Protein&coherence 3

Protein&coherence 3: Includes papers by Cheng and Fleming, Scholes, G., Francesca Fassioli, Alexandra Olaya-Castro, Caruso, F., Mohna Sarovar and Birgitta Whaley.

1.) Dynamics of Light Harvesting on Photosynthesis - Cheng & Fleming

2.) Biophysics: Green quantum computers - Scholes, G. - Unsatisfactory argument relative to comparison between processing in photosynthetic and neural protein.

3.) Limits of quantum speedup in photosynthetic light harvesting - Hoyer, S., Sarovar, M. & Whaley, Birgitta - Argues that coherence in photosynthetic protein is not a search engine but can increase the efficiency and robustness of energy transport.

4.) Entanglement and the entangling power of the dynamics in light harvesting complexes - Caruso, F. et al - Discusses efficacy of quantum entanglement in photosynthetic protein.

5.) Distribution of entanglement in light harvesting complexes and their quantum efficiency - Francesca Fassioli & Alexandra Olaya-Castro - Discusses quantum coherence and entanglement in photosynthetic protein with respect to responses to a variable environment.

1.)

Dynamics of Light Harvesting in Photosynthesis

Cheng, Y. & Fleming, R., University of California, Berkeley

Annual Review of Physical Chemistry, 2009, 60: pp. 241-62, doi:10.1146/annurev.physchem.040808.090259

This article discusses recent experimental advances in modelling and spectroscopic techniques, and their application to the study of electronic excitations involved in light harvesting by photosynthetic protein. These advances are connected to the both Engel (2007) and Collini (2010), who have made observations of long-lasting quantum coherence in photosynthetic systems.

In photosynthesis, peripheral antenna absorb light, and convert it into electronic excitations that are transferred to the reaction centre of the photosynthetic system. Photosynthetic organisms are characterised by a very high light-to-charge conversion efficiency of over 95%. The antennas and the reaction centres are connected by the Fenna-Matthews-Olson (FMO) complex. This is a trimer that comprises three identical subunits, each containing several tightly packed bacteriochlorophyll (BChl) pigments that support delocalised electronically excited states.

In the last decade, evidence has shown that the compact packing of this system means that it cannot be described by traditional classical means. The traditional theory of excitation energy transfer in these proteins did not involve coherence, but this view has proved inadequate, because of the close packing of the pigments. P. Scholes and Fleming (4.) have shown that excitation energy transfer between blocks of excitationally coupled molecules proceeds via delocalised exciton states. Delocalisation here means that the energy of an electron is spread over an extended region. Their model involves excitations delocalised over a small group of molecules.

The photosynthetic complex has dense almost equally spaced exciton levels and strong excitonic coupling. This structure involves the spatial overlap of exciton wave functions, and theory predicts rapid energy transfer between exciton states that have a strong overlap of their wave functions. Ultrafast studies of the antenna complex indicate that equations, known as Redfield equations, are needed to describe the long-lived coherence observed in the Engel et al (2007) experiment. Traditional theories assumed independent fluctuations of energy at different sites, but recent experiments (5.&6.) suggest that correlated energetic fluctuations might be important in pigment-protein complexes.

Ultrafast spectroscopic technology involving three laser pulses has been important for studying excitation energy transfer over time scales measured in femtoseconds. These have revealed delocalised excitations and couplings. The 2D form of srpectroscopy employed here is sensitive to the quantum phase evolution of photosynthetic systems. Quantum beats in the 2D spectra are related to the coherence dynamics of the system being studied. These type of quantum beats were observed in the Engel experiment. The spectroscopic studies are sensitive to the transition dipoles of excitons determined by the pigment arrangement, and the redistribution of the transition dipoles due to the electronic couplings. This process cannot be explained by localised molecular excitation, but only by the redistribution of transition dipole moments, due to the delocalisation of the exciton states.

The excitonic couplings and site energies of excited states in the FMO complex have been used to describe the dynamics of excitation transfer (Brixner et al, 5). Molecular transition dipole moments are redistributed due to the electronic couplings between BChls, and result in different positions and orientations of the dipoles. Brixner et al showed that the energy transport in the system depends on the spatial properties of the excited wave functions, as predicted by Redfield theory. The spatial/energetic nature of the complex allows the excitation to move to the lowest energy state (minima) in two or at most three steps.

Delocalisation states in pigment-protein complexes have been known to exist for some time, but it was only the development of two-dimensional spectroscopy that revealed the relevance of quantum coherence to the function of the complexes. Engel's 2007 study revealed a complex quantum beating pattern at time scales similar to the excitatory energy transfer of the system. It is thus argued that the classical random walk cannot fully describe the dynamics of light harvesting. The strong agreement between the observed beating signal and the beat system predicted from the systems excitonic structure indicates long-lasting quantum coherence.

Excitations are shown to move coherently through the FMO complex. On this basis, Engel et al propose that quantum coherence promotes light harvesting. They propose that the FMO complex runs a quantum search algorithm that is more efficient than a classical system. The algorithm enables a rapid and reversible search for the site that connects to the reaction complex (the minima). Reversibility guards against becoming trapped in a secondary minima, which could happen with a classical system.

Further to this, Fleming et al (4.) observed long-lasting coherence in a photosynthetic reaction centre. This could only be explained by correlations between protein motions that modulate the transition energies of neighbouring chromophores. This suggests that protein environments work to preserve electronic coherence in photosynthetic complexes and thus optimise excitatory energy transfer.

References:-
1.) Collini, Elizabetta et al, (2010) - Coherently wired light harvesting in photosynthetic marine algae at ambient temperature - Nature, 463, pp. 644-7 doi:10.1038/nature08811
2.) Engel, G. et al (2007) - Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems - Nature, 446, pp. 782-6
3.) van Grondelle et al, (2006) - Energy transfer in photosynthesis: experimental insights and quantitative models - Phys. Chem. Phys, 8: pp. 793-807 4.) Scholes, G. & Fleming, R., (2005) - Energy transfer and photosynthetic light harvesting - Adv. Chem. Phys., 132: pp. 57-130
5.) Brixner, T. et al, (2005) - Two-dimensional spectroscopy of electronic couplings in photosynthesis - Nature, 434: 625-628
6.) Lee, H., Cheng, Y. & Fleming, R., (2007) - Coherence dynamics in photosynthesis: protein protection of excitonic coherence - Science, 316: pp. 1462-65
7.) Renger, T. et al, (2007) - Refinement of the structural model of a pigment-protein complex - Journal Phys. Chem. B, 111: pp. 10487-501

2.)

Biophysics: Green quantum computers

Gregory Scholes, Centre for Quantum Information, University of Toronto

Nature Physics, 6, 402-403, 2010

In the photosynthetic systems of plants, algae and bacteria several proteins work together to convert solar energy. The process of photosynthesis has been central to the development of life on Earth. The Fenna-Matthews-Olson (FMO) complex is important in the photosynthetic processing of green sulphur bacteria. The FMO complex wires energy between two key areas. The first of these is an antenna for capturing sunlight and transiently storing this energy in excited chlorophyll molecules. These are described in this article as 'electron waves dancing in the confines of a molecule'. The other key area is a reaction-centre protein, similar to those also found in purple bacteria. The energy of photons from the sun is carried through the light harvesting protein to the seven bacteriochlorophyll molecules that are in each FMO complex before going to the reaction centre.

Recent experiments suggested that quantum coherence causes molecules to work collectively, and thus facilitate energy transfer. Sarovar et al suggested that this system might utilise quantum entanglement, where a change in the quantum state of one particle affects the quantum states of others at a distance. Entanglement is suggested to be related to the extent that excited electrons are delocalised. They predict that this entanglement persists over most of the life of the excited state. This is also stated to be true of purple bacteria. It is suggested here that entanglement might speed up the transfer of energy to the reaction centre, and in particular avoid trap states that prevent energy reaching the reaction centre.

The discussion towards the end of the article relative to the possibility that this type of quantum processing in protein might have implications for brain processing is perhaps predictably unsatisfactory given the general unpopularity of this topic, and a suspicion that associations with quantum consciousness could be a threat to funding. The assumption here appears to be a steam age one, where the brain has to be interpreted only in terms of large scale components, as originally described in 19^th century science. The main argument against relevance to brain processing is supposed to be that the photosynthetic systems described take place on a nanometre scale of size and picosecond scale of time. However, these are exactly the sort of scales that are relevant to processing within neurons, making the argument presented here appear irrelevant.

3.)

Limits of quantum speedup in photosynthetic light harvesting

Hoyer, S., Sarovar, M. & Whaley, Birgitta

Berkeley Quantum Information and Computation Centre & Dept. of Physics

arXiv:0910.1847v2 [quant-ph]

This paper deals with the Fenna-Matthews-Olson (FMO) complex found in green sulphur bacteria. There have been suggestions that quantum coherence in light-harvesting complexes supports a speed up in information processing analogous to quantum algorithms. However, this paper tries to show that the speed up in processing lasts for only 70 femtoseconds compared to quantum coherence that persists for about 500 femtoseconds.

Recent experiments have shown that there is long-lived quantum coherence in some photosynthetic systems, and there are suggestions that this coherence plays a role in the functioning of the system. The FMO complex acts as a quantum wire transporting excitations from a large disordered antennae complex to the reaction centre. Recent experimental studies have suggested that quantum coherence in this system may assist transport along this wire, and add to the overall efficiency of the system. The FMO complex comprises three identical sub-units each comprised of seven bacteriochlorophyll molecules in a protein cage. There are dipolar couplings between the seven chromophore molecules. In these light-harvesting complexes decoherence results from interactions with the protein cage, the reaction centre and the surrounding environment. However, it has been shown that some degree of dephasing or fluctuation of electronic transition energies increases the efficiency of transport in the FMO complex.

Conclusion: The conclusion of the paper is that quantum speed up requires both long-lived quantum coherence and excitons delocalised as a wave form across the entire complex, whether photosynthetic or artificial, as in the case of a manmade quantum computer. Such completely delocalised excitons do not exist in the FMO complex, and are thought unlikely to exist in other light harvesting complexes. The transfer of energy across the FMO complexes is not viewed by the authors as a quantum search. It is considered more likely that long-lived quantum coherence contributes to the overall efficiency and robustness, as in the ability to cope with variations in external conditions. In the LH2 complex of purple bacteria quantum coherence has been shown to enhance both the speed and robustness of energy transport.

4.)

Entanglement and the entangling power of the dynamics in light harvesting complexes

Caruso, F. et al, Imperial College

arXiv:0912.0122v1 [quant-ph] (2010)

This paper studies the evolution of quantum entanglement during exciton energy transfer (EET) in the Fenna-Matthews-Olson (FMO) complex in sulphur bacteria. In these bacteria energy from sunlight has to be transferred from antennae that collect it to the reaction centre which changes it into chemical energy. The efficiency of this energy transfer through light harvesting complexes, such as the FMO or a similar structure in other organisms known as the LH-1, is surprisingly high at 99%. In recent studies, such as Engel (2007), evidence of quantum coherence has been found in these structures, and it has been suggested that this could have a role in the high efficiency of energy transfer. Surprisingly the tendency for quantum states to decohere in the environment and the random noise of the environment is thought to play a positive role in energy transport.

Light harvesting complexes such as the FMO consist of several chromophore molecules coupled to one another by dipolar interactions, and situated within a protein scaffold. Sun light induced excitations on individual chromophores can undergo quantum coherent transfer from site to site and are thus delocalised as a wave form over multiple chromophore molecules. Quantum coherence is a necessary but not sufficient condition for the existence of quantum entanglement.

Efficient exciton energy transfer in light harvesting complexes is traced to the interplay between quantum coherent and incoherent processes, with the quantum correlations that are characteristic of coherence partially suppressed by noise, but not completely destroyed. The interplay between entanglement over short distances and times followed by the destruction of entanglement over longer distances and times is seen as necessary for optimal energy transport.

From the point of view of consciousness studies, there is an interesting contrast between the mixed coherent/incoherent systems discussed here, which appear to be functional in photosynthetic protein, and the insistence that any decoherence in the brain is a sudden death as far as the efficacy of quantum states is concerned. We may have to await further clarification of this.

5.)

Distribution of entanglement in light harvesting complexes and their quantum efficiency

Francesca Fassioli & Alexandra Olaya-Castro, Oxford University, University College London

arXiv:1003.3610v1 [quant-ph]

This paper suggests that electronic quantum coherence amongst distance donors could allow precise modulation of the light harvesting function. Photosynthesis is remarkable for the near 100% efficiency of energy transfer. The spatial arrangement of the pigment molecules and their electronic interaction is known to relate to this efficiency.

Recent experimental studies of photosynthetic protein have shown that it can sustain quantum coherence for longer than previously expected, and that this can happen at the normal temperature of biological processes. This has been taken to imply that quantum coherence may affect light harvesting processes. In photosynthesis, the energy of sunlight is transferred to a reaction centre with near 100% efficiency. The spatial arrangement of pigment molecules and their electronic interactions is known to be involved with this high efficiency. There is an implication that quantum coherence may affect the light harvesting process.

Some studies point to very efficient energy transport as the optimal result of the interplay of quantum coherent with decoherent mechanisms. Roles proposed for quantum coherence vary between avoidance of energy traps that are not at the overall lowest energy level, and actual searches for the overall lowest energy level. In this paper, it is suggested that the function of quantum coherence goes beyond efficiency of energy transport, and includes the modulation of the photosynthetic antennae complexes to deal with variations in the environment.

Role of quantum entanglement: There is some debate as to whether quantum entanglement plays a role in the functioning of the light-harvesting complexes, or is just a by-product of quantum states. The authors argue that entanglement may be involved in the efficiency of the system, and they use the FMO protein in green sulphur bacteria as the basis of their study. They suggest that entanglement could play a role in light-harvesting by allowing precise control of the rate at which excitations are transferred to the reaction centre. Interplay between quantum coherent and incoherent processes is also noticed, with one state being more or less efficient than the other depend on the type of coupling to the environment.

Long-lived quantum coherence: Long-range quantum correlations have been suggested to be important as a mechanism helping quantum coherence to survive at the high temperatures sustained in light harvesting antennae. Electronic coherence is distributed amongst pigment molecules, and it is suggested that it may adjust energy transport properties in relation to light intensity. This paper claims to show that in the FMO complex long-lived quantum coherence is spatially distributed in such a way that entanglement between pairs of molecules controls the efficiency profile needed to cope with variations in the environment. The ability to control energy transport under varying environmental conditions is seen as crucial for the robustness of photosynthetic systems. A mechanism involving quantum coherence and entanglement might be effective in controlling the response to different light intensities.

Consciousness: From the point of view of consciousness studies, the discussion in this paper might suggest greater caution in proposing simplistic dismissals of the possible influence of quantum coherence in neural tissues. This paper indicates the possibility that quantum entanglement helps to sustain coherence at biological temperatures, and also that fluctuations between coherent and decoherent mechanisms may be important within the same system.