Page 1

PubMed, a service of the US National Library of Medicine The ʻhard problemʼ and the quantum physicists. Part 2: Modern times C.U.M. Smith, a, Roger Penrose, Stuart Hameroff, microtubules and Orch-OR Nel 1989 Roger Penrose pubblicò il suo famoso libro “la nuova mente dellʼimperatore”, e nel 1994 proseguì con “ombre della mente”. In entrambi questi libri cercava di dimostrare che la mente umana era incommensurabile con la classica fisica newtoniana e con lʼintelligenza artificiale. Nel 1991 Stuart Hameroff, un anestesista che lavorava presso lʼUniversità dellʼArizona, lesse “la nuova mente dellʼimperatore” e si rese conto che le idee di Penrose completavano la sua personale, lunghissima ricerca sui microtubuli. Hameroff e Penrose decisero di collaborare per sviluppare una teoria quantica sulla coscienza. Battezzarono questa teoria “Orchestrated Objective Reduction (Orch-OR). Che cosa significa? Prima vediamo di chiarire la “riduzione oggettiva” (OR). Si ricorderà che la classica teoria dei quanti degli anni venti implicava che la natura, a livello Quantico, fosse indeterminata: consisteva in una sovrapposizione di stati (funzioni-onda), finché unʼosservazione (esterna) non causasse il collasso, o la riduzione, in uno od altri di questi stati. Questo ha sempre rappresentato un problema: sembra suggerire che il mondo della natura non possa esistere senza un osservatore. Penrose, tuttavia, suggerisce unʼalternativa: la riduzione oggettiva. In questa teoria ciascuna delle funzioni-onda sovrapposte, ha la sua propria geometria spazio-tempo, e quando questa geometria diverge fino ad un punto critico (connesso alla gravità quantica), si deve verificare un collasso in uno od altri stati. In contrasto con una “riduzione soggettiva”, Penrose chiamò questa “riduzione oggettiva”. Che legame cʼè con la coscienza? Qui entra in gioco il lavoro di Hameroff sui microtubuli. ([Hameroff and Watt, 1982] and [Hameroff, 1987]). Dove, nel cervello, potrebbe verificarsi una riduzione oggettiva di stati quantici sovrapposti? Questi stati dovrebbero rimanere isolati dallʼosservazione e dai legami ambientali, abbastanza a lungo per far sì che le loro geometrie spazio-tempo divergano fino al punto della riduzione oggettiva. Senza una adeguata protezione dallʼambiente caldo ed umido del cervello, ogni effetto quantico si perderebbe rapidamente nei movimenti casuali di questo ambiente. Inoltre, per avere effetto sul cervello, singole fluttuazioni quantiche dovrebbero essere moltiplicate enormemente da qualche forma di coerenza. Tali stati di coerenza, naturalmente, sono ben noti ai fisici come Condensati di Bose-Einstein, e si manifestano nel grande mondo con i fenomeni delle superfluidità e superconduttività. Ma questi condensati, in cui lo stato Quantico di grandi quantità di particelle si fonde in “lock step”, si trovano normalmente solo in condizioni estreme od a temperature vicine allo zero assoluto, dove anche le influenze esterne sono quasi ridotte allo zero. Dove, nel cervello, si potrebbero ottenere tali condizioni? Hameroff, che aveva lavorato sui microtubuli per almeno ventʼanni prima di leggere Penrose, suggerì che questi potessero costituire il luogo tanto ricercato. La teoria Penrose-Hameroff pertanto suggerisce che le sovrapposizioni quantiche nei microtubuli sono orchestrate (armonizzate) in modo tale che possono avvenire riduzioni oggettive su scala macroscopica (ma pur sempre da microscopio elettronico). Da qui il nome della teoria “Orchestrated Objective Reduction”. Ammettendo, per il momento, che questa teoria abbia un senso fisico e biologico, come risolve il “grave problema”? la risposta a questa domanda riguarda la convinzione di Penrose che il pensiero cosciente non può essere imitato da una macchina, che cioè, in altre parole, è “incalcolabile”. Le neuroscienze del cervello del ventesimo e ventunesimo secolo, rientrano appieno entro i paradigmi prospettati da Newton e dai suoi successori, e perciò descrivono un sistema che, sebbene complesso, è in definitiva ed in linea di principio suscettibile di essere calcolato. Penrose crede che lʼintuizione matematica umana sfugga a questa possibilità. È pertanto impossibile costruire un computer analogo. Questa convinzione è connessa ai teoremi dellʼincompletezza di Gödel ed al lavoro di Turin sui numeri calcolabili e sullʼimpossibilità di una macchina di calcolo universale, conosciuta anche come “il problema” (Turing, 1936). Lʼauto-collasso di uno stato quantico è nella sua essenza imprevedibile e perciò incalcolabile. In questo rispecchia la non calcolabilità della coscienza (Penrose, 1994, p. 356). Per questo, secondo Penrose, strumenti capaci di moltiplicare questo collasso sono buoni candidati per essere le basi fisiche della coscienza. Questo è naturalmente un approccio fisico-matematico alla coscienza, e non è appropriato qui


entrare nei dettagli della gravità quantica e del calcolo quantico. Tuttavia merita notare che cʼè stata una grande controversia circa la possibilità fisica della teoria di Penrose-Hameroff. Lʼastrofisico Max Tegmark ha pubblicato una critica particolarmente forte in Physical Review (Tegmark, 2000; see also Seife, 2000). La sua analisi matematica ha concluso che le sovrapposizioni di quanti abbracciano molti dimeri di tubulina, con ordini di grandezza decine e decine di volte minori rispetto alla scala dei classici fenomeno neurofisiologici come i potenziali dʼazione. Lʼanalisi di Tegmark non è rimasta senza risposta. Hagan, Hameroff and Tuszynski (2002) hanno criticato alcune delle assunzioni di Tegmark e Tegmark ha risposto a queste critiche (Tegmark, 2002). Lasciando i fisici al loro dibattito sulla fisica quantica, esaminiamo le implicazioni neurobiologiche. La teoria propone che gli eventi Orch-OR avvengano allʼinterno dei microtubuli. Si ricorda che i microtubuli sono parte, insieme ai microfilamenti ed ai filamenti intermedi, del citoscheletro di un neurone. I microtubuli sono costituiti da una proteina chiamata tubulina, che a sua volta è costituita da sub unità globulari. Queste sub unità sono di due tipi, alfa e beta-tubulina. Nei microfilamenti, si associano per formare dimeri, e questi, poi, si uniscono per le estremità a formare “proto filamenti”. 13 di questi microfilamenti si allineano in parallelo ed in circolo per formare un tubo cavo, del diametro di circa 24 nm e della lunghezza di circa 200 μm. Ciascun dimero di tubulina può esistere in due conformazioni, e si ritiene che la transizione dallʼuna allʼaltra, sia controllata da un elettrone posizionato al centro, che può spostarsi da una posizione allʼaltra (Hameroff and Watt, 1982). Chiaramente, siamo qui al livello in cui entra in gioco la fisica quantica, e la teoria di Penrose-Hameroff suggerisce che sia una magnificazione da questo livello attraverso le complessità della struttura del cervello, ciò che unisce coscienza e comportamento. Si ipotizza che la coerenza quantica si accumuli lungo i microtubuli fino a raggiungere un punto critico, in cui avviene la OR. In che modo questa coerenza è protetta dallʼambiente caldo ed umido intracellulare? Hameroff suggerisce varie possibilità, che includono strati strutturati di molecole dʼacqua sia dentro che fuori del microtubulo(Hameroff and Penfield, 1996). Unʼaltra possibilità è costituita da trasformazioni sol-gel del citoplasma circostante. Una copertura di gel dei microtubuli dovrebbe, secondo Hameroff, fornire un meccanismo di isolamento quantico ideale. Nel loro articolo del 1996 Hameroff e Penrose tirarono fuori delle cifre sulla Orch-OR nei microtubuli. I loro calcoli suggeriscono che circa 109 subunità di tubulina in coerenza Bose-Einstein, impiegherebbero circa 500 ms per raggiungere la riduzione oggettiva. Dopo lʼauto-collasso ricomincerebbe tutto di nuovo, crescendo ancora oltre 500 ms. alternativamente, per ottenere lʼOR in 25 ms, e perciò rendere conto della oscillazione coerente di 40 Hz che, secondo alcuni è ritenuta essere correlata alla coscienza, circa 2 x 1010 tubuline dovrebbero essere chiamate in causa (Hagan, Hameroff and Tuszinsky, 2002). Secondo la teoria di Penrose-Hameroff un momento di “coscienza” avverrebbe ad ogni collasso della funzione-onda, cioè ad ogni OR. Quanti microtubuli sarebbero coinvolti in questi casi di Orch-OR? Lo si calcola facilmente dal numero di sub unità richieste. Se ci sono circa 107 tubuline per neurone (Yu and Baas 1994) allora un condensato Bose-Einstein che si diffondesse attraverso circa 10° neuroni raggiungerebbe la OR in 500 ms. Per raggiungerla in 25 ms il condensato dovrebbe attraversare circa 20.000 cellule. In entrambi i casi queste sono stime approssimative. È improbabile che tutti i microtubuli di tutte le cellule siano coinvolti allo stesso momento. Se solo il 10% di tubuline è coinvolto, il sistema in questione potrebbe consistere di 1.000 cellule nel primo caso e 200.000 nel secondo. In che modo il condensato può passare di neurone in neurone? Le distanze di 30-50 nm delle classiche sinapsi chimiche sembrerebbero troppo grandi per la diffusione quantica. Hameroff, tuttavia, indica le sinapsi elettriche, in cui le distanze intercellulari sono di molto minori, 3-5 nm, permettendo la possibilità di effetti tunnel quantici (Hameroff, 1998). In effetti, alcuni hanno osservato sistemi di sinapsi elettriche funzionare come “un grande neurone”. Bisogna anche notare (un punto che Hameroff non sottolinea) che i neuroni e le loro glia circostanti sono di solito connessi da giunzioni. Queste cifre sembrano coincidere con la neurofisiologia convenzionale. Abbiamo notato in precedenza che il lavoro di Benjamin Libet può essere interpretato nel senso di dimostrare che circa 500 ms sono necessari per richiamare un numero di cellule sufficiente a procurare la “adeguatezza neuronale” necessaria per supportare la coscienza, ed un tempo di decoerenza di 25 ms è adeguato alla oscillazione di 40 Hz che viene proposta come il legame che unisce insieme i sistemi neuronali per procurare una coscienza unitaria. Rimane la questione più importante: perché la coscienza? Qualunque cosa si pensi della congettura


di Penrose-Hameroff, e per molti neurobiologi essa sembra più il sogno di un fisico-matematico, che una cosa che possa accadere nei caldi, umidi, agitati e biochimicamente attivi elementi del citoscheletro, perché la OR dovrebbe essere associata a momenti di coscienza? A parte lʼ equazione di Penrose della non computabilità della coscienza, non sembra esserci nessuna risposta ovvia. Ci sembra di essere in prossimità della fallacia del vecchio “post hoc ergo propter hoc”. Arriviamo finalmente alla plausibilità neurologica della congettura. Come prima cosa, è importante chiarire che i microtubuli non sono confinati ai neuroni, ma costituiscono parte del citoscheletro di tutte le cellule eucariote, dalla amebe, per esempio, alle cellule del fegato umano. In effetti, Hameroff è pronto ad ammettere che momenti di “coscienza” possano essere comparsi nelle prime forme metazoe, dallʼ”esplosione” cambriana in poi. Secondo, i microtubuli si sono evoluti fino ad avere numerose importanti funzioni nelle cellule ed in quelle nervose in particolare. Sono molto lontani dallʼessere quegli elementi strutturali statici che la loro definizione come parti del citoscheletro, e le prime rappresentazioni suggeriscono ( Bethe, 1898, Fig. 9). Sono profondamente coinvolti nel trasporto assoplasmatico, con vescicole attivate da kinesina e dineina che si muovono sia in senso anterogrado che retrogrado. Infine, ma non certo meno importante, i microtubuli sono in un continuo stato di sintesi ad una estremità, quella positiva, e di degradazione allʼaltra estremità, quella negativa. La microscopia ad alta definizione (AVEC-DIC) dimostra che i microtubuli sono il centro di uno sciame di attività (Weiss, 1986). I mitocondri si muovono a scatti su “binari” neuro tubulari in entrambe le direzioni lungo lʼassone; corpi multi vescicolari e multi lamellari si muovono lungo i microtubuli verso il pericario; densi banchi di vescicole di trasporto si muovono a diverse velocità in direzione opposta, verso il bottone sinaptico ([Nogales, 2001] e [Smith, 2002]). Al neurobiologo molecolare i microtubuli sembrano molto diversi dalla struttura in cui Penrose e Hameroff immaginano che i condensati Bose-Einstein vadano verso la OR. Sebbene le recenti pubblicazioni (Hagan, Hameroff and Tuszynki, 2002), suggeriscano che il caso è ancora aperto, la rappresentazione dei microtubuli della congettura Orch-OR di Penrose-Hameroff sembra improbabile, sia dal punto di vista della fisica quantica che dal punto di vista della neurobiologia molecolare (v. anche la critica di Koch and Hepp, 2006). Ciononostante, lʼidea generale potrebbe trovare validità nelle neuroscienze future. Come sottolinea Penrose, dalla sua prospettiva platonica, potrebbe essere che “lʼattuale attraente immagine del cervello e della mente non sia altro che una mera ombra del più profondo livello dellʼazione citoscheletrica – ed in questo livello più profondo dobbiamo cercare le basi fisiche della mente” (Penrose, 1994, p. 376).


PHYSICAL REVIEW E 80, 021912 !2009"

Penrose-Hameroff orchestrated objective-reduction proposal for human consciousness is not biologically feasible Laura K. McKemmish,1 Jeffrey R. Reimers,1,* Ross H. McKenzie,2 Alan E. Mark,3 and Noel S. Hush4 1

School of Chemistry, The University of Sydney, New South Wales 2006, Australia School of Mathematics and Physics, The University of Queensland, Queensland 4072, Australia 3 School of Chemistry and Molecular Biosciences and Institute for Molecular Biosciences, The University of Queensland, Queensland 4072, Australia 4 School of Molecular and Microbial Biosciences, The University of Sydney, New South Wales 2006, Australia !Received 15 November 2008; revised manuscript received 29 May 2009; published 13 August 2009" 2

Penrose and Hameroff have argued that the conventional models of a brain function based on neural networks alone cannot account for human consciousness, claiming that quantum-computation elements are also required. Specifically, in their Orchestrated Objective Reduction !Orch OR" model #R. Penrose and S. R. Hameroff, J. Conscious. Stud. 2, 99 !1995"$, it is postulated that microtubules act as quantum processing units, with individual tubulin dimers forming the computational elements. This model requires that the tubulin is able to switch between alternative conformational states in a coherent manner, and that this process be rapid on the physiological time scale. Here, the biological feasibility of the Orch OR proposal is examined in light of recent experimental studies on microtubule assembly and dynamics. It is shown that the tubulins do not possess essential properties required for the Orch OR proposal, as originally proposed, to hold. Further, we consider also recent progress in the understanding of the long-lived coherent motions in biological systems, a feature critical to Orch OR, and show that no reformation of the proposal based on known physical paradigms could lead to quantum computing within microtubules. Hence, the Orch OR model is not a feasible explanation of the origin of consciousness. DOI: 10.1103/PhysRevE.80.021912

PACS number!s": 87.15.R!, 03.67.Lx, 07.05.Mh, 87.16.Ka

I. INTRODUCTION

The nature of human consciousness is perhaps the most important of unsolved scientific problems. It is widely accepted that the consciousness is linked to the neural activity in the brain; however, the chemical interactions between neurons have been argued by Penrose #1,2$ to set restrictive limits on processing capacity. The most developed extended model of cognitive function is the Penrose-Hameroff orchestrated objective reduction #3–8$ !Orch OR" model, which proposes that the quantum computation occurs in microtubule assemblies within the neurons of the brain. Currently, there is great interest in both this and other proposals for nontrivial quantum effects in biology #9–11$. Figure 1 depicts the qubit in the Orch OR model and shows a proposed quantum computational cycle. Coherent superpositions of alternative conformational states of individual tubulins dimers are proposed to form the quantum computational elements !qubits". The coherent oscillation depicted in the figure interconverts the classical chemical conformational states in situ to facilitate the resonant superpositions !step 1", with coherence originating as a result of Fröhlich condensation #4,5$. This nuclear motion is then coupled to electronic motion, allowing the qubits to interact with each other while maintaining coherence, thus forming the quantum computer across an extensive network of microtubules. Figure 1 shows the formation of these extended superpositions and their spread to encompass many microtubules !steps 2 and 3" and

*Author to whom correspondence should be addressed. FAX: "61!2"93513329; reimers@chem.usyd.edu.au 1539-3755/2009/80!2"/021912!6"

even spread to include many neurons #7$. Quantum gravitational effects are proposed to decohere the system on the physiological time scale #4,6$. Decoherence causes the quantum state of each tubulin-dimer qubit in each participating microtubule to be reduced to one of its classical forms !step

FIG. 1. The physiological elements of a qubit and the operational cycle of the quantum computation within the PenroseHameroff model for cognitive function by orchestrated objective reduction, taken from Ref. #8$; reproduced with permission of MIT Press. Left: tubulin dimers within microtubules exist in two conformational states !shown black or white" and it is proposed that resonance coupling between these conformations acts to form qubits from quantum superpositions of the local vibronic wave functions !shown gray". Such superpositions require coherent motion in the vibrational modes, proposed to originate via Fröhlich condensation #4$, that interchange the two conformational states and move internal electrons !marked “e”". Right: four steps in the operational cycle starting at !1" superpositions start to appear from among classically localized states in the tubulin-dimer qubits, !2" coherent motions and superpositions grow to encompass large regions of this and neighboring microtubules, !3" superposition reaches critical mass inducing objective reduction to form !4" an ensemble of tubulin dimers throughout many microtubules containing the results of the quantum computation specified through their !classical" conformations.

021912-1

©2009 The American Physical Society


PHYSICAL REVIEW E 80, 021912 !2009"

MCKEMMISH et al.

4". This classical state then interacts with its chemical environment, possibly through the actin sol-gel cycles that control the microtubule network structure. As microtubules can influence the electrochemical properties of neurons #12$, the results of the quantum computation could by this means influence neural processing. The basic physical principle underlying the resonancebased chemical qubit sketched in Fig. 1 is a widely known motif throughout chemistry and biology. Originally quantum-mechanical “resonance” was conceptualized to describe the “aromatic” nature of benzene compared to the expected properties of its classical form, the hypothetical cyclohexatriene molecule. For benzene, the electron-phonon coupling involving the critical vibrational mode, #14 !see, e.g., #13$.", is insufficient to overpower the resonance stabilization and so a fully delocalized structure results #14$. A related problem that is more directly relevant to quantum computing !see, e.g., #15,16$" and Orch OR is the structure and dynamics of ammonia in the gas phase. For ammonia, the electron-phonon coupling in the relevant mode, the umbrella-inversion mode, does overpower the resonance interaction and so two mirror-image pyramidal classical chemical equilibrium structures result #14$. Coherent superpositions of the resulting vibronic states is a known process that in fact leads to the operation of the maser. Also pertinent to the Orch OR proposal are quantum phenomena in the Creutz-Taube ion #17$, a mixed valence bisruthenium complex of pyrazine in which charge transport is controlled through coherent motion #18$ involving long-range solvent vibrational modes #19$. This system is also very important in that it provided the model through which primary charge separation, quantum coherence, and charge transport was understood in bacterial and plant photosynthetic reaction centers #14,20$. More generally, all biological and chemical charge-transport processes are now known to be controlled by analogous interplays between vibrational motions and resonance couplings #21,22$, with a key feature being the time through which coherence is maintained. That such a process might give rise to quantum computation in biological tissues is thus a proposal worth considering. Indeed, a theory describing how resonating classical chemical structures can develop entangled states that function as quantum computer elements has recently been described #15$. Nonetheless, while the Penrose-Hameroff proposal contains many controversial aspects #7,23$, the most ambitious requirement is that the tubulin-dimer interconversion oscillation depicted in Fig. 1 remains coherent on a time scale relevant to neural processes #6$, 6–9 orders of magnitude longer than that for which any related process has been observed in chemistry or biology #16,18,20,24–26$. If either !i" the envisaged intradimer motion !Fig. 1 left" does not exist, !ii" the intradimer motion is not coherent for long enough, or !iii" if this coherence is not maintained over a network of coupled dimers !Fig. 1 right" sufficiently large to unite individual qubits into a complex quantum computer, then the Orch OR model becomes untenable. Alternatively, if the intradimer motion does exist and is coherent, then most other aspects of the proposal !e.g., the involvement of quantum gravity and the role of sol-gel cycles" could be replaced with other phenomena and the quantum computational element

retained #26,27$, although its function may manifest differently #4,8$. Here, we concentrate on the intradimer motion: !i" does it exist as envisaged in Fig. 1, and !ii" if it does not exist could any possible alternative process actually maintain coherence on the required time scale. The third critical issue concerning maintenance of coherence over the microtubule network is much more difficult to treat authoritatively and the only issue to have been widely discussed !see, e.g., #6–8,10,23,25,26$"; hence, it is not addressed herein. Specifically, we consider the feasibility of the Orch OR proposal in light of recent developments in the understanding of microtubule structure and function #12,28–45$, as well as in regard to the likelihood of extensive coherent oscillations in biology #46–49$ and in microtubules #50–53$. We show both that the original biochemical scenario envisaged in Orch OR is incorrect and that no possible modification of this proposal consistent with the biological facts can, using known physical padadigms, produce the required physical properties. Hence, if there are any nonelectrochemical contributions to cognitive function then they must arise by some mechanism other than the Penrose-Hameroff proposal. This gives hope to the vision that digital computing could achieve truly significant levels of artificial intelligence. II. EXISTENCE OF THE PROPOSED TUBULIN-DIMER VIBRATIONAL MOTION

The observed biochemical dynamics of tubulin dimers and their conformational states within microtubules is depicted in Fig. 2; a review of this dynamics, particularly in regard to microtubules in neurons, has recently been provided by Conde and Cáceres #12$. This figure is presented for comparison with the biochemical processes as envisaged in the Orch OR proposal shown previously in Fig. 1. Microtubules are cylindrical structures formed by the selfassociation of tubulin heterodimers. Primarily involved are two closely related tubulin isoforms !$ and %" that interact to form a stable heterodimer. Each subunit of the heterodimer contains one guanidinium phosphonucleotide !GTP or GDP" binding site #Fig. 2!a"$. The site on the $ subunit is nonexchangeable to which GTP is bound constitutively. The site on the % monomer is exchangeable, binding either GTP or GDP #54$. Self-association of tubulin to form microtubules is triggered by the binding of GTP to the % subunit of the free heterodimer !tubulin GTP" #Fig. 2!b"$ #33$. The growth of a microtubule involves the initial formation at a centrosome of a 13 membered ring of another tubulin isoform, & tubulin #12$, which then acts as a template for further growth via addition of tubulin GTP. Many slight variations in this process are possible, with the ring size possibly increasing to 17 and the relative orientations of the dimers with respect to each other changing !the so-called “microtubule-A” and “microtubule-B” structures #28$"; such variations affect the rates of subsequent processes and may be important in neurons #28,43$, but they do not affect the form of these processes #12,28,29$ and hence we do not focus on these features. Other possible variations such as the availability of different types of tubulins !eg., $1, $2, $4, %I, %II, %III, %IVa, and %IVb" and post-translational modifications to the

021912-2


PHYSICAL REVIEW E 80, 021912 !2009"

PENROSE-HAMEROFF ORCHESTRATED OBJECTIVE-…

FIG. 2. Current understanding of the biochemical processes that modify the conformational states of tubulin dimmers. A more modern symbol for the dimers is used compared to that used by Penrose and Hameroff !see Fig. 1" to facilitate a more complete description of the biochemical processes; while the microtubule-B lattice is shown #28$, the depicted processes are lattice independent #12,28–30$.

tubulins also preserve the form of the essential dynamical features #12$. Quite generally, some time after incorporation onto the microtubule, the GTP molecule bound to the % subunit is hydrolysed !Step 3, Fig. 2" #33$. Initially, the phosphate ion remains bound to the protein, leading to a metastable intermediate state called tubulin-GDP-Pi #Fig. 2!c"$ #31,32,39$. Finally, the phosphate ion is lost !Step 4, Fig. 2" yielding tubulin-GDP. The essential aspect of the Orch OR proposal depicted in Fig. 1 is that tubulin can adopt more than one conformational state and exist in a coherent quantum superposition of these states. Experimentally, the only identified aspect of the conformation of the tubulin heterodimer inside a microtubule depends on whether GTP or GDP is bound to the % subunit, an aspect that has profound consequences for the formation and function of microtubules. This aspect has been traditionally associated with proposals for computation in microtubules #55$ and is the only process to be ascribed to the conformational change depicted in Fig. 1 within the Orch OR proposal #5,45$. Free in solution, the isolated tubulin GTP adopts a straight conformation; in contrast, isolated tubulin GDP adopts a curved conformation #Fig. 2!e"$ #36,54$. To be incorporated in a microtubule, a tubulin dimer must be in the straight conformation !tubulin GTP". Even after the hydrolysis of the GTP to GDP !Steps 3 and 4, Fig. 2", tubulin GDP is constrained to remain similar to its original conformation #Fig. 2!c"$ #33,36$. This state differs slightly from the tubulin GTP straight structure, however, and involves a 2%–4% reduction in the length of the tubulin dimer #36,38$. It is higher in energy than the curved conformation so that the microtubule as a whole becomes under stress #i.e., in a higher energy state than the tubulin-GDP in solution depicted in Fig. 2!e"$ #32,36,40$. As a result, at the trailing end of the microtubule, individual tubulin GDP dimers are lost progressively !step 5, Fig. 2 #33$". Once free in solution the GDP can be exchanged with GTP and the tubulin GTP reattach at the growing end. The growing end is stabilized by a cap of tubulin GTP and tubulin-GDP-Pi #Fig. 2!c"$. Hence, microtubules continuously grow at one end and shrink at the other end, resulting in a treadmill arrangement where individual tubulin dimers move progressively along the microtubule; the length of the microtubule is determined by the kinetics of assembly versus disassembly. However, if GTP is removed from the system the GTP/GDP-Pi cap at the growing end is lost !Step 6, Fig. 2" and the microtubule undergoes a process of rapid and catastrophic disassembly !Steps 5 and 7, Fig. 2", leading to free tubulin GDP. Many factors control the stability of each end and hence the details of the kinetics, including the presence of Microtubule Associated Proteins !MAP" and chemical regulators #12$. There is considerable evidence to support the proposal that any conformational changes associated with the hydrolysis of tubulin GTP to tubulin GDP within the microtubule are small and occur only after the phosphate ion has been released #32,42$, i.e., during step 4 rather than step 3 in Fig. 2. The turnover of tubulin heterodimers within a microtubule is slow. The rate of GTP hydrolysis by tubulin-GTP incorporated at the growing end is approximately #56,57$ 30– 70 s−1 per microtubule, while the rate of growth of a microtubule is approximately #58$ 0.2– 1.2 'm / min, corre-

021912-3


PHYSICAL REVIEW E 80, 021912 !2009"

MCKEMMISH et al.

sponding to the addition of 5–30 tubulin heterodimers per second !based on a heterodimer length #54$ of ca. 80 Å and 13 dimers per layer". This suggests that tubulin-GTP is exclusively found in close proximity to the growing end #56$. Structural studies involving nonhydrolysable GTP analogs support these results #38$. Regardless of when the conformational transition within the microtubule occurs, it is clear that the transition within the microtubule from tubulin GTP to tubulin GDP is for practical purposes irreversible: radioactive labeling studies show that tubulin GDP is not phosphorelated back to tubulin GTP inside microtubules #29,30,42$. The core premise of the Penrose-Hameroff Orch OR model, that tubulin within stable microtubules can oscillate between two alternative conformations, as shown in Fig. 1, was postulated before the details of microtubule conformer dynamics was known. According to Orch OR, the quantum superposition of the two states via coherent motion along a specific vibrational mode of the dimer !Fig. 1" acts as a qubit in a quantum processor. However, the basic supposition expounded in Fig. 1, that tubulin repeatedly exchanges between the GTP and GTP bound forms within stable microtubules, is in stark contrast to the physiological description shown in Fig. 2 and is not supported by the available experimental evidence. III. COULD THE OBSERVED TREADMILLING BE UTILIZED TO FORM A QUANTUM QUBIT?

Next we consider if some revised Orch-OR model based on the known treadmilling microtubule dynamics could be useful as a quantum computer in the brain by considering the inherent time scale of the conformer interconversion cycle. An essential feature of Orch OR is that the tubulin dimer be able to interconvert between the alternative conformations a very large number of times #4,8$: the quantum computational cycle depicted in Fig. 1 must occur at least as fast as does the intrinsic neural processing, of order ms, and the underlying coherent oscillation must be very fast compared to this time scale. However, it is now very clear that each interconversion cycle requires the disassembly and reassembly of the whole microtubule. Exchange of GDP with GTP occurs only in free tubulin and not in the assembled microtubule #29,30,42$. Thus, the system could not interconvert between alternative conformational states, as is required for repeated quantum computation, on a time scale less than that of microtubule assembly. As noted above, the rate of tubulin addition onto a microtubule is approximately 5 – 30 s−1. Given the average length of a microtubule, this means that a tubulin dimer is incorporated at the growth end of the microtubule then released at the other end some seconds to hours later. Furthermore, in neurons, the binding of MAP #42$ to microtubules can result in lifetimes of an hour or greater #43$. Clearly, such time scales are too long to be of psychological relevance for oscillatory motions underpinning thought processes. IV. ALTERNATIVE BIOCHEMICAL MECHANISMS AND THE REQUIREMENT OF COHERENT MOTION

The possibility that a revised biochemical model for Orch OR involving stable microtubules could be developed con-

sistent with the observed biological processes is now considered. Such a revised model could in principle be conceived in many ways, exploiting for example the various forms of the $ and % tubulins #12$ or post-translational modification effects #12$ induced by external protein and chemicals. An essential feature of any such model must be the establishment of coherent motion between the two revised postulated structural forms involved in the qubit. This coherent motion must exist for a very long period of time compared to the sub-ps time scale on which motions associated with conformational change are usually decohered #24,25$. Indeed, consideration of physical mechanisms through which coherence could be maintained for the required time scale forms a central element of the original Orch OR proposal #4,5$ and of modern discussions #6–8,10,23,26$. One proposal involves the production of mechanical stability through either sol-gel formation, water ordering, and other macroscopic ordering processes #6–8$, but such effects could only support intradimer coherence on at most the ps time scale; something more profound is required for which the only proposal to date #4–6,26$ is the formation of a Fröhlich condensate #46–48$, a pseudo-Bose-Einstein condensate, in the biological medium. This is a critical aspect of the process depicted in Fig. 1 as originally proposed #4$. The core element of this proposal is that incoherent metabolic energy is used to force coherence in much the same way that coherence is induced in lasers. Three possible sources of this metabolic energy have been suggested #6$: GTP-GDP hydrolysis, dephosphorelation of MAPs, and ATP hydrolysis associated with actin polymerization, but of these only the GTP-GDP reaction is inherently associated with the tubulin conformational changes. Numerical simulation of Fröhlich’s model has shown that coherence times can be increased by up to 6 orders of magnitude, providing the type of dramatic effect that is critical to Orch OR #59$. We have examined the Fröhlich proposal in detail #49$ and identified scenarios under which the coherence requirements of Orch OR could in principle be met. The relevant regime is one in which the supplied energy corresponds to at least 1012 GTP-GDP reactions per second per tubulin dimer, ca. 10 orders of magnitude larger than the observed reaction rate. One necessary consequence of coherent Fröhlich condensation is coherent light emission #60,61$. This would most likely be expected in the terahertz region #62–65$ and is a feature observed as a result of similar processes #62–65$. While no such coherent radiation has ever been reported, nonthermal terahertz radiation has been observed from frog muscles #66$ and nonthermal radiation at 8.085 MHz has been observed from microtubules #50$. Nonthermal radiation can arise from various sources and does not necessarily imply either the formation of a Fröhlich condensate or the coherence of any formed condensate #50$. The possibility that the observed nonthermal radiation from microtubules arises from Fröhlich condensation has been championed by Pokorný #50–53$. Pokorný estimates that the net energy from GTP hydrolysis within the microtubule available to drive condensation is 1.7 kcal mol−1 !0.07 eV". As the conversion of tubulin GTP to tubulin GDP is associated with a large change in net dipole, Pokorný proposed that electrostatic interactions provide the long-range forces that give rise to coherence.

021912-4


PHYSICAL REVIEW E 80, 021912 !2009"

PENROSE-HAMEROFF ORCHESTRATED OBJECTIVE-…

Pokorný’s reasoning thus has much in common with aspects of the Orch OR proposal. However, the energy driving Pokorný’s proposed condensate is many orders of magnitude less than the energy required for the coherent condensate that is critical to Orch OR #49$. Quantitative analysis of Pokorný’s proposed condensation mechanism in terms of the fundamental parameters of Fröhlich’s model #46–49$ shows that the driving power s / kB is of the order of 100 Ks−1. Pokorný has argued that the power loss due to frictional forces is quite low #51$, with relaxation times extending up to 10−5 s. Expressed in terms of Fröhlich’s model, this result leads to a power loss of ( / kB = 20 Ks−1. As the formation of a Fröhlich condensate requires s / ( ) 1, it is thus feasible that the observed nonthermal radiation at 8.085 MHz in microtubules #50$ does result from the formation of a Fröhlich condensate. However, Fröhlich condensation does not ensure coherent motion, with coherent Fröhlich condensates #49$ requiring the power density in the mode to dramatically exceed s / (, a quantity that itself must dramatically exceed 1. The observed #50$ excess power density in the 8.085 MHz mode in microtubules is just 5 times the thermal energy, orders of magnitude smaller than that required to produce a coherent Fröhlich condensate. Indeed, thorough analysis #49$ of the Fröhlich model indicates that an excess radiative power of a factor of 5 is associated with only a weak condensate for which is s / ( is actually less than 1. Thus the weak Fröhlich condensate envisaged by Pokorný could not give rise to coherent motion and so contribute to cognitive function. No biologically feasible reformulation of the microtubule-based Orch OR proposal could deliver the essential element of coherent intramolecular vibrational motion via Fröhlich condensation. V. CONCLUSIONS

GDP for GTP occurring only after the tubulin has disassociated from the microtubule. As the cycling of tubulins within a microtubule is on the order of minutes to hours even if it were possible to generate the superposition of states required for quantum calculations, such processes could not occur on a psychologically relevant time scale. Further, we demonstrate that no alternative biochemical scheme could deliver the essential property of coherent intramolecular motion interchanging two conformers utilizing coherent Fröhich condensation. The available biochemical energy is at least 10 orders of magnitude too small to facilitate coherent Fröhich condensation, and experimentally envisaged possibilities for the involvement of Fröhlich condensates in microtubules do not deliver the essential property of coherent motion. Most significantly, if the proposed mechanism was correct, then one would observe stimulated emission of radiation from all biological tissues. No proposal of how coherence on the required time scale within an Orch-OR qubit has been suggested other than Fröhlich condensation, an effect that would produce in effect a new state of matter akin to a Bose-Einstein condensate, and no physical processes is known that could, in principle, deliver the requirements of Orch OR. The Penrose-Hameroff Orch OR model has attracted much attention and much debate since it was initially proposed in part because it holds the fascinating possibility of quantum mechanical effects playing a central role in cognitive function, and in part because, at least superficially, the model appears physically reasonable. Here we have shown that when tested objectively the basic physical assumptions upon which the Orch OR model depends simply do not hold either from a structural, dynamic or energetic perspective and we hope that with this work we can finally put to rest this intriguing but fundamentally flawed model of cognitive function.

We have demonstrated that quantum computation cannot take place as proposed in the Orch OR model using the conformational states of tubulins as qubits. This is because the individual tubulin dimers within the microtubule do not undergo a rapid interconversion between alternative conformational states, the most fundamental assumption used in the Orch OR proposal #8$. Instead, the conformational change that accompanies the self-assembly of tubulin to form a microtubule is essentially irreversible, with the exchange of

This work was stimulated and begun at an Exploratory Workshop on “Quantum Dynamics and Biomolecular Function,” supported by the International Institute for Complex Adaptive Matter !I2CAM" and the USA National Science Foundation !NSF". We thank the Australian Research Council !ARC" for funding this research and Dr. Meredith Jordan !The University of Sydney" for helpful discussions.

#1$ R. Penrose, The Emperor’s New Mind !Oxford Univ. Press, Oxford, 1989". #2$ R. Penrose, Shadows of the Mind !Oxford University Press, New York, 1994". #3$ R. Penrose and S. R. Hameroff, J. Conscious. Stud. 2, 99 !1995". #4$ S. Hameroff and R. Penrose, Math. Comput. Simul. 40, 453 !1996". #5$ S. Hameroff, Phil. Trans. R. Soc. London, Ser. A 356, 1869 !1998".

#6$ S. Hagan, S. R. Hameroff, and J. A. Tuszynski, Phys. Rev. E 65, 061901 !2002". #7$ S. R. Hameroff, Cogn. Sci. 31, 1035 !2007". #8$ S. R. Hameroff, in Towards a Science of Consciousness II: The Second Tucson Discussions and Debates, edited by S. R. Hameroff, A. Kaszniak, and A. C. Scott !MIT Press, Cambridge, MA, 1998", p. 197. #9$ P. C. W. Davies, Biosystems 78, 69 !2004". #10$ D. Abbott et al., Fluct. Noise Lett. 8, C5 !2008". #11$ D. Abbott et al., Proc. SPIE 6802, 680201 !2007".

ACKNOWLEDGMENTS

021912-5


PHYSICAL REVIEW E 80, 021912 !2009"

MCKEMMISH et al. #12$ C. Conde and A. Cáceres, Nat. Rev. Neurosci. 10, 319 !2009". #13$ M. J. Robey and E. W. Schlag, J. Chem. Phys. 67, 2775 !1977". #14$ J. R. Reimers and N. S. Hush, J. Am. Chem. Soc. 126, 4132 !2004". #15$ A. P. Hines, C. M. Dawson, R. H. McKenzie, and G. J. Milburn, Phys. Rev. A 70, 022303 !2004". #16$ M. P. A. Branderhorst et al., Science 320, 638 !2008". #17$ C. Creutz and H. Taube, J. Am. Chem. Soc. 91, 3988 !1969". #18$ P. J. Reid, C. Silva, P. F. Barbara, L. Karki, and J. T. Hupp, J. Phys. Chem. 99, 2609 !1995". #19$ J. R. Reimers, B. B. Wallace, and N. S. Hush, Phil. Trans. R. Soc. London, Ser. A 366, 15 !2008". #20$ H. Lee, Y.-C. Cheng, and G. R. Fleming, Science 316, 1462 !2007". #21$ R. A. Marcus and N. Sutin, Biochim. Biophys. Acta 811, 265 !1985". #22$ N. S. Hush, J. Electroanal. Chem. 460, 5 !1999". #23$ A. Litt, C. Eliasmith, F. W. Kroon, S. Weinstein, and P. Thagard, Cogn. Sci. 30, 593 !2006". #24$ J. Gilmore and R. H. McKenzie, J. Phys. Chem. A 112, 2162 !2008". #25$ M. Tegmark, Phys. Rev. E 61, 4194 !2000". #26$ L. P. Rosa and J. Faber, Phys. Rev. E 70, 031902 !2004". #27$ T. Hiramatsu, T. Matsui, and K. Sakakibara, Int. J. Mod. Phys. C 19, 291 !2008". #28$ A. Des Georges et al., Nat. Struct. Mol. Biol. 15, 1102 !2008". #29$ K. W. Farrell, M. A. Jordan, H. P. Miller, and L. Wilson, J. Cell Biol. 104, 1035 !1987". #30$ R. J. Stewart, K. W. Farrell, and L. Wilson, Biochemistry 29, 6489 !1990". #31$ D. Sept, H. J. Limbach, H. Bolterauer, and J. A. Tuszynski, J. Theor. Biol. 197, 77 !1999". #32$ R. Melki, M. F. Carlier, and D. Pantaloni, Biochemistry 29, 8921 !1990". #33$ E. Nogales, Annu. Rev. Biochem. 69, 277 !2000". #34$ E. M. Mandelkow, E. Mandelkow, and R. A. Milligan, J. Cell Biol. 114, 977 !1991". #35$ P. Carvalho, J. S. Tirnauer, and D. Pellman, Trends Cell Biol. 13, 229 !2003". #36$ L. A. Amos, Org. Biomol. Chem. 2, 2153 !2004". #37$ J. Howard and A. A. Hyman, Nature !London" 422, 753 !2003". #38$ A. A. Hyman, D. Chretien, I. Arnal, and R. H. Wade, J. Cell Biol. 128, 117 !1995".

#39$ P. T. Tran, R. A. Walker, and E. D. Salmon, J. Cell Biol. 138, 105 !1997". #40$ J. A. Tuszynski, J. A. Brown, and D. Sept, J. Biol. Phys. 29, 401 !2003". #41$ R. Heald and E. Nogales, J. Cell Sci. 115, 3 !2002". #42$ A. Desai and T. J. Mitchison, Annu. Rev. Cell Dev. Biol. 13, 83 !1997". #43$ L. Guillaud et al., J. Cell Biol. 142, 167 !1998". #44$ S. Okabe and N. Hirokawa, Nature !London" 343, 479 !1990". #45$ J. A. Tuszynski, J. A. Brown, and P. Hawrylak, Phil. Trans. R. Soc. London, Ser. A 356, 1897 !1998". #46$ H. Fröhlich, Int. J. Quantum Chem. 2, 641 !1968". #47$ H. Fröhlich, Phys. Lett. A 26, 402 !1968". #48$ H. Fröhlich, Nature !London" 228, 1093 !1970". #49$ J. R. Reimers, L. K. McKemmish, R. H. McKenzie, A. E. Mark, and N. S. Hush, Proc. Natl. Acad. Sci. U.S.A. 106, 4219 !2009". #50$ J. Pokorný, J. Hašek, F. Jelínek, J. Šaroch, and B. Palán, Electro- Magnetobiol. 20, 371 !2001". #51$ J. Pokorný, Electromagn. Biol. Med. 22, 15 !2003". #52$ J. Pokorný, Bioelectrochemistry 63, 321 !2004". #53$ J. Pokorný, Bioelectrochem. Bioenerg. 48, 267 !1999". #54$ E. Nogales, S. G. Wolf, and K. H. Downing, Nature !London" 391, 199 !1998". #55$ S. R. Hameroff and R. C. Watt, J. Theor. Biol. 98, 549 !1982". #56$ R. Melki, S. Fievez, and M. F. Carlier, Biochemistry 35, 12038 !1996". #57$ J. M. Hush, P. Wadsworth, D. A. Callaham, and P. K. Hepler, J. Cell Sci. 107, 775 !1994". #58$ M. Dogterom and B. Yurke, Science 278, 856 !1997". #59$ M. V. Mesquita, A. R. Vasconcellos, and R. Luzzi, Int. J. Quantum Chem. 60, 689 !1996". #60$ P. Stenius, W. Zhao, and A. Imamoglu Phys. Status Solidi A 164, 365 !1997". #61$ L. V. Butov et al., Phys. Rev. Lett. 86, 5608 !2001". #62$ A. V. Kuznetsov and C. J. Stanton, Phys. Rev. Lett. 73, 3243 !1994". #63$ M. L. Groot et al., Proc. Natl. Acad. Sci. U.S.A. 99, 1323 !2002". #64$ M. Först et al., Phys. Status Solidi B 244, 2971 !2007". #65$ G. I. Groma et al., Proc. Natl. Acad. Sci. U.S.A. 105, 6888 !2008". #66$ H. A. Gebbie and P. F. Miller, Int. J. Infrared Millim. Waves 18, 951 !1997".

021912-6


Consciousness-is-Not-Biologically  

Metafisica

Advertisement
Read more
Read more
Similar to
Popular now
Just for you