Abstract

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.

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.

Figure 1.

A depiction of the scales of biological length and complexity, as described in the text. Atomic-scale and, possibly, quantum mechanical effects govern the function of a protein. These details are lost as the system becomes more complex. In that case, certain emergent phenomena or functions are the primary observables.

Figure 1.

A depiction of the scales of biological length and complexity, as described in the text. Atomic-scale and, possibly, quantum mechanical effects govern the function of a protein. These details are lost as the system becomes more complex. In that case, certain emergent phenomena or functions are the primary observables.

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 and violet illumination, whose wavelengths “act so powerfully on most photographic preparations” (p. 279). Stokes reasoned that it is simply photon energy that matters, that more-energetic photons result in more favorable growing conditions. What Stokes did not account for was the fact that the molecules initiating photosynthesis undergo rapid energy relaxation after photoexcitation. The photosynthetic apparatus is composed of vast arrays of chlorophyll (or other highly colored) molecules (van Grondelle et al. 1994, Green and Parson 2003, Scholes et al. 2011). These molecules, known as chromophores, absorb certain wavelength bands of the incident light through their electronic wave function's making a quantum jump from a ground state to an excited state. The excitation relaxes rapidly to the lowest-energy state of the system, lying in the red region of the spectrum, so the extra energy of blue light is lost as heat. This explains Stokes's observation that the mustard seedlings did not grow more vigorously under blue light illumination; when a blue photon is absorbed, the molecule relaxes rapidly to the same state prepared directly by red-light absorption. The ­electronic excitation is ultimately transferred to reaction centers, where it can subsequently drive electron and proton transfer reactions across the thylakoid membrane. Figure 2 depicts the thylakoid membrane in which the photosynthetic apparatus is located. The resulting stored transmembrane electrochemical potential drives further chemical transformations, called dark reactions, to produce energy rich molecules that serve as fuel.

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.

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.

Duysens (1951) discovered that there are many more chlorophyll molecules and other accessory pigments than those in the reaction centers. Reaction center is a term that refers to the sites in the pigment–protein complexes at which photoexcitation drives electron transfer reactions. In fact, the vast 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 cross section of reaction centers is relevant because, in low to average sunlight, each chlorophyll receives about 0.1–1 excitation per second. With 200 chlorophylls per photosystem I or II reaction center, this implies 20–200 excitations per reaction center per second. Because the turnover time of the electron transfer chain is about 10 milliseconds, the two nicely match: The light-harvesting antenna allows the reaction centers of photosystem I and photosystem II to operate at their optimal capacity. At the same time, this simple calculation demonstrates that, at higher light intensities, the electron transfer chain becomes saturated, which leads to unwanted recombination reactions and the formation of triplet states in the reaction centers and light-harvesting chlorophyll molecules. That is a problem particularly in the reaction center of photosystem II, something that is avoided by basically switching off the light-harvesting antenna in a process called nonphotochemical quenching (Demmig-Adams and Adams 1992, Horton and Ruban 1992, Niyogi 2000).

Light harvesting is less tangible than many other biological processes, but it can still be viewed classically as a hopping of electronic excitation from one molecule to another in the spirit of a theory reported by Förster in 1948 (see van der Meer et al. 1994 and the citations therein, Scholes 2003, Renger 2009, Şener et al. 2011). Electronic excitation therefore executes a random walk among tens to hundreds of molecules in the antenna complexes until it is either trapped by a reaction center or decays to the ground state. Therefore, the efficiency of light harvesting depends on the rate of each energy transfer step (hop) compared with the lifetime of the excited state, which, for chlorophylls, is typically a few nanoseconds.

Until the mid-1980s, several theoretical physicists worked on the problem of how excitation energy diffuses through a random walk in a photosynthetic antenna, often represented by a regular lattice of some kind. A key finding of the work at that time is that, with a sufficiently fast hopping from one site to the next, the high trapping efficiency could be explained. Pearlstein (1967) modeled this problem of how excitation 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.

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).

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, ωexcite. 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, ωexcite. 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 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).

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.

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.

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 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 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, Ostroumov et al. 2013, Zigmantas et al. 2006), LHCII (plant light-harvesting complex II; Calhoun et al. 2009, Schlau-Cohen 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.

2DES to reveal energy transfer pathways. Our recent results on isolated photosystem I trimers (from Thermosynechococcus elongatus) suspended in solution at ambient temperature are summarized in figure 4. The structure of photosystem I 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).

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).

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).

2DES to reveal coherence. In 2010, we reported oscillations found at ambient temperature by performing 2DES experiments on cryptophyte algae antenna complexes (Collini et al. 2010). The linear absorption spectrum along with the 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.

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.

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.

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 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 (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 center-to-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 transfer is simply the sum of the probability of taking each path:  

\begin{equation*} P_{{\rm total}} = P_{{\rm AB}} + P_{{\rm ACB}} \end{equation*}

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:  

\begin{equation*} \Pi _{{\rm total}} = |A_{{\rm AB}} + A_{{\rm ACB}} |^2 \end{equation*}

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 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.

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.

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.

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 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.

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); 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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