Quantum coherence in biological systems

Seth Lloyd

Department of Mechanical Engineering, MIT

Abstract. This paper reviews the role of quantum mechanics in biological systems, and showshow the interplay between coherence and decoherence can strongly enhance quantum transportin photosynthesis.

Nature is the great nano-technologist. The chemical machinery that powers biological systemsconsists of complicated molecules structured at the nanoscale and sub-nanoscale. At these smallscales, the dynamics of the chemical machinery is governed by the laws of quantum mechanics.Quantum mechanics is well known to exhibit strange and counterintuitive effects. Accordingly,it makes sense to investigate the extent to which peculiarly quantum effects such as coherenceand entanglement play an important role in living systems.

Quantum mechanics and quantum coherence play a central role in chemistry. Quantumcoherence and entanglement determine the valence structure of atoms and the form of covalentbonds. Quantum mechanics fixes the set of allowed chemical compounds and sets the parametersof chemical reactions. Indeed, the very fact that there are only a countable, discrete setof possible chemical compounds arises from the fundamentally discrete nature of quantummechanics.

Chemistry, in turn, lays down the rules for what biological structures are possible and for howthey function. Biomolecules can contain many atoms (billions in the case of DNA). As moleculesbecome larger and more complex, quantum coherence becomes harder to maintain. Vibrationalmodes and interactions with the environment tend to decohere quantum superpositions.Consequently, most biomolecular mechanisms have traditionally been modeled as essentiallyclassical processes. For example, classical ‘ball and spring’ models of molecules can captureaccurately many aspects of molecular dynamics. As a result, for many years, the conventionalanswer to the question of whether quantum coherence and entanglement are important forbiological processes has been, not really.

Recently, however, strong evidence has emerged that quantum coherence is playing animportant role in certain selected biological processes [1-3]. The strongest evidence for quantumcoherence occurs in photosynthesis, which will form the main topic of this paper (a review ofthe mechanisms for photosynthesis can be found in [4]. Indirect evidence for quantum coherencealso appears in bird navigation [5-6] – the so-called ‘avian compass’ – and in the sense of smell[7-8]. Before turning to photosynthesis, I will review the evidence for quantum effects in thesebiological mechanisms.

(1) The avian compass. Some birds, such as homing pigeons, possess a small piece of magnetitein their beaks which functions as a compass, allowing them to tell North from South. Otherbirds, such as the European robin, seem to possess a different mechanism for sensing the earth’smagnetic field [5-6]. This mechanism (a) allows the birds to identify the angle the magnetic

International Symposium "Nanoscience and Quantum Physics 2011" IOP PublishingJournal of Physics: Conference Series 302 (2011) 012037 doi:10.1088/1742-6596/302/1/012037

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field lines make with the earth, but does not distinguish North from South; (b) is only activatedin blue or green light; and (c) is disrupted by oscillating fields a bit above one megahertz, atthe electron’s Larmor frequency in the earth’s magnetic field. These features are difficult toexplain using classical mechanisms. The only known mechanism consistent with these featuresis quantum mechanical.

The proposed mechanism postulates that absorption of blue or green light creates a radicalpair of electrons, separated within an oriented molecule (perhaps a cryptochrome) within thebird’s eye. The racial pair undergoes coherent quantum oscillations between entangled singletand triplet states, at a rate that depends on the orientation of the host molecule with respectto the earth’s magnetic field. A spin-dependent electron transition then allows current to flowonly if the spins in the pair are in a particular symmetry state. The rate of current flow thendepends on the molecule’s relative orientation to the field. This purely quantum mechanicalmechanism explains all peculiar observed features of the birds’ behavior, including their inabilityto tell North from South. Ongoing experimental and theoretical investigations are attemptingto identify the molecules or molecular complexes within which this mechanism can function, andto devise detailed and testable models for its operation.

(2) Sense of smell. The conventional mechanism postulated for smell is a lock and key model,in which different types of odorant molecule bind to different types of olfactory sensors. Thedifferent types of olfactory sensors in the human nose have been identified. In this model, theparticular smell of an odorant molecule depends only on its affinity to different sensors. Thereare several issues with this model. First of all, the smell of a molecule depends at most weaklyon shape, the primary determinant of the sensors to which the molecule binds in a lock and keymodel. Second, smell correlates well with the vibrational spectrum of the molecule: for example,a sulphur-less molecule whose vibrational spectrum exhibits a resonance at the same frequencyas the sulphur-hydrogen stretch mode, smells of sulphur. The nose is evidently a vibrationalspectrometer.

Again, the only known mechanism that can explain this vibrational sensitivity of the sense ofsmell is quantum mechanical [7-8]. The mechanism relies on inelastic tunneling. Once an odorantmolecule docks into the olfactory sensor, electrons can pass through the molecule, and currentcan flow, only by emitting a phonon of specific frequency to one of the molecule’s dominantvibrational modes. The strongest confirming evidence for this mechanism is the ability of fruitflies (drosophila) to smell the difference between an organic molecule and a deuterated versionof the same molecule. A molecule whose hydrogens have been replaced by deuterium shouldbind to the same receptors as the original molecule, with similar affinities. So if the shape-based lock and key mechanism were true, it should smell the same. By contrast, deuterium-carbon bonds vibrate at a rate

√2 slower than hydrogen-carbon bonds: deuteration significantly

changes the vibrational spectrum of the molecule. Ongoing work to validate further thispurely quantummechanical mechanism includes performing X-ray crystallography to identify theprecise geometry of the receptor molecules, and creating detailed quantum mechanical modelsto test and elucidate the specific mechanisms of inelastic tunneling.

Photosynthesis. I now turn to quantum coherence in photosynthesis, the primary topic of thisarticle. In the cases of the avian compass and sense of smell just described, the primary evidencefor quantum effects is observation of animal behavior, combined with a lack of plausible classicalmodels. By contrast, in photosynthesis, the evidence for the effects of quantum coherence isdirect and overwhelming [1-3].

In photosynthesis, a particle of light or photon is absorbed by a photocomplex, a set ofmolecular structures embedded in the membrane of a plant or bacterial cell. Part of the energyof the photon is converted into heat in the form of molecular vibrations, but most of it is

International Symposium "Nanoscience and Quantum Physics 2011" IOP PublishingJournal of Physics: Conference Series 302 (2011) 012037 doi:10.1088/1742-6596/302/1/012037

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captured as an exciton, a bound electron-hole pair that resides in a chromophore, a ‘light-carrying’ molecule such as a plant or bacterial chlorophyll. The exciton is so-called Frenkelexciton, tightly bound within a region a few angstroms on each side. Energy transfer occursvia the dipolar interaction between chromophores: a so-called Forster coupling between inducedor transition dipoles de-excites one chromophore while exciting a neighboring one. The excitonmust propagate through hundreds or thousands of chromophores in order to reach the reactioncenter, a special molecular complex in which charge separation takes place.

The exciton transport process is, of course, governed by the laws of quantum mechanics.For decades, however, this process was thought to be minimally quantum mechanical, in thesense that while quantum mechanics determined couplings between chromophores, the actualtransition rates could be calculated semi-classically using Fermi’s golden rule. In 2007, thispicture changed dramatically when the Fleming group in Berkeley used femtosecond two-dimensional spectroscopy based on four-wave mixing to demonstrate that quantum coherencewas at work the transfer process. The spectroscopic signature exhibited clear evidence ofquantum ‘beating’ at 77K, a result that was later confirmed at room temperature. The evidencefor quantum coherence in photosynthetic transport was essentially incontrovertible.

My own background is in quantum computation, not photochemistry. I became involved inthis field completely by accident. When the Fleming paper came out, the New York Timesreported it as claiming that green sulphur bacteria were performing a quantum computation.Quantum computers are devices that use quantum coherence to process information in waysthat classical computers can not. Specific methods for performing a quantum computation arecalled quantum algorithms. The Fleming paper speculated that the demonstrated coherence inexcitonic transport meant that bacteria were performing a quantum algorithm called ‘quantumsearch’ to allow the exciton to travel from the place and to find the reaction center. This claimcaused great hilarity in our quantum information theory group at MIT, as it seemed implausiblethat a quantum algorithm such as quantum search could be performed in the hot, wet, and noisyconditions inside a living cell. Despite our collective skepticism, conscientiousness obliged us totake a look. Moreover, Alan Aspuru-Guzik, an assistant professor of chemistry at Harvard, hadinteracted with the Fleming group and could vouch for the seriousness and accuracy of theirresults. So I read the paper and discussed it with Alan.

The paper was a masterwork. The evidence for quantum coherence was exceptionally strong.The line about quantum search algorithms was essentially an afterthought. Quantum searchalgorithms, invented by Lov Grover in 1996, take a unique form [9]: we were able to showright away that the bacteria were not performing a quantum search algorithm. To our surprise,however, the bacteria were in fact performing a different type of quantum algorithm, called aquantum walk.

A random walk is a transport mechanism in which the walker takes steps in random directionsthrough the network or structure to be traversed. In a classical random walk, the position of thewalker gradually diffuses throughout the network. Because the walker is equally likely to movein any direction, after time t the walker has moved from its original position by an distanceproportional to

√t. In a quantum walk, by contrast, the walker takes a quantum superposition

of paths through the network [10]. These paths can exhibit quantum interferences. If theinterference is destructive, the walker becomes stuck or ‘localized’ within the network. Bycontrast, if the interference is constructive, the walker moves from its original position by adistance proportional to t, a considerable improvement over the classical random walk. Thecoherence demonstrated by the Fleming group showed that the excitons were performing aquantum walk, at least over short distances.

Excited, we decided to make a detailed quantum mechanical model of the excitonic transportprocess, a model that took into account the strong role of quantum coherence. We were aidedby the fact that the quantum structure of the particular photosynthetic complex on which

International Symposium "Nanoscience and Quantum Physics 2011" IOP PublishingJournal of Physics: Conference Series 302 (2011) 012037 doi:10.1088/1742-6596/302/1/012037

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Fleming had performed his experiment was well-known. The Fenna-Matthews-Olsen complex,or FMO, had been exhaustively studied using both spectroscopy and by X-ray crystallography[1-3]. Consequently, we were able to make a full quantum model of the dynamics of excitonictransport through the complex, including its interaction with the environment. Because of thewell-studied nature of the complex, the only free parameter in our model was the temperature,which we could vary at will. All other parameters in the model were determined by pre-existingexperiments.

When Alan’s postdoc, Masoud Mohseni, and graduate student Patrick Rebentrost coded themodel into a computer and fired it up, we found that the efficiency of excitonic transport hada remarkable dependence on temperature [11-12]. (Subsequently but independently, MartinPlenio and co-workers at Imperial College developed a similar model which confirmed thisbehavior [13].) At low temperatures, the interference between paths in the excitonic walk waspredominantly destructive, localizing the exciton to within a few sites of its initial position. Athigher temperatures, however, the interaction with the environment decohered the quantum walksufficiently to remove that destructive interference, allowing the exciton to diffuse throughout theFMO complex towards the reaction center. At very high temperatures, the decoherence inducedby the environment was so destructive that it froze the exciton in place, reducing the efficiencyof the transport. The highest efficiency for transport was 290K, the average temperature of thewater in which the bacteria lived. Moreover, the transport was robust with respect to variationabout this optimal temperature, exhibiting almost 100% efficiency for a range of many tens ofdegrees K in both directions.

Our model gave a clear picture of the role of quantum coherence in excitonic transfer in FMO:quantum coherence allowed the exciton to spread rapidly and coherently over a small numberof sites, then environmentally induced decoherence kicked in to prevent the exciton from beinglocalized. The transport efficiency exhibited a distinctive signature as a function of temperature– low at low temperature, high for a range around some optimum temperature, then low againat high temperature. Because this particular signature was a function not of the individualsystem under investigated, but of any partially coherent transport process, we gave it the nameENAQT for Environmentally Assisted Quantum Transport. ENAQT applies to essentially anytype of partially coherent quantum transport through a disordered medium.

In addition, our model gave insight into the evolutionary mechanism underlying aphenomenon that had puzzled photochemists and biologists for decades – the convergence oftime scales in photosynthesis. Separation of time scales is a common phenomenon in physicalsystems. The initial absorption of a photon and creation of an exciton in a chromophore is a fastprocess, taking only a few femtoseconds. By contrast, the exciton lives for several nanosecondsbefore decaying. So there is a six order of magnitude separation of time scales between absorptionand decay. The physiological benefits of this particular separation of time scales is easy to see:fast absorption arises from strong coupling of the chromophore to light, and to absorption over abroad band of frequencies, both desirable characteristics. Long lifetimes increase the chance thatthe exciton will make it to the reaction center. All other time scales in the excitonic transportprocess, however – coupling constants, energy differences, decoherence rates, and environmentalcorrelation times – converged to the scale of a picosecond or so. Why?

The convergence of time scales makes excitonic transport in photosynthesis hard to model.When time scales are separated, different processes at different time scales can be modeledaccurately as perturbation to an underlying process. When time scales converge, no simplemodel is possible. So one explanation of why time scales converge is that Nature is modest andprefers not to reveal her secrets to scientists. A more physical explanation is that when timescales for different processes converge, the strong interaction between the processes can eitherhelp transport, or hurt it. In systems that have undergone a billion years of natural selection,it should come as little surprise that these temporally convergent processes help each other out.

International Symposium "Nanoscience and Quantum Physics 2011" IOP PublishingJournal of Physics: Conference Series 302 (2011) 012037 doi:10.1088/1742-6596/302/1/012037

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To test this hypothesis, we varied the parameters in our model to test the efficiency oftransport in non-physiological regimes where the time scales for different processes were notthe same [14]. These studies showed that when time scales failed to converge, the efficiency oftransport was lower. We call this effect the ‘quantum Goldilocks effect’ after the little girl inthe folk tale who enters a house in which there is three of everything – three chairs, three beds,three bowls of porridge on the table. One of the chairs is too large, one too small, and one is justthe right size. So Goldilocks sits on the chair that is just right. One of the bowls of porridge istoo cold, one too hot, and the third is just the right temperature. So she eats that one. Finally,she falls asleep on the bed that has just the right degree of softness. (At this point, the threebears who live in the house return home and become upset, but that is another story.)

The Goldilocks effect – natural selection chooses just the right degree for each effect – is wellknown in biology. There is also a Goldilocks principle for complexity of evolved or designedsystems [15]: too little complexity compromises function, while too much complexity diminishesrobustness. Well-designed or well-evolved systems typically exhibit just the right degree ofcomplexity. In the quantum Goldilocks effect, natural selection has made time scales converge,adding between quantum processes in photosynthesis until photosynthetic systems attain justthe right degree of quantum complexity. Our simulations that vary the different parameters ofthe FMO complex show that the FMO complex has attained just the right degree of quantumcomplexity to give essentially 100% efficiency while remaining robust.

Conclusion: Quantum coherence plays a strong role in photosynthetic energy transport, andmay also play a role in the avian compass and sense of smell. In retrospect, it should comeas no surprise that quantum coherence enters into biology. Biological processes are basedon chemistry, and chemistry is based on quantum mechanics. If an organism can attain anadvantage in reproduction, however slight, by putting quantum coherence to use, then overtime natural selection has a chance to engineer the necessary biochemical mechanisms to exploitthat coherence. Different types of quantum processes that operate at the same time scale caninteract strongly either to assist or to impede one another. In photosynthetic energy transfer,the convergence of quantum time scales gives rise to more efficient and robust transport. Evolvedbiological systems exhibit the quantum Goldilocks effect: natural selection pushes together timescales to allow quantum processes to help each other out.

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2007 Nature 446 782[2] Collini E, Wong C Y, Wilk K E, Curmi P M, Brumer P and Scholes G D 2010 Nature 463 644[3] Panitchayangkoon G, Hayes D, Fransted K A, Caram J R, Harel E, Wen J, Blankenship R E and Engel G

S 2010 Proc. Nat. Acad. Sci. 107 12766[4] Blankenship R E 2002 Molecular Mechanisms of Photosynthesis, (London: Blackwell Science)[5] Ritz T, Adem S and Schulten K 2000 Biophys. J. 78 707[6] Rodgers T and Hore P J 2009 Proc. Nat. Acad. Sci. USA 106 353[7] Turin L 1996 Chem. Senses 21 773[8] Franco M I, Turin L, Mershin A and Skoulakis E M C 2011 Proc. Nat. Acad. Sci. USA 108 3797[9] Grover L K 1996 Proc. 28th Ann. ACM Sym. Th. Comp. p 212

[10] Farhi E and Gutmann S 1998 Phys. Rev. A 58 915[11] Mohseni M, Rebentrost P, Lloyd S and Aspuru-Guzik A 2008 J. Chem. Phys. 129 174106[12] Rebentrost P, Mohseni M, Kassal I, Lloyd S and Aspuru-Guzik A 2009 New J. Phys. 11 033003[13] Plenio M B and Huelga S F 2008 New J. Phys. 10 113019[14] Shabani A, Mohseni M, Rabitz H and Lloyd S 2011 (in preparation)[15] Lloyd S, lecture at Santa Fe Institute, 1990, as reported by Gell-Mann M The Quark and the Jaguar, 1994

(New York: A. Knopf)

International Symposium "Nanoscience and Quantum Physics 2011" IOP PublishingJournal of Physics: Conference Series 302 (2011) 012037 doi:10.1088/1742-6596/302/1/012037

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