## Final Report Summary - PINADBIO (First principles study of photoinduced non-adiabatic dynamics in DNA repair by photolyases)

Photolyases are proteins capable of reusing the energy from sunlight to repair DNA damages due to the ultraviolet light from the sun. Understanding the mechanisms at play during the repair process in the photolyases is of major concern for designing new approaches to prevent from DNA damages and sunburns. Experimental studies cannot access the (microscopical) level of details in the repair mechanisms that is accessible by theoretical approaches. Understanding the repair process at the microscopical level is crucial to understand the factors governing the repair efficiency. PINADBio project aims at developing and using complementary theoretical tools in this task. In other words, during the three year of the research the researcher and scientist in charge have, with the help of the overseas scientist involved in the project, moved forward along the path of exploring novel and more accurate (or more carefully documented) methodologies for both the investigation of the force fields and dynamics of the repair process. In particular, the team have explored viable quantum dynamical methodologies and multiconfigurational electronic structure methods to provide a physically sounded description of critical repair steps. Due to the particularly ambitious task of the process the training phase for the researcher has been longer then expected but has finally converged into a testable computational protocol which has already been submitted for publication. The regular progress made over the three years will now been briefly described.

The repair processes involves electronic excited states that must be modeled using electronic structure methods that account for electronic correlation. The large size of the photolyases active sites complexed to the damaged DNA makes impossible the use of such methods. Hence, the first step of the project has been to design an active site molecular model capable to describe the repair process while being small enough to be studied. The dynamics of the photolyases on the electronic excited states show non-adiabatic transitions, which are cases of strong couplings between electrons and nuclei. However, the minimal molecular model is still too large for calculating the non-adiabatic couplings, which are essential to the description of the photolyases dynamics. The researcher implemented a numerical approach for obtaining these couplings. Using the developed methodology, the researcher studied the slow initial electron transfer in the cyclobutane pyrimidine dimer (CPD) photolyase, which is a key step for understanding the efficiency of the repair process. In parallel to this work, new methods have been developed to explore the electronic energy landscape in the nuclear coodinnate space (minimum energy paths through one or more potential energy surface crossings) and to map the corresponding potential energy surfaces. These methods have been exposed in peer reviewed papers (Journal of Computational Chemistry and Chemical Society Reviews).

Simulating the quantum dynamics of a molecular system necessitates first the construction of a model Hamiltonian. Owing to the large size of the molecular model, the number of nuclear degrees of freedom (DOF) is very large: 153 DOF. The first step is to reduce this number to a minimal set of active coordinates. To achieve this goal, the researcher made himself familiar with different schemes of coordinates dimensionality reduction, as can attest two published works in peer reviewed journal (both in Journal of Chemical Physics), and used this new skill to define active coordinates. Then, simple parametrized Hamiltonian models have been constructed by fitting the model over an important number of nuclear geometries. These models have then been used in combination with the Non-equilibrium Fermi golden rule (NFGR) method to estimate the electron transfer time scale and compare to experiment. For these models, different descriptions of the vibrational modes can be employed. Allowing for changes of orientations and frequencies of these modes requires using model Hamiltonians that are quadratic with the nuclear motions: quadratic vibronic coupling (QVC) type of models. NFGR was initially not derived for QVC models and has been extended during the project and was the subject of a peer reviewed publication (Journal of Chemical Physics). The simulated models gave good agreement with the experimental measurement. We found that a quadratic model is essential to the description of the process. We also found that a low energy vibrational mode plays an important role in regulating the electron transfer. Is it known that interference appear in case of non-adiabatic dynamics, which can drastically change the dynamics of an electron transfer. In the course of this project, a new approach has been found to assess the importance of such interference, which makes the full quantum treatment essential. This approach was recently submitted to a peer review journal and will be further used to study this interference in the CPD electron transfer.

In order to produce more quantitative calculations, we must account for the remaining coordinates. These coordinates are accounted for as an environment during the simulations. For these simulations, we needed first to obtain a Hamiltonian model for the environment. In this aim, the researcher elaborated a new approach to obtain such a model. The approach is based on the separation between the active modes and remaining ones and makes use of the already obtained small dimensional model for the active coordinates to simplify the construction of the full dimensional one. Then, only local (in nuclear coordinates) electronic structure data are necessary: electronic energy gradients and Hessians. The NFGR method scales favorably with the number of nuclear DOF so that we used it for simulating the full dimensional model. These results have recently been submitted to a peer review journal. The remaining modes were found to participate in assisting the electron transfer. Accounting for a larger environment, i.e. the protein environment, cannot be done using the same approach as was used so far because: electronic structure calculations cannot be employed for such large systems, and the flexibility of the protein environment necessitates non-local data for the nuclear coordinates. The researcher is currently working the construction of such environment's models by using statistical data obtained from more approximate but also more flexible simulations in the Boltzmann ensemble (semi-classical methods, molecular mechanics, or Monte Carlo).

The NFGR approach is valid for slow electron transfer in CPD. However, NFGR is perturbative in the electronic states coupling and is not valid anymore when this coupling becomes large as for fast transitions. In this case, a variational approach must be employed, at least for the active coordinates, in simulating the processes. These approaches are known as subsystem-bath methods and the researcher learned them as can attest a peer-reviewed paper (Journal of Chemical Physics) where he implemented a subsystem-bath type of simulation. In order to make the subsystem-bath methods more efficient, it is possible to use very flexible parametrization of the subsystem wavefunction as the variational Multiconfiguration Gaussian (vMCG) method. Unfortunately, this type of parametrization leads to severe unphysical behavior (e.g. energy is not conserved for an isolated subsystem). In order to solve this problem, the researcher developed a new approach that extends the Schrödinger equation for statistical mixture of quantum states. This new approach is promising for quantum statistics in general as it gives new perspectives on treating environment effects, and it solves the unphysical behavior of the quantum subsystem for any type of wavefunction parametrization (e.g. vMCG). This new approach is the subject of a peer reviewed paper (Journal of Chemical Physics). The vMCG method is of prime interest in quantum dynamics simulations because it can be used ''on-the-fly'' so that there is no need of a parametrized molecular Hamiltonian as a prerequisite. This is why the extended Schrödinger equation has been implemented for the vMCG wavefunction parametrization, published in a peer reviewed paper (Journal of Chemical Physics). However, this new approach has not yet been applied to the photolyases study due to the delay in implementing the method. Besides, much effort have been spent on mapping/computing the potential energy surfaces of molecular systems different from the one of the research target to facilitate the benchmarking studies of the vMCG methods under development as can attest the various publications in peer reviewed journals (e.g. Angewendte Chemie, Journal of Physical Chemistry Letters). These studies, mainly carried out in the lab of the scientist in charge but also involving the researcher, have explored alternative ways of computing the ground and excited state energies required for the dynamics simulations.These have comprised state-of-the art approaches up to QMC computations and various flavors of DFT theory for electronically excited states.

The project progresses toward the objectives is in agreement with the research proposal. Delays were accumulated: in the initial step of the electronic structure study due to an unexpected complication in calculating non-adiabatic couplings, and in the implementation of a method to study the fast transitions due to the unphysical behavior of the subsystem-bath methods for flexible parametrization of a subsystem wavefunction. Nevertheless, the researcher took advantage of these problems to explore new approaches and made himself an expert in statistical quantum mechanics, which was a priority in his training during the project. Furthermore, The new established collaborations will be pursued with ongoing works, giving to the researcher an international network of collaborators. This project was an opportunity for the researcher to acquire maturity in his research (e.g. reinforcement of his publication track record, oral communications at international conferences, students supervisions), which is already supported by the recently obtained interview for an academic position in France.

The repair processes involves electronic excited states that must be modeled using electronic structure methods that account for electronic correlation. The large size of the photolyases active sites complexed to the damaged DNA makes impossible the use of such methods. Hence, the first step of the project has been to design an active site molecular model capable to describe the repair process while being small enough to be studied. The dynamics of the photolyases on the electronic excited states show non-adiabatic transitions, which are cases of strong couplings between electrons and nuclei. However, the minimal molecular model is still too large for calculating the non-adiabatic couplings, which are essential to the description of the photolyases dynamics. The researcher implemented a numerical approach for obtaining these couplings. Using the developed methodology, the researcher studied the slow initial electron transfer in the cyclobutane pyrimidine dimer (CPD) photolyase, which is a key step for understanding the efficiency of the repair process. In parallel to this work, new methods have been developed to explore the electronic energy landscape in the nuclear coodinnate space (minimum energy paths through one or more potential energy surface crossings) and to map the corresponding potential energy surfaces. These methods have been exposed in peer reviewed papers (Journal of Computational Chemistry and Chemical Society Reviews).

Simulating the quantum dynamics of a molecular system necessitates first the construction of a model Hamiltonian. Owing to the large size of the molecular model, the number of nuclear degrees of freedom (DOF) is very large: 153 DOF. The first step is to reduce this number to a minimal set of active coordinates. To achieve this goal, the researcher made himself familiar with different schemes of coordinates dimensionality reduction, as can attest two published works in peer reviewed journal (both in Journal of Chemical Physics), and used this new skill to define active coordinates. Then, simple parametrized Hamiltonian models have been constructed by fitting the model over an important number of nuclear geometries. These models have then been used in combination with the Non-equilibrium Fermi golden rule (NFGR) method to estimate the electron transfer time scale and compare to experiment. For these models, different descriptions of the vibrational modes can be employed. Allowing for changes of orientations and frequencies of these modes requires using model Hamiltonians that are quadratic with the nuclear motions: quadratic vibronic coupling (QVC) type of models. NFGR was initially not derived for QVC models and has been extended during the project and was the subject of a peer reviewed publication (Journal of Chemical Physics). The simulated models gave good agreement with the experimental measurement. We found that a quadratic model is essential to the description of the process. We also found that a low energy vibrational mode plays an important role in regulating the electron transfer. Is it known that interference appear in case of non-adiabatic dynamics, which can drastically change the dynamics of an electron transfer. In the course of this project, a new approach has been found to assess the importance of such interference, which makes the full quantum treatment essential. This approach was recently submitted to a peer review journal and will be further used to study this interference in the CPD electron transfer.

In order to produce more quantitative calculations, we must account for the remaining coordinates. These coordinates are accounted for as an environment during the simulations. For these simulations, we needed first to obtain a Hamiltonian model for the environment. In this aim, the researcher elaborated a new approach to obtain such a model. The approach is based on the separation between the active modes and remaining ones and makes use of the already obtained small dimensional model for the active coordinates to simplify the construction of the full dimensional one. Then, only local (in nuclear coordinates) electronic structure data are necessary: electronic energy gradients and Hessians. The NFGR method scales favorably with the number of nuclear DOF so that we used it for simulating the full dimensional model. These results have recently been submitted to a peer review journal. The remaining modes were found to participate in assisting the electron transfer. Accounting for a larger environment, i.e. the protein environment, cannot be done using the same approach as was used so far because: electronic structure calculations cannot be employed for such large systems, and the flexibility of the protein environment necessitates non-local data for the nuclear coordinates. The researcher is currently working the construction of such environment's models by using statistical data obtained from more approximate but also more flexible simulations in the Boltzmann ensemble (semi-classical methods, molecular mechanics, or Monte Carlo).

The NFGR approach is valid for slow electron transfer in CPD. However, NFGR is perturbative in the electronic states coupling and is not valid anymore when this coupling becomes large as for fast transitions. In this case, a variational approach must be employed, at least for the active coordinates, in simulating the processes. These approaches are known as subsystem-bath methods and the researcher learned them as can attest a peer-reviewed paper (Journal of Chemical Physics) where he implemented a subsystem-bath type of simulation. In order to make the subsystem-bath methods more efficient, it is possible to use very flexible parametrization of the subsystem wavefunction as the variational Multiconfiguration Gaussian (vMCG) method. Unfortunately, this type of parametrization leads to severe unphysical behavior (e.g. energy is not conserved for an isolated subsystem). In order to solve this problem, the researcher developed a new approach that extends the Schrödinger equation for statistical mixture of quantum states. This new approach is promising for quantum statistics in general as it gives new perspectives on treating environment effects, and it solves the unphysical behavior of the quantum subsystem for any type of wavefunction parametrization (e.g. vMCG). This new approach is the subject of a peer reviewed paper (Journal of Chemical Physics). The vMCG method is of prime interest in quantum dynamics simulations because it can be used ''on-the-fly'' so that there is no need of a parametrized molecular Hamiltonian as a prerequisite. This is why the extended Schrödinger equation has been implemented for the vMCG wavefunction parametrization, published in a peer reviewed paper (Journal of Chemical Physics). However, this new approach has not yet been applied to the photolyases study due to the delay in implementing the method. Besides, much effort have been spent on mapping/computing the potential energy surfaces of molecular systems different from the one of the research target to facilitate the benchmarking studies of the vMCG methods under development as can attest the various publications in peer reviewed journals (e.g. Angewendte Chemie, Journal of Physical Chemistry Letters). These studies, mainly carried out in the lab of the scientist in charge but also involving the researcher, have explored alternative ways of computing the ground and excited state energies required for the dynamics simulations.These have comprised state-of-the art approaches up to QMC computations and various flavors of DFT theory for electronically excited states.

The project progresses toward the objectives is in agreement with the research proposal. Delays were accumulated: in the initial step of the electronic structure study due to an unexpected complication in calculating non-adiabatic couplings, and in the implementation of a method to study the fast transitions due to the unphysical behavior of the subsystem-bath methods for flexible parametrization of a subsystem wavefunction. Nevertheless, the researcher took advantage of these problems to explore new approaches and made himself an expert in statistical quantum mechanics, which was a priority in his training during the project. Furthermore, The new established collaborations will be pursued with ongoing works, giving to the researcher an international network of collaborators. This project was an opportunity for the researcher to acquire maturity in his research (e.g. reinforcement of his publication track record, oral communications at international conferences, students supervisions), which is already supported by the recently obtained interview for an academic position in France.