Photosynthesis tunes quantum-mechanical mixing of electronic and vibrational states to steer exciton energy transfer

Significance

Photosynthetic light-harvesting antennae transfer energy toward reaction centers with high efficiency, but in high light or oxidative environments, the antennae divert energy to protect the photosynthetic apparatus. For a decade, quantum effects driven by vibronic coupling, where electronic and vibrational states couple, have been suggested to explain the energy transfer efficiency, but questions remain whether quantum effects are merely consequences of molecular systems. Here, we show evidence that biology tunes interpigment vibronic coupling, indicating that the quantum mechanism is operative in the efficient transfer regime and exploited by evolution for photoprotection. Specifically, the Fenna–Matthews–Olson complex uses redox-active cysteine residues to tune the resonance between its excitons and a pigment vibration to steer excess excitation toward a quenching site.

Abstract

Photosynthetic species evolved to protect their light-harvesting apparatus from photoxidative damage driven by intracellular redox conditions or environmental conditions. The Fenna–Matthews–Olson (FMO) pigment–protein complex from green sulfur bacteria exhibits redox-dependent quenching behavior partially due to two internal cysteine residues. Here, we show evidence that a photosynthetic complex exploits the quantum mechanics of vibronic mixing to activate an oxidative photoprotective mechanism. We use two-dimensional electronic spectroscopy (2DES) to capture energy transfer dynamics in wild-type and cysteine-deficient FMO mutant proteins under both reducing and oxidizing conditions. Under reducing conditions, we find equal energy transfer through the exciton 4–1 and 4–2-1 pathways because the exciton 4–1 energy gap is vibronically coupled with a bacteriochlorophyll-a vibrational mode. Under oxidizing conditions, however, the resonance of the exciton 4–1 energy gap is detuned from the vibrational mode, causing excitons to preferentially steer through the indirect 4–2-1 pathway to increase the likelihood of exciton quenching. We use a Redfield model to show that the complex achieves this effect by tuning the site III energy via the redox state of its internal cysteine residues. This result shows how pigment–protein complexes exploit the quantum mechanics of vibronic coupling to steer energy transfer.

Photosynthetic organisms convert solar photons into chemical energy by taking advantage of the quantum mechanical nature of their molecular systems and the chemistry of their environment (1–4). Antenna complexes, composed of one or more pigment–protein complexes, facilitate the first steps in the photosynthesis process: They absorb photons and determine which proportion of excitations to move to reaction centers, where charge separation occurs (4). In oxic environments, excitations can generate highly reactive singlet oxygen species. These pigment–protein complexes can quench excess excitations in these environments with molecular moieties such as quinones and cysteine residues (1, 5–7).

The Fenna–Matthews–Olson (FMO) complex, a trimer of pigment–protein complexes found in the green sulfur bacterium Chlorobaculum tepidum (8), has emerged as a model system to study the photophysical properties of photosynthetic antenna complexes (9–19). Each subunit in the FMO complex contains eight bacteriochlorophyll-a site molecules (Protein Data Bank, ID code: 3ENI) that are coupled to form a basis of eight partially delocalized excited states called excitons (Fig. 1) (20–23). Previous experiments on FMO have observed the presence of long-lived coherences in nonlinear spectroscopic signals at both cryogenic and physiological temperatures (11, 13). The coherent signals are thought to arise from some combination of electronic (24–26), vibrational (16–18), and vibronic (27) coherences in the system (28–30). One previous study reported that the coherent signals in FMO remain unchanged upon mutagenesis of the protein, suggesting that the signals are ground state vibrational coherences (17). Others discuss the role of vibronic coupling, where electronic and nuclear degrees of freedom become coupled (29). Other dimeric model systems have demonstrated the regimes in which these vibronically coupled states produce coherent or incoherent transport and vibronic coherences (31–33). Recent spectroscopic data has suggested that vibronic coupling plays a role in driving efficient energy transfer through photosynthetic complexes (27, 31, 33, 34), but to date there is no direct experimental evidence suggesting that biological systems use vibronic coupling as part of their biological function.

Fig. 1.

(Left) Numbered sites and sidechains of cysteines C353 and C49 in the FMO pigment–protein complex (PDB ID code: 3ENI) (20). (Right) Site densities for excitons 4, 2, and 1 in reducing conditions with the energy transfer branching ratios for the WT oxidized and reduced protein. The saturation of pigments in each exciton denotes the relative contribution number to the exciton. The C353 residue is located near excitons 4 and 2, which have most electron density along one side of the complex, and other redox-active residues such as the Trp/Tyr chain. C353 and C49 surround site III, which contains the majority of exciton 1 density. Excitons 2 and 4 are generally delocalized over sites IV, V, and VII.

It has been shown that redox conditions affect excited state properties in pigment-protein complexes, yet little is known about the underlying microscopic mechanisms for these effects (1, 9). Many commonly studied light-harvesting complexes—including the FMO complex (20), light-harvesting complex 2 (LH2) (35), the PC645 phycobiliprotein (36), and the cyanobacterial antenna complex isiA (37)—contain redox-active cysteine residues in close proximity to their chromophores. As the natural low light environment of C. tepidum does not necessitate photoprotective responses to light quantity and quality, its primary photoprotective mechanism concerns its response to oxidative stress. C. tepidum is an obligate anaerobe, but the presence of many active anoxygenic genes such as sodB for superoxide dismutase and roo for rubredoxin oxygen oxidoreductase (38) suggests that it is frequently exposed to molecular oxygen (7, 39). Using time-resolved fluorescence measurements, Orf et al. demonstrated that two cysteine residues in the FMO complex, C49 and C353, quench excitons under oxidizing conditions (1), which could protect the excitation from generating reactive oxygen species (7, 40–42). In two-dimensional electronic spectroscopy (2DES) experiments, Allodi et al. showed that redox conditions in both the wild-type and C49A/C353A double-mutant proteins affect the ultrafast dynamics through the FMO complex (9, 43). The recent discovery that many proteins across the evolutionary landscape possess chains of tryptophan and tyrosine residues provides evidence that these redox-active residues may link the internal protein behavior with the chemistry of the surrounding environment (41, 43).

In this paper, we present data showing that pigment–protein complexes tune the vibronic coupling of their chromophores and that the absence of this vibronic coupling activates an oxidative photoprotective mechanism. We use 2DES to show that a pair of cysteine residues in FMO, C49 and C353, can steer excitations toward quenching sites in oxic environments. The measured reaction rate constants demonstrate unusual nonmonotonic behavior. We then use a Redfield model to determine how the exciton energy transfer (EET) time constants arise from changing chlorophyll site energies and their system-bath couplings (44, 45). The analysis reveals that the cysteine residues tune the resonance between exciton 4–1 energy gap and an intramolecular chlorophyll vibration in reducing conditions to induce vibronic coupling and detune the resonance in oxidizing conditions. This redox-dependent modulation of the vibronic coupling steers excitations through different pathways in the complex to change the likelihood that they interact with exciton quenchers.

Results

Redox-Dependent Exciton Steering by Cysteine Residues.

We investigate the excitonic pathways that give rise to the different 2DES signals to determine the roles of the cysteine C353 and C49 residues in exciton energy transfer (46). Two-dimensional electronic spectra map the couplings between excitonic states and show how the couplings evolve over time. The excitation energy (x axis) of the system is correlated with the detection energy (y axis) at each waiting time delay T. We can plot the intensity of peaks in the spectra with increased waiting time to observe the kinetic evolution of the exciton populations. For example, a cross-peak below the diagonal can report on energy absorbed at a higher-energy state and detected at a lower-energy state, indicating energy transfer between these states. Fig. 2 shows 2DES spectra taken at 77 K for the FMO wild-type, C353A and C49A single mutants, and C353A/C49A double-mutant samples under both oxidizing and reducing conditions at waiting time T = 1 ps. At later waiting times, the growth of below diagonal cross-peaks, where the excitation energy is greater than the detection energy, indicates that there is downhill EET in the system at subpicosecond rates. Using averaged time traces for each of these spectra, we extract the EET time constants for exciton 4–1, 4–2, and 2–1 energy transfer in each sample (see SI Appendix, Fig. S1 for overview; see SI Appendix for detailed description).

Fig. 2.

Absorptive 2D spectra of the eight FMO samples taken at 77 K at waiting time T = 1 ps under reducing (A–D, Top Row) and oxidizing (E–H, Bottom Row) conditions. In 2DES, the excitation energy of a system is correlated with the detection energy, and the waiting time T indicates the delay time between the pump and probe pulses. Spectra were normalized to the peak amplitude at time T = 0. The three peaks of the diagonal features in each spectrum represent excitons 4, 2, and 1. The growth of cross-peaks below the diagonal indicates downhill EET on the timescale of hundreds of femtoseconds.

Experimental time constant data in Table 1 show that the redox environment determines which pathways the excitation energy takes through the complex. Looking first at wild-type FMO under reducing conditions, we see that τ₄₁, τ₄₂, and τ₂₁ are comparable at 504 ± 12 fs, 408 ± 12 fs, and 455 ± 11 fs, respectively, indicating that exciton 4 is equally likely to transfer energy to exciton 1 through the direct 4–1 or indirect 4–2-1 pathways. The branching ratios representing relative probability of EET for these two pathways are 0.45 and 0.55, respectively (47). When the wild-type FMO is oxidized, τ₄₁ gets slower (1.5 ps), τ₄₂ gets faster (227 fs), and τ₂₁ does not change, indicating that exciton 4 is more likely to transfer energy through the indirect pathway under oxidizing conditions. Under these conditions, the branching ratios for the direct versus indirect pathway become 0.13 and 0.87, respectively. In the 4–2-1 pathway, the excitation is steered to generate higher electron density near the periphery of the system (exciton 2, Fig. 1). The amino acids near this region contain, among other redox-active residues, a Trp-Tyr chain which has been suggested to play a role in the redox-dependent ultrafast dynamics of the FMO complex (9). Given that τ₂₁ does not change, steering the excitation through the 4–2-1 pathway under oxidizing conditions would increase the likelihood of quenching at the cysteine 353 trapping site or charge transfer to the Trp-Tyr chain (SI Appendix, Fig. S12) (43). As shown in previous work (1, 9), we see that the long-time signal amplitudes of the oxidized wild-type complex decay faster than those of the reduced wild-type complex. The signal amplitudes of the oxidized wild-type (WT) complex also decay faster than those of the C353A/C49A double-mutant samples—which decay at similar rates under both redox conditions—indicating that the cysteines are responsible for the observed quenching (SI Appendix, Fig. S13).

Table 1.

Calculated changes made to the FMO Hamiltonian to reproduce the general trends in spectroscopic data (left), and 435 experimental energy transfer time constants for WT (bold), singly mutated, and DM FMO samples under reducing and oxidizing conditions extracted from 2D (right)

	Redfield theory									Experiment
	Site II change, cm−1	Site III change, cm−1	Site IV change, cm−1	Spectral density site II change, S/S0	Spectral density site III change, S/S0	Spectral density site IV change, S/S0	τ21, fs	τ41, fs	τ42, fs	τ21, fs	τ41, fs	τ42, fs
WT reduced	0	0	0	1	1	1	508	499	437	455 ± 11	504 ± 12	408 ± 12
C353A reduced	0	−60	10	1	0.8	1.1	537	1,601	397	544 ± 15	>5000	204 ± 20
C49A reduced	20	0	0	1	1	1	504	535	476	485 ± 13	558 ± 25	537 ± 25
C353A/C49A reduced	20	−60	10	1	0.8	1.1	525	1884	427	567 ± 20	>5000	205 ± 24
WT oxidized	40	120	70	1	1	1	264	1,532	412	439 ± 10	1,480 ± 11	227 ± 11
C353A oxidized	40	60	40	1	0.8	1.2	395	725	398	438 ± 11	853 ± 14	328 ± 14
C49A oxidized	20	20	10	1	1	1	455	504	443	452 ± 9	520 ± 19	524 ± 19
C353A/C49A oxidized	20	−40	−20	1	0.8	1.2	534	988	509	594 ± 17	1,642 ± 21	301 ± 21

The theoretical time constants were calculated using the Model C Redfield model described in the text. The trends in the time constants calculated with our Redfield model are mapped visually in Fig. 3 and SI Appendix, Fig. S4. The experimental time constants were extracted from 2D spectra using the extraction method described in SI Appendix.

Overall, we find that the C353 residue is responsible for exciton steering in reducing conditions, based on the drastic change in time constants in the C353A mutants in reducing conditions. However, we find that both C49 and C353 are active under oxidizing conditions. We observe that the patterns in the time constants are nonmonotonic and, in oxidizing conditions, noncooperative, as one would expect. A detailed analysis of all single- and double-mutant EET time constants can be found in the SI Appendix.

Redfield Model Reveals Vibronic Coupling Mechanism for Controlling Energy Transfer.

To understand the complex, nonmonotonic changes in the time constants for energy transfer as a function of both redox environment and mutation, we employ a Redfield model to show that the FMO protein structure facilitates redox-dependent exciton steering by tuning its resonant coupling with a vibrational mode in bacteriochlorophyll-a. The Redfield equation describes the relaxation of an exciton through the excited states of the complex after second-order perturbation by the system–bath coupling. The rate of energy transfer increases with the spatial overlap of excitons, resonance between the excitonic energy gap and bath oscillations through the spectral density, and the magnitude of coupling between the system and these bath modes (Huang–Rhys factor) (48, 49). An increased Huang–Rhys factor indicates that there is greater system–bath coupling, meaning that the bath more strongly couples to the excitonic states, and increases the rate of EET (48). Details of the model, our modifications to the parameters, and the approximations made in this model can be found in SI Appendix. We varied the pigment site energies and Huang–Rhys factors for bacteriochlorophyll-a sites II, III, and IV. These sites are proximal (within 10 Å) to C353 and C49 and are most likely to be electrostatically perturbed by cysteine mutation and oxidation (20). We use a log-normal spectral density with an added Gaussian curve centered at 260 cm⁻¹ representing coupling to a vibrational mode in bacteriochlorophyll-a (44, 45). The most illustrative energy transfer dynamics maps were for sites III and IV, shown in Fig. 3 B–D. The remaining maps can be found in SI Appendix, Fig. S3. In the maps, the x axis represents the relative change in Huang–Rhys factor for a given site, the y axis represents the change in site energy, the colormap represents the value of the energy transfer time constant as a function of these two variables, and the arrows represent changes upon mutation. Our results represent the only consistent set of changes that reproduce the experimental data. The calculated EET time constants can be found in Table 1. For example, in Fig. 3B the dashed blue line pointing downward from “WT oxidized” to “oC49A” shows that under oxidizing conditions, mutation of the C49 residue lowers the site III energy by 100 cm⁻¹ but does not affect the Huang-Rhys factor, in agreement with the difference in the corresponding calculated time constant in Table 1.

Fig. 3.

Calculated Redfield energy transfer rates of the FMO Hamiltonian upon changing the site energies and degree of system–bath coupling (Huang–Rhys factors, S) for pigments III (A and B) and IV (C and D). The center points (S/S₀ = 1; site energy change $\mathrm{\Delta }\nu$ = 0 cm⁻¹; plotted as red circle) represent the WT FMO in reducing conditions. The blue circles represent WT FMO in oxidizing conditions. (A) Overlap of the distribution of exciton 4–1 energy gaps in FMO with the spectral density for site III, representing relative vibronic coupling with an intramolecular vibration. Increased overlap with the spectral density indicates that the bath can more readily couple the two excitons, which increases the EET rate. (B) Change in the τ₄₁ time constant as site III energy and Huang–Rhys factor is changed. (C and D) Change in the τ₂₁ and τ₄₂ time constants as site IV is changed. The arrows represent how mutation changes each FMO sample. The “o” and “r “prefixes represent the oxidized and reduced parameters, respectively. For the reduced FMO samples, there is no change in the C49A parameters, and the C353A changes are the same as the double-mutant (DM) changes. In every case, the DM is a sum of the two single-mutant vectors. The calculated changes in all parameters and the associated energy transfer constants are shown in Table 1 under “Redfield theory.” The same plots but with arrows plotted as oxidation vectors are shown in SI Appendix.

Our Redfield model reveals that the FMO protein structure modulates different energy transfer rates by tuning its resonant coupling with the vibrational mode centered at 260 cm⁻¹. Fig. 3 A and B shows that when oxidized or reduced FMO is perturbed by mutation, the energy of site III changes such that the distribution of the exciton 4–1 energy gaps shifts in its resonance with the chlorophyll vibration. When site III energy is raised in this FMO Hamiltonian, the exciton 4–1 energy gap decreases. In the WT reduced Hamiltonian, the vibronic coupling between the energy gap distribution and the chlorophyll vibration produces a subpicosecond τ₄₁ time constant (23). The oxidized WT protein has a 120-cm⁻¹ increase in site III energy relative to the reduced WT; the slower time constant reflects the fact that the 4–1 energy gap is detuned from the chlorophyll mode (Fig. 3 A and B). In both oxidizing and reducing conditions, we find that the changes to the system Hamiltonian actually represent cooperative effects between mutations, meaning that the changes to the double mutant are a combination of the changes to the two single mutants (Table 1).

Generally, the effect of oxidation raises the site III energy based on the number of unmutated cysteines present, while the effect of mutation lowers the site III energy (Table 1). Our experimental data showed that τ₄₁ slowed down significantly (>5 ps) when the C353 residue was mutated under reducing conditions, discussed above. In the Redfield model, this change is least perturbatively achieved by lowering the energy of site III by >50 cm⁻¹, which increases the 4–1 energy gap and diminishes the vibronic coupling with the chlorophyll mode, as shown by the arrows representing site mutation in Fig. 3B. The reduced C49A time constants are relatively less changed, so we assume that the site energies for this mutant are roughly equal to the WT reduced parameters. The changes in the reduced double-mutant C49A/C353A parameters are thus exclusively caused by the C353A mutation.

In the oxidized samples, mutating C353 or C49 subsequently lowers the site III energy such that the vibronic resonance with the bacteriochlorophyll-a mode is increased in each single mutant and is decreased cooperatively in the double mutant. In Fig. 3B, we see that the calculated τ₄₁ time constants in the oxidized single mutants are faster than the double mutant because each single mutant is passing through the resonance vibronic coupling region. These changes to site III upon mutation of the oxidized cysteine residues shift the exciton 4–1 energy gap through various magnitudes of vibronic coupling with the intrinsic chlorophyll mode to facilitate steering of energy transfer pathways.

In the reduced FMO complex, the resonance between the 4–1 energy gap and the spectral density demonstrates that the chlorophyll vibration is able to couple the excitonic states and facilitate energy transfer. The cysteine residues manipulate the electronic Hamiltonian of FMO by tuning the degree of vibronic coupling between the exciton 4–1 energy gap and the intramolecular vibration centered at 260 cm⁻¹. The resulting assignments of site changes to the FMO Hamiltonian are supported within the limitations of Redfield theory because the mutations and redox conditions primarily perturb the excitonic Hamiltonian––not the system–bath coupling, as evident from the changes in peak position of the linear absorption spectra (SI Appendix, Fig. S5). In this new mechanism, the system steers the excited-state energy transfer toward quenching sites near the protein periphery in response to potentially dangerous oxic conditions.

Discussion

In this study, we show that redox-active residues in FMO steer energy transfer through different pathways in the complex by tuning the excitonic energy in and out of resonance with a vibrational mode of the pigments. In the oxidized WT protein and the reduced mutated C353A and C353A/C49A proteins, the vibronic coupling is detuned because the site III energy is changed, causing the exciton 4–1 energy gap to shift out of resonant coupling with an intramolecular vibration in the bacteriochlorophyll molecule. In these conditions, the indirect exciton 4–2–1 energy transfer pathway becomes more kinetically favorable than the direct exciton 4–1 pathway, increasing the likelihood of interacting with quenching sites in the protein. The redox-dependent vibronic coupling shown here exemplifies an evolutionary mechanism by which photosynthetic organisms can exploit the quantum mixing between electronic and vibrational states to control excited-state energy transfer dynamics.

Materials and Methods

Experimental Parameters.

Two-dimensional spectra of WT, C353A, C49A, and C535A/C49A FMO under oxidizing and reducing conditions were acquired at 77 K, as described in detail in a previous publication (9). Briefly, we used a cryostat containing liquid nitrogen (Oxford Instruments) to cool the sample to 77 K. To generate a glass, we mixed the protein buffer (CAPS, 20 mM, pH 10.5) with 50% glycerol and loaded the solution into a 200-μm quartz cuvette (Starna) coated with SigmaCote. We generated “oxidizing” conditions by handling the sample in ambient air prior to cooling. To create “reducing” conditions, we added sodium dithionite to a concentration of 10 mM.

For the spectroscopic measurements, using the output of a regenerative amplifier (Coherent Inc. Legend Elite USP, 35 fs, centered at 800 nm), we generated coherent light spanning from 775 to 840 nm via self-phase modulation in 15 psi of argon. The pulse was then temporally compressed to <20 fs using a pulse shaper (Biophotonic Solutions, MIIPS). We acquired 25 2DES spectra for each sample using our single-shot, GRadient Assisted Photon Echo Spectroscopy setup, described in detail elsewhere (50–53). We also collected pump–probe spectra of each sample to phase the data using the projection-slice theorem. We phased each spectrum separately and then averaged them to produce an averaged fully absorptive signal.

Extraction of Kinetic Parameters.

To obtain the time constants τ₂₁, τ₄₂, and τ₄₁ for each FMO sample, we averaged over the diagonal and below diagonal cross-peak signals using a circular window with a 70 cm⁻¹ range. The center points of the circles for each exciton pair were taken from the peaks of the respective linear absorption spectrum. The signals were then normalized, and the normalized diagonal signals were subtracted from the normalized cross-peak signals to remove the bleach recovery contribution. The subtracted signals were then fit to phenomenological kinetic equations for energy transfer. The time constant τ₂₁ was fit with the 2 diagonal and 2–1 cross-peak, and the τ₄₁ and τ₄₂ time constants were fit with the 4 diagonal and 4–1 cross-peak using the 4 diagonal time constant as a fit constraint.

Redfield Energy Transfer Calculations.

We calculated the Redfield energy transfer rates resulting from changing the FMO Hamiltonian. We used the “Model C” FMO Redfield model developed by Kell et al. (45) and their most recent FMO Hamiltonian as listed in ref. 23. Calculated rates using uncorrelated sites were averaged over static disorder with 5,000 Hamiltonians for each site using the same disorder parameters, Huang–Rhys factors, variances, and bath cutoff frequencies as listed in ref. 45. We added a Gaussian line centered at 260 cm⁻¹ with a full width at half maximum of 20 cm⁻¹ to the spectral density of each site. We calculate the energy rates after varying the site energies and Huang–Rhys factors for sites II, III, and IV. We fit to the set of changes for each FMO sample and constrained the set such that mutation and oxidation are consistent for all FMO samples.

Data Availability

Raw data and MATLAB Scripts data have been deposited in Dryad (https://doi.org/10.5061/dryad.0rxwdbrzd).