The fundamental role of quantized vibrations in coherent light harvesting by cryptophyte algae

Quantum mechanics of excitation transport in photosynthetic complexes: a key issues review

For a long time microscopic physical descriptions of biological processes have been based on quantum mechanical concepts and tools, and routinely employed by chemical physicists and quantum chemists. However, the last ten years have witnessed new developments on these studies from a different perspective, rooted in the framework of quantum information theory. The process that more, than others, has been subject of intense research is the transfer of excitation energy in photosynthetic light-harvesting complexes, a consequence of the unexpected experimental discovery of oscillating signals in such highly noisy systems. The fundamental interdisciplinary nature of this research makes it extremely fascinating, but can also constitute an obstacle to its advance. Here in this review our objective is to provide an essential summary of the progress made in the theoretical description of excitation energy dynamics in photosynthetic systems from a quantum mechanical perspective, with the goal of unifying the language employed by the different communities. This is initially realized through a stepwise presentation of the fundamental building blocks used to model excitation transfer, including protein dynamics and the theory of open quantum system. Afterwards, we shall review how these models have evolved as a consequence of experimental discoveries; this will lead us to present the numerical techniques that have been introduced to quantitatively describe photo-absorbed energy dynamics. Finally, we shall discuss which mechanisms have been proposed to explain the unusual coherent nature of excitation transport and what insights have been gathered so far on the potential functional role of such quantum features.

Coherent Exciton Dynamics in the Presence of Underdamped Vibrations

Recent ultrafast optical experiments show that excitons in large biological light-harvesting complexes are coupled to molecular vibration modes. These high-frequency vibrations will not only affect the optical response, but also drive the exciton transport. Here, using a model dimer system, the frequency of the underdamped vibration is shown to have a strong effect on the exciton dynamics such that quantum coherent oscillations in the system can be present even in the case of strong noise. Two mechanisms are identified to be responsible for the enhanced transport efficiency: critical damping due to the tunable effective strength of the coupling to the bath, and resonance coupling where the vibrational frequency coincides with the energy gap in the system. The interplay of these two mechanisms determines parameters responsible for the most efficient transport, and these optimal control parameters are comparable to those in realistic light-harvesting complexes. Interestingly, oscillations in the excitonic coherence at resonance are suppressed in comparison to the case of an off-resonant vibration.

Vibronically coherent speed-up of the excitation energy transfer in the Fenna-Matthews-Olson complex

We show that underdamped molecular vibrations fuel the efficient excitation energy transfer in the Fenna-Matthews-Olson molecular aggregate under realistic physiological conditions. By employing an environmental fluctuation spectral function derived from experiments, we obtain numerically exact results for the exciton quantum dynamics in the presence of underdamped vibrationally coherent quantum states. Assuming the prominent 180-cm(-1) vibrational mode to be underdamped, additional coherent transport channels for the excitation energy transfer open up and we observe an increase of the transfer speed towards the reaction center by up to 24%.

Limits and potentials of quantum chemical methods in modelling photosynthetic antennae

A critical overview of quantum chemical approaches to simulate the light-harvesting process in photosynthetic antennae is presented together with a perspective on the developments that need to be introduced to reach a quantitative predictive power.

Constrained geometric dynamics of the Fenna-Matthews-Olson complex: the role of correlated motion in reducing uncertainty in excitation energy transfer

The trimeric Fenna-Mathews-Olson (FMO) complex of green sulphur bacteria is a well-studied example of a photosynthetic pigment-protein complex, in which the electronic properties of the pigments are modified by the protein environment to promote efficient excitonic energy transfer from antenna complexes to the reaction centres. By a range of simulation methods, many of the electronic properties of the FMO complex can be extracted from knowledge of the static crystal structure. However, the recent observation and analysis of long-lasting quantum dynamics in the FMO complex point to protein dynamics as a key factor in protecting and generating quantum coherence under laboratory conditions. While fast inter- and intra-molecular vibrations have been investigated extensively, the slow, conformational dynamics which effectively determine the optical inhomogeneous broadening of experimental ensembles has received less attention. The following study employs constrained geometric dynamics to study the flexibility in the protein network by efficiently generating the accessible conformational states from the published crystal structure. Statistical and principle component analyses reveal highly correlated low frequency motions between functionally relevant elements, including strong correlations between pigments that are excitonically coupled. Our analysis reveals a hierarchy of structural interactions which enforce these correlated motions, from the level of monomer-monomer interfaces right down to the α-helices, β-sheets and pigments. In addition to inducing strong spatial correlations across the conformational ensemble, we find that the overall rigidity of the FMO complex is exceptionally high. We suggest that these observations support the idea of highly correlated inhomogeneous disorder of the electronic excited states, which is further supported by the remarkably low variance (typically <5%) of the excitonic couplings of the conformational ensemble.

Different Types of Vibrations Interacting with Electronic Excitations in Phycoerythrin 545 and Fenna-Matthews-Olson Antenna Systems

The interest in the phycoerythrin 545 (PE545) photosynthetic antenna system of marine algae and the Fenna-Matthews-Olson (FMO) complex of green sulfur bacteria has drastically increased since long-lived quantum coherences were reported for these complexes. For the PE545 complex, this phenomenon is clearly visible even at ambient temperatures, while for the FMO system it is more prominent at lower temperatures. The key to elucidate the role of the environment in these long-lived quantum effects is the spectral density. Here, we employ molecular dynamics simulations combined with quantum chemistry calculations to study the coupling between the biological environment and the vertical excitation energies of the bilin pigment molecules in PE545 and compare them to prior calculations on the FMO complex. It is found that the overall strength of the resulting spectral densities for the PE545 system is similar to the experiment-based counterpart but also to those in the FMO complex. Molecular analysis, however, reveals that the origin for the spectral densities in the low frequency range, which is most important for excitonic transitions, is entirely different. In the case of FMO, this part of the spectral density is due to environmental fluctuations, while, in case of PE545, it is essentially only due to internal modes of the bilin molecules. This finding sheds new light on possible explanations of the long-lived quantum coherences and that the reasons might actually be different in dissimilar systems.

Quantum Coherence in Photosynthesis for Efficient Solar Energy Conversion

The crucial step in the conversion of solar to chemical energy in Photosynthesis takes place in the reaction center where the absorbed excitation energy is converted into a stable charge separated state by ultrafast electron transfer events. However, the fundamental mechanism responsible for the near unity quantum efficiency of this process is unknown. Here we elucidate the role of coherence in determining the efficiency of charge separation in the plant photosystem II reaction centre (PSII RC) by comprehensively combining experiment (two-dimensional electronic spectroscopy) and theory (Redfield theory). We reveal the presence of electronic coherence between excitons as well as between exciton and charge transfer states which we argue to be maintained by vibrational modes. Furthermore, we present evidence for the strong correlation between the degree of electronic coherence and efficient and ultrafast charge separation. We propose that this coherent mechanism will inspire the development of new energy technologies.

Enhancement of vibronic and ground-state vibrational coherences in 2D spectra of photosynthetic complexes

A vibronic-exciton model is applied to investigate the recently proposed mechanism of enhancement of coherent oscillations due to mixing of electronic and nuclear degrees of freedom. We study a dimer system to elucidate the role of resonance coupling, site energies, vibrational frequency and energy disorder in the enhancement of vibronic-exciton and ground-state vibrational coherences, and to identify regimes where this enhancement is significant. For a heterodimer representing two coupled bachteriochloropylls of the FMO complex, long-lived vibronic coherences are found to be generated only when the frequency of the mode is in the vicinity of the electronic energy difference. Although the vibronic-exciton coherences exhibit a larger initial amplitude compared to the ground-state vibrational coherences, we conclude that, due to the dephasing of the former, both type of coherences have a similar magnitude at longer population time.

Coherent Oscillations in Chlorosome Elucidated by Two-Dimensional Electronic Spectroscopy

Chlorosomes are the most efficient photosynthetic light-harvesting complexes found in nature and consist of many bacteriochlorophyll (BChl) molecules self-assembled into supramolecular aggregates. Here we elucidate the presence and the origin of coherent oscillations in chlorosome at cryogenic temperature using 2D electronic spectroscopy. We observe coherent oscillations of multiple frequencies superimposed on the ultrafast amplitude decay of 2D spectra. Comparison of oscillatory features in the rephasing and nonrephasing 2D spectra suggests that an oscillation of 620 cm(-1) frequency arises from electronic coherence. However, this coherent oscillation can be enhanced by vibronic coupling with intermolecular vibrations of BChl aggregate, and thus it might originate from vibronic coherence rather than pure electronic coherence. Although the 620 cm(-1) oscillation dephases rapidly, the electronic (or vibronic) coherence may still take part in the initial step of energy transfer in chlorosome, which is comparably fast.

Photosynthetic light harvesting: excitons and coherence

Photosynthesis begins with light harvesting, where specialized pigment-protein complexes transform sunlight into electronic excitations delivered to reaction centres to initiate charge separation. There is evidence that quantum coherence between electronic excited states plays a role in energy transfer. In this review, we discuss how quantum coherence manifests in photosynthetic light harvesting and its implications. We begin by examining the concept of an exciton, an excited electronic state delocalized over several spatially separated molecules, which is the most widely available signature of quantum coherence in light harvesting. We then discuss recent results concerning the possibility that quantum coherence between electronically excited states of donors and acceptors may give rise to a quantum coherent evolution of excitations, modifying the traditional incoherent picture of energy transfer. Key to this (partially) coherent energy transfer appears to be the structure of the environment, in particular the participation of non-equilibrium vibrational modes. We discuss the open questions and controversies regarding quantum coherent energy transfer and how these can be addressed using new experimental techniques.

Non-classicality of the molecular vibrations assisting exciton energy transfer at room temperature

Advancing the debate on quantum effects in light-initiated reactions in biology requires clear identification of non-classical features that these processes can exhibit and utilize. Here we show that in prototype dimers present in a variety of photosynthetic antennae, efficient vibration-assisted energy transfer in the sub-picosecond timescale and at room temperature can manifest and benefit from non-classical fluctuations of collective pigment motions. Non-classicality of initially thermalized vibrations is induced via coherent exciton-vibration interactions and is unambiguously indicated by negativities in the phase-space quasi-probability distribution of the effective collective mode coupled to the electronic dynamics. These quantum effects can be prompted upon incoherent input of excitation. Our results therefore suggest that investigation of the non-classical properties of vibrational motions assisting excitation and charge transport, photoreception and chemical sensing processes could be a touchstone for revealing a role for non-trivial quantum phenomena in biology.

Molecular basis of the exciton–phonon interactions in the PE545 light-harvesting complex

A fully polarizable QM/MM approach is used in combination with classical MD simulations to predict the pigment-dependent spectral densities of the PE545 antenna complex and account for their effects on the exciton dynamics.

Toward Ab Initio Optical Spectroscopy of the Fenna-Matthews-Olson Complex

We present progress toward a first-principles parametrization of the Hamiltonian of the Fenna-Matthews-Olson pigment-protein complex, a molecule that has become key to understanding the role of quantum dynamics in photosynthetic exciton energy transfer. To this end, we have performed fully quantum mechanical calculations on each of the seven bacteriochlorophyll pigments that make up the complex, including a significant proportion of their protein environment (more than 2000 atoms), using linear-scaling density functional theory exploiting a recent development for the computation of excited states. Local pigment transition energies and interpigment coupling between optical transitions have been calculated and are in good agreement with the literature consensus. Comparisons between simulated and experimental optical spectra point toward future work that may help to elucidate important design principles in these nanoscale devices.

Disentangling electronic and vibronic coherences in two-dimensional echo spectra

The prevalence of long-lasting oscillatory signals in two-dimensional (2D) echo spectroscopy of light-harvesting complexes has led to a search for possible mechanisms. We investigate how two causes of oscillatory signals are intertwined: (i) electronic coherences supporting delocalized wavelike motion and (ii) narrow bands in the vibronic spectral density. To disentangle the vibronic and electronic contributions, we introduce a time-windowed Fourier transform of the signal amplitude. We find that 2D spectra can be dominated by excitations of pathways which are absent in excitonic energy transport. This leads to an underestimation of the lifetime of electronic coherences by 2D spectra.

Photodegradation of human growth hormone: a novel backbone cleavage between Glu-88 and Pro-89

The exposure of protein pharmaceuticals to light can cause loss of potency, oxidation, structural changes and aggregation. To elucidate the chemical pathways of photodegradation, we irradiated human growth hormone (hGH) at λ = 254 nm, λ ≈ 265-340 nm, and λ ≈ 295-340 nm (using the spectral cutoff of borosilicate glass) and analyzed the products by mass spectrometry. By means of LC-MS/MS analysis, we observed an unusual peptide backbone cleavage between Glu-88 and Pro-89. The crystal structure of hGH indicates that these residues are in proximity to Trp-86, which likely mediates this backbone cleavage. The two cleavage fragments observed by MS/MS analysis indicate the loss of CO from the amide bond and replacement of the Glu-C(═ O)Pro bond with a Glu-H bond, accompanied by double bond formation on proline. The reaction is oxygen-independent and likely involves hydrogen transfer to the Cα of Glu-88. To probe the influence of the protein fold, we irradiated hGH in its unfolded state, in 1:1 (v/v) acetonitrile/water, and also the isolated tryptic peptide Ile-78-Arg-90, which contains the Glu-88-Pro-89 sequence. In both cases, the cleavage between Glu-88 and Pro-89 was largely suppressed, while other cleavage pathways became dominant, notably between Gln-84 and Ser-85, as well as Ser-85 and Trp-86.

The FMO complex in a glycerol-water mixture

Experimental findings of long-lived quantum coherence in the Fenna-Matthews-Olson (FMO) complex and other photosynthetic complexes have led to theoretical studies searching for an explanation of this unexpected phenomenon. Extending in this regard our own earlier calculations, we performed simulations of the FMO complex in a glycerol-water mixture at 310 K as well as 77 K, matching the conditions of earlier 2D spectroscopic experiments by Engel et al. The calculations, based on an improved quantum procedure employed by us already, yielded spectral densities of each individual pigment of FMO, in water and glycerol-water solvents at ambient temperature that compare well to prior experimental estimates. Due to the slow solvent dynamics at 77 K, the present results strongly indicate the presence of static disorder, i.e., disorder on a time scale beyond that relevant for the construction of spectral densities.

Exploiting Structured Environments for Efficient Energy Transfer: The Phonon Antenna Mechanism

A nontrivial interplay between quantum coherence and dissipative environment-driven dynamics is becoming increasingly recognized as the key for efficient energy transport in photosynthetic pigment-protein complexes, and converting these biologically inspired insights into a set of design principles that can be implemented in artificial light-harvesting systems has become an active research field. Here we identify a specific design principle, the phonon antenna, by which interpigment coherence is able to modify and optimize the way that excitations spectrally sample their local environmental fluctuations. We provide numerical simulations that suggest that the Fenna-Matthews-Olson complex of green sulfur bacteria has an excitonic structure that is close to such an optimal operating point, and place the phonon antenna concept into a broader context that leads us to conjecture that this general design principle might well be exploited in other biomolecular systems.

Spatial and Electronic Correlations in the PE545 Light-Harvesting Complex

The recent discovery of long-lasting quantum coherence effects in photosynthetic pigment-protein complexes has challenged our view of the role that protein motions play in light-harvesting processes. Several groups have suggested that correlated fluctuations involving the pigments site energies and couplings could be at the origin of such unexpected behavior. Here we combine molecular dynamics simulations with quantum mechanics/molecular mechanics calculations to analyze the degree of correlated fluctuations in the PE545 complex of Rhodomonas sp. strain CS24. We find that correlations between the motions of the chromophores, which are significantly assisted by the water solvent, do not translate into appreciable site energy correlations but do lead to significant cross-correlations of energies and couplings. Such behavior, not observed in a recent study on the Fenna-Mathews-Olson complex, seems to provide phycobiliproteins with an additional fundamental mechanism to control quantum coherence and light-harvesting efficiency compared with chlorophyll-containing complexes.