Avian cryptochrome 4 binds superoxide.

Flavin-binding cryptochromes are blue-light sensitive photoreceptors that have been implicated with magnetoreception in some species. The photocycle involves an intra-protein photo-reduction of the flavin cofactor, generating a magnetosensitive radical pair, and its subsequent re-oxidation. Superoxide (O2•-) is generated in the re-oxidation with molecular oxygen. The resulting O2•--containing radical pairs have also been hypothesised to underpin various magnetosensitive traits, but due to fast spin relaxation when tumbling in solution would require immobilisation. We here describe our insights in the binding of superoxide to cryptochrome 4 from C. livia based on extensive all-atom molecular dynamics studies and density-functional theory calculations. The positively charged "crypt" region that leads to the flavin binding pocket transiently binds O2•- at 5 flexible binding sites centred on arginine residues. Typical binding times amounted to tens of nanoseconds, but exceptional binding events extended to several hundreds of nanoseconds and slowed the rotational diffusion, thereby realising rotational correlation times as large as 1 ns. The binding sites are particularly efficient in scavenging superoxide escaping from a putative generation site close to the flavin-cofactor, possibly implying a functional relevance. We discuss our findings in view of a potential magnetosensitivity of biological flavin semiquinone/superoxide radical pairs.

Use of Gaussian-Type Functions for Describing Fast Ion-Matter Irradiation with Time-Dependent Density Functional Theory.

The electronic stopping power is an observable property that quantifies the ability of swift ions to penetrate matter to transfer energy to the electron cloud. The recent literature has proven the value of Real-Time Time-Dependent Density Functional Theory to accurately evaluate this property from first-principles, but questions remain regarding the capability of computer codes relying on atom-centered basis functions to capture the physics at play. In this Perspective, we draw attention to the fact that irradiation by swift ions triggers electron emission into the continuum, especially at the Bragg peak. We investigate the ability of Gaussian atomic orbitals (AOC), which were fitted to mimic continuum wave functions, to improve electronic stopping power predictions. AOC are added to standard correlation-consistent basis sets or STO minimal basis sets. Our benchmarks for water irradiation by fast protons clearly advocate for the use of AOC, especially near the Bragg peak. We show that AOC only need to be placed on the molecules struck by the ion. The number of AOC that are added to the usual basis set is relatively small compared to the total number of atomic orbitals, making the use of such a basis set an excellent choice from a computational cost point of view. The optimum basis set combination is applied for the calculation of the stopping power of a proton in water with encouraging agreement with experimental data.

Ab initio derivation of flavin hyperfine interactions for the protein magnetosensor cryptochrome.

The radicals derived from flavin adenine dinucleotide (FAD) are a corner stone of recent hypotheses about magnetoreception, including the compass of migratory songbirds. These models attribute a magnetic sense to coherent spin dynamics in radical pairs within the flavo-protein cryptochrome. The primary determinant of sensitivity and directionality of this process are the hyperfine interactions of the involved radicals. Here, we present a comprehensive computational study of the hyperfine couplings in the protonated and unprotonated FAD radicals in cryptochrome 4 from C. livia. We combine long (800 ns) molecular dynamics trajectories to accurate quantum chemistry calculations. Hyperfine parameters are derived using auxiliary density functional theory applied to cluster and hybrid QM/MM (Quantum Mechanics/Molecular Mechanics) models comprising the FAD and its significant surrounding environment, as determined by a detailed sensitivity analysis. Thanks to this protocol we elucidate the sensitivity of the hyperfine interaction parameters to structural fluctuations and the polarisation effect of the protein environment. We find that the ensemble-averaged hyperfine interactions are predominantly governed by thermally induced geometric distortions of the flavin. We discuss our results in view of the expected performance of these radicals as part of a magnetoreceptor. Our data could be used to parametrize spin Hamiltonians including not only average values but also standard deviations.

Anisotropic magnetic field effects in the re-oxidation of cryptochrome in the presence of scavenger radicals.

The avian compass and many other of nature's magnetoreceptive traits are widely ascribed to the protein cryptochrome. There, magnetosensitivity is thought to emerge as the spin dynamics of radicals in the applied magnetic field enters in competition with their recombination. The first and dominant model makes use of a radical pair. However, recent studies have suggested that magnetosensitivity could be markedly enhanced for a radical triad, the primary radical pair of which undergoes a spin-selective recombination reaction with a third radical. Here, we test the practicality of this supposition for the reoxidation reaction of the reduced FAD cofactor in cryptochrome, which has been implicated with light-independent magnetoreception but appears irreconcilable with the classical radical pair mechanism (RPM). Based on the available realistic cryptochrome structures, we predict the magnetosensitivity of radical triad systems comprising the flavin semiquinone, the superoxide, and a tyrosine or ascorbyl scavenger radical. We consider many hyperfine-coupled nuclear spins, the relative orientation and placement of the radicals, their coupling by the electron-electron dipolar interaction, and spin relaxation in the superoxide radical in the limit of instantaneous decoherence, which have not been comprehensively considered before. We demonstrate that these systems can provide superior magnetosensitivity under realistic conditions, with implications for dark-state cryptochrome magnetoreception and other biological magneto- and isotope-sensitive radical recombination reactions.

Mechanistic Insights on Heme-to-Heme Transmembrane Electron Transfer Within NADPH Oxydases From Atomistic Simulations.

NOX5 is a member of the NADPH oxidase family which is dedicated to the production of reactive oxygen species. The molecular mechanisms governing transmembrane electron transfer (ET) that permits to shuttle electrons over the biological membrane have remained elusive for a long time. Using computer simulations, we report conformational dynamics of NOX5 embedded within a realistic membrane environment. We assess the stability of the protein within the membrane and monitor the existence of cavities that could accommodate dioxygen molecules. We investigate the heme-to-heme electron transfer. We find a reaction free energy of a few tenths of eV (ca. -0.3 eV) and a reorganization free energy of around 1.1 eV (0.8 eV after including electrostatic induction corrections). The former indicates thermodynamically favorable ET, while the latter falls in the expected values for transmembrane inter-heme ET. We estimate the electronic coupling to fall in the range of the µeV. We identify electron tunneling pathways showing that not only the W378 residue is playing a central role, but also F348. Finally, we reveal the existence of two connected O2-binding pockets near the outer heme with fast exchange between the two sites on the nanosecond timescale. We show that when the terminal heme is reduced, O2 binds closer to it, affording a more efficient tunneling pathway than when the terminal heme is oxidized, thereby providing an efficient mechanism to catalyze superoxide production in the final step. Overall, our study reveals some key molecular mechanisms permitting reactive oxygen species production by NOX5 and paves the road for further investigation of ET processes in the wide family of NADPH oxidases by computer simulations.

Molecular Simulations with in-deMon2k QM/MM, a Tutorial-Review.

deMon2k is a readily available program specialized in Density Functional Theory (DFT) simulations within the framework of Auxiliary DFT. This article is intended as a tutorial-review of the capabilities of the program for molecular simulations involving ground and excited electronic states. The program implements an additive QM/MM (quantum mechanics/molecular mechanics) module relying either on non-polarizable or polarizable force fields. QM/MM methodologies available in deMon2k include ground-state geometry optimizations, ground-state Born-Oppenheimer molecular dynamics simulations, Ehrenfest non-adiabatic molecular dynamics simulations, and attosecond electron dynamics. In addition several electric and magnetic properties can be computed with QM/MM. We review the framework implemented in the program, including the most recently implemented options (link atoms, implicit continuum for remote environments, metadynamics, etc.), together with six applicative examples. The applications involve (i) a reactivity study of a cyclic organic molecule in water; (ii) the establishment of free-energy profiles for nucleophilic-substitution reactions by the umbrella sampling method; (iii) the construction of two-dimensional free energy maps by metadynamics simulations; (iv) the simulation of UV-visible absorption spectra of a solvated chromophore molecule; (v) the simulation of a free energy profile for an electron transfer reaction within Marcus theory; and (vi) the simulation of fragmentation of a peptide after collision with a high-energy proton.

Simulating Electron Dynamics in Polarizable Environments.

We propose a methodology for simulating attosecond electron dynamics in large molecular systems. Our approach is based on the combination of real time time-dependent-density-functional theory (RT-TDDFT) and polarizable Molecular Mechanics (MMpol) with the point-charge-dipole model of electrostatic induction. We implemented this methodology in the software deMon2k that relies heavily on auxiliary fitted densities. In the context of RT-TDDFT/MMpol simulations, fitted densities allow the cost of the calculations to be reduced drastically on three fronts: (i) the Kohn-Sham potential, (ii) the electric field created by the (fluctuating) electron cloud which is needed in the QM/MM interaction, and (iii) the analysis of the fluctuating electron density on-the-fly. We determine conditions under which fitted densities can be used without jeopardizing the reliability of the simulations. Very encouraging results are found both for stationary and time-dependent calculations. We report absorption spectra of a dye molecule in the gas phase, in nonpolarizable water, and in polarizable water. Finally, we use the method to analyze the distance-dependent response of the environment of a peptide perturbed by an electric field. Different response mechanisms are identified. It is shown that the induction on MM sites allows excess energy to dissipate from the QM region to the environment. In this regard, the first hydration shell plays an essential role in absorbing energy. The methodology presented herein opens the possibility of simulating radiation-induced electronic phenomena in complex and extended molecular systems.

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. Charge separation involves chains of three or four tryptophan residues depending on the protein of interest. The molecular mechanisms of these processes are not completely clear. In the present work we investigate the relevance of quantum effects like the occurrence of nuclear tunneling and of coherences upon charge transfer in Arabidopsis thaliana cryptochromes. The possible breakdown of the Condon approximation is also investigated. We have devised a simulation protocol based on the realization of molecular dynamics simulations on diabatic potential energy surfaces defined at the hybrid constrained density functional theory/molecular mechanics level. The outcomes of the simulations are analyzed through various dedicated kinetics schemes related to the Marcus theory that account for the aforementioned quantum effects. MD simulations also provide a basic material to define realistic model Hamiltonians for subsequent quantum dissipative dynamics. To carry out quantum simulations, we have implemented an algorithm based on the Hierarchical Equations of Motion. With this new tool in hand we have been able to model the electron transfer chain considering either two- or three-state models. Kinetic models and quantum simulations converge to the conclusion that quantum effects have a significant impact on the rate of charge separation. Nuclear tunneling involving atoms of the tryptophan redox cofactors as well as of the environment (protein atoms and water molecules) is significant. On the other hand non-Condon effects are negligible in most simulations. Taken together, the results of the present work provide new insights into the molecular mechanisms controlling charge separation in this family of flavoproteins.

Energetics of Photoinduced Charge Migration within the Tryptophan Tetrad of an Animal (6-4) Photolyase.

Cryptochromes and photolyases are flavoproteins that undergo cascades of electron/hole transfers after excitation of the flavin cofactor. It was recently discovered that animal (6-4) photolyases, as well as animal cryptochromes, feature a chain of four tryptophan residues, while other members of the family contain merely a tryptophan triad. Transient absorption spectroscopy measurements on Xenopus laevis (6-4) photolyase have shown that the fourth residue is effectively involved in photoreduction but at the same time could not unequivocally ascertain the final redox state of this residue. In this article, polarizable molecular dynamics simulations and constrained density functional theory calculations are carried out to reveal the energetics of charge migration along the tryptophan tetrad. Migration toward the fourth tryptophan is found to be thermodynamically favorable. Electron transfer mechanisms are sought either through an incoherent hopping mechanism or through a multiple sites tunneling process. The Jortner-Bixon formulation of electron transfer (ET) theory is employed to characterize the hopping mechanism. The interplay between electron transfer and relaxation of protein and solvent is analyzed in detail. Our simulations confirm that ET in (6-4) photolyase proceeds out of equilibrium. Multiple site tunneling is modeled with the recently proposed flickering resonance mechanism. Given the position of energy levels and the distribution of electronic coupling values, tunneling over three tryptophan residues may become competitive in some cases, although a hopping mechanism is likely to be the dominant channel. For both reactive channels, computed rates are very sensitive to the starting protein configuration, suggesting that both can take place and eventually be mixed, depending on the state of the system when photoexcitation takes place.

QM/MM calculations with deMon2k.

The density functional code deMon2k employs a fitted density throughout (Auxiliary Density Functional Theory), which offers a great speed advantage without sacrificing necessary accuracy. Powerful Quantum Mechanical/Molecular Mechanical (QM/MM) approaches are reviewed. Following an overview of the basic features of deMon2k that make it efficient while retaining accuracy, three QM/MM implementations are compared and contrasted. In the first, deMon2k is interfaced with the CHARMM MM code (CHARMM-deMon2k); in the second MM is coded directly within the deMon2k software; and in the third the Chemistry in Ruby (Cuby) wrapper is used to drive the calculations. Cuby is also used in the context of constrained-DFT/MM calculations. Each of these implementations is described briefly; pros and cons are discussed and a few recent applications are described briefly. Applications include solvated ions and biomolecules, polyglutamine peptides important in polyQ neurodegenerative diseases, copper monooxygenases and ultra-rapid electron transfer in cryptochromes.

Electron transfer, decoherence, and protein dynamics: insights from atomistic simulations.

Electron transfer in biological systems drives the processes of life. From cellular respiration to photosynthesis and enzymatic catalysis, electron transfers (ET) are chemical processes on which essential biological functions rely. Over the last 40 years, scientists have sought understanding of how these essential processes function in biology. One important breakthrough was the discovery that Marcus theory (MT) of electron transfer is applicable to biological systems. Chemists have experimentally collected both the reorganization energies (λ) and the driving forces (ΔG°), two parameters of Marcus theory, for a large variety of ET processes in proteins. At the same time, theoretical chemists have developed computational approaches that rely on molecular dynamics and quantum chemistry calculations to access numerical estimates of λ and ΔG°. Yet another crucial piece in determining the rate of an electron transfer is the electronic coupling between the initial and final electronic wave functions. This is an important prefactor in the nonadiabatic rate expression, since it reflects the probability that an electron tunnels from the electron donor to the acceptor through the intervening medium. The fact that a protein matrix supports electron tunneling much more efficiently than vacuum is now well documented, both experimentally and theoretically. Meanwhile, many chemists have provided examples of the rich physical chemistry that can be induced by protein dynamics. This Account describes our studies of the dynamical effects on electron tunneling. We present our analysis of two examples of natural biological systems through MD simulations and tunneling pathway analyses. Through these examples, we show that protein dynamics sustain efficient tunneling. Second, we introduce two time scales: τcoh and τFC. The former characterizes how fast the electronic coupling varies with nuclear vibrations (which cause dephasing). The latter reflects the time taken by the system to leave the crossing region. In the framework of open quantum systems, τFC is a short time approximation of the characteristic decoherence time of the electronic subsystem in interaction with its nuclear environment. The comparison of the respective values of τcoh and τFC allows us to probe the occurrence of non-Condon effects. We use ab initio MD simulations to analyze how decoherence appears in several biological cofactors. We conclude that we cannot account for its order of magnitude by considering only the atoms or bonds directly concerned with the transfer. Decoherence results from contributions from all atoms of the system appearing with a time delay that increases with the distance from the primarily concerned atoms or bonds. The delay and magnitude of the contributions depend on the chemical nature of the system. Finally, we present recent developments based on constrained DFT for efficient and accurate evaluations of the electronic coupling in ab initio MD simulations. These are promising methods to study the subtle fluctuations of the electronic coupling and the mechanisms of electronic decoherence in biological systems.

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.

Calibration of forcefields for molecular simulation: sequential design of computer experiments for building cost-efficient kriging metamodels.

We present a global strategy for molecular simulation forcefield optimization, using recent advances in Efficient Global Optimization algorithms. During the course of the optimization process, probabilistic kriging metamodels are used, that predict molecular simulation results for a given set of forcefield parameter values. This enables a thorough investigation of parameter space, and a global search for the minimum of a score function by properly integrating relevant uncertainty sources. Additional information about the forcefield parameters are obtained that are inaccessible with standard optimization strategies. In particular, uncertainty on the optimal forcefield parameters can be estimated, and transferred to simulation predictions. This global optimization strategy is benchmarked on the TIP4P water model.

Statistical approaches to forcefield calibration and prediction uncertainty in molecular simulation.

Calibration of forcefields for molecular simulation should account for the measurement uncertainty of the reference dataset and for the model inadequacy, i.e., the inability of the force-field/simulation pair to reproduce experimental data within their uncertainty range. In all rigour, the resulting uncertainty of calibrated force-field parameters is a source of uncertainty for simulation predictions. Various calibration strategies and calibration models within the Bayesian calibration/prediction framework are explored in the present article. In the case of Lennard-Jones potential for Argon, we show that prediction uncertainty for thermodynamical and transport properties, albeit very small, is larger than statistical simulation uncertainty.

Water nanodroplets confined in zeolite pores.

We provide a comprehensive depiction of the behaviour of a nanodroplet of approximately equal to 20 water molecules confined in the pores of a series of 3D-connected isostructural zeolites with varying acidity, by means of molecular simulations. Both grand canonical Monte Carlo simulations using classical interatomic forcefields and first-principles Car-Parrinello molecular dynamics were used in order to characterise the behaviour of confined water by computing a range of properties, from thermodynamic quantities to electronic properties such as dipole moment, including structural and dynamical information. From the thermodynamic point of view, we have identified the all-silica zeolite as hydrophobic, and the cationic zeolites as hydrophilic; the condensation transition in the first case was demonstrated to be of first order. Furthermore, in-depth analysis of the dynamical and electronic properties of water showed that water in the hydrophobic zeolite behaves as a nanodroplet trying to close its hydrogen-bond network onto itself, with a few short-lived dangling OH groups, while water in hydrophilic zeolites "opens up" to form weak hydrogen bonds with the zeolite oxygen atoms. Finally, the dipole moment of confined water is studied and the contributions of water self-polarisation and the zeolite electric field are discussed.

Thermodynamics of water intrusion in nanoporous hydrophobic solids.

We report a joint experimental and molecular simulation study of water intrusion in silicalite-1 and ferrerite zeolites. The main conclusion of this study is that water condensation takes place through a genuine first-order phase transition, provided that the interconnected pores structure is 3-dimensional. In the extreme confinement situation (ferrierite zeolite), condensation takes place through a continuous transition, which is explained by a shift of both the first-order transition line and the critical point with increasing confinement. The present findings are at odds with the common belief that conventional phase transitions cannot take place in microporous solids such as zeolites. The most important features of the intrusion/extrusion process can be understood in terms of equilibrium thermodynamics considerations. We believe that these findings are very general for hydrophobic solids, i.e. for both nonwetting as well as wetting water-solid interface systems.

Dynamics and stability of E-cadherin dimers.

The extracellular domains of cadherins are known to play a major role in cell adhesion, although the structures involved in this process remain unclear. We have used molecular dynamics to characterize the conformational and thermodynamic properties of two of the dimer interfaces identified in E-cadherin crystals and involving the two outermost exodomains (EC1 and EC2): a dimer involving exchange of the N-terminal strand (referred to as the "swapped" dimer) and a "staggered" dimer involving an EC1-EC2 interface. The results show that the staggered dimer involves a much smaller interface area and is notably less stable than the swapped dimer. It is also found that, despite its stability, the swapped dimer undergoes a conformational transition leading to a structure closer to that experimentally observed for the homologous C-cadherin. Finally, comparing the simulated dimer structures with the sequences of E-, C-, and N-cadherins shows that the swapped dimer interface involves surprisingly few residues that vary from family to family and notably no changes between the E- and C-cadherin exodomains.

Secondary structure assignment that accurately reflects physical and evolutionary characteristics.

BACKGROUND: Secondary structure is used in hierarchical classification of protein structures, identification of protein features, such as helix caps and loops, for fold recognition, and as a precursor to ab initio structure prediction. There are several methods available for assigning secondary structure if the three-dimensional structure of the protein is known. Unfortunately they differ in their definitions, particularly in the exact positions of the termini. Additionally, most existing methods rely on hydrogen bonding, which means that important secondary structural classes, such as isolated beta-strands and poly-proline helices cannot be identified as they do not have characteristic hydrogen-bonding patterns. For this reason we have developed a more accurate method for assigning secondary structure based on main chain geometry, which also allows a more comprehensive assignment of secondary structure. RESULTS: We define secondary structure based on a number of geometric parameters. Helices are defined based on whether they fit inside an imaginary cylinder: residues must be within the correct radius of a central axis. Different types of helices (alpha, 3(10) or pi) are assigned on the basis of the angle between successive peptide bonds. beta-strands are assigned based on backbone dihedrals and with alternating peptide bonds. Thus hydrogen bonding is not required and beta-strands can be within a parallel sheet, antiparallel sheet, or can be isolated. Poly-proline helices are defined similarly, although with three-fold symmetry. CONCLUSION: We find that our method better assigns secondary structure than existing methods. Specifically, we find that comparing our methods with those of others, amino-acid trends at helix caps are stronger, secondary structural elements less likely to be concatenated together and secondary structure guided sequence alignment is improved. We conclude, therefore, that secondary structure assignments using our method better reflects physical and evolutionary characteristics of proteins. The program is available from http://www.bioinf.man.ac.uk/~lovell/segno.shtml.

Cadherin mechanics and complexation: the importance of calcium binding.

E-cadherins belong to a family of membrane-bound, cellular adhesion proteins. Their adhesive properties mainly involve the two N-terminal extracellular domains (EC1 and EC2). The junctions between these domains are characterized by calcium ion binding sites, and calcium ions are essential for the correct functioning of E-cadherins. Calcium is believed to rigidify the extracellular portion of the protein, which, when complexed, adopts a rod-like conformation. Here, we use molecular dynamics simulations to investigate the dynamics of the EC1-2 portion of E-cadherin in the presence and in the absence of calcium ions. These simulations confirm that apo-cadherin shows much higher conformational flexibility on a nanosecond timescale than the calcium-bound form. It is also shown that although the apo-cadherin fragment can spontaneously complex potassium, these monovalent ions are incapable of rigidifying the interdomain junctions. In contrast, removal of the most solvent-exposed calcium ion at the EC1-2 junction does not significantly perturb the dynamical behavior of the fragment. We have also extended this study to the cis-dimer formed from two EC1-2 fragments, potentially involved in cellular adhesion. Here again, it is shown that the presence of calcium is an important factor in both rigidifying and stabilizing the complex.