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

Multiscale enhanced path sampling based on the Onsager-Machlup action: application to a model polymer

We propose a novel path sampling method based on the Onsager-Machlup (OM) action by generalizing the multiscale enhanced sampling technique suggested by Moritsugu and co-workers [J. Chem. Phys. 133, 224105 (2010)]. The basic idea of this method is that the system we want to study (for example, some molecular system described by molecular mechanics) is coupled to a coarse-grained (CG) system, which can move more quickly and can be computed more efficiently than the original system. We simulate this combined system (original + CG system) using Langevin dynamics where different heat baths are coupled to the two systems. When the coupling is strong enough, the original system is guided by the CG system, and is able to sample the configuration and path space with more efficiency. We need to correct the bias caused by the coupling, however, by employing the Hamiltonian replica exchange, where we prepare many path replicas with different coupling strengths. As a result, an unbiased path ensemble for the original system can be found in the weakest coupling path ensemble. This strategy is easily implemented because a weight for a path calculated by the OM action is formally the same as the Boltzmann weight if we properly define the path "Hamiltonian." We apply this method to a model polymer with Asakura-Oosawa interaction, and compare the results with the conventional transition path sampling method.

Nylon-Oligomer Hydrolase Promoting Cleavage Reactions in Unnatural Amide Compounds

The active site of 6-aminohexanoate-dimer hydrolase, a nylon-6 byproduct-degrading enzyme with a β-lactamase fold, possesses a Ser112/Lys115/Tyr215 catalytic triad similar to the one of penicillin-recognizing family of serine-reactive hydrolases but includes a unique Tyr170 residue. By using a reactive quantum mechanics/molecular mechanics (QM/MM) approach, we work out its catalytic mechanism and related functional/structural specificities. At variance with other peptidases, we show that the involvement of Tyr170 in the enzyme-substrate interactions is responsible for a structural variation in the substrate-binding state. The acylation via a tetrahedral intermediate is the rate-limiting step, with a free-energy barrier of ∼21 kcal/mol, driven by the catalytic triad Ser112, Lys115, and Tyr215, acting as a nucleophile, general base, and general acid, respectively. The functional interaction of Tyr170 with this triad leads to an efficient disruption of the tetrahedral intermediate, promoting a conformational change of the substrate favorable for proton donation from the general acid.

Aqueous solutions: state of the art in ab initio molecular dynamics

The simulation of liquids by ab initio molecular dynamics (AIMD) has been a subject of intense activity over the last two decades. The significant increase in computational resources as well as the development of new and efficient algorithms has elevated this method to the status of a standard quantum mechanical tool that is used by both experimentalists and theoreticians. As AIMD computes the electronic structure from first principles, it is free of ad hoc parametrizations and has thus been applied to a large variety of physical and chemical problems. In particular, AIMD has provided microscopic insight into the structural and dynamical properties of aqueous solutions which are often challenging to probe experimentally. In this review, after a brief theoretical description of the Born-Oppenheimer and Car-Parrinello molecular dynamics formalisms, we show how AIMD has enhanced our understanding of the properties of liquid water and its constituent ions: the proton and the hydroxide ion. Thereafter, a broad overview of the application of AIMD to other aqueous systems, such as solvated organic molecules and inorganic ions, is presented. We also briefly describe the latest theoretical developments made in AIMD, such as methods for enhanced sampling and the inclusion of nuclear quantum effects.

Fast, metadynamics-based method for prediction of the stereochemistry-dependent relative free energies of ligand-receptor interactions

The computational approach applicable for the molecular dynamics (MD)-based techniques is proposed to predict the ligand-protein binding affinities dependent on the ligand stereochemistry. All possible stereoconfigurations are expressed in terms of one set of force-field parameters [stereoconfiguration-independent potential (SIP)], which allows for calculating all relative free energies by only single simulation. SIP can be used for studying diverse, stereoconfiguration-dependent phenomena by means of various computational techniques of enhanced sampling. The method has been successfully tested on the β2-adrenergic receptor (β2-AR) binding the four fenoterol stereoisomers by both metadynamics simulations and replica-exchange MD. Both the methods gave very similar results, fully confirming the presence of stereoselective effects in the fenoterol-β2-AR interactions. However, the metadynamics-based approach offered much better efficiency of sampling which allows for significant reduction of the unphysical region in SIP.

Silver and cesium diffusion dynamics at the β-SiC Σ5 grain boundary investigated with density functional theory molecular dynamics and metadynamics

The diffusion and release of silver-110m, a strong γ-radiation emitter, through silicon carbide in coated nuclear fuel particles has remained an unsolved topic since it was first observed 40 years ago. The challenge remains to explain why, contrary to other elements, silver is capable of escaping the ceramic diffusion barriers. The current work investigates the underlying differences in the diffusion of silver and cesium along a symmetric tilt Σ5 grain boundary of β-SiC through accelerated density functional theory molecular dynamics simulations. The energy barriers extracted from the simulations give diffusion coefficients that are in reasonable agreement with experiment for silver (2.19 × 10(-19) to 1.05 × 10(-17) m(2) s(-1)), but for cesium the equivalent calculated coefficients for this mechanism are much smaller (3.85 × 10(-23) to 2.15 × 10(-21) m(2) s(-1)) than those found experimentally. Analysis of the simulated structures and electron densities and comparisons with the calculations of other researchers suggest that diffusion of silver and cesium in β-SiC proceeds via different mechanisms. The mechanisms of cesium diffusion appear to be dominated by its relatively large size and repulsive interactions with the silicon and carbon atoms; β-SiC grain boundaries still offer higher energy barriers to diffusion. Silver, on the other hand, is not only smaller in size but, as we show for the first time, can also participate in weak bonding interactions with the host atoms where favorable geometries allow, thus reducing the energy barrier and enhancing the rate of diffusion.

Study of the B1-B2 transition in colloidal clusters

The possible mechanisms for the B1 (NaCl-type) to B2 (CsCl-type) transition in crystalline colloidal clusters of equally sized particles are studied by means of two computational techniques: metadynamics and nudged elastic band calculations. The system is modelled by a screened Coulomb potential. Different interaction ranges are considered. The transition from a perfect NaCl cubic cluster to a full CsCl cluster is forced by metadynamics, revealing a transition path with intermediate metastable configurations in which planes are shifted one by one. The presence of metastable configurations in the transition path, corresponding to a certain number of NaCl planes turned into CsCl, has clear analogies with the known Hyde and O'Keeffe mechanism for ionic crystals, with some important differences due to finite-size effects. These comprise the fact that the transition starts by shifting a surface plane by means of a row-by-row mechanism that has no analog in bulk crystals. The energy barriers between the local minima in the transition path are calculated, showing that the barriers strongly depend on the screening length, in such a way that the B1 metastable phase can have very long lifetimes when the interaction is sufficiently long-ranged.

Predicting pKa in Implicit Solvents: Current Status and Future Directions

Computational prediction of condensed phase acidity is a topic of much interest in the field today. We introduce the methods available for predicting gas phase acidity and pKas in aqueous and non-aqueous solvents including high-level electronic structure methods, empirical linear free energy relationships (LFERs), implicit solvent methods, explicit solvent statistical free energy methods, and hybrid implicit–explicit approaches. The focus of this paper is on implicit solvent methods, and we review recent developments including new electronic structure methods, cluster-continuum schemes for calculating ionic solvation free energies, as well as address issues relating to the choice of proton solvation free energy to use with implicit solvation models, and whether thermodynamic cycles are necessary for the computation of pKas. A comparison of the scope and accuracy of implicit solvent methods with ab initio molecular dynamics free energy methods is also presented. The present status of the theory and future directions are outlined.

QM/MM investigations of organic chemistry oriented questions

About 35 years after its first suggestion, QM/MM became the standard theoretical approach to investigate enzymatic structures and processes. The success is due to the ability of QM/MM to provide an accurate atomistic picture of enzymes and related processes. This picture can even be turned into a movie if nuclei-dynamics is taken into account to describe enzymatic processes. In the field of organic chemistry, QM/MM methods are used to a much lesser extent although almost all relevant processes happen in condensed matter or are influenced by complicated interactions between substrate and catalyst. There is less importance for theoretical organic chemistry since the influence of nonpolar solvents is rather weak and the effect of polar solvents can often be accurately described by continuum approaches. Catalytic processes (homogeneous and heterogeneous) can often be reduced to truncated model systems, which are so small that pure quantum-mechanical approaches can be employed. However, since QM/MM becomes more and more efficient due to the success in software and hardware developments, it is more and more used in theoretical organic chemistry to study effects which result from the molecular nature of the environment. It is shown by many examples discussed in this review that the influence can be tremendous, even for nonpolar reactions. The importance of environmental effects in theoretical spectroscopy was already known. Due to its benefits, QM/MM can be expected to experience ongoing growth for the next decade.In the present chapter we give an overview of QM/MM developments and their importance in theoretical organic chemistry, and review applications which give impressions of the possibilities and the importance of the relevant effects. Since there is already a bunch of excellent reviews dealing with QM/MM, we will discuss fundamental ingredients and developments of QM/MM very briefly with a focus on very recent progress. For the applications we follow a similar strategy.

Insights into the Cr(iii) catalyzed isomerization mechanism of glucose to fructose in the presence of water using ab initio molecular dynamics

In water, the partially hydrolyzed Cr complex [Cr(H₂O)₅OH]⁺²is the active species for glucose isomerization and not the unhydrolyzed, hexahydrated Cr⁺³.

Roadmaps through free energy landscapes calculated using the multi-dimensional vFEP approach

The variational free energy profile (vFEP) method is extended to two dimensions and tested with molecular simulation applications. The proposed 2D-vFEP approach effectively addresses the two major obstacles to constructing free energy profiles from simulation data using traditional methods: the need for overlap in the re-weighting procedure and the problem of data representation. This is especially evident as these problems are shown to be more severe in two dimensions. The vFEP method is demonstrated to be highly robust and able to provide stable, analytic free energy profiles with only a paucity of sampled data. The analytic profiles can be analyzed with conventional search methods to easily identify stationary points (e.g. minima and first-order saddle points) as well as the pathways that connect these points. These "roadmaps" through the free energy surface are useful not only as a post-processing tool to characterize mechanisms, but can also serve as a basis from which to direct more focused "on-the-fly" sampling or adaptive force biasing. Test cases demonstrate that 2D-vFEP outperforms other methods in terms of the amount and sparsity of the data needed to construct stable, converged analytic free energy profiles. In a classic test case, the two dimensional free energy profile of the backbone torsion angles of alanine dipeptide, 2D-vFEP needs less than 1% of the original data set to reach a sampling accuracy of 0.5 kcal/mol in free energy shifts between windows. A new software tool for performing one and two dimensional vFEP calculations is herein described and made publicly available.

Mechanism of acyl-enzyme complex formation from the Henry-Michaelis complex of class C β-lactamases with β-lactam antibiotics

Bacteria that cause most of the hospital-acquired infections make use of class C β-lactamase (CBL) among other enzymes to resist a wide spectrum of modern antibiotics and pose a major public health concern. Other than the general features, details of the defensive mechanism by CBL, leading to the hydrolysis of drug molecules, remain a matter of debate, in particular the identification of the general base and role of the active site residues and substrate. In an attempt to unravel the detailed molecular mechanism, we carried out extensive hybrid quantum mechanical/molecular mechanical Car-Parrinello molecular dynamics simulation of the reaction with the aid of the metadynamics technique. On this basis, we report here the mechanism of the formation of the acyl-enzyme complex from the Henry-Michaelis complex formed by β-lactam antibiotics and CBL. We considered two β-lactam antibiotics, namely, cephalothin and aztreonam, belonging to two different subfamilies. A general mechanism for the formation of a β-lactam antibiotic-CBL acyl-enzyme complex is elicited, and the individual roles of the active site residues and substrate are probed. The general base in the acylation step has been identified as Lys67, while Tyr150 aids the protonation of the β-lactam nitrogen through either the substrate carboxylate group or a water molecule.

From Atoms to Fullerene: Stochastic Surface Walking Solution for Automated Structure Prediction of Complex Material

It is of general concern whether the automated structure prediction of unknown material without recourse to any knowledge from experiment is ever possible considering the daunting complexity of potential energy surface (PES) of material. Here we demonstrate that the stochastic surface walking (SSW) method can be a general and promising solution to this ultimate goal, which is applied to assemble carbon fullerenes containing up to 100 atoms (including 60, 70, 76, 78, 80, 84, 90, 96, and 100 atoms) from randomly distributed atoms, a long-standing challenge in global optimization. Combining the SSW method with a parallel replica exchange algorithm, we can locate the global minima (GM) of these large fullerenes efficiently without being trapped in numerous energy-nearly degenerate isomers. Detailed analyses on the SSW trajectories allow us to rationalize how and why the SSW method is able to explore the highly complex PES, which highlights the abilities of SSW method for surmounting the high barrier and the preference of SSW trajectories to the low energy pathways. The work demonstrates that the parallel SSW method is a practical tool for predicting unknown materials.

The Janus-faced role of external forces in mechanochemical disulfide bond cleavage

Recent force microscopy measurements on the mechanically activated cleavage of a protein disulfide bond through reaction with hydroxide ions revealed that for forces greater than 0.5 nN, the acceleration of the reaction rate is substantially reduced. Here, using ab initio simulations, we trace this 'reactivity switch' back to a dual role played by the mechanical force, which leads to antagonistic effects. On the one hand, the force performs work on the system, and thereby accelerates the reaction. On the other hand, the force also induces a conformational distortion that involves the S-S-C-C dihedral angle, which drives the disulfide into a conformation that is shielded against nucleophilic attack because of steric hindrance. The discovery of force-induced conformational changes that steer chemical reactivity provides a new key concept that is expected to be relevant beyond this specific case, for example in understanding how 'disulfide switches' regulate protein function and for the rational design of mechanoresponsive materials.

Driven Metadynamics: Reconstructing Equilibrium Free Energies from Driven Adaptive-Bias Simulations

We present a novel free-energy calculation method that constructively integrates two distinct classes of nonequilibrium sampling techniques, namely, driven (e.g., steered molecular dynamics) and adaptive-bias (e.g., metadynamics) methods. By employing nonequilibrium work relations, we design a biasing protocol with an explicitly time- and history-dependent bias that uses on-the-fly work measurements to gradually flatten the free-energy surface. The asymptotic convergence of the method is discussed, and several relations are derived for free-energy reconstruction and error estimation. Isomerization reaction of an atomistic polyproline peptide model is used to numerically illustrate the superior efficiency and faster convergence of the method compared with its adaptive-bias and driven components in isolation.

Atom-Scale Reaction Pathways and Free-Energy Landscapes in Oxygen Plasma Etching of Graphene

We report first-principles molecular dynamics calculations combined with rare events sampling techniques that clarify atom-scale mechanisms of oxygen plasma etching of graphene. The obtained reaction pathways and associated free-energy landscapes show that the etching proceeds near vacancies via a two-step mechanism, formation of precursor lactone structures and the subsequent exclusive CO2 desorption. We find that atomic oxygen among the plasma components is most efficient for etching, providing a guidline in tuning the plasma conditions.

Free energy and electronic properties of water adsorption on the SnO2(110) surface

A molecular understanding of the adsorption of water on SnO2 surfaces is crucial for several applications of this metal oxide, including catalysis and gas sensing. We have investigated water adsorption on the SnO2(110) surface using a combination of dynamic and static calculations to gain fundamental insight into the reaction mechanism at room temperature. The reaction dynamics are studied by following water adsorption and dissociation on the SnO2 surface with metadynamics calculations at low and high coverage. The electronic structure in the relevant isolated minima is investigated through Mulliken charge analysis and projected density of states analysis. Surface bridging oxygen (Obr) is found to play a decisive role in water adsorption forming rooted hydroxyl groups with the water H atoms. Bond formation with H significantly changes the electronic configuration of Obr and presumably leads to reduced band bending at the SnO2 surface. The free-energy estimation indicates that on a clean SnO2(110) surface at room temperature both associative and dissociative adsorption occur, with the latter being thermodynamically favored. Oxygen coverage strongly affects the ratio between associatively and dissociatively adsorbed H2O, favoring associative adsorption at high oxygen coverage (oxidized surface) and dissociative adsorption at low oxygen coverage (reduced surface). Electronic analyses of isolated surface minima show the existence of two different electron-transfer phenomena occurring at the surface, depending on the water adsorption mechanism. The relevance of these findings in explaining the changes in electric conductivity occurring in SnO2-based gas sensors upon water adsorption is discussed. Whereas associative adsorption leads to electron enrichment of the metal oxide surface, dissociative adsorption induces surface electron depletion. Both mechanisms are consistent with the electrical conductivity changes occurring upon interaction of SnO2 with water, causing cross sensitivity to the latter. The theoretical results form the basis for correlating the existing atomistic models with the experimental data and offer a coherent description of the reaction events on the surface at room temperature.

Computational methods of studying the binding of toxins from venomous animals to biological ion channels: theory and applications

The discovery of new drugs that selectively block or modulate ion channels has great potential to provide new treatments for a host of conditions. One promising avenue revolves around modifying or mimicking certain naturally occurring ion channel modulator toxins. This strategy appears to offer the prospect of designing drugs that are both potent and specific. The use of computational modeling is crucial to this endeavor, as it has the potential to provide lower cost alternatives for exploring the effects of new compounds on ion channels. In addition, computational modeling can provide structural information and theoretical understanding that is not easily derivable from experimental results. In this review, we look at the theory and computational methods that are applicable to the study of ion channel modulators. The first section provides an introduction to various theoretical concepts, including force-fields and the statistical mechanics of binding. We then look at various computational techniques available to the researcher, including molecular dynamics, brownian dynamics, and molecular docking systems. The latter section of the review explores applications of these techniques, concentrating on pore blocker and gating modifier toxins of potassium and sodium channels. After first discussing the structural features of these channels, and their modes of block, we provide an in-depth review of past computational work that has been carried out. Finally, we discuss prospects for future developments in the field.

Recipes for free energy calculations in biomolecular systems

During the last decade, several methods for sampling phase space and calculating various free energies in biomolecular systems have been devised or refined for molecular dynamics (MD) simulations. Thus, state-of-the-art methodology and the ever increasing computer power allow calculations that were forbidden a decade ago. These calculations, however, are not trivial as they require knowledge of the methods, insight into the system under study, and, quite often, an artful combination of different methodologies in order to avoid the various traps inherent in an unknown free energy landscape. In this chapter, we illustrate some of these concepts with two relatively simple systems, a sugar ring and proline oligopeptides, whose free energy landscapes still offer considerable challenges. In order to explore the configurational space of these systems, and to surmount the various free energy barriers, we combine three complementary methods: a nonequilibrium umbrella sampling method (adaptively biased MD, or ABMD), replica-exchange molecular dynamics (REMD), and steered molecular dynamics (SMD). In particular, ABMD is used to compute the free energy surface of a set of collective variables; REMD is used to improve the performance of ABMD, to carry out sampling in space complementary to the collective variables, and to sample equilibrium configurations directly; and SMD is used to study different transition mechanisms.

Addressing open questions about phosphate hydrolysis pathways by careful free energy mapping

The nature and mechanism of phosphate hydrolysis reactions are of great interest in view of the crucial role of these reactions in key biological processes. Although it is becoming clearer that the ultimate way of resolving mechanistic controversies must involve reliable theoretical studies, it is not widely realized that such studies cannot be performed at present by using most existing automated ways and that only careful systematic studies can lead to meaningful conclusions. The present work clarifies the above point by considering the hydrolysis of phosphate monoesters. The clarification starts by defining the actual issues that should be addressed in careful studies and by highlighting the problems with studies that ignore the need for unique mechanistic definitions (e.g., works that confuse associative and dissociative pathways). We then focus on the analysis of the proton transfer (PT) pathways in phosphate hydrolysis and on recent suggestions that PT involves more than one water molecule. Here we point out that most of the studies that found a proton transfer through several water molecules have not involved a sufficient systematic search of the relevant reaction coordinates. This includes both energy minimization approaches as well as a recent metadynamics (MTD) simulation study. To illustrate the crucial need of exploring the potential surfaces reliably, rather than relying on automated approaches, we present here a very careful study of the free energy landscape along a 3D reaction coordinate (RC) exploring both the standard 2D RC, comprised of the attacking and leaving group reaction coordinates, as well as of the proton transfer (PT) coordinate. Our study points out that QM/MM minimization or MTD studies that concluded that the hydrolysis of phosphate monoesters involves a PT through several water molecules, have not explored carefully the single water (1W) path (that involves a direct PT form the attacking water molecule to the phosphate oxygen). Furthermore, we identified the most likely reason for the difficulty in finding the 1W path by QM/MM minimization methods, as well as by the current MTD simulations. We also discuss the problems with current studies that challenge the phosphate as a base mechanism and emphasize that all recent studies found associative/concerted paths (although many have not realized the meaning of their results). Finally, although we clearly do not have the last word about the 1W versus 2W paths we believe that we illustrated that the crucial mechanistic problems with alternative pathways should not be resolved by just running black box search approaches.

Exploring binding properties of agonists interacting with a δ-opioid receptor

Ligand-receptor interactions are at the basis of the mediation of our physiological responses to a large variety of ligands, such as hormones, neurotransmitters and environmental stimulants, and their tuning represents the goal of a large variety of therapies. Several molecular details of these interactions are still largely unknown. In an effort to shed some light on this important issue, we performed a computational study on the interaction of two related compounds differing by a single methyl group (clozapine and desmethylclozapine) with a -opioid receptor. According to experiments, desmethylclozapine is more active than clozapine, providing a system well suited for a comparative study. We investigated stable configurations of the two drugs inside the receptor by simulating their escape routes by molecular dynamics simulations. Our results point out that the action of the compounds might be related to the spatial and temporal distribution of the affinity sites they visit during their permanency. Moreover, no particularly pronounced structural perturbations of the receptor were detected during the simulations, reinforcing the idea of a strong dynamical character of the interaction process, with an important role played by the solvent in addition.