Efficient exploration of reactive potential energy surfaces using Car-Parrinello molecular dynamics

Temperature accelerated Monte Carlo (TAMC): a method for sampling the free energy surface of non-analytical collective variables

We introduce a new method to simulate the physics of rare events. The method, an extension of the Temperature Accelerated Molecular Dynamics, comes in use when the collective variables introduced to characterize the rare events are either non-analytical or so complex that computing their derivative is not practical. We illustrate the functioning of the method by studying the homogeneous crystallization in a sample of Lennard-Jones particles. The process is studied by introducing a new collective variable that we call Effective Nucleus Size N. We have computed the free energy barriers and the size of critical nucleus, which result in agreement with data available in the literature. We have also performed simulations in the liquid domain of the phase diagram. We found a free energy curve monotonically growing with the nucleus size, consistent with the liquid domain.

Ab initio thermochemistry of solid-state materials

In this contribution we introduce an electronic-structure-theory-based approach to a quantum-chemical thermochemistry of solids. We first deal with local and collective atomic displacements and explain how to calculate these. The fundamental importance of the phonons, their dispersion relations, their experimental determination as well as their calculation is elucidated, followed by the systematic construction of the thermodynamic potentials on this basis. Subsequently, we provide an introduction for practical computation as well as a critical analysis of the level of accuracy obtainable. We then show how different solid-state chemistry problems can be solved using this approach. Among these are the calculation of activation energies in perovskite-like oxides, but we also consider the use of theoretical vibrational frequencies for determining crystal structures. The pressure and temperature polymorphism of elemental tin which has often been classically described is also treated, and we energetically classify the metastable oxynitrides of tantalum. We also demonstrate, using the case of high-temperature superconductors, that such calculations may be used for an independent evaluation of thermochemical data of unsatisfactory accuracy. Finally, we show the present limits and the future challenges of the theory.

Cobalt-porphyrin catalyzed electrochemical reduction of carbon dioxide in water. 2. Mechanism from first principles

We apply first principles computational techniques to analyze the two-electron, multistep, electrochemical reduction of CO(2) to CO in water using cobalt porphyrin as a catalyst. Density functional theory calculations with hybrid functionals and dielectric continuum solvation are used to determine the steps at which electrons are added. This information is corroborated with ab initio molecular dynamics simulations in an explicit aqueous environment which reveal the critical role of water in stabilizing a key intermediate formed by CO(2) bound to cobalt. By use of potential of mean force calculations, the intermediate is found to spontaneously accept a proton to form a carboxylate acid group at pH < 9.0, and the subsequent cleavage of a C-OH bond to form CO is exothermic and associated with a small free energy barrier. These predictions suggest that the proposed reaction mechanism is viable if electron transfer to the catalyst is sufficiently fast. The variation in cobalt ion charge and spin states during bond breaking, DFT+U treatment of cobalt 3d orbitals, and the need for computing electrochemical potentials are emphasized.

Real-world predictions from ab initio molecular dynamics simulations

In this review we present the techniques of ab initio molecular dynamics simulation improved to its current stage where the analysis of existing processes and the prediction of further chemical features and real-world processes are feasible. For this reason we describe the relevant developments in ab initio molecular dynamics leading to this stage. Among them, parallel implementations, different basis set functions, density functionals, and van der Waals corrections are reported. The chemical features accessible through AIMD are discussed. These are IR, NMR, as well as EXAFS spectra, sampling methods like metadynamics and others, Wannier functions, dipole moments of molecules in condensed phase, and many other properties. Electrochemical reactions investigated by ab initio molecular dynamics methods in solution, on surfaces as well as complex interfaces, are also presented.

Protonation of a hydroxide anion bridging two divalent magnesium cations in water probed by first-principles metadynamics simulation

The protonation of a hydroxide anion (OH(-)) located between two magnesium cations (Mg(2+)) in aqueous solution has been investigated by first-principles metadynamics simulation. We observe that the complex Mg(2+)-OH(-)-Mg(2+) is stabilized by the coparticipation of the hydroxide anion to the first hydration shells of both the Mg(2+) cations. Contrary to the cases of OH(-) in pure water, the transfer of protons in the presence of the divalent metal ions turns out to be a slow chemical event. This can be ascribed to the decreased proton affinity of the bridging OH(-). Metadynamics simulation, used to overcome the difficulty of the long time scale required by the protonation of the bridging OH(-), has shown that the system possesses a great stability on the reactant state, characterized by a bioctahedral (6,6) solvation structure around the two Mg(2+) cations. The exploration of the free energy landscape shows that this stable bioctahedral configuration converts into a lower coordinated (5,6) structure, leading to a proton transfer from a water molecule belonging to the first solvation shell of the Mg(2+) ion having the lower coordination to the bridging OH(-); the free energy barrier for the protonation reaction is 11 kcal/mol, meaning that the bridging hydroxide is a weak base. During the proton transfer, the bridging OH(-) reverts to an H(2)O molecule, and this breaks the electrostatic coupling of the two Mg(2+) ions, which depart independently with their own hydration shells, one of which is entirely formed by water molecules. The second one carries the newly created OH(-). Our results show that the flexibility in the metal coordination plays a crucial role in both the protonation process of the bridging OH(-) and the separation of the metal cations, providing useful insight into the nature of proton transfer in binuclear divalent metal ions, with several biological implications, such as, for instance, transesterification of catalytic RNA.

H2CO3 forms via HCO3- in water

According to the generally accepted picture of CO(2) dissolution in water, the formation of H(2)CO(3) proceeds in a single step that involves the attack of a water oxygen on the CO(2) carbon in concert with a proton transfer to a CO(2) oxygen. In the present work, a series of ab initio molecular dynamics simulations have been carried out along with the metadynamics technique which reveals a stepwise mechanism: the reaction of a water molecule with CO(2) yields HCO(3)(-) as an intermediate and a hydronium ion, whereas the protonation of the CO(2) moiety occurs in a separate step representing a well-defined activation barrier toward the H(2)CO(3) molecule. This alternative scenario was already taken into consideration decades ago, but subsequent experiments and calculations have given preference to the concerted mechanism. Employing extended periodic models of the CO(2)-water system that mimic the bulk aqueous environment, the present simulations yield the complete free energy profile of the stepwise mechanism and provide a detailed microscopic mechanism of the elementary steps. HCO(3)(-) formation is found to be the rate-determining step of the entire CO(2) hydration process.

On the role of water in peroxidase catalysis: a theoretical investigation of HRP compound I formation

We have investigated the dynamics of water molecules in the distal pocket of horseradish peroxidase to elucidate the role that they may play in the formation of the principal active species of the enzymatic cycle (compound I, Por(o+)-Fe(IV)=O) upon reaction of the resting Fe(III) state with hydrogen peroxide. The equilibrium molecular dynamics simulations show that, in accord with experimental evidence, the active site access channel is hydrated with an average of two to three water molecules within 5 A from the bound hydrogen peroxide. Although the channel is always hydrated, the specific conformations in which a water molecule bridges H(2)O(2) and the distal histidine, which were found (Derat; et al. J. Am. Chem. Soc. 2007, 129, 6346.) to display a low-energy barrier for the initial acid-base step of the reaction, occur with low probability but are relevant within the time scale of catalysis. Metadynamics simulations, which were used to reconstruct the free-energy landscape of water motion in the access channel, revealed that preferred interaction sites within the channel are separated by small energy barriers (<1.5 kcal/mol). Most importantly, water-bridged conformations lie on a shoulder just 1 kcal/mol above one local minimum and thus are easily accessible. Such an energy landscape appears as a requisite for the effectiveness of compound I formation, whereby the H-bonding pattern involving reactants and catalytic residues (including the intervening water molecule) has to rearrange to deliver the proton to the distal OH moiety of the hydrogen peroxide and thereby lead to heterolytic O-O cleavage. Our study provides an example of a system for which the "reactive configurations" (i.e., structures characterized by a low barrier for the chemical transformation) correspond to a minor population of the system and show how equilibrium molecular dynamics and free-energy calculations may conveniently be used to ascertain that such reactive conformations are indeed accessible to the system. Once again, the MD and QM/MM combination shows that a single water molecule acts as a biocatalyst in the cycle of HRP.

ORAC: a molecular dynamics simulation program to explore free energy surfaces in biomolecular systems at the atomistic level

We present the new release of the ORAC engine (Procacci et al., Comput Chem 1997, 18, 1834), a FORTRAN suite to simulate complex biosystems at the atomistic level. The previous release of the ORAC code included multiple time steps integration, smooth particle mesh Ewald method, constant pressure and constant temperature simulations. The present release has been supplemented with the most advanced techniques for enhanced sampling in atomistic systems including replica exchange with solute tempering, metadynamics and steered molecular dynamics. All these computational technologies have been implemented for parallel architectures using the standard MPI communication protocol. ORAC is an open-source program distributed free of charge under the GNU general public license (GPL) at http://www.chim.unifi.it/orac.

Thermal nanostructure: an order parameter multiscale ensemble approach

Deductive all-atom multiscale techniques imply that many nanosystems can be understood in terms of the slow dynamics of order parameters that coevolve with the quasiequilibrium probability density for rapidly fluctuating atomic configurations. The result of this multiscale analysis is a set of stochastic equations for the order parameters whose dynamics is driven by thermal-average forces. We present an efficient algorithm for sampling atomistic configurations in viruses and other supramillion atom nanosystems. This algorithm allows for sampling of a wide range of configurations without creating an excess of high-energy, improbable ones. It is implemented and used to calculate thermal-average forces. These forces are then used to search the free-energy landscape of a nanosystem for deep minima. The methodology is applied to thermal structures of Cowpea chlorotic mottle virus capsid. The method has wide applicability to other nanosystems whose properties are described by the CHARMM or other interatomic force field. Our implementation, denoted SIMNANOWORLD, achieves calibration-free nanosystem modeling. Essential atomic-scale detail is preserved via a quasiequilibrium probability density while overall character is provided via predicted values of order parameters. Applications from virology to the computer-aided design of nanocapsules for delivery of therapeutic agents and of vaccines for nonenveloped viruses are envisioned.

Metadynamics convergence law in a multidimensional system

Metadynamics is a powerful sampling technique that uses a nonequilibrium history-dependent process to reconstruct the free-energy surface as a function of the relevant collective variables s . In Bussi [Phys. Rev. Lett. 96, 090601 (2006)] it is proved that, in a Langevin process, metadynamics provides an unbiased estimate of the free energy F(s) . We here study the convergence properties of this approach in a multidimensional system, with a Hamiltonian depending on several variables. Specifically, we show that in a Monte Carlo metadynamics simulation of an Ising model the time average of the history-dependent potential converge to F(s) with the same law of an umbrella sampling performed in optimal conditions (i.e., with a bias exactly equal to the negative of the free energy). Remarkably, after a short transient, the error becomes approximately independent on the filling speed, showing that even in out-of-equilibrium conditions metadynamics allows recovering an accurate estimate of F(s) . These results have been obtained introducing a functional form of the history-dependent potential that avoids the onset of systematic errors near the boundaries of the free-energy landscape.

Analysis of the reaction coordinate of alpha-L-fucosidases: a combined structural and quantum mechanical approach

The enzymatic hydrolysis of alpha-L-fucosides is of importance in cancer, bacterial infections, and fucosidosis, a neurodegenerative lysosomal storage disorder. Here we show a series of snapshots along the reaction coordinate of a glycoside hydrolase family GH29 alpha-L-fucosidase unveiling a Michaelis (ES) complex in a (1)C(4) (chair) conformation and a covalent glycosyl-enzyme intermediate in (3)S(1) (skew-boat). First principles metadynamics simulations on isolated alpha-L-fucose strongly support a (1)C(4)<-->(3)H(4)<-->(3)S(1) conformational itinerary for the glycosylation step of the reaction mechanism and indicate a strong "preactivation" of the (1)C(4) complex to nucleophilic attack as reflected by free energy, C1-O1/O5-C1 bond length elongation/reduction, C1-O1 bond orientation, and positive charge development around the anomeric carbon. Analysis of an imino sugar inhibitor is consistent with tight binding of a chair-conformed charged species.

Theoretical spectroscopy of floppy peptides at room temperature. A DFTMD perspective: gas and aqueous phase

Theoretical spectroscopy is mandatory for a precise understanding and assignment of experimental spectra recorded at finite temperature. We review here room temperature DFT-based molecular dynamics simulations for the purpose of interpreting finite temperature infrared spectra of peptides of increasing size and complexity, in terms of temperature-dependent conformational dynamics and flexibility, and vibrational anharmonicities (potential energy surface anharmonicities, vibrational mode couplings and dipole anharmonicities). We take examples from our research projects in order to illustrate the main key-points and strengths of dynamical spectra modeling in that context. The calculations are presented in relation to room temperature gas phase IR-MPD experiments and room temperature liquid phase IR absorption experiments. These illustrations of floppy polypeptides have been chosen in order to convey the following ideas: temperature-dependent spectra modeling is pivotal for a precise understanding of gas phase spectra recorded at room temperature, including conformational dynamics and vibrational anharmonicities; harmonic spectroscopy (as commonly performed in the literature) can be misleading and even erroneous for a proper interpretation of spectra recorded at finite temperature; taking into account vibrational anharmonicities is pivotal for a proper interplay between theory and experiments; amide I-III bands are not necessarily the most relevant fingerprints for unraveling the local structures of peptides and more complex systems; liquid phase simulations have unraveled relationships between the zwitterionic properties of the peptide bonds and infrared signatures. The review presents a state-of-the-art account of the domain and offers perspectives and new developments for future still more challenging applications.

Modelling components of future molecular devices

We discuss challenges involved in modelling different components of molecular devices and give several examples that demonstrate how computer modelling evolved over the last few years to become a comprehensive tool for designing molecules, predicting their adsorption and diffusion at surfaces, simulating atomic force microscopy imaging and manipulation of atoms and molecules at insulating surfaces and studying electron conduction in prototype molecular devices. We describe some of the computational techniques used for modelling adsorption, diffusion, imaging and manipulation of organic molecules at surfaces and challenges pertaining to these studies, give several examples of applications and discuss further prospects for theoretical modelling of complex organic molecules at surfaces.

The effects of water on beta-D-xylose condensation reactions

Car-Parrinello-based ab initio molecular dynamics simulations (CPMD) combined with metadynamics (MTD) simulations were used to determine the reaction energetics for the beta-D-xylose condensation reaction to form beta-1,4-linked xylobiose in a dilute acid solution. Protonation of the hydroxyl group on the xylose molecule and the subsequent breaking of the C-O bond were found to be the rate-limiting step during the xylose condensation reaction. Water and water structure was found to play a critical role in these reactions due to the proton's high affinity for water molecules. The reaction free energy and reaction barrier were determined using CPMD-MTD. We found that solvent reorganization due to proton partial desolvation must be taken into account in order to obtain the correct reaction activation energy. Our calculated reaction free energy and reaction activation energy compare well with available experimental results.

Peptide synthesis in aqueous environments: the role of extreme conditions on peptide bond formation and peptide hydrolysis

The mechanisms and free energetics underlying the formation of peptides from alpha-amino acids and alpha-amino acid N-carboxyanhydrides (NCAs) in bulk water at both ambient and extreme temperature and pressure conditions were investigated using accelerated ab initio molecular dynamics. In particular, peptide bond formation using an activated amino acid in form of its NCA, subsequent decarboxylation, as well as hydrolysis of the formed peptide were studied using glycine. It is shown to what extent thermodynamic conditions affect the reaction mechanisms qualitatively and the energetics quantitatively in solution. In particular, the zwitterionic intermediate in the peptidization step found in ambient water degenerates into a transient species in hot-pressurized water, whereas the hydrolysis reaction is found to follow qualitatively different pathways at ambient and extreme conditions. The work also quantifies the impact of extreme solvent conditions on both peptide bond formation and peptide hydrolysis in aqueous media. Beyond the specific case, the results provide important insights into how elevated temperatures and increased pressures affect organic reactions in aqueous solutions.

Examining ion channel properties using free-energy methods

Recent advances in structural biology have revealed the architecture of a number of transmembrane channels, allowing for these complex biological systems to be understood in atomistic detail. Computational simulations are a powerful tool by which the dynamic and energetic properties, and thereby the function of these protein architectures, can be investigated. The experimentally observable properties of a system are often determined more by energetic than dynamics, and therefore understanding the underlying free energy (FE) of biophysical processes is of crucial importance. Critical to the accurate evaluation of FE values are the problems of obtaining accurate sampling of complex biological energy landscapes, and of obtaining accurate representations of the potential energy of a system, this latter problem having been addressed through the development of molecular force fields. While these challenges are common to all FE methods, depending on the system under study, and the questions being asked of it, one technique for FE calculation may be preferable to another, the choice of method and simulation protocol being crucial to achieve efficiency. Applied in a correct manner, FE calculations represent a predictive and affordable computational tool with which to make relevant contact with experiments. This chapter, therefore, aims to give an overview of the most widely implemented computational methods used to calculate the FE associated with particular biochemical or biophysical events, and to highlight their recent applications to ion channels.

Theoretical studies of RNA catalysis: hybrid QM/MM methods and their comparison with MD and QM

Hybrid QM/MM methods combine the rigor of quantum mechanical (QM) calculations with the low computational cost of empirical molecular mechanical (MM) treatment allowing to capture dynamic properties to probe critical atomistic details of enzyme reactions. Catalysis by RNA enzymes (ribozymes) has only recently begun to be addressed with QM/MM approaches and is thus still a field under development. This review surveys methodology as well as recent advances in QM/MM applications to RNA mechanisms, including those of the HDV, hairpin, and hammerhead ribozymes, as well as the ribosome. We compare and correlate QM/MM results with those from QM and/or molecular dynamics (MD) simulations, and discuss scope and limitations with a critical eye on current shortcomings in available methodologies and computer resources. We thus hope to foster mutual appreciation and facilitate collaboration between experimentalists and theorists to jointly advance our understanding of RNA catalysis at an atomistic level.