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## investigating fine quantum effects in biological systems: toward a synergy between experimental and theoretical approaches?

#### Paris, FIAP Jean Monnet, Rue Cabanis, 14éme arrondissement

#### Organisers

**Important**:

We have now reached the capacity for attendance in this workshop.

A full program will be provided few weeks before the workshop. Tentatively, we will begin 9 AM on 28th May and finish by 5PM on 30th May.

In the recent years experimental measurements have uncovered fine quantum effects (FQE) in biological systems. These FQE may appear as surprising given the warm soft nature of biological media, as opposed to the cold hard world where quantum effects dominate. The observation of long-lived coherences within photosynthetic antennas at room temperature for hundreds of femtoseconds is one striking example of such FQE. The basic mechanism of energy transfer is described by Forster theory, but researchers have recently discovered important modifications to this theory that help explain the function of light-harvesting proteins.1 Recent 2D electronic spectroscopy experiments, for example, have provided evidence that long-lived quantum coherences can exist in various condensed-phase systems. Such coherences allow the possibility that quantum-mechanical effects might modify the flow of electronic excitations through light-harvesting proteins. The significance of quantum coherence to the mechanism and efficacy of energy transfer hinges on the timescale over which it survives. Up to now, it is not known whether coherent quantum dynamics is critical to make energy transfer highly efficient in large systems.2,3,4 Nevertheless, coherence presents opportunities for controlling energy transfer in multichromophoric assemblies because of the ways it modifies the random hopping mechanism assumed in the Förster model.

Other examples of FQE are given by electron tunneling (ET) between or within proteins. ET are ubiquitous in biology. Depending on the characteristic of the biosystems, ET can proceed through a myriad of competing mechanisms ranging from fully coherent to fully incoherent hopping. Electron transfers between the proteins of the cellular respiratory chains occur over ca. 10-20 Å and are usually assumed to follow the coherent super-exchange mechanism. When some molecular fragment(s) are susceptible to host the electron (or a hole) transiently on the way to the acceptor (donor) site, multistep (incoherent) hopping is likely to be the dominant mechanism. While the Marcus Theory of electron transfer has obtained remarkable successes for rationalizing super-exchange ET, the competition between coherent and incoherent electron transfers remains difficult to handle within this framework. It is a current central subject of research within the bio-chemistry community to probe the occurrence of hopping in biological ET processes. Remarkable experiments have been performed for example on DNA photolyases,5 cryptochromes,6 ribonucleotides reductases or on the photosynthetic reaction center.7 Similarly there are currently attempts to develop ET theories that go beyond the Marcus theory. The concept of "hopping maps"8 or the recent modification of the standard Marcus theory9 to include decoherence effects are examples of these attempts. Like for biological EET, the question of the possibility for biological systems to tune the coherence time lengths for catalytic purposes is an exciting, yet unsolved, perspective. Actually there is no doubt that experimental approaches with high spatial and temporal resolutions will bring fresh information, and also new interrogations, on the importance of coherences in biological ET

A third example of FQE came from the investigation of proton and hydrogen transfers in enzymatic reactions. Accumulating evidences coming from the measurements of kinetic isotope effects on enzymatic rates tend to shown that some enzymes kinetics largely exceeds the semi-classical limit (i.e. the standard Transition State Theory with zero point energy corrections). The persistent deviation of empirical observation led to the incorporation of the quantum mechanical nuclear tunneling into theoretical models. Many different proposals may be found in the literature like the Variational Transition State Theory or the adaptation of the Marcus Theory to hydrogen and proton tunneling. Recent models are mathematically flexible enough to cope with most of experimental rates, even those involving high tunneling contributions, but they also bring important questions about their limitations (like the non-equilibriums effects or the adiabatic vs. non-adiabatic kinetic character of the particle transfer) and the physics they capture.10 Generally speaking these models emphasize the importance of the fluctuations of the donor-acceptor distances and of the dynamics of the protein. It remains On the other hand little attention has been paid to the importance of coherences for this type of processes,11 at least it seems addressed in a different way than for EET and ET processes.

The last decades have seen a deeper and deeper exploration of biological systems up to the point of experimentally highlighting some quantum hallmarks of biological matter. The interpretation of the experimental data and the connections to fine quantum effects like coherences, decoherence, entanglement… is challenging due to the complexity of biological systems. A more detailed understanding of quantum coherent effects in exciton energy transfer, electron or proton/hydrogen atom tunneling demands thorough and comprehensive investigations combining the quantum dynamic theory with structure-based modeling based on quantum chemical calculations and molecular dynamics simulations. Computational approaches have to cope with the fact that biological systems are highly inhomogeneous and are characterized by multiscale dynamics. The workshop will be centered on questions concerning the measurement, prediction, and consequences of coherence in biological processes. It will provide a forum for exchanging ideas between experimental and theoretical approaches. The workshop will start with around half a day devoted to our understanding of coherences and decoherence in physical-chemistry in general. We will then especially focus on the role of the biological environment. How might the complex biological medium comprising protein, water, and ions—and characterized by a multiscale dynamics—wash out quantum effects? Or perhaps preserve them? How realistic do theoretical models need to be? Do we have molecular dynamics simulation tools to investigate such effects with atomic resolution? Are computational studies able to provide data for direct comparison with experiments (and vice versa) ?

Many simulations algorithms have been proposed for investigating the dynamics of multi-state systems in the presence of an environment. In principle, the investigation of coherences and other quantum features of the nuclei should be based on simulations at the quantum-mechanical level. However the complexity of the Time-Dependant Schrödinger equation, or, alternatively the Liouville-Von Neuman equations in the formalism of density matrices, makes the simulation of systems with more than few degrees of freedom intractable. Approximations need to the made to simplify the equations of motion. One possibility is to simulate the system using model Hamiltonians. The latter may calibrated following a bottom-up strategy using spectroscopic or quantum chemistry data. These approaches have been applied with great successes to model exciton energy transfers12,13,14 or enzymatic hydrogen tunneling.15 These methods will clearly continue to provide important understanding of the physics of non-BO processes, in particular given the fact that. We plan various presentations on these approaches during the workshop.

Actually the workshop will tend to insist more atomistic approaches. These approaches present the advantage to provide an atomistic description of non-Born-Oppenheimer processes. In view of the successes of atomistic approaches (for ex. hybrid QM/MM or MM approaches) for investigating the physical bases of enzymatic catalysis in the last decades, it sounds desirable to extend these methodologies for investigating coherences within biological systems. Such an objective however remains extremely challenging for various reasons. First one need to devise simulation algorithms that are based on semi-classical MD simulations but including as much as possible the quantum nature of the degrees of freedoms. The Ehrenfest approach, the Tully's surface hopping scheme are historical approaches of that type. Refined schemes including or coherence/decoherence effects have been proposed like the decay-of-mixing approaches16 or the decoherence-corrected surface hopping17 are promising working frameworks. In the last decade a family of promising mixed quantum-classical Liouville approaches in which both the electron and the nuclei are treated on equal footing have been devised.18,19 So far most applications of these sophisticated simulation algorithms have been applied using model Hamiltonians, and a challenge for the community is now to couple them to on-the-fly evaluations of the Hamiltonian elements by quantum chemistry computations.20 This requires fast and robust quantum chemistry methods for estimating the site energies and the couplings between the quantum states. Many progresses have been made in this direction in the recent years. For example, Hybrid QM/MM techniques combining Density Functional theory (DFT) and Time-dependent DFT to polarizable Molecular Mechanics methods seems to be a promising method for computing energetic and screening effects relevant to biological EET processes.21 For electron transfer reactions, an ensemble of method including the Empirical Valence Bond (EVB) scheme,22,23 the self-consistent-charge Tight-Binding DFT24 the frozen DFT approach,25 the fragment orbital approach26 or the constrained DFT 27,28,29 have appeared in the literature, and are candidates for non-Born-Oppenheimer MD simulations.

## References

**Canada**

Dennis Salahub (University of Calgary) - Organiser

Greg Scholes (University of Toronto) - Organiser & speaker

**Czech Republic**

Jan Rezac (Institute of Organic Chemistry and Biochemistry, Czech Academy of Science, Prague) - Organiser

**France**

Isabelle Demachy (University Paris-Sud, Orsay) - Organiser

Aurélien de la Lande (CNRS-University of Paris-Sud, Orsay ) - Organiser & speaker

**Italy**

Benedetta Mennucci (University of Pisa) - Organiser & speaker

**Spain**

Vicent Moliner (Universitat Jaume I) - Organiser & speaker