quantum coherence in biological systems-lloyd (m.i.t.) 2011

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International Symposium "Nanoscience and Quantum Physics 2011" Journal of Physics: Conference Series 302 (2011) 012037

IOP Publishing doi:10.1088/1742-6596/302/1/012037

Quantum coherence in biological systemsSeth LloydDepartment of Mechanical Engineering, MIT Abstract. This paper reviews the role of quantum mechanics in biological systems, and shows how the interplay between coherence and decoherence can strongly enhance quantum transport in photosynthesis.

Nature is the great nano-technologist. The chemical machinery that powers biological systems consists of complicated molecules structured at the nanoscale and sub-nanoscale. At these small scales, the dynamics of the chemical machinery is governed by the laws of quantum mechanics. Quantum mechanics is well known to exhibit strange and counterintuitive eects. Accordingly, it makes sense to investigate the extent to which peculiarly quantum eects such as coherence and entanglement play an important role in living systems. Quantum mechanics and quantum coherence play a central role in chemistry. Quantum coherence and entanglement determine the valence structure of atoms and the form of covalent bonds. Quantum mechanics xes the set of allowed chemical compounds and sets the parameters of chemical reactions. Indeed, the very fact that there are only a countable, discrete set of possible chemical compounds arises from the fundamentally discrete nature of quantum mechanics. Chemistry, in turn, lays down the rules for what biological structures are possible and for how they function. Biomolecules can contain many atoms (billions in the case of DNA). As molecules become larger and more complex, quantum coherence becomes harder to maintain. Vibrational modes and interactions with the environment tend to decohere quantum superpositions. Consequently, most biomolecular mechanisms have traditionally been modeled as essentially classical processes. For example, classical ball and spring models of molecules can capture accurately many aspects of molecular dynamics. As a result, for many years, the conventional answer to the question of whether quantum coherence and entanglement are important for biological processes has been, not really. Recently, however, strong evidence has emerged that quantum coherence is playing an important role in certain selected biological processes [1-3]. The strongest evidence for quantum coherence occurs in photosynthesis, which will form the main topic of this paper (a review of the mechanisms for photosynthesis can be found in [4]. Indirect evidence for quantum coherence also 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 eects in these biological mechanisms. (1) The avian compass. Some birds, such as homing pigeons, possess a small piece of magnetite in their beaks which functions as a compass, allowing them to tell North from South. Other birds, such as the European robin, seem to possess a dierent mechanism for sensing the earths magnetic eld [5-6]. This mechanism (a) allows the birds to identify the angle the magneticPublished under licence by IOP Publishing Ltd1

International Symposium "Nanoscience and Quantum Physics 2011" Journal of Physics: Conference Series 302 (2011) 012037

IOP Publishing doi:10.1088/1742-6596/302/1/012037

eld lines make with the earth, but does not distinguish North from South; (b) is only activated in blue or green light; and (c) is disrupted by oscillating elds a bit above one megahertz, at the electrons Larmor frequency in the earths magnetic eld. These features are dicult to explain using classical mechanisms. The only known mechanism consistent with these features is quantum mechanical. The proposed mechanism postulates that absorption of blue or green light creates a radical pair of electrons, separated within an oriented molecule (perhaps a cryptochrome) within the birds eye. The racial pair undergoes coherent quantum oscillations between entangled singlet and triplet states, at a rate that depends on the orientation of the host molecule with respect to the earths magnetic eld. A spin-dependent electron transition then allows current to ow only if the spins in the pair are in a particular symmetry state. The rate of current ow then depends on the molecules relative orientation to the eld. This purely quantum mechanical mechanism explains all peculiar observed features of the birds behavior, including their inability to tell North from South. Ongoing experimental and theoretical investigations are attempting to identify the molecules or molecular complexes within which this mechanism can function, and to 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 dierent types of odorant molecule bind to dierent types of olfactory sensors. The dierent types of olfactory sensors in the human nose have been identied. In this model, the particular smell of an odorant molecule depends only on its anity to dierent sensors. There are several issues with this model. First of all, the smell of a molecule depends at most weakly on shape, the primary determinant of the sensors to which the molecule binds in a lock and key model. 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 frequency as the sulphur-hydrogen stretch mode, smells of sulphur. The nose is evidently a vibrational spectrometer. Again, the only known mechanism that can explain this vibrational sensitivity of the sense of smell is quantum mechanical [7-8]. The mechanism relies on inelastic tunneling. Once an odorant molecule docks into the olfactory sensor, electrons can pass through the molecule, and current can ow, only by emitting a phonon of specic frequency to one of the molecules dominant vibrational modes. The strongest conrming evidence for this mechanism is the ability of fruit ies (drosophila) to smell the dierence between an organic molecule and a deuterated version of the same molecule. A molecule whose hydrogens have been replaced by deuterium should bind to the same receptors as the original molecule, with similar anities. So if the shapebased 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 signicantly changes the vibrational spectrum of the molecule. Ongoing work to validate further this purely quantum mechanical mechanism includes performing X-ray crystallography to identify the precise geometry of the receptor molecules, and creating detailed quantum mechanical models to test and elucidate the specic mechanisms of inelastic tunneling. Photosynthesis. I now turn to quantum coherence in photosynthesis, the primary topic of this article. In the cases of the avian compass and sense of smell just described, the primary evidence for quantum eects is observation of animal behavior, combined with a lack of plausible classical models. By contrast, in photosynthesis, the evidence for the eects of quantum coherence is direct and overwhelming [1-3]. In photosynthesis, a particle of light or photon is absorbed by a photocomplex, a set of molecular structures embedded in the membrane of a plant or bacterial cell. Part of the energy of the photon is converted into heat in the form of molecular vibrations, but most of it is


International Symposium "Nanoscience and Quantum Physics 2011" Journal of Physics: Conference Series 302 (2011) 012037

IOP Publishing doi:10.1088/1742-6596/302/1/012037

captured as an exciton, a bound electron-hole pair that resides in a chromophore, a lightcarrying molecule such as a plant or bacterial chlorophyll. The exciton is so-called Frenkel exciton, tightly bound within a region a few angstroms on each side. Energy transfer occurs via the dipolar interaction between chromophores: a so-called Frster coupling between induced o or transition dipoles de-excites one chromophore while exciting a neighboring one. The exciton must propagate through hundreds or thousands of chromophores in order to reach the reaction center, 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 the sense that while quantum mechanics determined couplings between chromophores, the actual transition rates could be calculated semi-classically using Fermis golden rule. In 2007, this picture changed dramatically when the Fleming group in Berkeley used femtosecond twodimensional spectroscopy based on four-wave mixing to demonstrate that quantum coherence was at work the transfer process. The spectroscopic signature exhibited clear evidence of quantum beating at 77K, a result that was later conrmed at room temperature. The evidence for quantum coherence in photosynthetic transport was essentially incontrovertible. My own background is in quantum computation, not photochemistry. I became involved in this eld completely by accident. When the Fleming paper came out, the New York Times reported it as claiming that green sulphur bacteria were performing a quantum computation. Quantum computers are devices that use quantum coherence to process information in ways that classical computers can not. Specic methods for performing a quantum computation are called quantum algorithms. The Fleming paper speculated that the demonstrated coherence in excitonic transport meant that bacteria were performing a quantum algorithm called quantum search to allow the exciton to travel from the place and to nd the reaction center. This claim caused great hilarity in


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