The brain is both neurocomputer and quantum computer

Stuart Hameroff M.D.

Copyright Cognitive Science Journal

Abstract: In their article “Is the brain a quantum computer?”, Litt et al (Cognitive Science 30, 593-603, 2006) criticize the Penrose-Hameroff Orch OR quantum computational model of consciousness, arguing instead for neurocomputation as an explanation for mental phenomena. Here I clarify and defend Orch OR, show how Orch OR and neurocomputation are compatible and question whether neurocomputation alone can physiologically account for coherent gamma synchrony EEG, a candidate for the neural correlate of consciousness. Orch OR is based on quantum computation in microtubules within dendrites in cortex and other regions linked by dendritic-dendritic gap junctions (dendritic webs) acting as laterally-connected input layers of the brain's neurocomputational architecture. Within dendritic webs, consciousness is proposed to occur as gamma EEG-synchronized sequences of discrete quantum computational events acting in integration phases of neurocomputational ‘integrate-and-fire’ cycles. Orch OR is a viable approach toward understanding how the brain produces consciousness.

 

1. Neurocompution and quantum compution are compatible – “dendritic webs”

 

In their article Is the brain a quantum computer? Litt et al (2006) argue that “neurocomputational rather than quantum mechanisms provide the most credible explanations of mental phenomena”, and criticize (among other quantum consciousness theories) the Orch OR (“orchestrated objective reduction”) model put forth by Sir Roger Penrose and me (Penrose  & Hameroff, 1995; Hameroff & Penrose, 1996a; Hameroff & Penrose, 1996b Hameroff, 1998a; Hameroff, 2006a). 

 

By ‘neurocomputational’ I assume Litt et al imply computation mediated by axonal action potentials (‘firings’, or spikes’) and axonal-dendritic (or axonal-somatic) chemical synaptic connections of variable strength between neurons. In this neural network paradigm, individual dendrites of each neuron receive and integrate multiple input-generated post-synaptic potentials, and when threshold is met, “fire”, i.e. trigger axonal action potential spikes as outputs (“integrate and fire”).

 

In the Orch OR model, quantum computations are proposed to occur in microtubules in cytoplasm within gap junction-linked dendrites (“dendritic webs” - Figure 1) of these same brain neurons in cortex and other regions, i.e. embedded in integration phases of integrate-and-fire cycles. The proposed quantum computations/integrations are discrete events of roughly 25 milliseconds duration (coupled to gamma synchrony EEG) with each quantum computation culminating in a conscious moment, e.g. at 40 Hz. In neural network parlance, the site of consciousness is proposed to occur in laterally-connected inputs of a hidden layer, able to selectively trigger axonal firings as outputs in specific neurons and thus govern behavior. Orch OR and neurocomputation are compatible, and consciousness may occur primarily in dendrites, as proposed previously by Karl Pribram (1991), Sir John Eccles (1992) and others.

         

                   

Figure 1. Dendrites and cell bodies of schematic neurons connected by dendritic-dendritic gap junctions form a laterally connected input layer (“dendritic web”) within a neurocomputational architecture. Dendritic web dynamics are temporally coupled to gamma synchrony EEG, and correspond with integration phases of “integrate and fire” cycles. Axonal firings provide input to, and output from, integration phases (only one input, and three output axons are shown). Cell bodies/soma contain nuclei shown as black circles; microtubule networks pervade the cytoplasm. According to the Orch OR theory, gamma EEG-synchronized integration phases include quantum computations in microtubule networks which culminate with conscious moments. Insert closeup shows a gap junction through which microtubule quantum states entangle among different neurons, enabling macroscopic quantum states in dendritic webs extending throughout cortex and other brain regions.

 

 

 

2. Specific issues in Is the brain a quantum computer?

 

Here I respond to specific issues raised by Litt et al in their article.

 

2.1. Nothing special about microtubules.

 

Litt et al state “Found throughout the plant and animal kingdoms, their distribution in neurons is wholly unexceptional”. This is false. 1) Brain neuronal microtubules are composed of 17 different isozymes of subunit proteins (“tubulins”), far greater genetic diversity (and information capacity) than microtubules in other cells (Lee et al, 1986). 2) Microtubules are densely arrayed and overly abundant in neurons compared to all other cells because of the large and highly asymmetrical neuronal shape. 3) Only neuronal dendrites have mixed polarity, short microtubules interconnected in anti-parallel network arrays (e.g. Woolf, 1998; Woolf & Hameroff, 2001) simulations of which are suitable for learning (Rasmussen et al, 1990). 4) Only in the brain are many such arrays interconnected in gap junction-linked dendritic webs.

 

Orch OR attributes consciousness to a sequence of discrete conscious moments, each a quantum computation terminated by an objective threshold for quantum state reduction proposed by Penrose (objective reduction—“OR”). The quantum computations in dendritic microtubules are proposed to be “orchestrated” by axonal firings, synaptic inputs, memory etc (hence “Orch OR”).

 

According to Orch OR, dendritic cytoplasmic microtubules are isolated from their classical/non-quantum environment (e.g. by actin gelation) in quantum state phases of superpositioned entanglement. The quantum isolated (“integrate”) phases cycle at gamma synchrony frequency with open, communicative (“fire”) phases for inputs to, and outputs from, isolated quantum computations. Quantum states of unconscious possibilities evolve and compute according to the mathematical laws of quantum mechanics until reaching threshold for objective reduction/OR (and a conscious moment) by the indeterminacy principle E=h/t. E is the energy/amount of superpositioned mass—e.g. the number of quantum superpositioned tubulin proteins, h is Planck’s constant over 2π, and t is the time until objective reduction and a conscious moment occur. OR events select specific classical output states (e.g. patterns of tubulin protein conformations within dendritic microtubules) which can trigger axonal spikes and govern behavior.

 

E is also proposed to correlate with intensity of conscious experience. Due to the inverse relation between E and t, large E superpositions (assuming they are isolated/shielded to avoid decoherence) reach threshold quickly (small t, high intensity experience), and small isolated superpositions require long times (small E, large t, low intensity experience). Consequently only in the brain may a sufficiently large number of quantum superpositioned neuronal microtubules be entangled and isolated (in dendritic webs) so that OR/consciousness threshold is reached in relevant time scales. For example setting t equal to 25 msec (duration of one gamma synchrony cycle at 40 Hz), E is equivalent to superpositioned and entangled microtubules in a dendritic web of roughly 100,000 neurons.  

 

Litt et al ask: “Are we to believe that carrots and rutabagas also exhibit quantum computation, or are conscious?” No, we are not. Plant cells have very few microtubules (very small E); whether they have quantum isolation and quantum computation is unknown. But assuming they did, by E=h/t a carrot or rutabaga (small E, long t) might have a single, very low intensity conscious moment once per month or so. (Avoiding decoherence for this duration is extremely unlikely.) Apparently high intensity conscious experience (e.g. in meditating Tibetan monks) correlates with extremely high frequency, amplitude and coherence (very high E, low t) of global gamma EEG synchrony (Lutz et al, 2004). Orch OR provides consciousness with ontological distinction as sequences of a specific type of physical event—OR-mediated quantum state reductions coupled to neurophysiology.

 

 

2.2. Timescale/decoherence.

 

Technological quantum computations apparently require low temperature to avoid “decoherence”, disruption of quantum states by thermal energy in the classical (non-quantum) environment. Decoherence must be avoided long enough for quantum computation to occur (and in Orch OR, for threshold to be reached by E=h/t). Thus many physicists are skeptical of quantum computation occurring in the “warm, wet brain”.

 

The authors cite Tegmark’s (2000) calculations indicating that microtubule quantum states decohere far too quickly (10-13 seconds) at brain temperature to exert useful neurophysiological effects. However Tegmark’s calculations ignored Orch OR stipulations to avoid decoherence. In a footnote, Litt et al refer to a paper in which we (Hagan, Hameroff & Tuszynski, 2001) used Tegmark’s decoherence formula with Orch OR stipulations and calculated microtubule decoherence times in hundreds of milliseconds or longer—sufficient for neurophysiological effects. Litt et al misinterpret those findings, concluding they apply only locally to microtubule subunit proteins—too small a scale to be significant. On the contrary, anti-decoherence stipulations of Orch OR include 1) transiently encasing bundles of dendritic microtubules in actin gel—an isolated, shielded and water-ordered non-liquid environment for quantum processes, 2) quantum states extending among dendritic gel environments via quantum tunneling and/or entanglement through window-like gap junctions of dendritic webs, 3) microtubule quantum error correction topology (Hameroff et al, 2002) and 4) biomolecular quantum states pumped by, rather than disrupted by, heat energy. Indeed, Ouyang & Awschalom (2003) showed that quantum spin transfer through organic biomolecules is enhanced at warm brain temperature. And warm quantum states have recently been demonstrated in semiconductors (Lau et al, 2006; Stern et al, 2006; c.f. Amin et al, 2006). 

 

2.3. Synaptic transmission

 

Litt et al cite philosopher Patricia Churchland, a vocal critic of Orch OR who said: “…the explanatory vacuum is catastrophic. Pixie dust in the synapses is about as explanatorily powerful as quantum coherence in the microtubules” (Churchland, 1998).

 

(The term “quantum coherence” is vague. We refer specifically to quantum computation involving OR-mediated state reductions of entangled superpositions which we claim provide sequences of discrete conscious moments, e.g. at 40 Hz.)

 

But if pixie dust molecules bound to dendritic receptors, how would they differ from neurotransmitters? Where is the explanatory power in neurocomputation? Aspects of mental phenomena should extend to the molecular level (e.g. Thagard, 2002) so the apparent answer lies in specific properties of psychoactive neurotransmitters and their receptors. Recent evidence suggests that interactions between odorant molecules and nasal smell receptor proteins involve not only lock-and-key chemical binding, but also quantum correlations between odorant and receptor molecular electron resonance orbitals (Brookes et al, 2006). Potency of hallucinogenic drug molecules correlate with their quantum electron resonance effects on receptors (Snyder & Merrill,1965; Kang & Green, 1970 and Nichols, 1986). Thus significant quantum correlations may be expected between electron resonance orbitals of psychoactive neurotransmitter molecules (e.g. the indole ring of serotonin, the benzene ring of dopamine etc.) and their brain receptors.

   

Litt et al cite two Churchland critiques of Orch OR (Grush and Churchland, 1995; Churchland, 1998) but unfairly fail to cite our detailed replies to each (Penrose & Hameroff, 1995; Hameroff, 1998b).  

 

2.4. Penrose OR is unproven.

 

The fate of isolated quantum superpositions remains unexplained; Penrose OR (Penrose, 1989; 1994; 1996) is one tentative proposal which is testable, and can also account for consciousness. It is true, as Litt et al state, that if Penrose OR is proven correct then quantum theory would have to be rewritten. But quantum theory as it stands is incomplete: it must be rewritten.

 

2.5. Anesthesia

 

The authors cite my 1998 paper (Hameroff, 1998c) which proposed quantum London forces in hydrophobic pockets of dendritic brain proteins as the origin for both 1) quantum states leading to consciousness and 2) anesthetic action. They then state subsequent work has shown that all anesthetics act on one or more ligand-gated ion channels/receptors, and that my “…quantum mechanical theory of anesthesia has been surpassed by biochemical explanations…”.

 

My more recent paper in Anesthesiology (Hameroff, 2006b) points out: 1) many drugs bind to these channels/receptors but do not cause anesthesia, 2) anesthetics have varying and confusing effects on channels/receptors (e.g. anesthetics may potentiate excitatory channels and/or inhibit inhibitory channels), 3) within ligand-gated channels/receptors (and other dendritic proteins), anesthetic gases act via quantum London forces in hydrophobic pockets to inhibit electron resonance and thereby selectively prevent consciousness. And 4) anesthetic gas molecules are chemically inert and do not form (bio)chemical bonds with protein targets, acting solely through quantum London forces instead. Thus, to argue that biochemical explanations account for anesthesia is a non sequitur.

 

2.6. Bird flight

 

The non-dependence of bird flight on quantum effects is irrelevant, because 1) bird flight is understood and consciousness is not, and 2) there is no suggestion of macroscopic quantum states relating to bird flight.  

 

3. The role and function of consciousness

 

Although Litt et al did not discuss it, the role/function of consciousness is perhaps the most important question we face. Because evoked potentials and other measurable brain electrical activity correlating with conscious perceptions occur after subjects have responded to those perceptions (e.g. Velmans, 1991), neurocomputationalists conclude that consciousness is epiphenomenal and illusory (Dennett, 1991; Dennett & Kinsbourne, 1992; Koch & Crick, 2001; Wegner, 2002). The party line in cognitive neuroscience is that we react unconsciously, after which (a third of a second behind reality) we construct and falsely remember being and acting in the here and now. “We are merely helpless spectators” as T.H. Huxley put it. Even unified conscious experience is deemed a mirage (e.g. Dennett, 1991). Maybe so, but evidence suggests backward time effects occur in the brain (e.g. Libet et al, 1979). Quantum entanglement apparently depends on seemingly backward time effects which, as unconscious quantum information, can potentially rescue consciousness from the unfortunate position of illusory epiphenomenon (Hameroff, 2006a).   

 

4. Aspects of the brain requiring quantum effects

 

Litt et al state “The onus is on those who would appeal to quantum theory to show the existence of aspects of the brain that are not explained by neurocomputational theories, and that can be explained by quantum computation or associated mechanisms”.

 

In my opinion, neurocomputational theories fail to explain essential features of consciousness like binding, transition from unconscious activities to consciousness, non-algorithmic processing and the “hard problem” of subjective experience (Chalmers, 1996). However these are all arguable.

 

Instead I point to gamma synchrony electroencephalography (“EEG”), a candidate for the “neural correlate of consciousness” (the “NCC”). Gamma synchrony EEG (30 to 90 Hz) has been observed in hundreds of animal and human studies using multi-unit scalp, surface and implanted electrodes, and occurs within and across cortical areas, hemispheres, thalamus and even spinal cord (Schoffelen et al, 2005).

 

Loss of consciousness associated with onset of general anesthesia is characterized by disappearance of frontal-posterior gamma EEG coherence which returns when patients awaken (John and Prichep, 2005; Imas et al, 2005; John, 2001). During general anesthesia in the absence of consciousness, neurocomputation in the brain continues, evidenced by evoked potentials, sub-gamma EEG, autonomic control etc. For reviews of evidence linking gamma synchrony with consciousness, see Singer (1999) and Hameroff (2006a).

 

Despite the evidence, gamma synchrony is often questioned as the NCC perhaps because axonal spikes are not coherent (e.g. Shadlen & Movshon, 1999; Koch, 2004). But in any case, brain-wide gamma synchrony does occur, and is clearly “an aspect of the brain”. 

 

Gamma synchrony involves gap junctions, or electrical synapses—direct open windows between adjacent cells formed by paired collars consisting of classes of proteins called connexins (Herve 2004, Rouach et al 2002) and pannexins (Ray et al, 2005). Gap junctions occur between brain neuronal dendrites, between axons and axons, between neurons and glia, between glia, and between axons and dendrites—bypassing chemical synapses and electrically coupling neuronal depolarizations (Traub et al 2001, Froes & Menezes 2002, Traub et al 2002, Bezzi & Volterra 2001; Fukuda et al, 2006).

 

Cortical inhibitory interneurons are particularly studded with gap junctions, potentially connecting each cell to 20 to 50 others (Amitai et al 2002). Pyramidal cells and other primary neurons have far fewer gap junctions, the numbers decreasing from development to become necessarily sparse (but present; e.g. Ray et al, 2005) in adult primary neurons. Traub et al (2002) showed that 3 or more open/active gap junctions per primary neuron (e.g. pyramidal cells, each with thousands of chemical synapses) would cause excessive and dysfunctional coupling.

 

Dendritic-dendritic gap junction circuits of cortical interneurons and selected primary neurons (in concert with GABA inhibitory chemical synapses) specifically mediate gamma synchrony (Dermietzel 1998, Draguhn et al 1998, Hormuzdi et al 2004, Bennett and Zukin 2004, Lebeau et al 2003, Friedman and Strowbridge 2003, Buhl et al 2003, Rozental et al 2000, Perez-Velazquez and Carlen 2000, Tamas et al, 2000; Galaretta and Hestrin 1999, Gibson et al 1999). Thus gamma synchrony occurs in the same gap junction-connected “dendritic webs” within whose cytoplasm Orch OR conscious events are proposed to occur.   

While gap junctions are required for gamma synchrony, they still impart some phase delay—i.e. gap junctions are necessary but not sufficient to account for the precise global coherence. Recent reviews (Freeman and Vitiello, 2006; c.f. John, 2001) concluded that thalamic pacing, recurrent feedback, reciprocal connections, electric fields and/or gap junction membrane coupling cannot account for precise global coherence of gamma synchrony EEG, and that long range quantum correlations may be required.

Litt et al and other proponents of neurocomputation should attempt to show how global brain gamma synchrony can be explained by classical (non-quantum) neural mechanisms.     

 

5. Conclusion

 

Orch OR is a theory of consciousness spanning scale and discipline. It relies on as-yet unproven biology and physics, but is consistent with known science, falsifiable and generates testable predictions (Hameroff, 1998a; Hameroff, 2006a). Orch OR involves quantum computations in microtubule networks embedded within gap junction-linked cortical dendrites ("dendritic webs") acting as laterally connected input layers of the brain's neurocomputational architecture. According to Orch OR, consciousness is a sequence of discrete quantum computations, each culminating in a conscious moment in gamma EEG-synchronized integration phases of neurocomputational "integrate-and-fire" cycles. Orch OR is a specific and viable scientific proposal for consciousness. 

 

 

 

References

 

      Amin, M.H.S., Love, P.J., & Truncik, C.J.S. (2006).   Thermally assisted adiabatic quantum computation. arXiv:cond-mat/o609332 v1.

 

       Amitai, Y., Gibson, J.R., Beierlein, M., Patrick, S.L., Ho, A.M., Connors, B.W., & Golomb, D. (2002) The spatial dimensions of electrically coupled networks of interneurons in the neocortex. The Journal of Neuroscience 22(10): 4142-52

 

      Bennett, M.V., & Zukin, R.S. (2004) Electrical coupling and neuronal synchronization in the mammalian brain. Neuron. 41(4):495-511.

 

       Brookes J.C., Hartoutsiou F., Horsfield A.P. & Stoneham A.M. (2006) Could humans recognize odor by phonon assisted tunneling? http://www.arxiv.org/abs/physics/0611205

      Buhl, D.L., Harris, K.D, Hormuzdi, S.G., Monyer, H., & Buzsaki, G. (2003) Selective impairment of hippocampal gamma oscillations in connexin-36 knock-out mouse in vivo. Journal of Neuroscience. 23(3):1013-8.

 

      Chalmers, D. J., (1996) The conscious mind - In search of a fundamental theory. Oxford University Press, New York

 

     Churchland, P.S. (1998) Brainshy: Nonneural theories of conscious experience. In S.R. Hameroff, A.W. Kaszniak & A.C. Scott (Eds.), Toward a Science of Consciousness II:  ­ The Second Tucson Discussions and Debates, (pp. 109-126). Cambridge, MA: MIT Press.

 

              Dennett, D.C. (1991) Consciousness explained. Boston, MA:  Little, Brown and Company.

 

              Dennett, D.C. & Kinsbourne, M. (1992). Time and the observer: the where and when of consciousness. Behavioral and Brain Sciences, 15, 183-247.

 

      Dermietzel, R. (1998) Gap junction wiring: a 'new' principle in cell-to-cell communication in the nervous system? Brain Research Reviews. 26(2-3):176-83

 

      Draguhn, A., Traub, R.D., Schmitz, D., Jefferys, J.G. (1998) Electrical coupling underlies high-frequency oscillations in the hippocampus in vitro. Nature. 394(6689):189-92.

 

              Eccles, J.C. (1992). Evolution of consciousness. Proceedings of the National Academy of Sciences, 89, 7320-24.

 

              Freeman, W.J., & Vitiello, G. (2006). Nonlinear brain dynamics as macroscopic many-body field dynamics. Physics of Life Reviews, 3, 93-118.

 

       Friedman, D., & Strowbridge, B.W. (2003) Both electrical and chemical synapses mediate fast network oscillations in the olfactory bulb. Journal of Neurophysiology 89(5):2601-10.

 

       Froes, M.M. & Menezes, J.R. (2002) Coupled heterocellular arrays in the brain. Neurochemistry International. 41(5):367-75.

 

              Fukuda, T., Kosaka, T., Singer, W., & Galuske, R.A. (2006). Gap junctions among dendrites of
cortical GABAergic neurons establish a dense and widespread intercolumnar network. Journal of Neuroscience, 26(13), 3434-43.

 

              Galarreta, M, & Hestrin, S. (1999). A network of fast-spiking cells in the neocortex connected by electrical synapses. Nature, 402, 72-75.

 

            Gibson, J.R., Beierlein, M., & Connors, B.W. (1999) Two networks of electrically coupled inhibitory neurons in neocortex. Nature, 402:75-79.

 

              Grush, R., & Churchland, P.S. (1995). Gaps in Penrose’s toilings. Journal of Consciousness Studies, 

2(1), 10-29.

 

              Hagan, S., Hameroff, S., & Tuszynski, J. (2002). Quantum Computation in Brain Microtubules?  Decoherence and Biological Feasibility, Physical Reviews E, 65, 061901.

 

              Hameroff, S.R., & Penrose, R. (1996a) Orchestrated reduction of quantum coherence in brain microtubules: A model for consciousness. In S.R. Hameroff, A.W. Kaszniak & A.C. Scott (Eds.) Toward a Science of Consciousness II:  ­ The Second Tucson Discussions and Debates (pp. 507-540). Cambridge, MA: MIT Press. Also published in Mathematics and Computers in Simulation (1996) 40, 453-480. http://www.consciousness.arizona.edu/hameroff/or.html.

 

              Hameroff, S.R., & Penrose, R. (1996b).  Conscious events as orchestrated spacetime selections. Journal of Consciousness Studies, 3(1), 36-53.

http://www.u.arizona.edu/~hameroff/penrose2

 

              Hameroff, S. (1998a) Quantum computation in brain microtubules?  The Penrose-

Hameroff "Orch OR" model of consciousness. Philosophical Transactions of the Royal Society,  London Series A, 356, 1869-1896. http://www.consciousness.arizona.edu/hameroff/royal2.html.

 

              Hameroff, S. (1998b).  More neural than thou (A reply to Patricia Churchland). In S.R. Hameroff, A.W. Kaszniak & A.C. Scott (Eds.) Toward a Science of Consciousness II:  ­ The Second Tucson Discussions and Debates (pp. 197-213). Cambridge, MA: MIT Press.


              Hameroff, S. (1998c). Anesthesia, consciousness and hydrophobic pockets – A unitary quantum hypothesis of anesthetic action. Toxicology Letters 100/101, 31-39.

 

       Hameroff, S., Nip, A., Porter, M., & Tuszynski, J. (2002) Conduction pathways in microtubules, biological quantum computation and microtubules. Biosystems 64(13):149-68

 

              Hameroff, S. (2006a). Consciousness, neurobiology and quantum mechanics – The case for a connection. In. J. Tuszynski (Ed.) The emerging physics of consciousness, (pp 193-253). Berlin, Germany: Springer.

 

              Hameroff, S. (2006b). The entwined mysteries of anesthesia and consciousness – Is there a common underlying mechanism? Anesthesiology 105, 400-412.

 

       Herve, J-C. (2004) The connexins Biochimica et Biophysica Acta (BBA) Biomembrane 1662, 1-2.

 

       Hormuzdi, S.G., Filippov, M.A., Mitropoulou,G., Monyer, H., Bruzzone, R. (2004). Electrical synapses: a dynamic signaling system that shapes the activity of neuronal networks. Biochimica et Biophysica Acta. 1662(1-2):113-3.

 

              Imas, O.A., Ropella, K.M., Ward, B.D., Wood, J.D., & Hudetz, A.G. (2005). Volatile anesthetics disrupt frontal-posterior recurrent information transfer at gamma frequencies in rat. Neuroscience Letters, 387, 145-150.

 

              John, E.R., & Prichep, L.S. (2005). The anesthetic cascade. A theory of how anesthesia suppresses consciousness.  Anesthesiology, 102, 447-471.

 

              John, E.R. (2001). A field theory of consciousness. Consciousness & Cognition, 10(2), 184-213.

 

             Kang S, Green JP M(1970)  Steric and electronic relationships among some hallucinogenic compounds Proc. Natl. Acad. Sci. USA 67(1):62-67

 

              Koch, C. & Crick, F.C.R. (2001). The zombie within.  Nature, 411, 893.

 

       Koch, C.K. (2004) The quest for consciousness: A neurobiological approach. Englewood, Colorado, Roberts and Company.

 

       Lau, W.H.,  Sih, V., Stern, N.P., Myers, R.C., Buell, D.A., & Awschalom, D.D. (2006). Room temperature electron spin coherence in telecom-wavelength quaternary quantum wells  Applied Physics Letters 89,142104.

 

       LeBeau, F.E., Traub, R.D., Monyer, H., Whittington, M.A., & Buhl, E.H. (2003) The role of electrical signaling via gap junctions in the generation of fast network oscillations. Brain Research Bulletin 62(1):3-13.

 

              Lee, J. C., Field, D.J., George, H.J., & Head, J. (1986). Biochemical and chemical properties of tubulin subspecies. Annals of the New York Academy of Sciences 466, 111-128.

 

       Libet, B., Wright, E.W. Jr., Feinstein, B., & Pearl, D.K. (1979) Subjective referral of the timing for a conscious sensory experience. Brain 102, 193-224.

 

       Litt, A., Eliasmith, C., Kroon, F.W., Weinstein, S., & Thagard, P. (2006). Is the brain a quantum computer, Cognitive Science 30, 593-603 .

 

       Lutz, A., Greischar, L.L., Rawlings, N.B., Ricard, M. and Davidson, R.J. (2004) Long-term meditators self-induce high-amplitude gamma synchrony during mental practice The Proceedings of the National Academy of Sciences USA 101(46)16369-16373.

 

       Nichols DE (1986) Studies of the relationship between molecular structure and hallucinogenic activity Pharmacology Biochemistry and Behavior 24:335-340

 

       Ouyang, M., & Awschalom, D.D., (2003).  Coherent spin transfer between molecularly bridged quantum dots. Science 301, 1074-78.

 

        Penrose, R. (1989). The emperor’s new mind. Oxford: University Press.

 

        Penrose, R. (1994). Shadows of the mind: a search for the missing science of consciousness. Oxford:  University Press.

 

         Penrose, R. (1996).  On gravity's role in quantum state reduction. General Relativity and Gravitation 28(5), 581-600.

 

         Penrose R., & Hameroff S.R. (1995). What gaps? Reply to Grush and Churchland. Journal of Consciousness Studies, 2, 98-112.

 

         Perez Velazquez, J.L., & Carlen, P.L. (2000) Gap junctions, synchrony and seizures. Trends in Neurosciences. 23(2):68-74.

 

         Pribram, K.H. (1991). Brain and Perception. New Jersey: Lawrence Erlbaum.

 

         Rasmussen, S., Karampurwala, H., Vaidyanath, R., Jensen, K.S., & Hameroff, S. (1990). Computational connectionism within neurons: A model of cytoskeletal automata subserving neural networks. Physica D 42, 428-49.

 

         Ray, A., Zoidi, G., Weickert, S., Wahle, P., Dermietzel, R. (2005) Site-specific and developmental expression of pannexin1 in the mouse nervous system. European Journal of Neuroscience 21(12):3277-3290

 

        Rouach, N., Avignone, E., Meme, W., Koulakoff, A., Venance, L., Blomstrand, F., & Giaume, C. (2002) Gap junctions and connexin expression in the normal and pathological central nervous system.  Biology of the Cell 94(7-8):457-75.

 

         Rozental, R., Giaume, C. & Spray. D.C., (2000) Gap junctions in the nervous system. Brain Research Reviews 32(1):11-5.

 

         Schoffelen JM, Oostenveld R, and Fries P (2005): Neuronal coherence as a mechanism of effective corticospinal interaction. Science 308(5718): 111-113.

 

          Shadlen, M.N., & Movshon, J.A. (1999) Synchrony unbound: A critical evaluation of the temporal binding hypothesis. Neuron 24:67-77.

          

          Singer, W.  (1999) Neuronal synchrony: a versatile code for the definition of relations. Neuron 24:111-125.

 

          Snyder SH, Merrill CR (1965) A relationship between the hallucinogenic activity of drugs and their electronic configuration Proc. Natl. Acad. Sci. USA 54:258-266


           Stern, P., Ghosh, S., Xiang, G., Zhu, M., Samarth, N., & Awschalom, D.D. (2006) Current-induced polarization and the spin Hall effect at room temperature Physics Reviews Letters 97, 126603.

 

              Tamas, G., Buhl, E.H., Lorincz, A., & Somogyi, P. (2000).  Proximally targeted GABAergic synapses and gap junctions synchronize cortical interneurons. Nature Neuroscience 3, 366-71.

 

              Tegmark, M. (2000).  The importance of quantum decoherence in brain processes. Physica Rev E  61, 4194-4206.

 

             Thagard P. (2002) How molecules matter to mental computation) Philosophy of Science 69: 497-518

 

             Traub, R.D., Kopell, N., Bibbig, A., Buhl, E.H., LeBeau, F.E. (2001) Gap junctions between interneuron dendrites can enhance synchrony of gamma oscillations in distributed networks.  Journal of Neuroscience 21(23):9478-86.

 

             Traub, R.D., Draguhn, A., Whitingon, M.A., Baldeweg, T., Bibbig, A., Buhl, E.H. (2002) Axonal gap junctions between principal neurons: a novel source of network oscillations, and perhaps epileptogenesis.  Reviews in the Neurosciences 13(1):1-30.

 

             Velmans, M. (1991). Is human information processing conscious? Behavioral and Brain Sciences 14, 651-69.

 

            Wegner, D.M. (2002). The illusion of conscious will. Cambridge MA: MIT Press.

 

            Woolf, N.J.  (1998). A structural basis for memory storage in mammals. Progress in Neurobiology 55, 59-77.

 

           Woolf, N.J. & Hameroff, S.R. (2001) A quantum approach to visual consciousness. Trends in Cognitive Science 5, 472-78.