Exploring Intramolecular Reactions in Complex Systems with Metadynamics: The Case of the Malonate Anions

First-Principle Molecular Dynamics Study of Selected Schiff and Mannich Bases: Application of Two-Dimensional Potential of Mean Force to Systems with Strong Intramolecular Hydrogen Bonds

Car-Parrinello Molecular Dynamics simulations were performed for selected anharmonic systems, i.e., Schiff and Mannich base-type compounds, to investigate the vibrational properties associated with O-H stretching. All calculations were performed in the gas phase to compare them with available experimental data. First the vibrational properties of the two compounds were analyzed on the basis of well-established approaches:  Fourier transformation of the autocorrelation function of both the atomic velocities and dipole moments. Then path integral molecular dynamics simulations were performed to demonstrate the influence of quantum effects on the proton's position in the hydrogen bridge. In addition, quantum effects were incorporated a posteriori into calculations of O-H stretching envelopes for the Schiff and Mannich bases. Proton potential snapshots were extracted from the ab initio molecular dynamics trajectory. Vibrational Schrödinger equations (one- and two-dimensional) were solved numerically for the snapshots, and the O-H stretching envelopes were calculated as a superposition of the 0→1 transitions. Subsequently, one- and two-dimensional potentials of mean force (1D and 2D pmf) were calculated for the proton stretching mode from the proton vibrational eigenfunctions and eigenvalues incorporating statistical sampling and nuclear quantum effects. The results show that the applied methodologies are in good agreement with experimental infrared spectra. Additionally, it is demonstrated that the 2D pmf method could be applied in systems with strong anharmonicity to describe the properties of the O-H stretching mode more accurately. Future applications of the 2D pmf technique include, in principle, large biomolecular systems treated within the QM/MM framework.

Paradynamics: an effective and reliable model for ab initio QM/MM free-energy calculations and related tasks

Recent years have seen tremendous effort in the development of approaches with which to obtain quantum mechanics/molecular mechanics (QM/MM) free energies for reactions in the condensed phase. Nevertheless, there remain significant challenges to address, particularly, the high computational cost involved in performing proper configurational sampling and, in particular, in obtaining ab initio QM/MM (QM(ai)/MM) free-energy surfaces. One increasingly popular approach that seems to offer an ideal way to progress in this direction is the elegant metadynamics (MTD) approach. However, in the current work, we point out the subtle efficiency problems associated with this approach and illustrate that we have at hand what is arguably a more powerful approach. More specifically, we demonstrate the effectiveness of an updated version of our original idea of using a classical reference potential for QM(ai)/MM calculations [J. Phys. Chem. 1995, 99, 17516)], which we refer to as paradynamics (PD). This approach is based on the use of an empirical valence bond (EVB) reference potential, which is already similar to the real ab initio potential. The reference potential is fitted to the ab initio potential by an iterative and, to a great degree, automated refinement procedure. The corresponding free-energy profile is then constructed using the refined EVB potential, and the linear response approximation (LRA) is used to evaluate the QM(ai)/MM activation free-energy barrier. The automated refinement of the EVB surface (and thus the reduction of the difference between the reference and ab initio potentials) is a key factor in accelerating the convergence of the LRA approach. We apply our PD approach to a test reaction, namely, the S(N)2 reaction between a chloride ion and methyl chloride, and demonstrate that, at present, this approach is far more powerful and cost-effective than the metadynamics approach (at least in its current implementation). We also discuss the general features of the PD approach in terms of its ability to explore complex systems and clarify that it is not a specialized approach limited to only accelerating QM(ai)/MM calculations with proper sampling, but rather can be used in a wide variety of applications. In fact, we point out that the use of a reference (CG) potential coupled with its PD refinement, as well as our renormalization approach, provides very general and powerful strategies that can be used very effectively to explore any property that has been studied by the MTD approach.

Correlation between fractal dimension and surface characterization by small angle X-ray scattering in marble

Among several analysis techniques applied to the study of surface passivation using dicarboxylic acids, small angle X-ray scattering (SAXS) has proved to be relevant in the physicochemical interpretation of the surface association resulting between calcium carbonate and the molecular structure of malonic acid. It is possible to establish chemical affinity principles through bidimensional geometric analysis in terms of the fractal dimension obtained experimentally by SAXS. In this Article, we present results about the adsorption of malonic acid on calcite, using theoretical and mathematical principles of the fractal dimension.

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.

Progress in ab initio QM/MM free-energy simulations of electrostatic energies in proteins: accelerated QM/MM studies of pKa, redox reactions and solvation free energies

Hybrid quantum mechanical/molecular mechanical (QM/MM) approaches have been used to provide a general scheme for chemical reactions in proteins. However, such approaches still present a major challenge to computational chemists, not only because of the need for very large computer time in order to evaluate the QM energy but also because of the need for proper computational sampling. This review focuses on the sampling issue in QM/MM evaluations of electrostatic energies in proteins. We chose this example since electrostatic energies play a major role in controlling the function of proteins and are key to the structure-function correlation of biological molecules. Thus, the correct treatment of electrostatics is essential for the accurate simulation of biological systems. Although we will be presenting different types of QM/MM calculations of electrostatic energies (and related properties) here, our focus will be on pKa calculations. This reflects the fact that pKa's of ionizable groups in proteins provide one of the most direct benchmarks for the accuracy of electrostatic models of macromolecules. While pKa calculations by semimacroscopic models have given reasonable results in many cases, existing attempts to perform pKa calculations using QM/MM-FEP have led to discrepancies between calculated and experimental values. In this work, we accelerate our QM/MM calculations using an updated mean charge distribution and a classical reference potential. We examine both a surface residue (Asp3) of the bovine pancreatic trypsin inhibitor and a residue buried in a hydrophobic pocket (Lys102) of the T4-lysozyme mutant. We demonstrate that, by using this approach, we are able to reproduce the relevant side chain pKa's with an accuracy of 3 kcal/mol. This is well within the 7 kcal/mol energy difference observed in studies of enzymatic catalysis, and is thus sufficient accuracy to determine the main contributions to the catalytic energies of enzymes. We also provide an overall perspective of the potential of QM/MM calculations in general evaluations of electrostatic free energies, pointing out that our approach should provide a very powerful and accurate tool to predict the electrostatics of not only solution but also enzymatic reactions, as well as the solvation free energies of even larger systems, such as nucleic acid bases incorporated into DNA.

Adaptively biased molecular dynamics for free energy calculations

We present an adaptively biased molecular dynamics (ABMD) method for the computation of the free energy surface of a reaction coordinate using nonequilibrium dynamics. The ABMD method belongs to the general category of umbrella sampling methods with an evolving biasing potential and is inspired by the metadynamics method. The ABMD method has several useful features, including a small number of control parameters and an O(t) numerical cost with molecular dynamics time t. The ABMD method naturally allows for extensions based on multiple walkers and replica exchange, where different replicas can have different temperatures and/or collective variables. This is beneficial not only in terms of the speed and accuracy of a calculation, but also in terms of the amount of useful information that may be obtained from a given simulation. The workings of the ABMD method are illustrated via a study of the folding of the Ace-GGPGGG-Nme peptide in a gaseous and solvated environment.

The free energy landscape of small peptides as obtained from metadynamics with umbrella sampling corrections

There is considerable interest in developing methodologies for the accurate evaluation of free energies, especially in the context of biomolecular simulations. Here, we report on a reexamination of the recently developed metadynamics method, which is explicitly designed to probe "rare events" and areas of phase space that are typically difficult to access with a molecular dynamics simulation. Specifically, we show that the accuracy of the free energy landscape calculated with the metadynamics method may be considerably improved when combined with umbrella sampling techniques. As test cases, we have studied the folding free energy landscape of two prototypical peptides: Ace-(Gly)(2)-Pro-(Gly)(3)-Nme in vacuo and trialanine solvated by both implicit and explicit water. The method has been implemented in the classical biomolecular code AMBER and is to be distributed in the next scheduled release of the code.

Deprotonation of solvated formic acid: Car-Parrinello and metadynamics simulations

The deprotonation of solvated formic acid was investigated theoretically with ab initio simulations. With the Car-Parrinello method, deprotonation and reprotonation by means of a proton wire were observed. The microscopics of these reactions were analyzed, and reveal the key role played by nearby water molecules in catalyzing the reactions. A constrained molecular dynamics calculation was carried out to estimate the dissociation free energy. Deprotonation of formic acid was further investigated with the recently developed metadynamics method using the formic acid oxygen coordination numbers as the collective variables. The determined free-energy landscape gives barriers similar to that obtained with the constrained free-energy calculation.

Equilibrium free energies from nonequilibrium metadynamics

In this Letter we propose a new formalism to map history-dependent metadynamics in a Markovian process. We apply this formalism to model Langevin dynamics and determine the equilibrium distribution of a collection of simulations. We demonstrate that the reconstructed free energy is an unbiased estimate of the underlying free energy and analytically derive an expression for the error. The present results can be applied to other history-dependent stochastic processes, such as Wang-Landau sampling.