Download A Little Coherence in Photosynthetic Light Harvesting

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A Little Coherence in Photosynthetic
Light Harvesting
JESSICA M. ANNA, GREGORY D. SCHOLES, AND RIENK
van
GRONDELLE
How could quantum mechanics possibly be important in biology? We will discuss this question in the light of recent experiments that suggest
that quantum mechanics—or at least coherence—is at play after photosynthesis is initiated by light. First, we give a brief description of light
harvesting in photosynthesis. We follow this with an introduction to two-dimensional electronic spectroscopy, in which we demonstrate how this
spectroscopic technique can be used to indicate coherent contributions to energy transfer dynamics. As a final point, we focus on the possible role
that coherence may play in photosynthetic biological systems.
Keywords: energy transfer, coherence, light harvesting, photosynthesis, femtosecond spectroscopy
A
biological system is incredibly complex, and the complexity hardly diminishes even as we focus on processes occurring in the cell, such as respiration or the action
of enzymes. Biologists therefore describe an average process
rather than map out every possibility that transpires in each
cell each time the process occurs. As a consequence of this
statistical approach, quantum mechanical (or coherent) phenomena are hidden in the average response of a very complex system. Schrödinger pioneered this idea in his (1944)
book What is Life? As was summarized in a lucid lecture by
McFadden (2012), Schrödinger hypothesized that quantum
mechanical effects in living systems may be evident, and
indeed active, if the number of particles in the system of
interest is very small. In this article, we illustrate the idea by
discussing recent evidence that coherences, whether they
are classical (e.g., promoted by coherent motion of classical
modes) or quantum (e.g., interference of Feynman paths),
are involved in the initial events of photosynthesis.
To understand what Schrödinger’s statement means, first
consider a process being performed by the particles, where
particle could describe an enzyme, for instance. Let us
assume that we need quantum mechanics to describe the
mechanism of this process. However, the behavior of the
particle—for example, its position or energy levels along a
reaction coordinate—fluctuates randomly and is therefore
unpredictable. The average over many particles washes away
the evidence of quantum mechanics, because we lose the
ability to distinguish the signature of wavelike behavior:
its phase. Schrödinger reasoned that if the number of particles involved in the process is small enough, the quantum
mechanical effects could be preserved from start to end and
could, therefore, play a role in the mechanism. Nowadays, we
know this viewpoint is a bit too simplistic, but it is a useful
way to start thinking about the issue of why we do not usually consider quantum mechanics in biology, even though it
may be relevant.
Schrödinger hypothesized that, as the size of a statistical system diminishes, quantum effects start to appear
­(figure 1). We should define this size not as the physical size
of a molecule or enzyme but, instead, as the size of configuration space that is sampled as we watch a process happen
repeatedly. Configuration space can include the positions
and orientations of reactants and their relative energies,
all of which fluctuate randomly because of thermal effects
(Frauenfelder and Wolynes 1985, Voth and Hochstrasser
1996). Schrödinger’s idea is evident, then, when we reduce
configuration space by confining molecules to isolated
environments. But what about in a biological environment?
To address this issue, we should ask, first, what the nature
of the quantum effect of interest is and, second, how we can
detect it.
The nature of quantum effects in light-harvesting
complexes
Higher plants, algae, and phototropic bacteria use solar
energy to synthesize high-energy molecular species that
power life (Blankenship 2002). More than 10 quadrillion
photons of light strike a leaf each second. Incredibly, almost
every visible photon (those with wavelengths between 400
and 700 nanometers [nm]) is captured by pigments and
initiates the steps of plant growth. Stokes (1887) was puzzled
that mustard seedlings grew equally well whether they were
illuminated with red light or with blue and violet light. He
hypothesized the growth to be more vigorous under blue
BioScience 64: 14–25. © The Author(s) 2013. Published by Oxford University Press on behalf of the American Institute of Biological Sciences. All rights
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doi:10.1093/biosci/bit002
Advance Access publication 5 December 2013
14 BioScience • January 2014 / Vol. 64 No. 1
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Overview Articles
majority of chlorophylls are not found
in the reaction centers but are used
solely for light harvesting. That is, they
absorb sunlight and transfer that energy
through a network of intervening chlorophylls to the reaction centers with
an efficiency approaching 90% (van
Grondelle et al. 1994, van Amerongen
et al. 2000, Blankenship 2002). The
result is that the absorption cross section of the reaction centers is effectively
increased by a factor of 200–300. These
light-harvesting chlorophylls thereby
allow a higher flux of excitation to
arrive at each reaction center than do
the isolated reaction centers.
Enhancing the effective absorption
Figure 1. A depiction of the scales of biological length and complexity, as
cross section of reaction centers is reledescribed in the text. Atomic-scale and, possibly, quantum mechanical effects
vant because, in low to average sunlight,
govern the function of a protein. These details are lost as the system becomes
each chlorophyll receives about 0.1–1
more complex. In that case, certain emergent phenomena or functions are the
excitation per second. With 200 chloroprimary observables.
phylls per photosystem I or II reaction
center, this implies 20–200 excitations
per reaction center per second. Because the turnover time of
and violet illumination, whose wavelengths “act so powerthe electron transfer chain is about 10 milliseconds, the two
fully on most photographic preparations” (p. 279). Stokes
nicely match: The light-harvesting antenna allows the reacreasoned that it is simply photon energy that matters, that
tion centers of photosystem I and photosystem II to opermore-energetic photons result in more favorable growing
ate at their optimal capacity. At the same time, this simple
conditions. What Stokes did not account for was the fact
calculation demonstrates that, at higher light intensities,
that the molecules initiating photosynthesis undergo rapid
the electron transfer chain becomes saturated, which leads
energy relaxation after photoexcitation. The photosynthetic
to unwanted recombination reactions and the formation
apparatus is composed of vast arrays of chlorophyll (or other
of triplet states in the reaction centers and light-harvesting
highly colored) molecules (van Grondelle et al. 1994, Green
chlorophyll molecules. That is a problem particularly in the
and Parson 2003, Scholes et al. 2011). These molecules,
reaction center of photosystem II, something that is avoided
known as chromophores, absorb certain wavelength bands
by basically switching off the light-harvesting antenna in a
of the incident light through their electronic wave function’s
process called nonphotochemical quenching (Demmig-Adams
making a quantum jump from a ground state to an excited
and Adams 1992, Horton and Ruban 1992, Niyogi 2000).
state. The excitation relaxes rapidly to the lowest-energy
Light harvesting is less tangible than many other biological
state of the system, lying in the red region of the spectrum,
processes, but it can still be viewed classically as a hopping
so the extra energy of blue light is lost as heat. This explains
of electronic excitation from one molecule to another in
Stokes’s observation that the mustard seedlings did not
the spirit of a theory reported by Förster in 1948 (see van
grow more vigorously under blue light illumination; when
der Meer et al. 1994 and the citations therein, Scholes 2003,
a blue photon is absorbed, the molecule relaxes rapidly to
Renger 2009, Şener et al. 2011). Electronic excitation therefore
the same state prepared directly by red-light absorption.
executes a random walk among tens to hundreds of molecules
The ­electronic excitation is ultimately transferred to reacin the antenna complexes until it is either trapped by a reaction centers, where it can subsequently drive electron and
tion center or decays to the ground state. Therefore, the effiproton transfer reactions across the thylakoid membrane.
ciency of light harvesting depends on the rate of each energy
Figure 2 depicts the thylakoid membrane in which the photransfer step (hop) compared with the lifetime of the excited
tosynthetic apparatus is located. The resulting stored transstate, which, for chlorophylls, is typically a few nanoseconds.
membrane electrochemical potential drives further chemical
Until the mid-1980s, several theoretical physicists worked
transformations, called dark reactions, to produce energy
on the problem of how excitation energy diffuses through a
rich molecules that serve as fuel.
random walk in a photosynthetic antenna, often represented
Duysens (1951) discovered that there are many more chloby a regular lattice of some kind. A key finding of the work at
rophyll molecules and other accessory pigments than those
that time is that, with a sufficiently fast hopping from one site
in the reaction centers. Reaction center is a term that refers to
to the next, the high trapping efficiency could be explained.
the sites in the pigment–protein complexes at which photoPearlstein (1967) modeled this problem of how excitation
excitation drives electron transfer reactions. In fact, the vast
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Overview Articles
Figure 2. The photosynthetic apparatus associated with the light-dependent reactions of photosynthesis. The energy
transfer pathways involved in photosynthesis are depicted as red arrows, electron transfer pathways as blue arrows, and
the proton transfer pathways as black arrows. For further details, refer to Jon Nield’s Web site (http://macromol.sbcs.qmul.
ac.uk), where the original figure can be found. The thylakoid membrane-bound pigment–protein complexes, photosystem I
and photosystem II, use the energy of an absorbed photon to drive electron transfer reactions. Light-harvesting chlorophyll
molecules act to absorb sunlight and transfer this energy to the reaction center, where the photochemistry takes place. In
photosystem II, the electron transfer reaction is linked to the splitting of water (H2O), creating a proton gradient, which
eventually drives the formation of adenosine triphosphate (ATP). Photosystem I drives a transmembrane electron transfer
reaction, which leads to the reduction of nicotinamide adenine dinucleotide phosphate (NADP+) to NADPH, which is
subsequently linked to carbon fixation. Source: Reprinted from Boeker and van Grondell (2011) with permission from
John Wiley and Sons, copyright (2011). Abbreviations: ADP, adenine dinucleotide phosphate; CF, photosynthetic coupling
factor; Fd, ferredoxin; H, hydrogen; hv, energy from the sun; nm, nanometers; O, oxygen; PC, plastocyanin; Pi, phosphate;
PQH2, dihydroplastoquinone; PQ, plastoquinone; Q, quinone; QH2, plastoquinol.
energy diffuses through a random walk in photosynthetic
antenna complexes. He calculated that for N molecules
arranged in a square lattice, where one of those molecules
is a trap (a reaction center), it takes on average (1/p)N ×
log N jumps to reach the trap, where p is the probability of a
jump. Considering the relatively short excited-state lifetime
of a typical molecule (say, approximately 2 nanoseconds)
and an antenna containing 400 molecules, an energy transfer
jump time of about 300 femtoseconds (fs; 10–15 seconds) is
required to attain a 90% quantum efficiency of trapping at a
reaction center. On the basis of excitation annihilation experiments in which the efficiency for two excitations to meet on
the same site was measured, excitation hopping times of the
same order of magnitude were estimated (Bakker et al. 1983,
den Hollander et al. 1983). Later, transient absorption (Visser
et al. 1995) and fluorescence depolarization (Bradforth et al.
1995) experiments led to very similar estimates. Energy
transfer is therefore an extremely fast process compared with
typical biological functions.
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Spectroscopic experimental results collected over the past
15 years augmented by recent experiments using the new
technique of two-dimensional (2-D) electronic spectroscopy
strongly challenge this description of photosynthetic light
harvesting that uses entirely localized, hopping excitations
moving around incoherently—that is, without any memory of
phase. For detailed reviews and background, see Sundström
(2000), Yang and colleagues (2003), van Grondelle and
Novoderezhkin (2006), Cheng and Fleming (2009), Renger
(2009), Novoderezhkin and van Grondelle (2010), Scholes
(2010), Schlau-Cohen and colleagues (2012a), Scholes and
colleagues (2012). They suggest that, although incoherent
hopping of excitation energy is an excellent first approximation, it is not the whole story. We need to introduce concepts
from quantum mechanics to satisfactorily explain the mechanism. The explanation requires us to resort to this deeper
layer of theory; therefore, photosynthetic light harvesting is
an example of “quantum biology” (Wolynes 2009, Fleming
et al. 2011, Lambert et al. 2013).
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The detection of quantum effects
With the advent of femtosecond spectroscopy, the possibility of exploring quantum mechanical effects (i.e., coherences) in natural photosynthetic complexes became an
experimental reality (Martin and Vos 1992, Fleming and
van Grondelle 1997, Zewail 2000). Some of the earlier work
in this area included the observation of oscillatory intensity
modulations in pump–probe measurements on natural
photosynthetic complexes (Vos et al. 1991, Martin and Vos
1992, Chachisvilis et al. 1994, Savikhin et al. 1997, Arnett
et al. 1999). Although there has been much previous work
in this area, there has been a recent revival in the field since
Engel and colleagues (2007) described evidence for remarkably long-lived electronic coherences after excitation of the
Fenna–Matthews–Olson (FMO) complex. Those observations were facilitated by the experimental spectroscopic
technique of 2-D electronic spectroscopy (2DES), a method
that yields a clearer measurement of dynamic coherences
than other femtosecond spectroscopic experiments. These
experiments stimulated a rapid increase in the number of
theoretical (Mohseni et al. 2008, Caruso et al. 2009, Cheng
and Fleming 2009, Ishizaki and Fleming 2009, Hoyer et al.
2010, Chin et al. 2013, Tiwari et al. 2013) and experimental
(Lee et al. 2007, Collini et al. 2010, Panitchayangkoon et al.
2010, Harel and Engel 2012, Turner et al. 2012, Hildner et al.
2013) studies in which the possible role that coherences may
play in photosynthetic complexes was explored.
To demonstrate how 2DES has been important in providing these new insights, we first describe how this information is manifested in a 2-D spectrum for a model system.
The 2DES experiment uses femtosecond laser pulses to
excite electronic absorption bands of the system being
studied (e.g., a protein dispersed in solution) and monitors
how these excited states change over time. This allows for
information on how energy has been redistributed among
the exited states—for example, by the energy transfer process causing excitation energy to flow from one molecule to
another. In fact, 2DES is very similar to pump–probe spectroscopy, in which a probe pulse arrives at various times after
the pump and is used to examine how an excited-state population has redistributed among the excited states. One main
way in which 2DES differs from pump–probe spectroscopy
is that the pump pulse is spectrally resolved in a 2-D electronic spectrum. For a 2-D spectrum, one can think of the
pump pulse as effectively labeling the system according to
the electronic absorption bands and reporting this labeled
state along the excitation axis, wexcite. Then, after some time,
the waiting time (t2), in which the system is free to evolve,
the probe pulse interacts to effectively “read out” the current
state of the previously labeled system, and that current state
is recorded along the detection axis, wexcite. In this manner, a
frequency–frequency correlation map is generated, on which
each excitation frequency is correlated to each detection
­frequency (Jonas 2003, Cho 2008).
The experimental details for obtaining this frequency–­
frequency correlation map are quite involved and go beyond
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the scope of this article. The following books and review
articles offer a comprehensive account of the experimental
details: Mukamel (2000), Jonas (2003), Cho (2008, 2009),
Hamm and Zanni (2011). Although we do not discuss the
experimental techniques here, we would like to comment on
some of the limitations associated with 2DES before moving
on to the model system. 2DES is based on Fourier transform
techniques and, therefore, requires attosecond (10–18-second)
timing precision and mechanisms for phase stabilization
(for a detailed account of experimental techniques for
overcoming these issues, see Ogilvie and Kubarych 2009).
Therefore, although 2DES can be used to obtain more direct,
unambiguous information regarding the system, one of the
drawbacks of employing this technique is that it is harder to
implement experimentally than pump–probe spectroscopies
are. Another limitation lies in the difficulty of extracting
kinetics from the wealth of information contained in the
2-D spectra. However, progress has been made in this area by
the Ogilvie group (Myers et al. 2010) and the Scholes group
(Ostroumov et al. 2013), who have extended well-established
techniques for extracting kinetics from 1-D pump–probe
spectra to 2-D electronic spectra.
To demonstrate how information can be extracted from
the 2-D spectra, we first consider a model system. The model
system is shown in figure 3, which consists of three identical
chromophores, A, B, and C, in a protein scaffold (e.g., the
chlorin ring of chlorophyll molecules in light-harvesting
pigment–protein complexes). The energy level diagram and
the linear electronic absorption spectrum are also shown in
figure 3. Owing to pigment–protein and pigment–pigment interactions, the three identical chromophores give rise to three
resolvable peaks in the electronic absorption spectrum. The
chromophores lie in different local protein environments,
which leads to shifts in the transition frequencies associated
with the individual chromophores (the site energies). In the
model system, chromophore C is shifted to a higher energy
with respect to chromophores A and B. The electronic structure is further perturbed because of the pigment–pigment
interactions. Chromophores A and B lie in close proximity
to each other and, after photoexcitation, the wave function is
shared coherently over A and B, like a wave that has a specific arrangement of peaks and troughs at the position of the
molecules. This kind of delocalized excited electronic state
is known as a molecular exciton (van Amerongen et al. 2000,
Scholes and Rumbles 2006, Spano 2010).
Schematic representations of two 2-D spectra at different
waiting times are also shown in figure 3. The peaks lying
along the diagonal correspond to the peaks in the linear
spectrum. At early waiting times, before dynamic processes
occur, in figure 3d, the cross-peaks indicate that the corresponding diagonal peaks, a and b, arise from transitions with
common ingredients—common molecular orbitals or a pair
of exciton states. The 2DES experiment uses the properties
of short laser pulse photoexcitation to probe the properties
of the electronic states in light-harvesting complexes. The
femtosecond pulse contains a spectrum of colors that are all
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Overview Articles
Figure 3. A model system consisting of three identical chromophores in a protein scaffold (a) along with the corresponding
linear spectrum (b) and energy level diagram (c). Schematic two-dimensional spectra at t2 = 0 femtoseconds (fs) (d) and
a later waiting time (e). At early waiting times, cross-peaks indicate that the corresponding diagonal peaks are electronic
transitions involving common electronic orbitals. At later waiting times, the appearance of cross-peaks indicates energy
transfer between the different electronic transitions.
in phase. Therefore, it can photoexcite absorption bands in
phase. This gives the cross-peaks in the 2-D spectrum additional properties when the absorption bands have a common character. From these cross-peaks, information, such
as the magnitude of coupling and the relative orientation of
the exciton states, can be extracted (see Schlau-Cohen et al.
2011 and the references therein). These cross-peaks also
have a well-characterized waiting time dependence: Their
amplitudes are modulated as a result of a superposition (i.e.,
quantum coherence) created between the exciton states a
and b (Mukamel 2000, Jonas 2003, Hamm and Zanni 2011).
As t2 increases, the amplitude of these cross-peaks will oscillate at a frequency given by the difference in energy between
the two strongly coupled states. By monitoring these oscillations, which are typically rapidly damped, we can determine
the lifetime of the coherence.
From the schematic spectra at later waiting times, we
see the appearance of cross-peaks among weakly coupled
exciton states. These cross-peaks indicate that energy is
transferred between the corresponding diagonal peaks. In
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figure 3e, the appearance of cross-peaks below the diagonal
indicates that energy is transferred downhill from state c to
states a and b, whereas the appearance of cross-peaks above
the diagonal indicates uphill energy transfer from states a
and b to state c. Monitoring the time-dependent amplitudes
of these cross-peaks thereby allows detailed information on
energy flow pathways to be determined.
These aspects of 2DES were applied to explore a wide
range of photosynthetic complexes (Brixner et al. 2005,
Zigmantas et al. 2006, Engel et al. 2007, Cho 2008, Calhoun
et al. 2009, Schlau-Cohen et al. 2009, 2011, 2012a, 2012b,
Collini et al. 2010, Myers et al. 2010, Panitchayangkoon et al.
2010, Anna et al. 2012, Dostál et al. 2012, Harel and Engel
2012, Lewis and Ogilvie 2012, Turner et al. 2012, Ostroumov
et al. 2013), including electronic energy transfer in reaction
centers (Myers et al. 2010, Schlau-Cohen et al. 2012b), the
chlorosome (Dostál et al. 2012), trimeric photosystem I
(Anna et al. 2012), the FMO complex (Brixner et al. 2005,
Engel et al. 2007, Panitchayangkoon et al. 2010), LH2 (a
bacterial light-harvesting complex; Harel and Engel 2012,
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Figure 4. The linear absorption spectrum of photosystem I trimers from Thermosynechococcus elongatus in the (a)
Qy spectral region along with (b) the 2.5-angstrom resolution crystal structure (Jordan et al. 2001). (c) The chlorophyll
molecules for the monomer are shown and colored according to the site energies from Byrdin and colleagues (2002), which
were calculated on the basis of the structure of photosystem I: blue, 660–665 nanometers (nm); cyan, 665–670 nm; green,
670–675 nm; yellow, 675–680 nm; orange, 680–690 nm; brown, 690–700 nm; red, 700–720 nm. The chromophores that have
an electronic coupling greater than 120 wavenumbers are indicated with shaded ovals (calculated using the point dipole
approximation; see Byrdin et al. 2002 for more details). The ovals with dashed outlines indicated that the chromophores
are found near the lumen surface, and the solid outlines indicate that the chromophores are found near the protoplasmic
surface. (d) Two representative two-dimensional (2-D) electronic spectra (λ, wavelength) at an early and a later waiting
time. (e) The amplitudes for traces taken at the points indicated in the 2-D spectra are plotted as a function of waiting time.
The off-diagonal traces grow in with a time scale of 50 femtoseconds (fs). Source: Adapted from Anna and colleagues (2012).
Ostroumov et al. 2013, Zigmantas et al. 2006), LHCII (plant
light-harvesting complex II; Calhoun et al. 2009, SchlauCohen et al. 2009), and phycobiliproteins (Collini et al. 2010,
Turner et al. 2012). Here, we briefly summarize our recent
results on two different light-harvesting complexes: photosystem I (Anna et al. 2012) and PC645 (phycocyanin-645;
Collini et al. 2010, Turner et al. 2012). Our results for
PC645 illustrate how electronic coherences (superpositions
between different electronic states) are observed by 2DES,
whereas our results on photosystem I demonstrate how
2DES elucidates electronic energy transfer pathways.
is shown along with the linear absorption spectrum that
has contributions from approximately 300 chlorophyll
molecules. Comparing the two 2-D spectra at different
­­
waiting times (figure 4d), we observe a change in the line
shape that indicates that energy is being redistributed among
the chlorophyll molecules and partly transferred from the
higher lying states to the lower lying states. This occurs on a
time scale of approximately 50 fs, which corresponds to the
average time scale for energy equilibration among strongly
coupled chromophores within an exciton manifold (indicated in figure 4c as shaded ovals; Byrdin et al. 2002).
2DES to reveal energy transfer pathways. Our recent results on
2DES to reveal coherence. In 2010, we reported oscillations
isolated photosystem I trimers (from Thermosynechococcus
elongatus) suspended in solution at ambient temperature
are summarized in figure 4. The structure of photosystem I
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found at ambient temperature by performing 2DES experiments on cryptophyte algae antenna complexes (Collini
et al. 2010). The linear absorption spectrum along with the
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Figure 5. (a) The linear absorption and (b) the structure of the cryptophyte light-harvesting antenna complex PC645
from Chroomonas sp. Strain CCMP270. (c) The waiting-time-dependent amplitude (in arbitrary units) of the cross-peak
(indicated with an arrow in the two-dimensional [2-D] electronic spectra). The electronic coherence, determined
from analyzing different contributions to the 2-D electronic spectra, was found to dephase with a time constant of
170 femtoseconds (fs). (d–f) 2-D electronic spectra at three different waiting times recorded at ambient temperature. The
appearance and disappearance of the ­cross-peak is indicated with an arrow. Source: Adapted from Collini and colleagues
(2010) and Turner and colleagues (2011). Abbreviation: THz, terahertz.
structure of one of the cryptophyte (Chroomonas sp.) antenna
complexes, known as PC645, is displayed in figure 5a,
5b. There are eight chromophores contributing to the linear
electronic absorption spectrum, and the electronic transition
frequencies associated with the system are indicated as sticks
in the spectrum. The 2-D spectra at three different waiting
times are displayed in figure 5d–5f, with the cross-peak
between the states that coherently share excitation indicated
with an arrow. The waiting-time-dependent amplitude of the
cross-peak is plotted in figure 5c, where it can be seen that
oscillations persist for hundreds of femtoseconds.
Identifying the electronic coherences has been a challenge, because molecular spectroscopy involves electronic
excitations as well as excitations of the vibrational energy
levels of the molecules. For example, in figure 4a (the linear
absorption spectrum of photosystem I), there are three
resolvable peaks in the linear absorption spectrum, at 590,
625, and 680 nm. The two lower-energy bands are assigned
to the Qy transition and the higher energy band to the Qx.
The peak at 680 nm is assigned to the Qy(0–0) absorption
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band, which is the purely electronic absorption band,
meaning that the vibrational state of the molecule does not
change on excitation. The Qy(0–1) vibronic band at approximately 625 nm arises because the vibrational state of the
molecule changes on electronic excitation. This is just one
example that demonstrates how both vibrational and electronic states of molecules can be explored with electronic
spectroscopy.
Owing to the vibronic nature of the spectroscopy of molecules, on excitation with a short optical laser pulse (with a
broad spectral bandwidth), vibrational wave packets, coherent superpositions between vibrational levels, and possible
electronic superpositions can be prepared (Heller 1981, Bitto
and Huber 1992, Jonas and Fleming 1995, Zewail 2000).
These vibrational frequencies are often quite similar in
magnitude to the difference in energy between the exciton
states, and one of the challenges in 2DES is assigning the
waiting-time-dependent oscillations to vibrational and electronic coherences. It turns out that more-detailed analysis of
2DES can discriminate electronic and vibrational coherences
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(Turner et al. 2011, Butkus et al. 2012). On that basis, it was
concluded that a long-lived electronic coherence ­(having
a dephasing time of 170 fs) contributes to the oscillatory
amplitude of the cross-peak in PC645. Although 170 fs is
incredibly short on the time scale of biology, it is comparable
to the time scale of the most rapid energy transfer processes,
as was seen in the photosystem I example above.
What does coherence do for energy transfer?
To understand why we are interested in coherent superpositions of states—and, particularly, in how long they survive—in these systems, it will help to briefly review how to
think about energy transfer from the perspective of Förster
theory. Electronic energy transfer requires two factors. First,
there needs to be an electronic interaction between pairs of
molecules. Such an interaction is turned on by the absorption of light. Then the transition dipole for deexcitation of
the photoexcited molecule couples to the transition dipole
for excitation of a nearby ground-state molecule, promoting
a radiationless jump of electronic excitation from one molecule to another. This is a quantum mechanical phenomenon,
but the interaction and its distance dependence resemble
the classical electrostatic interaction between two dipoles—
in this case, interaction between the transition dipoles of
the donor and the acceptor (Andrews 1989, Krueger et al.
1998). The second requirement for energy transfer is that
the energy is conserved. In practice, that means that the
fluorescence spectrum of the photoexcited molecule should
overlap in frequency with the absorption spectrum of the
energy acceptor.
The quantum mechanical aspect of light harvesting can
be traced to the assumption in Förster theory that electronic
coupling between the molecules is extremely weak (compared with line broadening). However, the chromophores
(e.g., chlorophyll) in light-harvesting complexes are packed
at a high density. As a consequence, the average centerto-center separation of neighboring molecules is typically
only about 10 angstroms; therefore, the electron couplings
are moderately large. One ramification of this is that several chromophores can act cooperatively in the absorption
and transfer of electronic excitation (Sauer et al. 1996, van
Amerongen et al. 2000, Scholes 2003, Renger 2009). When
chromophores carry electronic excitation cooperatively, it
means not only that there is a good chance of finding the
excitation simultaneously on more than one chromophore
but also that the excitation is spread with a defined amplitude across those molecules. This amplitude factor carries
information on the relative sign of the excitation wave on
each molecule.
What does quantum mechanics do for energy transfer?
The short answer is that it changes the way we think about
the energy jumps in Pearlstein’s random-walk model. Let
us say that there are two pathways for transferring excitation from molecule A to molecule B in a light-harvesting
complex: directly from A to B (PAB) and by way of a third
molecule, C (PACB). Classically, the probability of the energy
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transfer is simply the sum of the probability of taking each
path:
Ptotal = PAB + PACB
In quantum mechanics, however, that probability law is
modified, resulting in the common explanation that both
paths are taken simultaneously. What happens is that the
probability of energy transfer from A to B is calculated differently: We assign a probability amplitude to each path, sum
those amplitudes, then convert the sum to a probability by
taking the modulus squared:
≥total = |AAB + AACB|2
The result of that procedure is that the pathways can interfere, as if we represented each as a wave, then we added those
waves. If the crests of the waves are lined up for the two
paths, constructive interference boosts the energy transfer
rate relative to the classical calculation. The quantum law
reduces to the familiar probability law when we lose the
ability to discriminate the waves—a process called decoherence—or when a system is so intrinsically complex that all
the constructive and destructive interferences cancel on
average—an idea exploited in semiclassical simulations of
dynamics (Miller 2012).
As was discussed in the model system, the 2DES experiment can be used to gain rather direct information on
coherent dynamics. In the model system, we demonstrated
how information on the frequency and lifetime of electronic
coherences among strongly coupled exciton states is manifested in the 2-D spectrum. By monitoring these oscillations,
we can gain insight into the energy transfer mechanisms: If
the oscillations are long lived, the Förster hopping model for
energy transfer breaks down. A question to consider is precisely how to interpret the experimental results to improve
theoretical models that predict the energy transfer mechanism occurring in nature. The question arises because the
2DES experiments are carried out using ultrashort broadband laser pulses, not under natural-light conditions, and the
properties of the incoming laser pulses are known to be able
to influence the experimentally measured outcome (Freed
1972, Brumer and Shapiro 1992, Warren et al. 1993, Zewail
2000). We stress that directly comparing the results obtained
using femtosecond pulses to that of the dynamics that occur
under natural excitation conditions is not a trivial matter. Nevertheless, from the 2DES experiments, we can still
learn much about these natural light-harvesting complexes,
including information on the excited-electronic states, the
coupling strength between chromophores, and how energy
flows among these excited states.
Conclusions
We have shown that 2DES is a spectroscopic technique with
femtosecond time resolution that can be used to gain rather
direct information on electronic energy transfer time scales
January 2014 / Vol. 64 No. 1 • BioScience 21
Overview Articles
Figure 6. Structural models of (a, c) LHCII from peas
(Standfuss et al. 2005); the red molecules are chlorophyll a,
and the blue molecules are chlorophyll b. (b, d) LH2 from
Rhodopseudomonas acidophila strain 10050. Here, the
green bacteriochlorophyll a molecules compose the B850
ring, and the light blue ones compose the B800 ring. The
carotenoids are drawn in gray.
and coherence dynamics, but it can be difficult to appreciate
why these properties observed through 2DES matter. Are
these measured properties that are influenced by the incoming coherent light source relevant in nature? The main point
is that the experiments expose unforeseen properties of the
electronic structure of the antenna complex. Specifically,
those effects that require theoretical models beyond Förster
theory. Biophysicists are interested in these mechanistic
aspects of the process of electronic energy transfer and
how it causes excitation to move among the chromophores.
Understanding how it works, in detail, will help reveal differences between the various light-harvesting complexes
found in nature. For example, there is a striking difference
between the arrangements of molecules in the LH2 complex
from purple bacteria compared with LHCII from higher
plants (figure 6). Why? Does one structure function more
efficiently than the other? Answering such questions will, in
turn, yield guidance for the design of artificial systems for
energy conversion, sensing, or even processing of excitation
energy.
It is possible that the interplay between the coherence and
appropriate vibrational levels of the chromophores could
be beneficial for rapid energy jumps (Kolli et al. 2012, Chin
et al. 2013, Pullerits et al. 2013, Tiwari et al. 2013). One qualitative illustration of the possible role of the protein matrix
22 BioScience • January 2014 / Vol. 64 No. 1
in ultrafast energy and electron transfer can be considered
as follows: In a disordered energy landscape, an excitation
could move from one site to another, but because the roughness of the energy landscape has a molecular length scale,
the localized excitation might be easily trapped and might
be unsuccessful in reaching the reaction center. Suppose that
one specific protein vibrational mode is resonant with the
difference between the electronic energy levels, a mode or
deformation that steers the excitation toward the reaction
center. Then the roughness of the energy landscape would
be overcome. It would be like kicking a football on a rough
playground, and, at the moment the ball is kicked, a channel
opens that moves coherently with the ball to guide it toward
its goal. The interaction between the ball (the excitation)
and the playground (the protein) must be coherent, in the
sense that they travel together, and this would, of course,
dramatically increase the chance of scoring a goal (i.e., the
excitation’s being trapped by the reaction center). In this
way, the long-lived vibrational coherences observed in photosynthetic light-harvesting systems can dramatically affect
the efficiency by which reaction centers trap the excitations
of the surrounding 200 chlorophylls. The challenge is to discover these vibrational modes and how nature has managed
to select them and suppress others.
This article leads to the key question: Coherence is
detected in femtosecond laser experiments used to examine
photoinduced processes in various light-harvesting complexes, but is it exploited in biological function? Because
of the strong interactions between chromophores and the
environment and because the antenna complexes are inherently complex (there are many pathways through space that
the excitation can traverse on its way to the reaction center),
quantum coherent effects should be lost over long lengths
and time scales, but they can have a significant influence on
the initiation of ultrafast processes. The role of coherence
appears to be the way it interplays with incoherent transport
rather than dominating how excitation flows (Chang and
Cheng 2012, Hoyer et al. 2012). These kinds of arguments
indicate that we should not think of quantum coherence as
providing a smoother and more efficient passage of excitation energy through the antenna complex. Instead, we should
inquire how coherence on short length and time scales might
seed some kind of property or function of the system that is
not itself quantum in nature. We have in mind here emergent
phenomena (sensu Anders and Wiesner 2011). Researchers
acquainted with that field will appreciate how difficult it will
be to unravel biological functions to expose the roles played
by quantum effects, and we see this as one of the next big
challenges. The difficulty in pinpointing such an effect lies
in the immense complexity of biological systems.
Acknowledgments
This work was supported by DARPA (the Defense Advanced
Research Project Agency) under the Quantum Effects in
Biological Environments program; the US Air Force Office of
Scientific Research (through grant no. FA9550-10-1-0260);
http://bioscience.oxfordjournals.org
Overview Articles
the Natural Sciences and Engineering Research Council
of Canada (to GDS); Technology Opportunities Program
grant no. 700.58.305 from the Netherlands Organization
for Scientific Research’s Division of Chemical Sciences; and
Advanced Investigator Grant no. 267333 (PHOTPROT)
from the European Research Council (to RvG).
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Jessica M. Anna and Gregory D. Scholes ([email protected]) are
affiliated with the Department of Chemistry at the University of Toronto, in
Ontario, Canada. Rienk van Grondelle is affiliated with the Department of
Biophysics, in the Faculty of Sciences, at VU University (Vrije Universiteit), in
Amsterdam, the Netherlands.
January 2014 / Vol. 64 No. 1 • BioScience 25