Quantum Biology

O

n the face of it, quantum effects and living organisms seem to occupy utterly different realms. The former are usually observed only on the nanometre scale, surrounded by hard vacuum, ultra-low temperatures and a tightly controlled laboratory environment. The latter inhabit a macroscopic world that is warm, messy and anything but controlled. A quantum phenomenon such as

‘coherence’, in which the wave patterns of every part of a system stay in step, wouldn’t last a microsecond in the tumultuous realm of the cell.

Or so everyone thought. But discoveries in recent years suggest that nature knows a few tricks that physicists don’t: coherent quantum pro- cesses may well be ubiquitous in the natural world. Known or suspected examples range from the ability of birds to navigate using Earth’s mag- netic field to the inner workings of photosynthesis — the process by

The key to practical quantum computing and high-efficiency solar cells may lie in the messy green world outside the physics lab.

The dawn of

biology quantum

BY P H I L I P BA L L

DAREN NEWMAN

2 7 2 | N A T U R E | V O L 4 7 4 | 1 6 J U N E 2 0 1 1

© 2011 Macmillan Publishers Limited. All rights reserved

Quantum Biology

the dawn of

Hsiu-Hau Lin

National Tsing Hua Univ.

outline

• introduction to quantum biology

• photosynthesis

• olfactory receptors

• theory and predictions

• conclusions

2

quantum biology

3

REVIEW ARTICLE

PUBLISHED ONLINE: 9 DECEMBER 2012 | DOI: 10.1038/NPHYS2474

Quantum biology

Neill Lambert

¹

* , Yueh-Nan Chen

²

, Yuan-Chung Cheng

³

, Che-Ming Li

⁴

, Guang-Yin Chen

²

and Franco Nori

^1,5

*

Recent evidence suggests that a variety of organisms may harness some of the unique features of quantum mechanics to gain a biological advantage. These features go beyond trivial quantum effects and may include harnessing quantum coherence on physiologically important timescales. In this brief review we summarize the latest results for non-trivial quantum effects in photosynthetic light harvesting, avian magnetoreception and several other candidates for functional quantum biology. We present both the evidence for and arguments against there being a functional role for quantum coherence in these systems.

B

efore the twentieth century, biology and physics rarely crossed paths. Biological systems were often seen as too complex to be penetrable with mathematical methods. After all, how could a set of differential equations or physical principles shed light on something as complex as a living being? In the early twentieth century, with the advent of more powerful microscopes and techniques, researchers began to delve more deeply into possible physical and mathematical descriptions of microscopic biological systems¹. Some famous examples^1–3 (among many) include Turing patterns and morphogenesis, and Schrödinger’s lecture series and book ‘What is Life?’, in which he predicted several of the functional features of DNA. The pace of progress in this field is now rapid, and many branches of physics and mathematics have found applications in biology; from the statistical methods used in bioinformatics, to the mechanical and factory-like properties observed at the microscale within cells.

This progress leads naturally to the question: can quantum mechanics play a role in biology? In many ways it is clear that it already does. Every chemical process relies on quantum mechanics³. However, in many ways quantum mechanics is still a concept alien to biology, especially on a scale that can have a physiological impact⁴. Recent technological progress in physics in harnessing quantum mechanics for information processing and encryption puts the question in a different light: are there any biological systems that use quantum mechanics to perform a task that either cannot be done classically, or can do that task more efficiently than even the best classical equivalent? In other words, do some organisms take advantage of quantum mechanics to gain an advantage over their competitors? Many attempts to find examples of such phenomenon have been met with fierce criticism by both physicists and biologists (see, for example, refs 5,6). However, over the past decade a range of experiments have suggested that there may be some cases in which quantum mechanics is harnessed for a biological advantage.

In what form do these quantum effects usually appear? In quantum information, arguably the most important quantum effect is that quantum bits can exist in superpositions whereas classical bits cannot. In quantum biology, the role of quantum effects can be subtle and will be described for each system we discuss in this review. However, we may consider a biological system that exploits coherent superpositions of states for some practical purpose to be

1Advanced Science Institute, RIKEN, Saitama 351-0198, Japan,²Department of Physics and National Center for Theoretical Sciences, National Cheng Kung University, Tainan 701, Taiwan,³Department of Chemistry and Center for Quantum Science and Engineering, National Taiwan University, Taipei 106,

Taiwan,⁴Department of Engineering Science and Supercomputing Research Center, National Cheng Kung University, Tainan 701, Taiwan,⁵Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, USA. *e-mail: nwlambert@riken.jp; fnori@riken.jp.

the clearest example of functional quantum biology. Some of the systems we discuss are thought to fit into this category, but not all.

Here we present a very brief overview of some of these cases in which quantum effects may assist or enhance a biological function.

Our goal is to give a clear basic introduction to each system and to outline in what way quantum coherence or other quantum effects might be harnessed by this system. We also attempt to present the latest evidence both for and against these quantum effects actually being functional. We begin by discussing the observation of quantum coherence (superpositions) at room temperature in the transport of excitation energy through photosynthetic systems.

We briefly summarize the latest research about the role this coherence might play in the efficiency of photosynthesis in bacteria and plants. We then move onto an entirely different system: the radical-pair model used to describe the magnetic sense of some avian species. The evidence supporting the radical-pair model is primarily based on behavioural experiments, although very recent in vitro experiments⁷ on candidate radical pairs are in its favour. The possibility that a macroscopic cognitive species could respond to fundamentally quantum effects is fascinating, but a cautious approach of course needs to be taken to fully verify and understand this phenomenon. Finally, we will briefly discuss several other biological functions in which quantum mechanics may play a vital but less direct role, including long-range tunnelling of electrons through proteins and the rapid photoisomerization in photoreceptors. Some of these last examples could be considered as a class of quantum phenomena in biological systems that depends only on trivial quantization and discrete energy levels, not on quantum coherence. A brief list of selected works that demonstrate quantum effects in the examples we discuss here is shown in Table 1.

Quantum coherent energy transport in photosynthesis

Photosynthesis provides energy for almost all life on Earth. This energy, in the form of photons, is absorbed by light-harvesting antennas as an electronic excitation^8,9. This excitation is then transported from each antenna to a reaction centre where charge separation creates more stable forms of chemical energy. The precise biological structures and pigment constituents used, from the antenna to the reaction centre and onwards, vary between organisms^9,10. For example, purple bacteria use highly symmetric

10 NATURE PHYSICS | VOL 9 | JANUARY 2013 | www.nature.com/naturephysics

Nature Physics 9, 10 (2013)

Can we find quantum coherence in biology?

potential candidates

4

NATURE PHYSICS

DOI: 10.1038/NPHYS2474

REVIEW ARTICLE

Table 1|Summary of a selection of the main experimental and theoretical works on functional quantum biology.

Biological system Reference

Photosynthesis Cryogenic-temperature quantum coherence ^12,14

Ambient/room-temperature quantum coherence (FMO) ¹⁶

Ambient/room-temperature quantum coherence (algae) ¹⁵

Environment-assisted transport 19,26,27,29

Entanglement, tests of quantumness ^48,49,103

Alternative views ^46,47,51

Radical-pair magnetoreception Early proposals and evidence ^60,66

Mathematical models ^66,67

Indirect evidence (light dependence, magnetic field) 58,61,64,65,78,104

Experiments on radical pairs 7,71–73,105

Other examples Olfaction ^92,93

Vision ^97,99

Long-range electron transfer ^81,82

Enzyme catalysis ^84,85

ring-like structures for light harvesting¹¹, whereas green plants and cyanobacteria have photosystems with chlorophylls (light- absorbing pigment molecules) that seem to be randomly arranged.

Moreover, most photosynthetic organisms use arrangements of such chlorophyll molecules complexed with proteins, but cyanobacteria and red algae use a unique chromophore called a phycobillin. This diversity in light-harvesting apparatus reflects the necessity for photosynthetic organisms to adapt in response to different physiological conditions and natural habitats¹⁰. One of the simplest and most well-studied examples is the light-harvesting apparatus of green-sulphur bacteria (Fig. 1). These have a very large chlorosome antenna that allows them to thrive in low-light conditions. The energy collected by these chlorosomes is transferred to the reaction centre through a specialized structure called the Fenna–Matthews–Olson (FMO) complex. Owing to its relatively small size and solubility in water, the FMO complex has attracted much research attention and as a result has been well characterized.

What is remarkable is the observed efficiency of this and other photosynthetic units. Almost every photon (nearly 100%) that is absorbed is successfully transferred to the reaction centre, even though the intermediate electronic excitations are very short-lived (⇠1 ns). In 2007, Fleming and co-workers demonstrated evidence for quantum coherent energy transfer in the FMO complex¹², and since then the FMO protein has been one of the main subjects of research in quantum biology.

The FMO complex itself normally exists in a trimer of three complexes, of which each complex consists of eight bacteriochlorophyll a (BChl-a) molecules. These molecules are bound to a protein scaffold, which is the primary source of decoherence and noise, but which also may assist in protecting the coherent excitations in the complex and play a role in promoting high transport efficiency¹³. The complex is connected to the chlorosome antenna through what is called a baseplate. Excitations enter the complex from this baseplate, exciting one of the BChl molecules into its first singlet excited state. The molecules are in close proximity to one another (roughly 1.5 nm), enabling the excitation energy to transfer from one BChl molecule to another, until it reaches the reaction centre.

Quantum properties. As mentioned, direct evidence for the pres- ence of quantum coherence over appreciable length scales and timescales in the FMO complex was observed by Engel et al.¹² in 2007. They presented the spectroscopic observation, at low tem- perature (77 K), of quantum coherent dynamics (that is, coherent superpositions evolving in time) of an electronic excitation across multiple pigments within the FMO complex. Since that time a huge

body of literature has arisen, and further experiments^14–17 suggest that the coherence is non-negligible even at room temperature, for up to 300 fs. If quantum coherent dynamics are present at room temperature in the FMO complex (and other parts of a light-harvesting apparatus), what purpose does it serve? As we will discuss in the next section, a higher transport efficiency¹⁸ is the typical answer, and a large variety of theoretical models have been employed to explain if, how and why nature uses quantum coherence to move this electronic excitation through the FMO complex¹⁹ more efficiently than classically possible. The closest equivalent classical model against which one can compare such quantum effects is the Förster model that treats the transfer of the excitation between sites as an incoherent rate, and neglects all coherences or superpositions between sites. One should also note that the excitonic nature of the system, manifested in the co- herent delocalization of photoexcitation among several molecular sites, is also important and strongly influences the spectroscopic properties and energy relaxation of the complex, which should be discussed independently^20–22.

At first the notion of observing quantum coherence at room temperature in a biological system may be quite surprising.

However, even a naive comparison^23,24 of the relevant energy scales suggests that in fact quantum effects could be important in this case.

These energy scales are the environment’s temperature (⇠300 K), the coupling strength between the excitation in the FMO complex and the protein environment (⇠100 cm ¹) and the electronic coupling strength that transfers the excitation between BChl molecules (⇠100 cm ¹). Precisely calculating or measuring the energies and coupling strengths in a photosynthetic complex such as FMO requires a combination of spectroscopy and ab initio quantum chemistry methods based on atomistic models^23,24. Fortunately FMO is one of the most well-studied models, and generally speaking both measurements and calculations of the coupling strengths and energies agree quantitatively²⁵.

Environment-assisted transport. One can argue that the goal of the FMO complex is to maximize the efficiency of transporting a single excitation from the BChl-a molecule nearest the antenna to the BChl-a nearest the reaction centre (see Fig. 1). To this end, apart from the energy and couplings mentioned earlier, there are two other important timescales to be considered. One is the rate at which the excitation leaves the target molecule and enters the reaction centre (⇠1 ps). The other is the rate at which the excitation in any of the BChl is lost owing to fluorescence relaxation (⇠1 ns).

It is this latter rate that the excitation must beat, in its race to reach the reaction centre. Remarkably, the excitation is almost

NATURE PHYSICS | VOL 9 | JANUARY 2013 | www.nature.com/naturephysics 11

Focus on photosynthesis and olfaction in this talk.

photosynthesis

5

FMO is a trimer with 7 pigments inside

each monomer.

FMO complex

6

Chlorosome complex

FMO

complex reaction center

Published: June 03, 2011

r2011 American Chemical Society 8609 dx.doi.org/10.1021/jp202619a

|

J. Phys. Chem. B 2011, 115, 8609–8621

ARTICLE pubs.acs.org/JPCB

From Atomistic Modeling to Excitation Transfer and Two-Dimensional Spectra of the FMO Light-Harvesting Complex

Carsten Olbrich, ^† Thomas L. C. Jansen, ^‡ J€org Liebers, ^† Mortaza Aghtar, ^† Johan Str€umpfer, ^§ Klaus Schulten, ^§ Jasper Knoester, ^‡ and Ulrich Kleinekath€ofer* ^,†

†

School of Engineering and Science, Jacobs University Bremen, Campus Ring 1, 28759 Bremen, Germany

‡

Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands

§

Center for Biophysics and Computational Biology and Beckman Institute, University of Illinois at Urbana!Champaign, Urbana, Illinois 61801, United States

ABSTRACT:

The experimental observation of long-lived quantum coherences in the Fenna!Matthews!Olson (FMO) light-harvesting complex at low temperatures has challenged general intuition in the field of complex molecular systems and provoked considerable theoretical effort in search of explanations. Here we report on room-temperature calculations of the excited-state dynamics in FMO using a combination of molecular dynamics simulations and electronic structure calculations. Thus we obtain trajectories for the Hamiltonian of this system which contains time-dependent vertical excitation energies of the individual bacteriochlorophyll molecules and their mutual electronic couplings. The distribution of energies and couplings is analyzed together with possible spatial correlations. It is found that in contrast to frequent assumptions the site energy distribution is non-Gaussian. In a subsequent step, averaged wave packet dynamics is used to determine the exciton dynamics in the system. Finally, with the time-dependent Hamiltonian, linear and two-dimensional spectra are determined. The thus-obtained linear absorption line shape agrees well with experimental observation and is largely determined by the non-Gaussian site energy distribution. The two-dimensional spectra are in line with what one would expect by extrapolation of the experimental observations at lower temperatures and indicate almost total loss of long-lived coherences.

’ INTRODUCTION

In photosynthesis the energy of sunlight is converted into chemical energy. Light harvesting and charge separation are the primary steps in this process. Specific pigment!protein aggre- gates, the so-called light-harvesting (LH) complexes, have the function of absorbing light and transporting the energy to the photosynthetic reaction center (RC). Within the RC the excita- tion is subsequently converted into charge separation.

¹

Many of the structural and functional details of these protein complexes have been elucidated already.

^2!4

One of the extensively studied LH systems is the Fenna!

Matthews!Olson (FMO) complex of green sulfur bacteria.

⁵

For the bacterium Prosthecochloris aestuarii, the crystal structure was already solved three decades ago,

⁶

the first time that this was achieved for a pigment!protein complex. Meanwhile the structure

has been characterized at atomic resolution 1.9 Å.

⁷

Recently, the structure of the FMO complex of Chlorobaculum tepidum has been determined as well.

⁸

Under physiological conditions, the FMO complex forms a homotrimer consisting of eight bacteriochloro- phyll-a (BChl a) molecules per monomer. The existence of an eighth BChl molecule in the structure of each monomer has been shown only recently;

⁸

many earlier studies refer to just seven BChls per monomer. The biological function of the FMO trimer is to transfer excitation energy from the chlorosome, i.e., the main LH antenna system of green sulfur bacteria, to the RC, which is embedded into the membrane.

⁵

The optical properties of FMO

Received: March 20, 2011

Revised: June 2, 2011

exciton transport

7 experiment (0.37). We reproduce the presence of negative regions (dashed contour lines in Fig. 1c, f) corresponding to excited-state absorption to the two-exciton states, as well as the shape-contour change around the central diagonal peak, that is, its horizontal elongation towards region B. Some differences between experiment and simulation also occur. First, the build-up of cross peak A is slower in the simulations (Fig. 1f) than in experiment (Fig. 1c), implying that the calculated rate of populating level 1 is too slow;

that is, the ratios of the amplitude of cross peak A to that of diagonal peaks C and D in the experimental (theoretical) spectra at T ¼ 1 ps are 2.07 (1.41) and 0.76 (0.48), respectively. Second, the experi- mental cross peak near A (Fig. 1c) extends horizontally between exciton states 2 and 5, whereas in the simulation (Fig. 1f) separate peaks appear. This is at least partly the result of our limited (40 cm²¹) q_t-frequency resolution.

Nevertheless, considering the complexity of the physical system, the agreement with the key 2D features is very promising. On the basis of our model, we now analyse how the excitation propagates between the different BChl molecules; that is, we follow the energy transfer in space and time. First we consider the delocalization of the exciton wavefunctions. Most excitons are delocalized mainly over only one or two neighbouring BChl molecules. This is indicated by the coloured shading in Fig. 2a. For example, excitons 3 and 7 (green, bold numbers) are both delocalized over the same BChls 1 and 2 (italic numbers). Second, from the exciton transfer-rate matrix obtained with the modified Fo¨rster/Redfield theory we can then identify the two major energy transport pathways shown by red and green arrows. In terms of energy levels, the results are displayed in Fig. 2b. An important factor for efficient energy transport is the mutual wavefunction overlap between initial and final states.

Stronger overlap leads to faster transfer.

Consider first the ‘green’ pathway, starting with exciton 6 (on BChls 5 and 6). Because of its strong wavefunction overlap with exciton 5 (located on the same two pigments), the excitation is transferred efficiently (green ellipse). From there, exciton 4 can be reached, which in turn transfers to exciton 2 (again because of the strong spatial overlap as both excitons 2 and 4 are located on BChls 4 and 7). Alternatively, exciton 2 is reached directly from exciton 5.

Note that in either case exciton 3 is not involved because it does not have strong spatial overlap with exciton 4 or 5. From exciton 2, the transport proceeds to exciton 1, and ultimately to the reaction centre where it is turned into chemical energy. The second pathway (red arrows) starts with exciton 7 and proceeds through excitons 3

and 2 to 1. Using similar arguments, it is clear that the good spatial overlap between excitons 7 and 3 and the weak coupling of corresponding BChls 1 and 2 to the remaining pigments prevents energy transfer from exciton 7 to excitons 4, 5 or 6. We conclude that the energy is not simply transferred stepwise down the energy ladder as has been conjectured previously^15,28. Instead, distinct pathways emerge (Fig. 2b) in which some energetically intermediate states are left out.

As illustrated by these findings, 2D femtosecond photon-echo spectroscopy remedies the deficiency of conventional types of spectroscopy in which only the evolutions of populations over time can be determined directly, but not the mechanisms that underlie these temporal changes. Thus we get detailed insight into the driving force of biological light harvesting, and applications to larger photosynthetic systems are possible. By noting that the magnitudes of electronic couplings and exciton relaxation rates are essentially dependent on the spatio-energetic distribution of chromophores, analysis of the exciton delocalization pattern leads to spatial information on the molecular scale. Hence, in general, the combination of these fully self-consistent calculations and experiments allows us to follow energy transport through space and time with nanometre spatial resolution and femtosecond temporal resolution. This methodology also opens the door to similar investigations of electronic couplings and energy transport in any photoactive assembly, macromolecule or other nanoscale

system. A

Methods

Experiment and data analysis

Our implementation of inherently phase-stabilized two-dimensional Fourier-transform femtosecond spectroscopy for electronic transitions has been described in detail

elsewhere^20,21. In brief, 50-fs, 805-nm, 3-kHz laser pulses from a home-built Ti:sapphire regenerative-amplifier laser system are used for three-pulse photon-echo spectroscopy in a diffractive-optic-based^29,30 non-collinear four-wave mixing set-up with phase-matched box geometry. Time delays are introduced with better than l/100 precision by movable glass wedges, and passive interferometric phase stability is maintained over several hours^20,21. The third-order signal is completely characterized by spectral interferometry with the help of a heterodyning local-oscillator pulse¹⁷. Automated subtraction of scattering terms removes experimental artefacts caused by sample imperfections. To resolve individual spectral features, we perform the experiment at low temperature (77 K) in a liquid-nitrogen cryostat (Oxford Instruments).

For any given population time (waiting time) T, the coherence time t is scanned in 5-fs steps from 2440 fs toþ440 fs, moving excitation pulse 1 (2) in the second (first) half of the scanning period. Spectral interferograms are recorded with a 16-bit, 100-pixel £ 1,340- pixel, thermoelectrically cooled charge-coupled device camera (Princeton Instruments) and a 0.3-m imaging spectrometer (Acton). These parameters lead to a spectral resolution of 40 cm²¹for qt and 2 cm²¹for q_t. The spot diameter at the sample position is 84 mm (1/e²intensity level), and the excitation energy is 20 nJ per pulse for the 2D traces shown. Repetitions with 30% of the laser power led to essentially the same results within the experimental uncertainties (though at decreased signal-to-noise ratio). Data analysis by Fourier transformation yields the desired 2D traces whose absolute phase is obtained by means of the projection-slice theorem and comparison with separately recorded spectrally resolved pump–probe data^8,21. Each 2D trace is the average of three separate scans.

The FMO complex of Chlorobium tepidum was prepared in a buffer of 50 mM Tris HCl at pH 8.0 and 10 mM sodium ascorbate¹⁰. To avoid cracking of samples at low

temperature, we used a water/glycerol (35:65 v/v) mixture between plastic windows (thickness 0.3 mm) with a 0.4 mm optical path length. The optical density peak value was 0.37 at 77 K. After each series of 2D scans for different population times, we repeated the first of the scans in the same sample spot for comparison. This gave qualitatively the same 2D results within the experimental noise limits as those shown, and the absolute decrease in 2D signal due to sample degradation was below 30%.

Theory and numerical simulations

The Frenkel exciton hamiltonian matrix elements, denoted by H_jk, were obtained by simultaneously fitting to the absorption and time-resolved 2D photon-echo spectra. The diagonal elements, H_jj, for BChl molecules j¼ 1,…,7 (Fig. 2a), are 280, 420, 0, 175, 320, 360 and 260 cm²¹. The off-diagonal matrix elements are identical to those presented previously¹⁴, except that H56¼ H⁶⁵was reduced to 40 cm²¹because the corresponding diagonal frequencies were readjusted in the present work. The general nonlinear response functions were obtained^3,22, but the Laplace (stationary-phase approximation) method was used to calculate the corresponding 2D Fourier spectrum approximately. The site energy fluctuation was assumed to be uncorrelated with those of other sites. The frequency–

frequency correlation function determining line broadening processes was expressed in terms of an ohmic-type spectral density, that is, rðqÞ ¼ ðl="q^cÞq²¹expð2q=q^cÞ; where 7

6 5

5, 6

4 3 3, 7

2 2, 4

1 1

Figure 2 Exciton delocalization and energy transport. a, The FMO structural arrangement of the seven BChl molecules (italic numbers) is overlaid qualitatively with the delocalization patterns of the different excitons (coloured shading, bold numbers). Two main

photoexcitation transfer pathways are indicated by red and green arrows.b, The energy transport is not just a simple process of stepwise energy decrease from one level to the next level below; rather, intermediate states are left out if they have insufficient spatial overlap with potential transfer partners.

letters to nature

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© 2005 Nature Publishing Group

Can we detect the

excitonic states by simple pump-probe experiments?

Nature 434, 625 (2005)

pump and probe

On resonance, the output frequency echoes the input

frequency.

off-diagonal peaks

The real biological systems seem to be more complicated. Off-diagonal peaks show up!

transition dipoles, and nonlinear optical transitions involving two different exciton states are allowed and produce off-diagonal peaks even at T¼ 0. The transitions above and below the diagonal involve different one-exciton and two-exciton states, with correspondingly different oscillator strengths. Accordingly, the cancellation between bleaching/stimulated emission features and excited-state absorp- tion features is different in the two half-planes, giving rise to the stronger cross peaks below the diagonal. For cross peak A, the system is in an electronic coherence state of the ground and fifth excitonic states during t and of the lowest one-exciton and ground states during t. This cross peak indicates that the BChl pigments that make up excitons 1 and 5 are coupled; feature B shows the same for excitons 2 and 5. The negative regions (dark blue in Fig. 1a) can be attributed to two-exciton contributions, that is, excited-state absorption.

The electronic couplings lead to energy transfer, which is observed for population times T . 0. As an example, we show two snapshots at T ¼ 200 fs (Fig. 1b) and T ¼ 1,000 fs (Fig. 1c).

With these 2D spectra, not only do we measure the population evolution as in conventional pump–probe experiments, we also follow the state-to-state energy transfer pathway. Between 200 and 1,000 fs, the amplitude of the lowest-energy diagonal peak increases and the main diagonal peak (D) shifts to lower energies, indicating a sizeable downward population transfer. The concentration of features below the diagonal also indicates that ‘downhill’ transfer, from higher to lower energies, dominates. The cross peaks in Fig. 1b, c demonstrate the sensitivity of this method to pigment–pigment interactions. Focusing on the two dominant off-diagonal peaks near regions A and B, the 2D spectra show increasing amplitudes as

a function of waiting time T. This reveals, for example, the relaxation from exciton states 4 and 5 to exciton state 2 (B) and exciton state 1 (A) as a function of time. Other features can be discussed qualitatively in an analogous fashion.

For quantitative simulations we use a Frenkel exciton hamil- tonian with electronic coupling constants and site energies obtained by fitting the resulting absorption and 2D spectra. A single ohmic spectral density (representing the chromophore–bath coupling- strength distribution) and modified Fo¨rster/Redfield theory^26,27 are employed for fully self-consistent calculations of the exciton transfer rates, the linear absorption spectrum (Fig. 1d, dashed black line) and the time-dependent 2D spectra (Fig. 1e, f). By using modified Fo¨rster/Redfield theory, we can self-consistently describe the excited states as either localized or delocalized (excitonic) depending on the magnitude of the coupling constants²⁷. Most of the exciton states are delocalized over two or three molecules, but the lowest exciton is essentially localized on BChl 3 (refs 14, 28). The transport of excitation is treated as reversible; finite temperature and detailed balance are correctly incorporated. The comparison between experiment and theory shows that the positions of the peaks in the 2D frequency space are reproduced. In addition, the relative timescales associated with the appearance/disappearance of the specific features are also well described. For example, in both theory and experiment the amplitudes in cross peaks A and B increase with population time T as a result of downhill energy transfer. The experimental (and theoretical) ratios of the amplitude of cross peak B to diagonal peaks C and D at T¼ 1 ps are 1.49 (1.45) and 0.55 (0.5), respectively. The calculated relative amplitude of diagonal peak C to D (0.34) at T¼ 1 ps is also close to that from

Figure 1 Experimental and theoretical spectra (real parts) of the FMO complex from Chlorobium tepidum at 77 K.a–c, The experimental 2D spectra (upper three panels) are shown for population times T¼ 0 fs (a), T ¼ 200 fs (b) and T ¼ 1,000 fs (c). Contour lines are drawn in 10% intervals at ^5%, ^15%, …, ^95% of the peak amplitude, with solid lines representing positive contributions (‘more light’) and dashed lines negative features. Horizontal and vertical grid lines indicate exciton levels 1–7 as labelled.d, The

experimental linear absorption spectrum (solid black) is reproduced by theory (dashed black), with individual exciton contributions as shown (dashed–dotted green). The laser spectrum used in the 2D experiments (red) covers all transition frequencies.

e, f, Simulations of 2D spectra are shown for T¼ 200 fs (e) and T ¼ 1,000 fs (f ).

Off-diagonal features such as those labelled A and B are indicators of electronic coupling and energy transport; they are discussed in more detail in the text.

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Diagonal peaks (C,D) expected.

Off-diagonal peaks (A,B) show up... What

happens?

three-pulse pump-probe

Engel et al. have demonstrated using two- dimensional (2D) electronic spectroscopy that surprisingly long-lived (>660 fs) quantum coher- ences between excitonic states play an important role in the dynamics of energy transfer in pho- tosynthetic complexes—i.e., the energy transfer is described by wavelike coherent motion instead of incoherent hopping (4).

To understand the origins of such long-lived coherences and the role of the protein matrix in its preservation, an experiment specifically de- signed to monitor electronic coherences between excited states is required. Here, we describe a two-color electronic coherence photon echo ex- periment (2CECPE) that produces a direct probe of electronic coherences between two exciton states. We applied the method to the coherence between bacteriopheophytin and accessory bac- teriochlorophyll in the purple bacteria reaction center (RC). The measurement quantifies dephasing dynamics in the system and provides strong evidence that the collective long-range electrostatic response of the protein environment to the electronic excitations is responsible for the long-lasting quantum coherence. In other words, the protein environment protects electronic coherences and plays a role in the optimization of excitation energy transfer in photosynthetic complexes.

The RC from the photosynthetic purple bac- terium Rhodobacter sphaeroides includes a bacteriochlorophyll dimer called the special pair (P) in the center, an accessory bacteriochlo- rophyll flanking P on each side (BChl; B

_L

and B

_M

, for the L and M peptides, respectively), and a bacteriopheophytin (BPhy; H

_L

and H

_M

for the L and M peptides, respectively) next to each BChl (5). (We use H and B to denote excitonic states whose major contributions are from monomeric BPhy and accessory BChl in the RC, respectively.) In addition to electron trans- fer with near-unity efficiency (6), energy trans- fer occurs between the excitonically coupled chromophores—for example, from H to B in about 100 fs and from B to P in about 150 fs—in the isolated RC (7–10). In our experiments, the primary electron donor (P) is chemically oxidized by K

₃

Fe(CN)

₆

(11), which blocks electron trans- fer from P to H

_L

, but does not affect the dy- namics of energy transfer (8). This modification eliminates interference from the charge-transfer dynamics. The absorption spectrum of the P- oxidized RC at 77 K (Fig. 1A) shows the H band at 750 nm and the B band at 800 nm.

In our 2CECPE (11) (Fig. 1B), three ~40-fs laser pulses interact with the sample and generate a signal field in the phase-matched direction k

_s

. The first two pulses have different colors and are respectively tuned for resonant excitation of the H transition at 750 nm and the B transition at 800 nm (Fig. 1A). This is different from conventional two-color three-pulse photon echo technique in which the first two pulses have the same color (12). In our experiment, the first pulse (750 nm) creates an optical coherence

(electronic superposition) between the ground state and the H excitonic state (|g 〉〈H| coherence).

The coherence evolves for time delay t

₁

until the second pulse (800 nm) interacts with the sample to form a coherence between B and H (|B 〉〈H|

coherence) that evolves for a time t

₂

. Finally, the third pulse (750 nm) interacts with the system to generate a photon echo signal if, and only if, B and H are mixed. The integrated intensity of the echo signal is recorded at different delay times t

₁

and t

₂

. The central idea of the experiment is that if two chromophores are coupled and create two exciton bands (H and B in this case) in the ab- sorption spectrum, then excitation resonant with one transition (|g 〉→|H〉), followed by excitation resonant with the other (|g 〉→|B〉) converts the initial coherence (|g 〉〈H|) into a coherence of the two exciton bands (|B 〉〈H|). This experiment is distinct from conventional two-color three-pulse photon echo measurements because different colors in the first two pulses are used to optically select the contributions to the third-order re- sponse function that arise from coherence path- ways involving electronic superposition between two exciton states in the t

₂

period. Because the system is in a coherence state in time t

₂

, popu- lation dynamics only contribute to dephasing and do not generate additional echo signals; therefore, this technique is specifically sensitive to the co- herence dynamics and provides a probe for the protein environment of the chromophores. A similar pulse ordering was applied in dual- frequency 2D infrared spectroscopy to study vibrational coherence transfer and mode cou- plings (13, 14).

The 2CECPE signals for the RC as a function of t

₁

and t

₂

measured at 77 K and 180 K are shown in Fig. 2, A and B, respectively. These figures provide a 2D representation of the sys- tem, which propagates as a |g 〉〈H| coherence dur- ing the t

₁

period and as a |B 〉〈H| coherence during the t

₂

period. The result is a map showing the dephasing dynamics of the |g 〉〈H| coherence along the t

₁

axis and the dynamics of the |B 〉〈H|

coherence along the t

₂

axis. Clearly, the decay of the |g 〉〈H| coherence is much faster than the de- cay of the |B 〉〈H| coherence. Moreover, following the black curve that connects the maximum of integrated echo signal at fixed t

₂

, we see that the signals exhibit a sawtooth-shaped beating pattern that persists for longer than t

₂

> 400 fs. This oscillatory behavior is not from excitonic beating, given that we detect signal intensities in which the oscillatory phase factor vanishes; instead, this beating indicates electronic coupling to vibra- tional modes. Notably, the pattern is also pe- culiarly slanted along the antidiagonal direction;

this slant arises because the vibrational coher- ence is induced by the first laser pulse and prop- agates in time t

₁

+ t

₂

, making the peaks of the beats parallel to the antidiagonal (t

₁

+ t

₂

is fixed).

The signals show substantial peak shift [i.e., shift from t

₁

= 0 (12)], indicating correlation of the excitation energies between the H and B transitions (12).

To analyze the |B 〉〈H| coherence dynamics, we plotted the integrated signal at t

₁

= 30 fs (across the maxima of the first beat) as a function of t

₂

(Fig. 3). Clearly, the dephasing is enhanced at higher temperature, as expected. The decay of the echo signal as a function of t

₂

is not de- scribed by a single exponential decay because of its highly non-Markovian nature and the vibration- al modulation. A Gaussian-cosine fit of the signal shows that the main component of the coherence signal decays with a Gaussian decay time (t

_g

) of 440 and 310 fs at 77 and 180 K, respectively (eq. S1 and fig. S1). These dephasing times are substantially longer than the experimentally estimated excitation energy transfer time scale of about 250 fs from H to B to P

⁺

(8). The surprisingly long-lived |B 〉〈H| coherence indi- cates that the excitation energy transfer in the RC cannot be described by Förster theory, which neglects the coherence between donor and accep- tor states (15). In addition, the decay of the |g 〉〈H|

coherence is much faster than the decay of the

|B 〉〈H| coherence. Considering that the dephasing of the |g 〉〈H| coherence is caused by the transition energy fluctuations on H, whereas the dephasing of the |B 〉〈H| coherence is due to the fluctuations on the gap between H and B transition energies, the transition energy fluctuations on B and H must be strongly correlated, because in-phase energy fluctuations do not destroy coherence.

Such a strong correlation can arise for two possible reasons: strong electronic coupling between B and H and/or strong correlation be- tween nuclear modes that modulate transition frequency fluctuations of localized BChl and

1

0.5

0700 750 800 850 900

Wavelength(nm)

Normalized Absorption (a.u.)

H

B

k

¹

k

³

k

²

k

^s

=-k

¹

+k

²

+k

³

t

¹

t

²

B A

Fig. 1. The 2CECPE experiment. (A) The 77 K absorption spectrum (black) of the P-oxidized RC from the photosynthetic purple bacterium R. sphaeroides and the spectral profiles of the

~40-fs laser pulses (blue, 750 nm; red, 800 nm) used in the experiment. (B) The pulse sequence for the 2CECPE experiment. We detect the in- tegrated intensity in the phase-matched direc- tion k

_s

= –k

₁

+ k

₂

+ k

₃

. a.u., arbitrary units.

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Three-pulse pump-probe:

The first two pulses pump and entangled two excitonic states

and the third one probe the

entangled dynamics.

quantum coherence

11

BPhy excitations. Our theoretical analysis found that strong electronic coupling alone cannot re- produce the sawtooth pattern and a dephasing time as long as that observed (11). Instead, cross- correlation between nuclear modes modulating the energy levels of localized BChl and BPhy excitations is required.

We modeled the 2CECPE signals using im- pulsive limit third-order response functions for a coupled heterodimer based on the transition fre- quency correlation functions for each localized excitation (11, 16). The model correlation func- tions contain a sum of a Gaussian component representing solvent reorganization and a con- stant term representing the inhomogeneous static contribution:

C_iðtÞ ¼ 〈Dw²i〉expð−t²=t_i²Þ þ D²i ð1Þ where〈Dw²〉^1/2is the fluctuation amplitude that is determined by the reorganization energy l, t is the bath relaxation time, D is the standard de- viation of Gaussian static distribution, and i = h, b, and hb denote the localized BPhy, BChl exci- tations, and the cross-correlation between them, respectively. For C_h(t) and C_b(t), we adopted parameters established by previous photon echo experiments on the neutral RC and by quantum chemistry calculations (17–20). For simplicity, we used a single coefficient c to describe the cross-correlation and assume l_hb ¼ c ⋅pffiffiffiffiffiffiffiffiffil_hl_band D²_hb ¼ c ⋅ D^hD_b. The cross-correlation coefficient c represents the extent to which nuclear motions modulating the transition frequencies of localized BPhy and BChl excitations are correlated with

each other. With c = 0.9 and the addition of a vibrational mode coupled to the localized BPhy excitation (w = 250 cm⁻¹; Huang-Rhys factor S = 0.4; damping time > 0.6 ps; phase shift 0.28 rad), the model semiquantitatively reproduces the measurements at 77 and 180 K simultaneously;

a c value of 0.6 substantially diminishes agree- ment with experiment (Figs. 2 and 3). Adding more terms to the model correlation functions improves the fit to experiments, but does not change any conclusions.

A c value near unity implies that nuclear modes coupled to H and B exhibit almost iden- tical motions immediately after excitation. In other words, the two chromophores, H and B, are effectively embedded in the same protein envi- ronment and feel a similar short-time Gaussian component of their energy-level fluctuations.

Most likely, this short-time component is the electrostatic response of the protein environment to the electronic excitations. Molecular dynamics simulations of the RC support this conclusion and show that interactions with the solvent en- vironment (protein and water), rather than the intramolecular contributions, dominate the tran- sition energy fluctuations of the P dimer excited state (21).

Theories for excitation energy transfer in pigment-protein complexes usually assume an independent bath for each of the individual chro- mophores (1–3, 15, 22, 23). However, our result suggests that in densely packed pigment-protein complexes, the assumption of independent bath environments for each site is not correct. Indeed, a previous molecular dynamics simulation on the

RC of Rhodopseudomonas viridis also showed that nuclear motions of adjacent chromophores are strongly correlated (24). Given that closely packed pigment-protein complexes are a ubiqui- tous configuration for efficient energy harvesting and trapping in photosynthetic organisms, the long-range correlated fluctuations indicated by our results are unlikely to be unique.

What are the likely consequences of long- lived electronic coherence in the RC? First, such coherence enables the excitation to move rapidly and reversibly in space, allowing a very efficient search for the energetic trap, in this case the primary electron donor, P. The almost complete correlation of the H and B fluctuations (on the few hundred–femtosecond time scale) and the likely significant correlation of the fluctuations of both exciton states of P with those of B will also enable bath-induced coherence transfers between the various pairs of excitons (25–27). We suggest that the overall effect of the protection of electronic coherence is to substantially enhance the energy transfer efficiency for a given set of electronic couplings over that obtainable when electronic dephasing is fast compared with transfer times.

It will be important to confirm this proposal by carrying out experiments similar to the one described here, but with excitation wavelengths resonant with B and P and with H and P. The

t2(fs)

Integrated Intensity (a.u.)

50 100 150 200 250 300 350 400 450

Experiment c=0.9 c=0.6

Integrated Intensity (a.u.)

50 100 150 200 250 300 350 400 450

A

B

77K

180K

Fig. 3. Integrated echo signals as a function of t₂ at t1= 30 fs. Because the system evolves as a coherence between the H and B excitons during the t₂ period, this plot represents the dephasing dynamics of the |B^〉〈H| coherence. Measurements at 77 K (A) and 180 K (B) are shown in solid circles, and the theoretical curves are shown in red (c = 0.9) or blue (c = 0.6) lines. a.u., arbitrary units.

Fig. 2. Two-dimensional maps of experimental (A and B) and simulated (C and D) integrated echo signals as a function of the two delay times, t₁ and t₂, from the RC. The black lines follow the maximum of the echo signal at a given t₂. The data at t₂ < 75 fs are not shown because the conventional two-color three-pulse photon echo signal (750-750-800 nm) overwhelms the 2CECPE signal in this region, due to the pulse overlap effect.

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without K (fig. S4). This is another indication of NEA because K deposition onto a positive elec- tron affinity semiconductor will lead to a shift of the low–kinetic energy cutoff and strong enhance- ment of the secondary electron background.

On a typical NEA surface, electrons excited into unoccupied states relax to the bottom of the conduction band as a result of inelastic scatter- ing, a process normally referred to as the second- ary cascade. A number of secondary electrons will then accumulate at the bottom of the con- duction band. For a surface with positive elec- tron affinity (as occurs in almost all untreated semiconductor surfaces), these accumulated elec- trons cannot escape. For an NEA surface, these accumulated electrons can be emitted directly be- cause the vacuum level lies below the bottom of conduction band. As a result, a peak will be ob- served at the low–kinetic energy threshold in PES (4, 17–19, 23, 24).

However, on diamondoid SAM surfaces, there is only a single layer of diamondoid molecules.

The detailed mechanism responsible for the high- ly monochromatic emission is unknown at this stage. Naïvely, one may consider that photoex- cited electrons lose energy by creating phonons in the molecules, but this would likely lead to the destruction of the molecules. A plausible scenario is that most of the photoexcited electrons come from the substrate. These electrons first thermalize in the metal, producing many more low-energy electrons. Electrons with energies above the diamondoid conduction-band minimum may get transferred to diamondoid molecules, reach the bottom of the conduction band by creating phonons, and get emitted. This proposal is shown schematically in Fig. 4. Another difference be- tween our results and those of other typical NEA systems (4, 17–19, 23, 24) is that our data show a spike in the spectra rather an exponential rise of the secondary tail toward the threshold, suggesting that a single energy level, resulting from the mo- lecular nature of nanometer-sized diamondoids, and/or a strong resonance process are involved.

Our results suggest that diamondoid mono- layers may have promising utility. Not only can functionalized diamondoids be easily grown into large area SAMs with NEA properties, they also naturally circumvent the long-standing electron- conductivity issues encountered for wide-gap bulk NEA semiconductors (4, 26). On a diamondoid SAM surface, electron conduction from the elec- tron reservoir (metal substrates) to the emission surface is through a single molecule, which suc- cessfully avoids the low-conductivity problem and enhances the electron emission. Additional- ly, the possibility of different functionalizations (3, 4) allows one to optimize the NEA and other properties of diamondoids. Although many techni- cal issues need to be addressed before diamondoid SAMs can be used as electron emitters, diamond- oids provide intrinsic advantages over bulk materials because of their special molecular characteristics—for example, narrow energy dis- tribution of the electronic states.

References and Notes

1. J. E. Dahl, S. G. Liu, R. M. K. Carlson, Science 299, 96 (2003).

2. B. A. Tkachenko et al., Org. Lett. 8, 1767 (2006).

3. P. R. Schreiner et al., J. Org. Chem. 71, 8532 (2006).

4. A. Paoletti, A. Tucciarone, Eds., The Physics of Diamond, Proceedings of the International School of Physics Enrico Fermi (IOS Press, Amsterdam, 1997).

5. N. D. Drummond, A. J. Williamson, R. J. Needs, G. Galli, Phys. Rev. Lett. 95, 096801 (2005).

6. Materials and methods are available as supporting material on Science Online.

7. A. Ulman, Chem. Rev. 96, 1533 (1996).

8. J. Stöhr, NEXAFS Spectroscopy (Springer, Berlin, 1992).

9. G. Hähner, Chem. Soc. Rev. 35, 1244 (2006).

10. M. Zharnikov, M. Grunze, J. Phys. Condens. Matter 13, 11333 (2001).

11. T. M. Willey et al., Phys. Rev. Lett. 95, 113401 (2005).

12. T. M. Willey et al., Phys. Rev. B 74, 205432 (2006).

13. P. E. Laibinis et al., J. Am. Chem. Soc. 113, 7152 (1991).

14. A. Shaporenko et al., Langmuir 21, 4370 (2005).

15. J. C. Love et al., Chem. Rev. 105, 1103 (2005).

16. D. G. Castner, K. Hinds, D. W. Grainger, Langmuir 12, 5083 (1996).

17. F. J. Himpsel, J. A. Knapp, J. A. VanVechten, D. E. Eastman, Phys. Rev. B 20, 624 (1979).

18. B. B. Pate, Surf. Sci. 165, 83 (1986).

19. J. van der Weide, R. J. Nemanich, Appl. Phys. Lett. 62, 1878 (1993).

20. W. L. Yang et al., Science 300, 303 (2003).

21. C. D. Bain et al., J. Am. Chem. Soc. 111, 321 (1989).

22. The lack of a strong secondary electron component on the annealed sample may indicate that the transmission efficiency of the spectrometer is poor at low kinetic energies. This suggests that the peak from SAM surface could have been even stronger. Artificial effects on the peak have been ruled out by testing with different bias voltages.

23. L. W. James, J. L. Moll, Phys. Rev. 183, 740 (1969).

24. R. C. Eden, J. L. Moll, W. E. Spicer, Phys. Rev. Lett. 18, 597 (1967).

25. For NEA materials, the difference between photoemission spectral width and the excitation energy should match the band-gap value (4, 17–19). Although there is no precise gap value reported for [121]tetramantane-6-thiol, and it is difficult to define a precise photoemission spectral width of an insulating monolayer system (owing to the difficulty in determining the spectral onset), the estimate obtained from our spectra is consistent with the DMC calculation (5), considering that the thiol groups are likely to change the gap value by only a few tenths of an electron volt.

26. R. L. Bell, Negative Electron Affinity Devices (Clarendon, Oxford, 1973).

27. We acknowledge helpful discussions with Z. Liu,

D.-H. Lee, and H. Padmore. W.L.Y. thanks Y. Y. Wang for sharing information on diamondoid film deposition and J. Pepper and S. DiMaggio for technical support. The work at Stanford Synchrotron Radiation Laboratory and the Advanced Light Source is supported by the U.S. Department of Energy, Office of Basic Energy Science, Division of Material Science, under contracts DE-FG03-01ER45929-A001 and DE-AC03-765F00515, respectively. The work at Stanford is also supported by Chevron through the Stanford-Chevron Program on Diamondoid Nano-Science.

Supporting Online Material

www.sciencemag.org/cgi/content/full/316/5830/1460/DC1 Materials and Methods

Figs. S1 to S4 References

27 February 2007; accepted 30 April 2007 10.1126/science.1141811

Coherence Dynamics in

Photosynthesis: Protein Protection of Excitonic Coherence

Hohjai Lee, Yuan-Chung Cheng, Graham R. Fleming*

The role of quantum coherence in promoting the efficiency of the initial stages of photosynthesis is an open and intriguing question. We performed a two-color photon echo experiment on a bacterial reaction center that enabled direct visualization of the coherence dynamics in the reaction center. The data revealed long-lasting coherence between two electronic states that are formed by mixing of the bacteriopheophytin and accessory bacteriochlorophyll excited states.

This coherence can only be explained by strong correlation between the protein-induced fluctuations in the transition energy of neighboring chromophores. Our results suggest that correlated protein environments preserve electronic coherence in photosynthetic complexes and allow the excitation to move coherently in space, enabling highly efficient energy harvesting and trapping in photosynthesis.

H

ighly efficient solar energy harvesting and trapping in photosynthesis relies on sophisticated molecular machinery built from pigment-protein complexes (1, 2). Although the pathways and time scales of excitation energy

transfers within and among these photosynthetic complexes are well studied, less is known about the precise mechanism responsible for the energy transfer. In particular, to what extent quantum coherence contributes to the efficiency of energy transfer is largely unknown. Only recently have nonlinear optical spectroscopy and theoretical modeling started to reveal that coherences between electronic excitonic states can have a substantial impact on excitation energy transfer in photosynthetic systems (2–4). For example,

Department of Chemistry and QB3 Institute, University of California, Berkeley and Physical Bioscience Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA.

*To whom correspondence should be addressed. E-mail:

GRFleming@lbl.gov

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So, quantum coherence is detected in FMO complex

by pump-probe photon echo experiment.

Science 316, 1462 (2007)

at ambient temp

12

Now observed at room temperature!

Nature 463, 644 (2010)

olfactory receptors

13

how do we smell?

14

odorant receptors

15

Linda Buck and Richard Axel

discovered olfactory receptors in 1991.

olfaction pathway

16

• Odorant molecules bind to receptors

• Olfactory receptor cells are activated

• Signals are relayed in glomerulus

• Final processing in higher regions of the brain

Nature 413, 211 (2001)

many, many receptors...

17

This number of genes specific to the olfactory system is about 3% of our whole genome, second only to those of

the immune system.

It is now known that there are about 350 functional odorant receptors in human being and twice more for all (including inactive) odorant

receptors.