Nonadiabatic QM/MM Simulations of Fast Charge Transfer in Escherichia coli DNA Photolyase

Non-adiabatic molecular dynamics simulations provide new insights into the exciton transfer in the Fenna-Matthews-Olson complex

A trajectory surface hopping approach, which uses machine learning to speed up the most time-consuming steps, has been adopted to investigate the exciton transfer in light-harvesting systems. The present neural networks achieve high accuracy in predicting both Coulomb couplings and excitation energies. The latter are predicted taking into account the environment of the pigments. Direct simulation of exciton dynamics through light-harvesting complexes on significant time scales is usually challenging due to the coupled motion of nuclear and electronic degrees of freedom in these rather large systems containing several relatively large pigments. In the present approach, however, we are able to evaluate a statistically significant number of non-adiabatic molecular dynamics trajectories with respect to exciton delocalization and exciton paths. The formalism is applied to the Fenna-Matthews-Olson complex of green sulfur bacteria, which transfers energy from the light-harvesting chlorosome to the reaction center with astonishing efficiency. The system has been studied experimentally and theoretically for decades. In total, we were able to simulate non-adiabatically more than 30 ns, sampling also the relevant space of parameters within their uncertainty. Our simulations show that the driving force supplied by the energy landscape resulting from electrostatic tuning is sufficient to funnel the energy towards site 3, from where it can be transferred to the reaction center. However, the high efficiency of transfer within a picosecond timescale can be attributed to the rather unusual properties of the BChl a molecules, resulting in very low inner and outer-sphere reorganization energies, not matched by any other organic molecule, e.g., used in organic electronics. A comparison with electron and exciton transfer in organic materials is particularly illuminating, suggesting a mechanism to explain the comparably high transfer efficiency.

Directed ultrafast conformational changes accompany electron transfer in a photolyase as resolved by serial crystallography

Charge-transfer reactions in proteins are important for life, such as in photolyases which repair DNA, but the role of structural dynamics remains unclear. Here, using femtosecond X-ray crystallography, we report the structural changes that take place while electrons transfer along a chain of four conserved tryptophans in the Drosophila melanogaster (6-4) photolyase. At femto- and picosecond delays, photoreduction of the flavin by the first tryptophan causes directed structural responses at a key asparagine, at a conserved salt bridge, and by rearrangements of nearby water molecules. We detect charge-induced structural changes close to the second tryptophan from 1 ps to 20 ps, identifying a nearby methionine as an active participant in the redox chain, and from 20 ps around the fourth tryptophan. The photolyase undergoes highly directed and carefully timed adaptations of its structure. This questions the validity of the linear solvent response approximation in Marcus theory and indicates that evolution has optimized fast protein fluctuations for optimal charge transfer.

Tryptophan to Tryptophan Hole Hopping in an Azurin Construct

Electron transfer (ET) between neutral and cationic tryptophan residues in the azurin construct [ReI(H126)(CO)3(dmp)](W124)(W122)CuI (dmp = 4,7-Me2-1,10-phenanthroline) was investigated by Born-Oppenheimer quantum-mechanics/molecular mechanics/molecular dynamics (QM/MM/MD) simulations. We focused on W124•+ ← W122 ET, which is the middle step of the photochemical hole-hopping process *ReII(CO)3(dmp•-) ← W124 ← W122 ← CuI, where sequential hopping amounts to nearly 10,000-fold acceleration over single-step tunneling (ACS Cent. Sci. 2019, 5, 192-200). In accordance with experiments, UKS-DFT QM/MM/MD simulations identified forward and reverse steps of W124•+ ↔ W122 ET equilibrium, as well as back ET ReI(CO)3(dmp•-) → W124•+ that restores *ReII(CO)3(dmp•-). Strong electronic coupling between the two indoles (≥40 meV in the crossing region) makes the productive W124•+ ← W122 ET adiabatic. Energies of the two redox states are driven to degeneracy by fluctuations of the electrostatic potential at the two indoles, mainly caused by water solvation, with contributions from the protein dynamics in the W122 vicinity. ET probability depends on the orientation of Re(CO)3(dmp) relative to W124 and its rotation diminishes the hopping yield. Comparison with hole hopping in natural systems reveals structural and dynamics factors that are important for designing efficient hole-hopping processes.

Drug Design in the Exascale Era: A Perspective from Massively Parallel QM/MM Simulations

The initial phases of drug discovery - in silico drug design - could benefit from first principle Quantum Mechanics/Molecular Mechanics (QM/MM) molecular dynamics (MD) simulations in explicit solvent, yet many applications are currently limited by the short time scales that this approach can cover. Developing scalable first principle QM/MM MD interfaces fully exploiting current exascale machines - so far an unmet and crucial goal - will help overcome this problem, opening the way to the study of the thermodynamics and kinetics of ligand binding to protein with first principle accuracy. Here, taking two relevant case studies involving the interactions of ligands with rather large enzymes, we showcase the use of our recently developed massively scalable Multiscale Modeling in Computational Chemistry (MiMiC) QM/MM framework (currently using DFT to describe the QM region) to investigate reactions and ligand binding in enzymes of pharmacological relevance. We also demonstrate for the first time strong scaling of MiMiC-QM/MM MD simulations with parallel efficiency of ∼70% up to >80,000 cores. Thus, among many others, the MiMiC interface represents a promising candidate toward exascale applications by combining machine learning with statistical mechanics based algorithms tailored for exascale supercomputers.

Hybrid Quantum Mechanical/Molecular Mechanical Methods For Studying Energy Transduction in Biomolecular Machines

Hybrid quantum mechanical/molecular mechanical (QM/MM) methods have become indispensable tools for the study of biomolecules. In this article, we briefly review the basic methodological details of QM/MM approaches and discuss their applications to various energy transduction problems in biomolecular machines, such as long-range proton transports, fast electron transfers, and mechanochemical coupling. We highlight the particular importance for these applications of balancing computational efficiency and accuracy. Using several recent examples, we illustrate the value and limitations of QM/MM methodologies for both ground and excited states, as well as strategies for calibrating them in specific applications. We conclude with brief comments on several areas that can benefit from further efforts to make QM/MM analyses more quantitative and applicable to increasingly complex biological problems.

Adiabatic Excited-State Molecular Dynamics with an Explicit Solvent: NEXMD-SANDER Implementation

We present a method to link the Nonadiabatic EXcited-state Molecular Dynamics (NEXMD) package to the SANDER package supplied by AMBERTOOLS to provide excited-state adiabatic quantum mechanics/molecular mechanics (QM/MM) simulations. NEXMD is a computational package particularly developed to perform simulations of the photoexcitation and subsequent nonadiabatic electronic and vibrational energy relaxation in large multichromophoric conjugated molecules involving several coupled electronic excited states. The NEXMD-SANDER exchange has been optimized in order to achieve excited-state adiabatic dynamics simulations of large conjugated materials in a QM/MM environment, such as an explicit solvent. Dynamics of a substituted polyphenylene vinylene oligomer (PPV3-NO₂) in vacuum and different explicit solvents has been used as a test case by performing comparative analysis of changes in its optical spectrum, state-dependent conformational changes, and quantum bond orderings. The method has been tested and compared with respect to previous implicit solvent implementations. Also, the impact on the expansion of the QM region by including a variable number of solvent molecules has been analyzed. Altogether, these results encourage future implementations of NEXMD simulations using the same combination of methods.

Molecular Rectifiers with a Very High Rectification Ratio Enabled by Oxidative Damage in Double-Stranded DNA

In this work, we report a novel strategy to construct highly efficient molecular diodes using oxidatively damaged DNA molecules. Being exposed to several endogenous and exogenous events, DNA suffers from constant oxidative damage, leading to the oxidation of guanine to 8-oxoguanine (8oxoG). Here, we study the charge migration properties of native and oxidatively damaged DNA using a multiscale multiconfigurational methodology comprising molecular dynamics, density functional theory, and kinetic Monte Carlo simulations. We perform a comprehensive study to understand the effect of different concentrations and locations of 8oxoG in a dsDNA sequence on its charge-transport properties and find tunable rectifier properties having potential applications in molecular electronics such as molecular switches and molecular rectifiers. We also discover the negative differential resistance properties of the fully oxidized Drew-Dickerson sequence. The presence of 8oxoG guanine leads to the trapping of charge, thus operating as a charge sink, which reveals how oxidized guanine saves the rest of the genome from further oxidative damage.

Scalable Ehrenfest Molecular Dynamics Exploiting the Locality of Density-Functional Tight-Binding Hamiltonian

To explore the science behind excited-state dynamics in high-complexity chemical systems, a scalable nonadiabatic molecular dynamics (MD) technique is indispensable. In this study, by treating the electronic degrees of freedom at the density-functional tight-binding level, we developed and implemented a reduced scaling and multinode-parallelizable Ehrenfest MD method. To achieve this goal, we introduced a concept called patchwork approximation (PA), where the effective Hamiltonian for real-time propagation of the electronic density matrix is partitioned into a set of local parts. Numerical results for giant icosahedral fullerenes, which comprise up to 6000 atoms, suggest that the scaling of the present PA-based method is less than quadratic, which yields a significant advantage over the conventional cubic scaling method in terms of computational time. The acceleration by the parallelization on multiple nodes was also assessed. Furthermore, the electronic and structural dynamics resulting from the perturbation by the external electric field were accurately reproduced with the PA, even when the electronic excitation was spatially delocalized.

Photoinduced hole hopping through tryptophans in proteins

Hole hopping through tryptophan/tyrosine chains enables rapid unidirectional charge transport over long distances. We have elucidated structural and dynamical factors controlling hopping speed and efficiency in two modified azurin constructs that include a rhenium(I) sensitizer, Re(His)(CO)₃(dmp)⁺, and one or two tryptophans (W₁, W₂). Experimental kinetics investigations showed that the two closely spaced (3 to 4 Å) intervening tryptophans dramatically accelerated long-range electron transfer (ET) from Cu^I to the photoexcited sensitizer. In our theoretical work, we found that time-dependent density-functional theory (TDDFT) quantum mechanics/molecular mechanics/molecular dynamics (QM/MM/MD) trajectories of low-lying triplet excited states of Re^I(His)(CO)₃(dmp)⁺-W₁(-W₂) exhibited crossings between sensitizer-localized (*Re) and charge-separated [Re^I(His)(CO)₃(dmp^•-)/(W₁ ^•+ or W₂ ^•+)] (CS1 or CS2) states. Our analysis revealed that the distances, angles, and mutual orientations of ET-active cofactors fluctuate in a relatively narrow range in which the cofactors are strongly coupled, enabling adiabatic ET. Water-dominated electrostatic field fluctuations bring *Re and CS1 states to a crossing where *Re(CO)₃(dmp)⁺←W₁ ET occurs, and CS1 becomes the lowest triplet state. ET is promoted by solvation dynamics around *Re(CO)₃(dmp)⁺(W₁); and CS1 is stabilized by Re(dmp^•-)/W₁ ^•+ electron/hole interaction and enhanced W₁ ^•+ solvation. The second hop, W₁ ^•+←W₂, is facilitated by water fluctuations near the W₁/W₂ unit, taking place when the electrostatic potential at W₂ drops well below that at W₁ ^•+ Insufficient solvation and reorganization around W₂ make W₁ ^•+←W₂ ET endergonic, shifting the equilibrium toward W₁ ^•+ and decreasing the charge-separation yield. We suggest that multiscale TDDFT/MM/MD is a suitable technique to model the simultaneous evolution of photogenerated excited-state manifolds.

Electron Transfer-Induced Active Site Structural Relaxation in 64-Photolyase of Drosophila melanogaster

While catalytic electron flow and photoreactivation of CPD-photolyases are increasingly understood, the microscopic details of the 64-photolyase repair mechanism are perpetually debated. Here, we investigate in long-time (μs) molecular dynamics simulations combined with extensive quantum mechanical/molecular mechanical (QM/MM) simulations the primary electron transfer (ET) reactions in 64-photolyase of Drosophila melanogaster (D. melanogaster). The characterization of the relative energetics of locally excited and charge separated states in the (6-4) photoproduct enzyme repair complex reveals a charge-separated state involving the adenine moiety of the FADH^- cofactor that facilitates reduction of the photoproduct. Microscopic details of the collective reaction coordinate of ET reactions are identified that involve the reorganization of the hydrogen bond network and structural relaxation of the active site. The simulations reveal complex active site relaxation dynamics involving distinguished amino acids (Lys246, His365, and His369), conformational reorganization of the hydroxyl group of the (6-4) photoproduct, and a strengthening of hydrogen bonds with immobilized water molecules. In particular, rotation of the Lys246 side chain is found to impose a double-well character along the reaction coordinate of the ET reaction. Our findings suggest that the primary ET reactions in the (6-4) photoproduct enzyme repair complex of D. melanogaster are governed by a complex multi-minima active site relaxation dynamics and potentially precede the equilibration of the protein. ET pathways mediated by the adenine moiety and the 5' side of the photoproduct are proposed to be relevant for triggering the catalytic (6-4) photoproduct reactivation.

Speed-dependent adaptive partitioning in QM/MM MD simulations of displacement damage in solid-state systems

Solids undergo displacement damage (DD) when interacting with energetic particles, which may happen during the fabrication of semiconductor devices, in harsh environments and in certain analysis techniques. Simulations of DD generation are usually carried out using classical molecular dynamics (MD), but classical MD does not account for all the effects in DD, as demonstrated by ab initio calculations of model systems in the literature. A complete ab initio simulation of DD generation is impractical due to the large number of atoms involved. In my previous paper [Yang, Phys. Chem. Chem. Phys., 2020, 22, 19307], I developed an adaptive-center (AC) method for the adaptive-partitioning (AP) of quantum mechanics/molecular mechanics (QM/MM) simulations, allowing the active region centers and the QM/MM partition to be determined on-the-fly for energy-conserving AP-QM/MM methods. I demonstrated that the AC-AP-QM/MM is applicable to the simulation of DD generation, so that the active regions can be treated using an ab initio method. The AC method could not be used to identify the fast-moving recoil ions in DD generation as active region centers, however, and the accuracy is negatively affected by the rapid change in the QM/MM partition of the system. In this paper, I extend the AC method and develop a speed-dependent adaptive-center (SDAC) method for accurate AP-QM/MM simulations of DD. The SDAC method is applicable to general problems with speed-dependent active regions, and is compatible with all existing energy-conserving partitioning-by-distance AP-QM/MM methods. The artifact due to the speed-dependent potential energy surface can be made small by choosing suitable criteria. I demonstrate the SDAC method by simulations of DD generation in bulk silicon.

Biological relevance of charge transfer branching pathways in photolyases

The repair of sun-induced DNA lesions by photolyases is driven by a photoinduced electron transfer from a fully reduced FAD to the damaged DNA. A chain of several aromatic residues connecting FAD to solvent ensures the prior photoreduction of the FAD cofactor. In PhrA, a class III CPD photolyase, two branching tryptophan charge transfer pathways have been characterized. According to previous experiments, both pathways play a role in the FAD photoreduction. To provide a molecular insight to the charge transfer abilities of both pathways, we perform multiscales simulations where the protein motion and the positive charge are simultaneously propagated. Our computational approach reveals that one pathway drives a very fast charge transfer whereas the other pathway provides a very good thermodynamic stabilization of the positive charge. During the simulations, the positive charge firstly moves on the fast triad, while a reorganization of the close FAD˙^- environment occurs. Then, backward transfers can lead to the propagation of the positive charge on the second pathway. After one nanosecond, we observe a nearly equal probability to find the charge at ending tryptophan of either pathway; eventually the charge distribution will likely evolve towards a charge stabilization on the last tryptophan of the slowest pathway. Our results highlight the role the protein environment, which manages the association of a kinetic and a thermodynamic pathways to trigger a fast and efficient FAD photoreduction.

What accounts for the different functions in photolyases and cryptochromes: a computational study of proton transfers to FAD

Photolyases (PL) and cryptochromes (CRY) are light-sensitive flavoproteins, respectively, involved in DNA repair and signal transduction. Their activation is triggered by an electron transfer process, which partially or fully reduces the photo-activated FAD cofactor. The full reduction additionally requires a proton transfer to the isoalloxazine ring. In plant CRY, an efficient proton transfer takes place within several μs, enabled by a conserved aspartate working as a proton donor, whereas in E. coli PL a proton transfer occurs in the 4 s timescale without any obvious proton donor, indicating the presence of a long-range proton transfer pathway. Unexpectedly, the insertion of an aspartate as a proton donor in a suitable position for proton transfer in E. coli PL does not initiate a transfer process similar to plant CRY, but even prevents the formation of a protonated FAD. In the present work, thanks to a combination of classical molecular dynamics and state-of-the-art DFTB3/MM simulations, we identify a proton transfer pathway from bulk to FAD in E. coli PL associated with a free energy profile in agreement with the experimental kinetics data. The free energy profiles of the proton transfer between aspartate and FAD show an inversion of the driving force between plant CRY and E. coli PL mutants. In the latter, the proton transfer from the aspartate is faster than in plant CRY but also thermodynamically disfavoured, in agreement with the experimental data. Our results further illustrate the fine tuning of the electrostatic FAD environment and the adaptability of the FAD pocket to ensure the divergent functions of the members of the PL-CRY family.

Molecular Insights into Variable Electron Transfer in Amphibian Cryptochrome

Cryptochrome proteins are activated by the absorption of blue light, leading to the formation of radical pairs through electron transfer in the active site. Recent experimental studies have shown that once some of the amino acid residues in the active site of Xenopus laevis cryptochrome DASH are mutated, radical-pair formation is still observed. In this study, we computationally investigate electron-transfer pathways in the X. laevis cryptochrome DASH by extensively equilibrating a previously established homology model using molecular dynamics simulations and then mutating key amino acids involved in the electron transfer. The electron-transfer pathways are then probed by using tight-binding density-functional theory. We report the alternative electron-transfer pathways resolved at the molecular level and, through comparison of amino acid sequences for cryptochromes from different species, we demonstrate that one of these alternative electron-transfer pathways could be general for all cryptochrome DASH proteins.

Why Are DNA and Protein Electron Transfer So Different?

The corpus of electron transfer (ET) theory provides considerable power to describe the kinetics and dynamics of electron flow at the nanoscale. How is it, then, that nucleic acid (NA) ET continues to surprise, while protein-mediated ET is relatively free of mechanistic bombshells? I suggest that this difference originates in the distinct electronic energy landscapes for the two classes of reactions. In proteins, the donor/acceptor-to-bridge energy gap is typically several-fold larger than in NAs. NA ET can access tunneling, hopping, and resonant transport among the bases, and fluctuations can enable switching among mechanisms; protein ET is restricted to tunneling among redox active cofactors and, under strongly oxidizing conditions, a few privileged amino acid side chains. This review aims to provide conceptual unity to DNA and protein ET reaction mechanisms. The establishment of a unified mechanistic framework enabled the successful design of NA experiments that switch electronic coherence effects on and off for ET processes on a length scale of multiple nanometers and promises to provide inroads to directing and detecting charge flow in soft-wet matter.

Reassessment of the Four-Point Approach to the Electron-Transfer Marcus-Hush Theory

The Marcus-Hush theory has been successfully applied to describe and predict the activation barriers and hence the electron-transfer (ET) rates in several physicochemical and biological systems. This theory assumes that in the ET reaction, the geometry of the free Gibbs energy landscape is parabolic, with equal curvature near the local minimum for both reactants and products. In spite of its achievements, more realistic models have included the assumption of the two parabolas having not the same curvature. This situation is analyzed by the Nelsen's four-point method. As a benchmark to compare the Marcus-Hush approximation to a precise calculation of the excitation energy, we studied the non-ET process of the electronic excitation of the aluminum dimer that has two local minima (³∑_g ^- and ³∏_u electronic states) and allows to obtain analytically the Marcus-Hush nonsymmetric parameters. We appraise the ability of the Marcus-Hush formula to approximate the analytical results by using several averages of the two reorganization energies associated with the forward and backward transitions and analyze the error. It is observed that the geometric average minimizes the relative error and that the analytical case is recovered. The main results of this paper are obtained by the application of the Nelsen's four-point method to compute the reorganization energies of a large set of potential π-conjugated molecules proposed for organic photovoltaic devices using the above-mentioned averages for the Marcus-Hush formula. The activation energies obtained with the geometric average are significantly larger for some donor-acceptor pairs in comparison with the previously employed arithmetic average, their differences being suitable for experimental testing.

Functional role of an unusual tyrosine residue in the electron transfer chain of a prokaryotic (6-4) photolyase

Cryptochromes and photolyases form a flavoprotein family in which the FAD chromophore undergoes light induced changes of its redox state. During this process, termed photoreduction, electrons flow from the surface via conserved amino acid residues to FAD. The bacterial (6-4) photolyase PhrB belongs to a phylogenetically ancient group. Photoreduction of PhrB differs from the typical pattern because the amino acid of the electron cascade next to FAD is a tyrosine (Tyr391), whereas photolyases and cryptochromes of other groups have a tryptophan as direct electron donor of FAD. Mutagenesis studies have identified Trp342 and Trp390 as essential for charge transfer. Trp342 is located at the periphery of PhrB while Trp390 connects Trp342 and Tyr391. The role of Tyr391, which lies between Trp390 and FAD, is however unclear as its replacement by phenylalanine did not block photoreduction. Experiments reported here, which replace Tyr391 by Ala, show that photoreduction is blocked, underlining the relevance of Tyr/Phe at position 391 and indicating that charge transfer occurs via the triad 391-390-342. This raises the question, why PhrB positions a tyrosine at this location, having a less favourable ionisation potential than tryptophan, which occurs at this position in many proteins of the photolyase/cryptochrome family. Tunnelling matrix calculations show that tyrosine or phenylalanine can be involved in a productive bridged electron transfer between FAD and Trp390, in line with experimental findings. Since replacement of Tyr391 by Trp resulted in loss of FAD and DMRL chromophores, electron transfer cannot be studied experimentally in this mutant, but calculations on a mutant model suggest that Trp might participate in the electron transfer cascade. Charge transfer simulations reveal an unusual stabilization of the positive charge on site 391 compared to other photolyases or cryptochromes. Water molecules near Tyr391 offer a polar environment which stabilizes the positive charge on this site, thereby lowering the energetic barrier intrinsic to tyrosine. This opens a second charge transfer channel in addition to tunnelling through the tyrosine barrier, based on hopping and therefore transient oxidation of Tyr391, which enables a fast charge transfer similar to proteins utilizing a tryptophan-triad. Our results suggest that evolution of the first site of the redox chain has just been possible by tuning the protein structure and environment to manage a downhill hole transfer process from FAD to solvent.

Charge Transport in Molecular Materials: An Assessment of Computational Methods

The booming field of molecular electronics has fostered a surge of computational research on electronic properties of organic molecular solids. In particular, with respect to a microscopic understanding of transport and loss mechanisms, theoretical studies assume an ever-increasing role. Owing to the tremendous diversity of organic molecular materials, a great number of computational methods have been put forward to suit every possible charge transport regime, material, and need for accuracy. With this review article we aim at providing a compendium of the available methods, their theoretical foundations, and their ranges of validity. We illustrate these through applications found in the literature. The focus is on methods available for organic molecular crystals, but mention is made wherever techniques are suitable for use in other related materials such as disordered or polymeric systems.

Microsecond Simulation of Electron Transfer in DNA: Bottom-Up Parametrization of an Efficient Electron Transfer Model Based on Atomistic Details

The transfer of electrons over long distances in complex molecular systems is a phenomenon of significance in both biochemistry and technology. In recent years, we have been developing efficient models to study ET in complex systems, including DNA as a prominent example. Ab initio and model approaches have been combined in an "on-the-fly" calculation of ET parameters, which can be used to propagate nuclear and electronic degrees of freedom simultaneously. These previous efforts have aimed at deriving an efficient nonadiabatic quantum mechanical-molecular mechanical (QM/MM) simulation scheme for ET, making nanosecond simulations of ET in realistic systems possible. This, however, is still insufficient for the treatment of large donor-bridge-acceptor systems, like the ET in DNA, overcoming long adenine bridges. Therefore, we have constructed a theoretical model in a bottom-up manner. All quantum-chemical as well as force-field calculations are substituted by theoretical models of the involved phenomena on a molecular level, including polarization and relaxation of the molecular environment, which are often omitted in other recently developed theoretical models of ET. A nonadiabatic simulation scheme is employed, and no assumptions regarding the ET mechanism are needed. Thus, the predictive power of the simulations is preserved, while pushing the limits of the accessible time scales beyond microseconds. This model-based simulation scheme is applied to ET in various DNA species. Good agreement with the "full" atomistic nonadiabatic QM/MM scheme is observed for the archetypal DNA ET systems, the polyA sequence, as well as the sequences GT_nGGG, containing adenines as bridge sites. Furthermore, ET in larger, more complex DNA sequences is simulated, and the results are discussed.

Insights into Light-driven DNA Repair by Photolyases: Challenges and Opportunities for Electronic Structure Theory

Ultraviolet radiation causes two of the most abundant mutagenic and cytotoxic DNA lesions: cyclobutane pyrimidine dimers and 6-4 photoproducts. (6-4) Photolyases are light-activated enzymes that selectively bind to DNA and trigger repair of mutagenic 6-4 photoproducts via photoinduced electron transfer from flavin adenine dinucleotide anion (FADH^- ) to the lesion triggering repair. This review provides an overview of the sequential steps of the repair process, that is light absorption and resonance energy transfer, photoinduced electron transfer and electron-induced splitting mechanisms, with an emphasis on the role of theory and computation. In addition, theoretical calculations and physical properties that can be used to classify specific mechanism are discussed in an effort to trace the fundamental aspects of each individual step and assist the interpretation of experimental data. The current challenges and suggested future directions are outlined for each step, concluding with a view on the future.

Electron flow through biological molecules: does hole hopping protect proteins from oxidative damage?

Biological electron transfers often occur between metal-containing cofactors that are separated by very large molecular distances. Employing photosensitizer-modified iron and copper proteins, we have shown that single-step electron tunneling can occur on nanosecond to microsecond timescales at distances between 15 and 20 Å. We also have shown that charge transport can occur over even longer distances by hole hopping (multistep tunneling) through intervening tyrosines and tryptophans. In this perspective, we advance the hypothesis that such hole hopping through Tyr/Trp chains could protect oxygenase, dioxygenase, and peroxidase enzymes from oxidative damage. In support of this view, by examining the structures of P450 (CYP102A) and 2OG-Fe (TauD) enzymes, we have identified candidate Tyr/Trp chains that could transfer holes from uncoupled high-potential intermediates to reductants in contact with protein surface sites.

Polarizability of the active site of cytochrome c reduces the activation barrier for electron transfer

Enzymes in biology’s energy chains operate with low energy input distributed through multiple electron transfer steps between protein active sites. The general challenge of biological design is how to lower the activation barrier without sacrificing a large negative reaction free energy. We show that this goal is achieved through a large polarizability of the active site. It is polarized by allowing a large number of excited states, which are populated quantum mechanically by electrostatic fluctuations of the protein and hydration water shells. This perspective is achieved by extensive mixed quantum mechanical/molecular dynamics simulations of the half reaction of reduction of cytochrome c. The barrier for electron transfer is consistently lowered by increasing the number of excited states included in the Hamiltonian of the active site diagonalized along the classical trajectory. We suggest that molecular polarizability, in addition to much studied electrostatics of permanent charges, is a key parameter to consider in order to understand how enzymes work.

Quantum effects in ultrafast electron transfers within cryptochromes

Cryptochromes and photolyases are flavoproteins that may undergo ultrafast charge separation upon electronic excitation of their flavin cofactors.

Quantifying electron transfer reactions in biological systems: what interactions play the major role?

Various biological processes involve the conversion of energy into forms that are usable for chemical transformations and are quantum mechanical in nature. Such processes involve light absorption, excited electronic states formation, excitation energy transfer, electrons and protons tunnelling which for example occur in photosynthesis, cellular respiration, DNA repair, and possibly magnetic field sensing. Quantum biology uses computation to model biological interactions in light of quantum mechanical effects and has primarily developed over the past decade as a result of convergence between quantum physics and biology. In this paper we consider electron transfer in biological processes, from a theoretical view-point; namely in terms of quantum mechanical and semi-classical models. We systematically characterize the interactions between the moving electron and its biological environment to deduce the driving force for the electron transfer reaction and to establish those interactions that play the major role in propelling the electron. The suggested approach is seen as a general recipe to treat electron transfer events in biological systems computationally, and we utilize it to describe specifically the electron transfer reactions in Arabidopsis thaliana cryptochrome-a signaling photoreceptor protein that became attractive recently due to its possible function as a biological magnetoreceptor.

Electronic couplings for molecular charge transfer: benchmarking CDFT, FODFT and FODFTB against high-level ab initio calculations. II

A new database (HAB7-) of electronic coupling matrix elements (Hab) for electron transfer in seven medium-sized negatively charged π-conjugated organic dimers is introduced. Reference data are obtained with spin-component scaled approximate coupled cluster method (SCS-CC2) and large basis sets. Assessed DFT-based approaches include constrained density functional theory (CDFT), fragment-orbital DFT (FODFT), self-consistent charge density functional tight-binding (FODFTB) and the recently described analytic overlap method (AOM). This complements the previously reported HAB11 database where only cationic dimers were considered. The CDFT method in combination with a functional based on PBE and including 50% of exact exchange (HFX) was found to provide best estimates, with a mean relative unsigned error (MRUE) of 8.2%. CDFT couplings systematically increase with decreasing fraction of HFX as a consequence of increasing delocalisation of the SOMO orbital. The FODFT method is found to be very robust underestimating electronic couplings by 28%. The FODFTB and AOM methods, although orders of magnitude more efficient in terms of computational effort than the DFT approaches, perform well with reasonably small errors of 54% and 29%, respectively, translating in errors in the non-adiabatic electron transfer rate of a factor of 2.4 and 1.7, respectively. We discuss carefully various sources of errors and the scope and limitations of all assessed methods taking into account the results obtained for both HAB7- and HAB11 databases.

Progress and challenges in simulating and understanding electron transfer in proteins

This Review presents an overview of the most common numerical simulation approaches for the investigation of electron transfer (ET) in proteins. We try to highlight the merits of the different approaches but also the current limitations and challenges. The article is organized into three sections. Section 2 deals with direct simulation algorithms of charge migration in proteins. Section 3 summarizes the methods for testing the applicability of the Marcus theory for ET in proteins and for evaluating key thermodynamic quantities entering the reaction rates (reorganization energies and driving force). Recent studies interrogating the validity of the theory due to the presence of non-ergodic effects or of non-linear responses are also described. Section 4 focuses on the tunneling aspects of electron transfer. How can the electronic coupling between charge transfer states be evaluated by quantum chemistry approaches and rationalized? What interesting physics regarding the impact of protein dynamics on tunneling can be addressed? We will illustrate the different sections with examples taken from the literature to show what types of system are currently manageable with current methodologies. We also take care to recall what has been learned on the biophysics of ET within proteins thanks to the advent of atomistic simulations.

Computational modeling of photoexcitation in DNA single and double strands

The photoexcitation of DNA strands triggers extremely complex photoinduced processes, which cannot be understood solely on the basis of the behavior of the nucleobase building blocks. Decisive factors in DNA oligomers and polymers include collective electronic effects, excitonic coupling, hydrogen-bonding interactions, local steric hindrance, charge transfer, and environmental and solvent effects. This chapter surveys recent theoretical and computational efforts to model real-world excited-state DNA strands using a variety of established and emerging theoretical methods. One central issue is the role of localized vs delocalized excitations and the extent to which they determine the nature and the temporal evolution of the initial photoexcitation in DNA strands.

Could tyrosine and tryptophan serve multiple roles in biological redox processes?

Single-step electron tunnelling reactions can transport charges over distances of 15-20 Åin proteins. Longer-range transfer requires multi-step tunnelling processes along redox chains, often referred to as hopping. Long-range hopping via oxidized radicals of tryptophan and tyrosine, which has been identified in several natural enzymes, has been demonstrated in artificial constructs of the blue copper protein azurin. Tryptophan and tyrosine serve as hopping way stations in high-potential charge transport processes. It may be no coincidence that these two residues occur with greater-than-average frequency in O(2)- and H(2)O(2)-reactive enzymes. We suggest that appropriately placed tyrosine and/or tryptophan residues prevent damage from high-potential reactive intermediates by reduction followed by transfer of the oxidizing equivalent to less harmful sites or out of the protein altogether.

Photoactivation of cryptochromes from Drosophila melanogaster and Sylvia borin: insight into the chemical compass mechanism by computational investigation

Although behavioral studies demonstrated light-induced magnetoreception in the insect Drosophila melanogaster, gaining insight into the possibility that a radical-pair mechanism accounts for the magnetic response of the cryptochrome (DmCry1) is complicated by a number of factors. In addition, the mechanism of magnetoreception for the cryptochrome from the garden warbler bird Sylvia borin (gwCry1a), which demonstrated a long-lived radical pair by transient optical absorption measurements, has also not been rationalized. To assess potential feasibility of a radical-pair mechanism in DmCry1 and gwCry1a, formed by excitation and electron transfer between a Trp-triad and flavin adenine dinucleotide (FAD), further separated by electron transfer within the triad, we applied a combination of theoretical methods, including homology modeling and molecular dynamics (MD) for structure refinement, high-level ab initio theory, and MD simulations using a polarizable force-field for prediction of pKa and the electron transfer rate. Calculated excitation energies, followed by electron transfer in model compounds of DmCry1 that assume proton transfer in conjunction with electron transfer from Trp (W420) to FAD and the predicted pKa for the proximate residue to FAD (Cys416), support a radical-pair mechanism. Furthermore, free-energy and reorganization energies for the Trp-triad in DmCry1 demonstrate facile electron transfer, explained by the local protein environment and exposure to solvent, which in turn enables a large enough distance separation for the radical-pair partners. Results for gwCry1a demonstrated the importance of accounting for relaxed excited-state geometries in validating the first stage of a radical-pair mechanism. This work provides insight into the so-called chemical compass mechanism to explain magnetic-field sensing in DmCry1 and gwCry1a, expanding on previous work on the cyrptochrome from the plant Arabidopsis thaliana (Solov'yov et al. J. Am. Chem. Soc. 2012, 134, 18046-18052. Solov'yov et al., Sci. Rep. 2014, 4, 1-8.).

Electronic couplings for molecular charge transfer: benchmarking CDFT, FODFT, and FODFTB against high-level ab initio calculations

We introduce a database (HAB11) of electronic coupling matrix elements (H(ab)) for electron transfer in 11 π-conjugated organic homo-dimer cations. High-level ab inito calculations at the multireference configuration interaction MRCI+Q level of theory, n-electron valence state perturbation theory NEVPT2, and (spin-component scaled) approximate coupled cluster model (SCS)-CC2 are reported for this database to assess the performance of three DFT methods of decreasing computational cost, including constrained density functional theory (CDFT), fragment-orbital DFT (FODFT), and self-consistent charge density functional tight-binding (FODFTB). We find that the CDFT approach in combination with a modified PBE functional containing 50% Hartree-Fock exchange gives best results for absolute H(ab) values (mean relative unsigned error = 5.3%) and exponential distance decay constants β (4.3%). CDFT in combination with pure PBE overestimates couplings by 38.7% due to a too diffuse excess charge distribution, whereas the economic FODFT and highly cost-effective FODFTB methods underestimate couplings by 37.6% and 42.4%, respectively, due to neglect of interaction between donor and acceptor. The errors are systematic, however, and can be significantly reduced by applying a uniform scaling factor for each method. Applications to dimers outside the database, specifically rotated thiophene dimers and larger acenes up to pentacene, suggests that the same scaling procedure significantly improves the FODFT and FODFTB results for larger π-conjugated systems relevant to organic semiconductors and DNA.

ATP binding and aspartate protonation enhance photoinduced electron transfer in plant cryptochrome

Cryptochromes are flavoproteins encountered in most vegetal and animal species. They play a role of blue-light receptors in plants and in invertebrates. The putative resting state of the FAD cofactor in these proteins is its fully oxidized form, FADox. Upon blue-light excitation, the isoalloxazine ring (ISO) may undergo an ultrafast reduction by a nearby tryptophan residue W400. This primary reduction triggers a cascade of electron and proton transfers, ultimately leading to the formation of the FADH° radical. A recent experimental study has shown that the yield of FADH° formation in Arabidopsis cryptochrome can be strongly modulated by ATP binding and by pH, affecting the protonation state of D396 (proton donor to FAD°(-)). Here we provide a detailed molecular analysis of these effects by means of combined classical molecular dynamics simulations and time-dependent density functional theory calculations. When ATP is present and D396 protonated, FAD remains in close contact with W400, thereby enhancing electron transfer (ET) from W400 to ISO*. In contrast, deprotonation of D396 and absence of ATP introduce flexibility to the photoactive site prior to FAD excitation, with the consequence of increased ISO-W400 distance and diminished tunneling rate by almost two orders of magnitude. We show that under these conditions, ET from the adenine moiety of FAD becomes a competitive relaxation pathway. Overall, our data suggest that the observed effects of ATP and pH on the FAD photoreduction find their roots in the earliest stage of the photoreduction process; i.e., ATP binding and the protonation state of D396 determine the preferred pathway of ISO* relaxation.

Density functional tight binding: values of semi-empirical methods in an ab initio era

Semi-empirical (SE) methods are derived from Hartree-Fock (HF) or Density Functional Theory (DFT) by neglect and approximation of electronic integrals. Thereby, parameters are introduced which have to be determined from reference calculations and/or by fitting to available experimental data. This leads to computational methods that are about 2-3 orders of magnitude faster than the standard HF/DFT methods using medium sized basis sets while being about 3 orders of magnitude slower than empirical force field methods (Molecular Mechanics: MM). Therefore, SE methods are most appropriate for a specific range of applications. These include the study of systems that contain a large number of atoms and therefore being too large for ab initio or DFT methods and also problems where dynamic or entropic effects are particularly important. In the latter case, the errors made by considering a very limited number of molecular structures or neglecting entropic contributions can be much larger than the accuracy lost due to the use of SE methods. Another area where SE methods are attractive concerns the analysis of systems for which reliable MM models are not readily available. Therefore, even in an era when rapid progress is being made in ab initio methods, there is considerable interest in further developing SE methods. We illustrate this point by focusing on the discussion of recent development and application of the Density Functional Tight Binding method.

Computational reference data for the photochemistry of cyclobutane pyrimidine dimers

The cis-syn cyclobutane pyrimidine dimer is one of the major classes of carcinogenic UV-induced DNA photoproducts. In this work, diverse high-level quantum-chemical methods were used to determine the spectroscopic properties of neutral (singlet and triplet) and charged (cation and anion) species of thymine dimers. Maps of potential energy, charge distribution, electron affinity, and ionization potential of the thymidine dimers were computed along the two dimerization coordinates for neutral and charged species, as well as for the singlet excited state. This set of data aims at providing consistent results computed with the same methods as for photodamage and repair. Based on these results, several different photo-, heat-, and charge-induced mechanisms of dimerization and repair are characterized and discussed. Additionally, a new stable dimer with methylmethylidene-hexahydropyrimidine structure was found in the S0 state.

Charge transfer in strongly correlated systems: an exact diagonalization approach to model Hamiltonians

We study charge transfer in bridged di- and triruthenium complexes from a theoretical and computational point of view. Ab initio computations are interpreted from the perspective of a simple empirical Hamiltonian, a chemically specific Mott-Hubbard model of the complexes' π electron systems. This Hamiltonian is coupled to classical harmonic oscillators mimicking a polarizable dielectric environment. The model can be solved without further approximations in a valence bond picture using the method of exact diagonalization and permits the computation of charge transfer reaction rates in the framework of Marcus' theory. In comparison to the exact solution, the Hartree-Fock mean field theory overestimates both the activation barrier and the magnitude of charge-transfer excitations significantly. For triruthenium complexes, we are able to directly access the interruthenium antiferromagnetic coupling strengths.

Dynamic Determination of Active-Site Reactivity in Semiquinone Photolyase by the Cofactor Photoreduction

Photolyase contains a flavin cofactor in a fully reduced form as its functional state to repair ultraviolet-damaged DNA upon blue light absorption. However, after purification, the cofactor exists in its oxidized or neutral semiquinone state. Such oxidization eliminates the repair function, but it can be reverted by photoreduction, a photoinduced process with a series of electron-transfer (ET) reactions. With femtosecond absorption spectroscopy and site-directed mutagenesis, we completely recharacterized such photoreduction dynamics in the semiquinone state. Comparing with all previous studies, we identified a new intramolecular ET pathway, determined stretched ET behaviors, refined all ET time scales, and finally evaluated the driving forces and reorganization energies for eight elementary ET reactions. Combined with the oxidized-state photoreduction dynamics, we elucidated the different active-site properties of the reduction ability and structural flexibility in the oxidized and semiquinone states, leading to the dramatically different ET dynamics and photoreduction efficiency in the two states.