as in molecular scale `cellular automata'. Dipolecoupling mediates logical interactions among neighboring tubulins, resulting in self-organizing patterns capable of informationprocessing, memory and learning ( Fig. 4).

In a series of simulations (e.g. Hameroffand Rasmussen) Frhlich's excitations were used as a clocking mechanism andelectrostatic dipole coupling forces as `transition rules' for cellular automata behavior by dynamic conformational states oftubulins within MTs. In Fig. 3, each tubulin dimer conformation is ruled by a single London force electron pair coupling. Forautomata behavior, the dipole strength of each dimer is coupled to its six surrounding tubulin neighbors at each `Frhlich

coherent' time step (e.g. 10-910-11s). The net electrostatic force Fnetfrom the six surrounding neighbors acting on each tubulin

can then be calculated as:

whereyiand riare inter-tubulin distances, eis the electron charge, and is the average protein permittivity. MT automata

simulations (Fig. 5) show conformational pattern behaviors including standing waves, oscillators and gliders traveling one dimer

length (8 nm) per time step (10 -910-11s) for a velocity range of 8800 m s-1, consistent with the velocity of propagating nerveaction potentials.

MT automata patterns can thus represent and process information through each cell; gliders may convey signals which regulatesynaptic strengths, represent binding sites for MAPs (and thus neuronal and synaptic connectionist architecture) or material to betransported. Information could become `hardened' in MTs by tubulin modifications or stored in neurofilaments via MAPs.


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2.2. Tryptophan and histidine locations in tubulin

In conventional computers the `currency' of information in semiconductors is electrons. Microtubule automata could utilizeFrhlich phonons for information currency, although other quasi-particles such as solitons, excitons, instantons, anyons, as wellas photons, electrons and protons could serve. Electron propagation would be extremely useful, as conformational energy (e.g. inthe form of phonons) could be coupled to electrons and both classical and quantum processes could be supported. However,proteins have never been considered especially conductive, nor in most cases semiconductive (of course neither has DNA whichhas recently been shown to be highly conductive, and perhaps superconductive (Bartonand Kasumov)).

Electron (or proton) transfer within and among specific amino acid residues within proteins may mediate protein function. Forexample catalysis in the enzyme class 1 ribonuclease reductase utilizes electron or proton transfer over 3.5 nm from a tyrosine toa cysteine. Photoactivation inE. coliDNA photolyase enzyme involves electron `hopping' or tunneling along a chain of threeseparate tryptophans (Aubert et al., 2000). Electron tunneling over significant distances within proteins has now been shownexperimentally, and there is evidence of electron transfer from intra-protein tryptophan to DNA ( Wagenknecht et al., 2000).

The amino acids tryptophan and tyrosine are convenient depots for electron hopping or tunneling because of the highpolarizability of their ring structure. The àromatic' amino acids such as tyrosine, tryptophan, phenylalanine and histidine haveresidues with resonant ring structures in which electrons are mobile and delocalizable.

Tyrosine, phenylalanine and histidine have single rings; each tyrosine and phenylalanine have six-carbon benzene-like rings, andhistidine has a ring with three carbons and two nitrogens. Tryptophan has a particular double ring (an ìndole ring')a six carbon

ring conjoined with a five ring with one nitrogen and four carbons. The extra lines between the atoms in the rings in Fig. 1signify shared, delocalized, or resonant electrons. Thus tryptophan has the greatest electron resonance (and thus is the mostfluorescent), and histidine the lowest electron mobility, and least fluorescent. Becker et al. (1975)showed fluorescent resonanceenergy transfer (non-radiative photon exchange) between tryptophan and other aromatics in adjacent tubulins in MTs, andbetween MTs and membranes. Tryptophan is the most highly suited amino acid for transiting electrons and exchanging photons.In this study, we have begun to examine and map intra-tubulin locations of the aromatic amino acids tryptophan and histidine.

)

Fig. 1. Model of protein conformational switching. Tubulin is depicted as an example, and for simplicity one pair of electrons coupled byLondon forces is shown in a single hydrophobic pocket. Top: coupled electrons in one configuration in a single hydrophobic pocketcorrespond to òpen' (black) conformation. In the opposite London force electron coupling the protein is `closed' (white). Bottom: sinceLondon forces are quantum mechanical, the electron pair may occupy both states, and the protein exist in a quantum superposition of bothopen and closed conformations. By going from bottom (quantum superposition) to top (one particular conformation) the protein functions asa qubit.


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Fig. 2. The neuronal cytoskeleton. Immunoelectron micrograph of dendritic MTs interconnected by dendrite-specific MAPs. Some MTs havebeen sheared, revealing internal hollow core. The granular `corn-cob' surface of MTs is barely evident to close inspection. Scale bar, lowerleft: 100 nms. With permission from Hirokawa, 1991.

Fig. 3. Left: microtubule, a cylindrical lattice of tubulin proteins. Right (Fig. 1): coupled to position of a pair of quantum coupled electrons inan internal hydrophobic pocket, each tubulin may occupy two classical conformations (top) or exist in quantum superposition of bothconformational states (bottom). A tubulin may thus act as a classical bit (top) or as a quantum bit, or `qubit'.

Fig. 4. Microtubule automaton simulation (fromRasmussen et al., 1990). Black and white tubulins correspond to states shown inFig. 4. Eightns time steps of a segment (eight of 13 protofilaments) of one microtubule are shown in `classical computing' mode in which patterns

(`gliders') move, evolve, interact and lead to emergence of new patterns.

Tyrosine Phenylalanine Histidine Tryptophan

Fig. 5. The "aromatic" amino acids contain ring structures with resonant (shared) electrons. Tyrosine, phenylalanine and histidine have single

rings; each tyrosine and phenylalanine have 6-carbon benzene-like rings, and tryptophan and histidine have double rings.

Tubulin dimers are 8 nm in length, and 4 nm wide (and 4 nm `deep'). The peanut-shaped dimer is composed of two roughly equal


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monomers, alpha tubulin and beta tubulin each approximately 444 nm. The distances between the tryptophans is thus no morethan 2 nm. The 3-D crystallographic structure of tubulin was solved in 1998 by Nogales, Wolf and Downing (Nogales et al.,1998). Recently Alex Nip (now at University de Montreal) and Jack Tuszynski (University of Alberta, Starlab.org) simulated thelocations of tryptophans and other aromatics in tubulin. Those results for tryptophan and histidine in 2-D projection are shownhere. Tryptophan locations in the tubulin dimer are shown in Fig. 6,Fig. 7and Fig. 8,and histidine locations in Fig. 9,Fig. 10and Fig. 11.

Fig. 6. Tryptophans (black) in the tubulin dimer. Left: front view (looking at the outer MT surface), Middle: side view (from within the MTwall), Right: top view (looking down on the MT protofilament).

Fig. 7. Histidines (black) in the tubulin dimer. Left: front view, Middle: side view, Right: top view.

Fig. 8. Tryptophans in the tubulin dimer. Left: trypyophan locations in front view. Right: tryptophans interconnected by estimated shortestpaths (2-D approximation). Typical separations are 2 nm, close enough for `through-bond' hopping. The path separates near the cleft, orhinge of the dimer.


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Fig. 9. Histidines in the tubulin dimer. Left: histidine locations in front view. Right: Histidines interconnected by estimated shortest paths.Typical separations are 1 nm.

Fig. 10. Helical winding patterns of tubulin subunits within MTs. The windings repeat on any given protofilament according to the Fibonacci

series: from left to right, 3, 5, 8 and 13 step repeats. The 3-step repeat is based on monomers, whereas the 5 and 8 step repeats are based ondimmrs. The 13-step repeat is simply the direct path along the vertical protofilaments. These patterns form the basis for attachment patternsof MAPs.


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Fig. 11. A lattice neighborhood of seven tubulin dimers as found in a microtubule with tryptophans highlighted in black.

Fig. 6shows the `front view'of tryptophan locations, looking at the tubulin dimer as looking at the microtubule from the outside,e.g. as in Fig. 3.However, the front view gives only a 2-D picture. We gain 3-D perspective by also looking at `side' (within theMT wall) and `top' (down the protofilament). There are eight tryptophans, four in the alpha (top) monomer, and four in the beta(bottom) monomer. Two tryptophans (one from each monomer) are in the neck, or hinge of the dimer.

The side view indicates that two of the tryptophans are alone in the extended portion of each monomer, separated from eachother by exactly 4 nm. The other tryptophans are close to the inner surface and arrayed vertically. The top view shows that thetryptophans are arrayed vertically along three specific axes within the dimer.

Histidines are more numerous than tryptophans, 22 per dimer, and their arrangement is more complex (Fig. 7).

We next consider possible electron pathways between tryptophans and histidines within tubulin.

2.3. Conduction pathways within tubulin

Conventional wisdom indicates that electron tunneling or hopping in proteins is only possible over distances under 1 nm. This isthe `Foerster distance' (maximum length of an excitation to travel). However the Foerster distance pertains to free hopping via aninert medium like an ionic solution. Within proteins electron movements may be facilitated by `through bond hopping' overdistances of 3 nm or more. Furthermore, if there are sufficient available electrons to fill half or more of the available sites, thenconditions can exist within proteins at physiological temperature for (semi)conductivity comparable with silicon or even semi-metals (e.g. Brown, 1999). With dynamic water ordered at the protein surface, conductivity may be even further enhanced, andproton conduction can also occur.

As described earlier, in some enzymes electron hopping between amino acid residues may span 3.5 nm or more, and electronhopping along 3 tryptophans is known to occur in some enzymes. Based on a qualitative 2-D approximation, Fig. 8estimatesshortest direct paths between tryptophans in the tubulin dimer.

The tryptophan paths are mostly vertical, along the protofilament axis. The path separates near the cleft, or hinge of the tubulin.Occupation of one path versus the other path may control the dimer conformation, for example bending at the hinge.

In Fig. 9, we examine possible paths between histidines.

Estimation of shortest paths between histidines shows multiple loops and alternate possible routes. The average distance betweenhistidines is about 1 nm.


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Electron conduction between aromatic tryptophan and histidine amino acid residues is within range of known conductionmechanisms in proteins (tunneling, `hopping', semiconduction).

2.4. Inter-tubulin conduction pathways in microtubules

Tubulin dimers are arranged not only in vertical protofilament chains, but form a particular skewed hexagonal lattice whosecrystal structure gives rise to helical winding patterns with regular repeat intervals. Increasingly steep winding patterns completeone cycle around the cylinder at a certain number of tubulins above where the cycle started (Fig. 10). These numbers, 3, 5, 8, 13,21 etc. follow the well known `Fibonacci series' found throughout nature. The repeating patterns also determine binding sites of

MAPs'.A neighborhood of seven tubulin dimers with tryptophans represented in black is shown in Fig. 11.

If we then show the intra-tubulin tryptophan paths in the lattice format by connecting nearest tryptophans (as in Fig. 12), we seethat the tryptophan paths extend vertically along each protofilament.

Fig. 12. Left: a lattice of seven tubulin dimers as found in the microtubule lattice. Black lines connect tryptophans. Right: vertical path alongprotofilament (`13 start' winding pattern) which corresponds with tryptophan conduction path.

Tryptophans seem oriented vertically whereas histidine locations suggest helical paths. When added to tryptophan, all possible

structural winding pathways appear available (Fig. 13and Fig. 14). In Section 4, we will discuss the possible implications fortopological quantum error correction in microtubular computation.


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Fig. 13. A lattice neighborhood of seven tubulin dimers as found in a microtubule with histidines highlighted in black.

Fig. 14. Left: a lattice of seven tubulin dimers as found in the microtubule lattice. Black lines connect histidines. Right: 3, 5 and 8 start helical

winding patterns in MTs. Histidine pathways in the lattice may be seen to follow these winding patterns.

3. Quantum computation in microtubules


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3.1. PenroseHameroff Òrch OR' model

Quantum theory and consciousness have been intertwined since the days of Schrdinger's cat when conscious observation wasbelieved to cause collapse of the wave function. More recently, consciousness has itself been viewed as a collapse process,analogous to quantum computation. Penroseand Penrosecorrelated the multiple possibilities of quantum superposition withmultiple sub-conscious, or pre-conscious possibilities `collapsing' to distinct choices or perceptions (cf. Stapp, 1993). In his earlywork in this area, Penrose suggested quantum superpositions of neurons both firing and not firing, collapsing or reducing (by hisquantum gravity òbjective redution' process, OR) to either firing or not firing. Thus the neuron was acting as qubit. However, fora variety of reasons MTs within each neuron were deemed better candidates for biological quantum computation, with individual

tubulins within MTs acting as qubits.The PenroseHameroff Òrch OR' model portrays consciousness as quantum computation in MTs which collapse or reduce by anobjective factor related to quantum gravity. For detailed explanations see Penrose; Hameroffand Hameroff; HameroffandHameroff, etc. The basic ideas are these:

Conformational states of individual tubulins within neuronal MTs are determined by quantum mechanical London forces withinthe tubulin interiors which can induce conformational quantum superposition (Fig. 3).While in superposition, tubulins communicate/compute with entangled tubulins in the same microtubule, and in other MTs in

the same neuron.Quantum states in MTs in any given neuron may extend to MTs in neighboring neurons, and through macroscopic regions of

brain via tunneling through gap junctions (see Section 3.3, Fig. 16).Quantum states of tubulin/MTs are isolated/protected from environmental decoherence by biological mechanisms which include

phases of actin gelation, ordered water, coherent pumping and topological quantum error correction (see Section 3.2).Microtubule quantum computations/superpositions are tuned or òrchestrated' by MAPs during a classical, liquid phase which

alternates (e.g. at 40 Hz) with a quantum, solid state phase.Following periods of pre-conscious quantum computation (e.g. on the order of tens to hundreds of milliseconds) tubulin

superpositions reduce or collapse by Penrose quantum gravity òbjective reduction' (OR Fig. 15). The classical output stateswhich result from the OR process are chosen non-algorithmically (`non-computably') and then govern neurophysiological eventsby binding of MAPs, regulating synapses and membrane functions etc.The reduction or `self-collapse' in the orchestrated objective reduction Òrch OR' model is suggested to be a `conscious

moment', linked to Penrose's quantum gravity mechanism which ties the process to fundamental spacetime geometry. Thisconnection enables a pan-protopsychist approach to the `hard problem' of subjective experience ( Chalmers, 1996a).

Fig. 15. An Orch OR event. (a) Microtubule simulation in which classical computing (step 1) leads to emergence of quantum coherentsuperposition and quantum computing (steps 2, 3) in certain (gray) tubulins. Step 3 (in coherence with other microtubule tublins) meetscritical threshold related to quantum gravity for selfcollapse (Orch OR). A conscious event (Orch OR) occurs in the step 3 to 4 transition.Tubulin states in step 4 are noncomputably chosen in the collapse, and evolve by classical computing to regulate neural function. (b)Schematic graph of proposed quantum coherence (number of tubulins) emerging versus time in MTs. Area under curve connects superposedmass energyEwith collapse time Tin accordance withE=h-bar/T.Emay be expressed asNt,the number of tubulins whose mass separation


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(and separation of underlying space time) for time Twill selfcollapse. For T=25 ms (e.g. 40 Hz oscillations),Nt=21010tubulins.

Fig. 16. Schematic representation of a gap junction connecting two dendrites in which MTs are in quantum superposition/quantumcomputation `tuned' by interconnecting MAP proteins as suggested in the PenroseHameroff Orch OR model. On either side of the gap

junction, dendritic lamellar bodies (DLBs) containing mitochondria may act as tunneling diodes to convey the quantum state between thedendrites.

Other quantum models related to consciousness include those of Marshall; Beck; Stappand Jibu.

Quantum models have potential explanatory value for the enigmatic features of consciousness ( Table 3), but face at least twoconceptual obstacles: (1) the apparent likelihood of rapid `decoherence' (loss of quantum state) due to environmental thermalinteractions in the seemingly-too-warm brain (Tegmarkand Seife); and (2) the question of how a quantum state or field locatedwithin neurons might extend across membranes and anatomical regions to approach `brain-wide' proportions. The next sectiondeals with these issues.

Table 3. Enigmatic features of consciousness and possible solutions via the Orch OR model)

3.2. Quantum states in the brain? Decoherence and biological feasibility

Quantum computing surpasses classical computing in certain critical functions (e.g. Grover's quantum search algorithm) andwould be of extreme benefit to biological organisms for survival and adaptation. Billions of years of evolution may have solvedthe problems of decoherence and spatiotemporal spread. A number of mechanisms to prevent environmental decoherence havebeen suggested, specifically for quantum computation in MTs. These include (1) coherent pumping of the environment; (2)


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screening due to counterion Debye double layers surrounding MTs; (3) screening by actin gelation and ordered water; (4)quantum error correction; (5) topological effects of the microtubule cylindrical lattice. Recent calculations of protein decoherencetimes indicate quantum superpositions may indeed survive for neurophysiological time durations (Hagan et al., 2000), and brainimaging by `quantum coherence MRI' utilizes quantum couplings of proton spins in proteins and water to give a neuroanatomicalcorrelate of consciousness ( Richterand Rizi). This quantum coherence is a MRI-induced artifact, but shows that quantumcoherence of some sort can indeed occur in the brain.

Technological quantum computation became feasible with the advent of quantum error correction codes. This means thatalgorithms run on the quantum computer which detect and correct errors (random localized decoherence) before they destroy theglobal quantum state. In some cases topological structure of the quantum computer enhances the error correction. For example

toroidal surfaces (e.g. Kitaev, 1997) may have global, topological degrees of freedom which are protected from local errors anddecoherence. Topological quantum computation and error correction have been suggested to occur in MTs by Porter (2001)andthe helical windings discussed in Section 2 may correspond to quantum-computational `basis states' distinguished by `windingnumber' ( Fig. 12and Fig. 14).

3.3. Spatio-temporal spread of quantum states in the brain

Regarding spatial extension of a quantum (or `quantum-like' (John, 2001)) field throughout the brain, a possible solution may begap junctions-window-like `electrical' connections between cells including neurons (e.g. Dermietzel and Spray, 1993). Gapjunctions are more primitive and less numerous connections than chemical synapses, and occur between dendrites, axons, cellbodies and/or glial cells. Dendriticdendritic gap junctions in particular have been implicated in the mediation of consciousprocesses ( Pribramand Eccles). Cell interiors (cytoplasm) are continuous through gap junctions so that cells connected by gap

junctions have actually one complex interior. Quantum states isolated in one cell interior may thus extend to neighboring cells byquantum tunneling of electrons across the 4 nm gap junction. Specific intracellular organelles have been discovered in dendrites,immediately adjacent to dendriticdendritic gap junctions. These are layers of membrane covering a mitochondrion, and arecalled `dendritic lamellar bodies' ( De Zeeuw et al., 1995). The dendritic lamellar bodies are tethered to small cytoskeletalproteins anchored to MTs, and it is suggested that the mitochondria within the bodies provide free electrons for tunneling,forming a tunneling diode pair or Josephson junction between cells ( Fig. 16). As few as three gap junction connections percortical neuron (with perhaps thousands of chemical synapses) to neighboring neurons and glia which in turn have gap junctionconnections elsewhere may permit spread of cytoplasmic quantum states throughout significant regions of the brain, weaving awidespread syncytium whose unified interior hosts a unified quantum state or field ( Hameroff; Hameroffand Woolf).

Kandel et al. (1991)remarked that neurons connected by gap junctions fire synchronously, behaving like `one giant neuron', andE.R. John (2001) has suggested that gap junction-connected neurons (`hyper-neurons') mediate zero phase lag coherence.

Dendritic lamellar bodies are associated with synchronously firing neurons ( De Zeeuw et al., 1997) and several studies (Galarreta; Gibsonand Velasquez) implicate gap junction-connected interneurons in the mediation of coherent (`40 Hz')oscillations. These gap junction-connected interneurons form `dual' connections (gap junctions and GABAergic chemicalsynapses) with pyramidal cells and other cortical neurons. GABA inhibition could quiet membrane activities, avoidingdecoherence to enable quantum states in neuronal cytoplasmic interiors to develop and spread among many gap junction-linkedcells across wide areas of the brain. Thus gap junction-connected coherent 40 Hz neurons may support spatially extendedquantum states.

4. Conclusion

Scientists speak of `levels of theory', a hierarchy of models ranked by physical detail. The ultimate level would be a `Theory ofEverything'. One possible over-arching approach (suggested by Roger Penrose) attributes quantum state reduction to gravity. The

Orch OR model asserts that this ultimate level is relevant to the physics of consciousness.

The discovery of the aromatic lattice within the microtubule has no immediately discernible implications at this ultimate level,but it suggests a host of new possibilities at simpler levels of theory (one-body quantum models, many-body quantum models,and quantum-field models). For example, in the Orch OR model it is assumed that neighboring dimers become entangled by thedipoledipole interaction, which appears in the classical cellular automaton models of the microtubule. But it may be that mobileelectrons following these newly recognized pathways contribute more to the entanglement process; tubulin dimers may becomeentangled indirectly, by way of interaction with strongly correlated mobile electrons.

Table 4and Table 5list a few theoretical approaches to motion of electrons within the lattice of aromatic amino acids. These andothers need to be explored and their predictions calculated (Brown and Tuszynski (2001)is a promising starting point). Thestructures of other biomolecules must also be examined, in order to show whether these pathways are unique to tubulin or found

in many proteins. Logical candidates for examination include actin and other cytoskeletal proteins, the bacterial protein FtsZ,which is related to tubulin, and microtubule associated proteins such as MAP-2, MAP-4 and tau (Eva Nogales, personalcommunication).

Table 4. Potential single-body approaches to microtubule electronics


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Table 5. Potential many body theory approaches to microtubule electronics

Acknowledgements

MOLMOL and POVRAY were used for rendering high quality images and script programs written in Python were to customize

images and perform the required numerical analyses. Simulations were done on a Pentium II 300 MHZ with 128 MB RAMrunning 7.1 ( kernel 2.2.13). Artwork was done by Dave Cantrell. Mitchell Porter thanks Eva Nogalesfor a stimulating conversation about electron transport in proteins. Stuart Hameroff is grateful to the Fetzer Institute, the YeTaDelFoundation, Biophan and Starlab, as well as the Center for Consciousness Studies. The authors are grateful to Roger Penrose forunderlying inspiration.

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