Abstract
The role of quantum mechanics in biological organisms has been a fundamental question of twentieth-century biology. It is only now, however, with modern experimental techniques, that it is possible to observe quantum mechanical effects in bio-molecular complexes directly. Indeed, recent experiments have provided evidence that quantum effects such as wave-like motion of excitonic energy flow, delocalization and entanglement can be seen even in complex and noisy biological environments (Engel et al 2007 Nature 446 782; Collini et al 2010 Nature 463 644; Panitchayangkoon et al 2010 Proc. Natl Acad. Sci. USA 107 12766). Motivated by these observations, theoretical work has highlighted the importance of an interplay between environmental noise and quantum coherence in such systems (Mohseni et al 2008 J. Chem. Phys. 129 174106; Plenio and Huelga 2008 New J. Phys. 10 113019; Olaya-Castro et al 2008 Phys. Rev. B 78 085115; Rebentrost et al 2009 New J. Phys. 11 033003; Caruso et al 2009 J. Chem. Phys. 131 105106; Ishizaki and Fleming 2009 J. Chem. Phys. 130 234111). All of this has led to a surge of interest in the exploration of quantum effects in biological systems in order to understand the possible relevance of non-trivial quantum features and to establish a potential link between quantum coherence and biological function. These studies include not only exciton transfer across light harvesting complexes, but also the avian compass (Ritz et al 2000 Biophys. J. 78 707), and the olfactory system (Turin 1996 Chem. Sens. 21 773; Chin et al 2010 New J. Phys. 12 065002).
These examples show that the full understanding of the dynamics at bio-molecular length (10 Å) and timescales (sub picosecond) in noisy biological systems can uncover novel phenomena and concepts and hence present a fertile ground for truly multidisciplinary research.
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All contributions to the focus issue are listed and available to read here.
The 'quantum effects and noise in biomolecules' focus issue, motivated by recent developments concerning both experimental and theoretical aspects, collects a select list of research results that explore from a variety of angles the question of whether quantum effects exist in biological systems and, if they do, what possible functional role quantum effects may play.
Thanks to pioneering experiments on exciton transfer [1–3] and subsequent theoretical work linking environmental noise and quantum coherence [4–9], the exploration of this interplay in photosynthetic complexes and the development of relevant spectroscopic techniques represent an emphasis of current research. On the theoretical side, this focus issue reports the work of [13], which explores the detailed mechanisms that underly noise-assisted transport further and applies these to the Fenna–Matthew–Olson (FMO) complex to explain how noise alters the pathways of energy transfer across the complex, suppressing ineffective pathways and facilitating direct ones to the reaction center. Building on this, detailed studies of the external parameters that help maximize the efficiency [14] can then be carried out and understood.
While Chin et al [13] and previous work [4–9] suggests that the fundamental mechanisms underpinning noise-assisted transport are robust, the specific details of the exciton–phonon coupling may result in variations of dynamical features. Indeed, it is expected that the nature of the environmental correlations does play a significant role in the dynamics of the excitation energy transport. In [15], for example, a model for bath-induced electronic transitions is developed and then applied to study the dynamics of electronic dephasing in the FMO complex using two-dimensional Fourier transform electronic spectroscopy. This paper provides evidence that the protein matrix protects coherences by globally correlating fluctuations in transition energies and that the lifetimes of individual coherences are distinct, thus suggesting that the FMO complex has been locally tuned by natural selection to optimize transfer efficiency by exploiting quantum coherence. The effect of spatial correlations on quantum coherent bio-molecular energy transfer is also investigated in detailed and numerically exact studies in [16], where it is shown in a simple toy model of a single donor–acceptor pair that quantum coherent transfer of excitations between bio-molecular chromophores is strongly influenced by spatial correlations of environmental fluctuations. Hossein-Nejad and Scholes [17] study analytically the dynamics of energy transfer and dephasing in a molecular dimer with degenerate energies interacting with an anti-correlated, collective vibrational bath and find that, under the influence of a collective phonon bath, coherence survives longer in systems with weak electronic couplings. Correlated fluctuations may also play a role in the exciton dynamics and spectroscopy of DNA, which is in turn of relevance for an understanding of photodamage (Dijkstra and Tanimura [18]). It also noted in this focus issue that the transport dynamics in networks will not only be affected by dephasing noise, but also by oscillatory perturbations which may lead to enhancement or strong suppression of transport, as in [19, 20].
The energy transfer dynamics in a photosynthetic membrane is another example of current interest that is studied in this focus issue. Empirical findings of an illumination-driven transition in the bio-molecular membrane architecture of the purple bacteria Rhodospirillum photometricum are the motivation for studies of the interplay between excitation kinetics and reaction-center dynamics in purple bacteria reported in [21]. It is suggested that the shift in preferred architectures can be traced back to the interplay between the excitation kinetics and the reaction center dynamics. The net effect is that the bacteria profit from efficient metabolism at low illumination intensities while using dissipation to avoid an oversupply of energy at high illumination intensities. Such findings might depend sensitively on the specifics of the modeling of the system–environment coupling. Hsin et al [22] in turn provide evidence to the contrary in an examination of the excitation transfer dynamics in a single RCLH1PufX core complex dimer and show that the generalized Förster theory provides accurate transfer rates.
The mounting evidence of electronic coherence during excitation energy transfer in photosynthetic antenna complexes has reinvigorated the discussion concerning the role that coherence and entanglement may play in the functionality of these molecular systems. These issues are explored in several papers in this focus issue. The study reported in [23] aims to establish quantitative relationships between the yield of a light-harvesting complex and the distribution of entanglement among its components in the FMO complex and finds that there is an inverse relationship between the quantum efficiency and the average entanglement between distant donor sites. Ishizaki and Fleming [24] explores the quantum entanglement among the chlorophyll molecules in light-harvesting complex II (LHII) and find robust quantum entanglement under physiological conditions for the case of a single elementary excitation. However, spectroscopically detectable delocalized states are entangled states as long as one follows the formal definition of quantum entanglement, and the benefit of considering entanglement measures lies in their potential to more accurately characterize delocalized states [25]. The role of the method of excitation is discussed in [26], and this continues to be subject to lively debate.
One might speculate that the presence of entanglement in light-harvesting complexes may be used to achieve a speed-up analogous to those found in quantum algorithms. To decide this question, Hoyer et al [27] compares the dynamics in light-harvesting systems to the dynamics of quantum walks. For the FMO complex they find that while there is indeed speed-up at short times, it is short lived (70 fs) and hence negligible compared to the total transfer time and long-lived quantum coherences that extend to pico-second timescales. These results suggest that quantum coherent effects in biological systems might be optimized for efficiency or robustness, but not for a possible quantum speed-up [28]. Notably, though, the situation might change in assemblies of, for example, nano-engineered light-harvesting complexes. Indeed, Lloyd and Mohseni [29] suggests that symmetry-enhanced supertransfer of delocalized quantum states might enhance the speed and distance across which energy transfer is possible and may play a role in recent observations of anomalously long diffusion lengths in nano-engineered assembly of light-harvesting complexes [30].
The previous examples were mostly concerned with electronic coherence, but vibrational coherence is also of interest. Indeed, in carotenoids of the LHII complex two-color vibronic coherence spectroscopy can be used to observe long-lived vibrational coherences in the ground electronic state of carotenoid molecules, with decoherence times in excess of 1 ps, as reported in [31]. Here, it is also observed that the vibrational coherence time increases significantly for the carotenoid in the complex, providing further support to suggestions that long-lived electronic coherences in light-harvesting complexes are facilitated by correlated motion of the chromophores and surrounding proteins. Vibrational energy flow may also be affected by quantum effects, which may lead to localization and hence influence biomolecule function, including control of reaction kinetics. The authors of [32] studied these effects and find that simplified treatments based on golden-rule calculations often overestimate the mode-damping rate.
The interplay between theory and experiment will benefit not only from improved theoretical methods and questions, but also depends on the development of more sensitive experimental methods. More information may be extracted, for instance with the help of higher order spectroscopic techniques such as fifth-order two-dimensional electronic spectroscopy. Non-perturbative calculations, for example, show clear patterns that correspond to the electronic structure of one- and two-exciton manifolds of a FMO light-harvesting complex [33]. As reported in [34], the incorporation of the effects of three-exciton correlations in the simulation of population and coherence relaxation dynamics also induces new peaks that are absent or much weaker when the three-exciton variables are factorized and thus aid the interpretation of observations in a recent experiment [1]. In these investigations the response functions are computed from effective equations that neglect the detailed atomistic structure of the systems. Jeon and Cho [35] examine the extent to which a refined and accurate picture is computationally feasible. They present a new computational method that calculates nonlinear response function in the classical limit from a series of classical molecular dynamics simulations, employing a quantum mechanical/molecular mechanical force field and applying it to the two-dimensional IR spectroscopy of carbon monoxide and N-methylacetamide, each solvated in a water cluster.
While excitation energy transport concerns very light quasi-particles, such as excitons, biological systems also depend crucially on the transport of heavier species such as protons to support, for example, proton transfer reactions in enzymes or even ion channels that regulate the flow of particular ions across the cell membrane and are important in a variety of processes, including neuronal communications. Indeed, Bothma et al [36] explore the role of quantum effects in proton transfer reactions in enzymes and examine in some detail whether quantum tunneling can play a role in noisy environments. Vaziri and Plenio [20] explore the related question of whether quantum coherence may exist and play a functional a role in the properties of the selectivity filter of ion channels such as the potassium channel, and they propose several experimental procedures to test this hypothesis.
This issue also reports work on a variety of other topics, including the exploration of the quantization of conformational changes in α-helical proteins [37] and the exploration of an intricate interplay between the quantum Zeno effect and the coherent excitation of radical-ion pairs, which is proposed in [38] to lead to a high angular sensitivity of radical pair reactions, and might be of relevance for the avian compass.
In summary, this focus issue of New Journal of Physics presents a series of complementary analyses of the rich interplay between quantum coherence and decoherence in a wide variety of systems of biological relevance during an interesting period of active research and rapid development. The whole picture is still far from complete and we anticipate that exciting developments lie ahead.