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

Investigating rare events with nonequilibrium work measurements. II. Transition and reaction rates

We present a formalism for investigating transition pathways and transition probabilities for rare events in biomolecular systems. The formalism is based on combining Transition Path Theory with the results of nonequilibrium work relations, and shows that the equilibrium and nonequilibrium transition rates are in fact related. Aside from its fundamental importance, this allows for the calculation of relative equilibrium reaction rates with driven nonequilibrium simulations such as Steered Molecular Dynamics. The workings of the formalism are illustrated with a few typical numerical examples.

Free energy and hidden barriers of the β-sheet structure of prion protein

On-the-fly free-energy parametrization is a new collective variable biasing approach akin to metadynamics with one important distinction: rather than acquiring an accelerated distribution via a history-dependent bias potential, sampling on this distribution is achieved from the beginning of the simulation using temperature-accelerated molecular dynamics. In the present work, we compare the performance of both approaches to compute the free-energy profile along a scalar collective variable measuring the H-bond registry of the β-sheet structure of the mouse Prion protein. Both methods agree on the location of the free-energy minimum, but free-energy profiles from well-tempered metadynamics are subject to a much higher degree of statistical noise due to hidden barriers. The sensitivity of metadynamics to hidden barriers is shown to be a consequence of the history dependence of the bias potential, and we detail the nature of these barriers for the prion β-sheet. In contrast, on-the-fly parametrization is much less sensitive to these barriers and thus displays improved convergence behavior relative to that of metadynamics. While hidden barriers are a frequent and central issue in free-energy methods, on-the-fly free-energy parametrization appears to be a robust and preferable method to confront this issue.

Extended Phase-Space Methods for Enhanced Sampling in Molecular Simulations: A Review

Molecular Dynamics simulations are a powerful approach to study biomolecular conformational changes or protein-ligand, protein-protein, and protein-DNA/RNA interactions. Straightforward applications, however, are often hampered by incomplete sampling, since in a typical simulated trajectory the system will spend most of its time trapped by high energy barriers in restricted regions of the configuration space. Over the years, several techniques have been designed to overcome this problem and enhance space sampling. Here, we review a class of methods that rely on the idea of extending the set of dynamical variables of the system by adding extra ones associated to functions describing the process under study. In particular, we illustrate the Temperature Accelerated Molecular Dynamics (TAMD), Logarithmic Mean Force Dynamics (LogMFD), and Multiscale Enhanced Sampling (MSES) algorithms. We also discuss combinations with techniques for searching reaction paths. We show the advantages presented by this approach and how it allows to quickly sample important regions of the free-energy landscape via automatic exploration.

Ab Initio Molecular Dynamics Simulations of Amino Acids in Aqueous Solutions: Estimating pKa Values from Metadynamics Sampling

Changes in the protonation and deprotonation of amino acid residues in proteins play a key role in many biological processes and pathways. Here, we report calculations of the free-energy profile for the protonation-deprotonation reaction of the 20 canonical α amino acids in aqueous solutions using ab initio Car-Parrinello molecular dynamics simulations coupled with metadynamics sampling. We show here that the calculated change in free energy of the dissociation reaction provides estimates of the multiple pKa values of the amino acids that are in good agreement with experiment. We use the bond-length-dependent number of the protons coordinated to the hydroxyl oxygen of the carboxylic and the amine groups as the collective variables to explore the free-energy profiles of the Bronsted acid-base chemistry of amino acids in aqueous solutions. We ensure that the amino acid undergoing dissociation is solvated by at least three hydrations shells with all water molecules included in the simulations. The method works equally well for amino acids with neutral, acidic and basic side chains and provides estimates of the multiple pKa values with a mean relative error, with respect to experimental results, of 0.2 pKa units.

Carbohydrate-protein interactions: molecular modeling insights

The article reviews the significant contributions to, and the present status of, applications of computational methods for the characterization and prediction of protein-carbohydrate interactions. After a presentation of the specific features of carbohydrate modeling, along with a brief description of the experimental data and general features of carbohydrate-protein interactions, the survey provides a thorough coverage of the available computational methods and tools. At the quantum-mechanical level, the use of both molecular orbitals and density-functional theory is critically assessed. These are followed by a presentation and critical evaluation of the applications of semiempirical and empirical methods: QM/MM, molecular dynamics, free-energy calculations, metadynamics, molecular robotics, and others. The usefulness of molecular docking in structural glycobiology is evaluated by considering recent docking- validation studies on a range of protein targets. The range of applications of these theoretical methods provides insights into the structural, energetic, and mechanistic facets that occur in the course of the recognition processes. Selected examples are provided to exemplify the usefulness and the present limitations of these computational methods in their ability to assist in elucidation of the structural basis underlying the diverse function and biological roles of carbohydrates in their dialogue with proteins. These test cases cover the field of both carbohydrate biosynthesis and glycosyltransferases, as well as glycoside hydrolases. The phenomenon of (macro)molecular recognition is illustrated for the interactions of carbohydrates with such proteins as lectins, monoclonal antibodies, GAG-binding proteins, porins, and viruses.

Linear Response Path Following: A Molecular Dynamics Method To Simulate Global Conformational Changes of Protein upon Ligand Binding

Molecular functions of proteins are often fulfilled by global conformational changes that couple with local events such as the binding of ligand molecules. High molecular complexity of proteins has, however, been an obstacle to obtain an atomistic view of the global conformational transitions, imposing a limitation on the mechanistic understanding of the functional processes. In this study, we developed a new method of molecular dynamics (MD) simulation called the linear response path following (LRPF) to simulate a protein's global conformational changes upon ligand binding. The method introduces a biasing force based on a linear response theory, which determines a local reaction coordinate in the configuration space that represents linear coupling between local events of ligand binding and global conformational changes and thus provides one with fully atomistic models undergoing large conformational changes without knowledge of a target structure. The overall transition process involving nonlinear conformational changes is simulated through iterative cycles consisting of a biased MD simulation with an updated linear response force and a following unbiased MD simulation for relaxation. We applied the method to the simulation of global conformational changes of the yeast calmodulin N-terminal domain and successfully searched out the end conformation. The atomistically detailed trajectories revealed a sequence of molecular events that properly lead to the global conformational changes and identified key steps of local-global coupling that induce the conformational transitions. The LRPF method provides one with a powerful means to model conformational changes of proteins such as motors and transporters where local-global coupling plays a pivotal role in their functional processes.

Elucidation of Ligand-Dependent Modulation of Disorder-Order Transitions in the Oncoprotein MDM2

Numerous biomolecular interactions involve unstructured protein regions, but how to exploit such interactions to enhance the affinity of a lead molecule in the context of rational drug design remains uncertain. Here clarification was sought for cases where interactions of different ligands with the same disordered protein region yield qualitatively different results. Specifically, conformational ensembles for the disordered lid region of the N-terminal domain of the oncoprotein MDM2 in the presence of different ligands were computed by means of a novel combination of accelerated molecular dynamics, umbrella sampling, and variational free energy profile methodologies. The resulting conformational ensembles for MDM2, free and bound to p53 TAD (17-29) peptide identify lid states compatible with previous NMR measurements. Remarkably, the MDM2 lid region is shown to adopt distinct conformational states in the presence of different small-molecule ligands. Detailed analyses of small-molecule bound ensembles reveal that the ca. 25-fold affinity improvement of the piperidinone family of inhibitors for MDM2 constructs that include the full lid correlates with interactions between ligand hydrophobic groups and the C-terminal lid region that is already partially ordered in apo MDM2. By contrast, Nutlin or benzodiazepinedione inhibitors, that bind with similar affinity to full lid and lid-truncated MDM2 constructs, interact additionally through their solubilizing groups with N-terminal lid residues that are more disordered in apo MDM2.

Life as we know it depends on interactions between proteins. There is substantial evidence that many interactions between proteins involve very flexible protein regions. These disordered regions may undergo disorder/order transitions upon forming an interaction with another protein. Many successful approaches to medicinal chemistry are based on mimicking the interactions of biological molecules with man-made small molecules. However how drug-like small-molecules may modulate protein disorder is currently poorly understood, largely because it is difficult to measure in details this type of interaction with experimental methods. Here we have used computer simulations to resolve with great details the process by which different small-molecules modulate the flexibility of a disordered region of the protein MDM2. This protein is overexpressed in many cancers and small-molecules that recognize MDM2 have been developed over the last decade as possible novel anti-cancer agents. We show that the flexible MDM2 “lid” region adopts different conformational states in the presence of different small-molecules. Our results suggest why some classes of small-molecules form favorable interactions with the lid region, whereas others do not. These findings may prove crucial to develop new and more effective MDM2 inhibitors, and more generally to help drug designers target disordered proteins regions with small-molecules.

Dividing a complex reaction involving a hypervalent iodine reagent into three limiting mechanisms by ab initio molecular dynamics

The electrophilic N-trifluoromethylation of MeCN with a hypervalent iodine reagent to form a nitrilium ion, that is rapidly trapped by an azole nucleophile, is thought to occur via reductive elimination (RE). A recent study showed that, depending on the solvent representation, the S(N)2 is favoured to a different extent over the RE. However, there is a discriminative solvent effect present, which calls for a statistical mechanics approach to fully account for the entropic contributions. In this study, we perform metadynamic simulations for two trifluoromethylation reactions (with N- and S-nucleophiles), showing that the RE mechanism is always favoured in MeCN solution. These computations also indicate that a radical mechanism (single electron transfer) may play an important role. The computational protocol based on accelerated molecular dynamics for the exploration of the free energy surface is transferable and will be applied to similar reactions to investigate other electrophiles on the reagent. Based on the activation parameters determined, this approach also gives insight into the mechanistic details of the trifluoromethylation and shows that these commonly known mechanisms mark the limits within which the reaction proceeds.

Aqueous dye-sensitized solar cells

This review highlights the efforts towards the realization of an artificial photosynthetic system able to convert sunlight into electricity by using a unique solvent, water, the solvent of life.

Estimating successive pKa values of polyprotic acids from ab initio molecular dynamics using metadynamics: the dissociation of phthalic acid and its isomers

pKa values of polyprotic acids estimated from ab initio molecular dynamics computation of the change in free energy upon dissociation.

Unraveling the degradation of artificial amide bonds in nylon oligomer hydrolase: from induced-fit to acylation processes

To unravel the factor that provides the ability to degrade non-biological amide bond with nylon oligomer hydrolase, we investigated the process from induced-fit to acylation by a combination of different theoretical methods.

Solvation dynamics and energetics of intramolecular hydride transfer reactions in biomass conversion

Solvent dynamics and non-equilibrium solvation alter the energetics of the hydride transfer step and thus, can significantly affect reaction kinetics.

Enhanced sampling techniques in biomolecular simulations

Biomolecular simulations are routinely used in biochemistry and molecular biology research; however, they often fail to match expectations of their impact on pharmaceutical and biotech industry. This is caused by the fact that a vast amount of computer time is required to simulate short episodes from the life of biomolecules. Several approaches have been developed to overcome this obstacle, including application of massively parallel and special purpose computers or non-conventional hardware. Methodological approaches are represented by coarse-grained models and enhanced sampling techniques. These techniques can show how the studied system behaves in long time-scales on the basis of relatively short simulations. This review presents an overview of new simulation approaches, the theory behind enhanced sampling methods and success stories of their applications with a direct impact on biotechnology or drug design.

Discovering chemistry with an ab initio nanoreactor

Chemical understanding is driven by the experimental discovery of new compounds and reactivity, and is supported by theory and computation that provides detailed physical insight. While theoretical and computational studies have generally focused on specific processes or mechanistic hypotheses, recent methodological and computational advances harken the advent of their principal role in discovery. Here we report the development and application of the ab initio nanoreactor – a highly accelerated, first-principles molecular dynamics simulation of chemical reactions that discovers new molecules and mechanisms without preordained reaction coordinates or elementary steps. Using the nanoreactor we show new pathways for glycine synthesis from primitive compounds proposed to exist on the early Earth, providing new insight into the classic Urey-Miller experiment. These results highlight the emergence of theoretical and computational chemistry as a tool for discovery in addition to its traditional role of interpreting experimental findings.

Small endohedral metallofullerenes: exploration of the structure and growth mechanism in the Ti@C2n (2n = 26-50) family

Analysis of the structure and the bottom-up growth mechanism in the family of small endohedral metallofullerenes Ti@C_2n (2n = 26–50).

The formation of the smallest fullerene, C₂₈, was recently reported using gas phase experiments combined with high-resolution FT-ICR mass spectrometry. An internally located group IV metal stabilizes the highly strained non-IPR C₂₈ cage by charge transfer (IPR = isolated pentagon rule). Ti@C₄₄ also appeared as a prominent peak in the mass spectra, and U@C₂₈ was demonstrated to form by a bottom-up growth mechanism. We report here a computational analysis using standard DFT calculations and Car–Parrinello MD simulations for the family of the titled compounds, aiming to identify the optimal cage for each endohedral fullerene and to unravel key aspects of the intriguing growth mechanisms of fullerenes. We show that all the optimal isomers from C₂₆ to C₅₀ are linked by a simple C₂ insertion, with the exception of a few carbon cages that require an additional C₂ rearrangement. The ingestion of a C₂ unit is always an exergonic/exothermic process that can occur through a rather simple mechanism, with the most energetically demanding step corresponding to the closure of the carbon cage. The large formation abundance observed in mass spectra for Ti@C₂₈ and Ti@C₄₄ can be explained by the special electronic properties of these cages and their higher relative stabilities with respect to C₂ reactivity. We further verify that extrusion of C atoms from an already closed fullerene is much more energetically demanding than forming the fullerene by a bottom-up mechanism. Independent of the formation mechanism, the present investigations strongly support that, among all the possible isomers, the most stable, smaller non-IPR carbon cages are formed, a conclusion that is also valid for medium and large cages.

First principle chemical kinetics in zeolites: the methanol-to-olefin process as a case study

To optimally design next generation catalysts a thorough understanding of the chemical phenomena at the molecular scale is a prerequisite. Apart from qualitative knowledge on the reaction mechanism, it is also essential to be able to predict accurate rate constants. Molecular modeling has become a ubiquitous tool within the field of heterogeneous catalysis. Herein, we review current computational procedures to determine chemical kinetics from first principles, thus by using no experimental input and by modeling the catalyst and reacting species at the molecular level. Therefore, we use the methanol-to-olefin (MTO) process as a case study to illustrate the various theoretical concepts. This process is a showcase example where rational design of the catalyst was for a long time performed on the basis of trial and error, due to insufficient knowledge of the mechanism. For theoreticians the MTO process is particularly challenging as the catalyst has an inherent supramolecular nature, for which not only the Brønsted acidic site is important but also organic species, trapped in the zeolite pores, must be essentially present during active catalyst operation. All these aspects give rise to specific challenges for theoretical modeling. It is shown that present computational techniques have matured to a level where accurate enthalpy barriers and rate constants can be predicted for reactions occurring at a single active site. The comparison with experimental data such as apparent kinetic data for well-defined elementary reactions has become feasible as current computational techniques also allow predicting adsorption enthalpies with reasonable accuracy. Real catalysts are truly heterogeneous in a space- and time-like manner. Future theory developments should focus on extending our view towards phenomena occurring at longer length and time scales and integrating information from various scales towards a unified understanding of the catalyst. Within this respect molecular dynamics methods complemented with additional techniques to simulate rare events are now gradually making their entrance within zeolite catalysis. Recent applications have already given a flavor of the benefit of such techniques to simulate chemical reactions in complex molecular environments.

High energy conformers of M(+)(APE)(H2O)(0-1)Ar(0-1) clusters revealed by combined IR-PD and DFT-MD anharmonic vibrational spectroscopy

IR-PD vibrational spectroscopy and DFT-based molecular dynamics simulations are combined in order to unravel the structures of M(+)(APE)(H2O)0-1 ionic clusters (M = Na, K), where APE (2-amino-1-phenyl ethanol) is commonly used as an analogue for the noradrenaline neurotransmitter. The strength of the synergy between experiments and simulations presented here is that DFT-MD provides anharmonic vibrational spectra that unambiguously help assign the ionic clusters structures. Depending on the interacting cation, we have found that the lowest energy conformers of K(+)(APE)(H2O)0-1 clusters are formed, while the lowest energy conformers of Na(+)(APE)(H2O)0-1 clusters can only be observed through water loss channel (i.e. without argon tagged to the clusters). Trapping of higher energy conformers is observed when the argon loss channel is recorded in the experiment. This has been rationalized by transition state energies. The dynamical anharmonic vibrational spectra unambiguously provide the prominent OH stretch due to the OH···NH2 H-bond, within 10 cm(-1) of the experiment, hence reproducing the 240-300 cm(-1) red-shift (depending on the interacting cation) from bare neutral APE. When this H-bond is not present, the dynamical anharmonic spectra provide the water O-H stretches as well as the rotational motion of the water molecule at finite temperature, as observed in the experiment.

QM/MM molecular dynamics studies of metal binding proteins

Mixed quantum-classical (quantum mechanical/molecular mechanical (QM/MM)) simulations have strongly contributed to providing insights into the understanding of several structural and mechanistic aspects of biological molecules. They played a particularly important role in metal binding proteins, where the electronic effects of transition metals have to be explicitly taken into account for the correct representation of the underlying biochemical process. In this review, after a brief description of the basic concepts of the QM/MM method, we provide an overview of its capabilities using selected examples taken from our work. Specifically, we will focus on heme peroxidases, metallo-β-lactamases, α-synuclein and ligase ribozymes to show how this approach is capable of describing the catalytic and/or structural role played by transition (Fe, Zn or Cu) and main group (Mg) metals. Applications will reveal how metal ions influence the formation and reduction of high redox intermediates in catalytic cycles and enhance drug metabolism, amyloidogenic aggregate formation and nucleic acid synthesis. In turn, it will become manifest that the protein frame directs and modulates the properties and reactivity of the metal ions.

Efficient and Minimal Method to Bias Molecular Simulations with Experimental Data

A primary goal in molecular simulations is to modify the potential energy of a system so that properties of the simulation match experimental data. This is traditionally done through iterative cycles of simulation and reparameterization. An alternative approach is to bias the potential energy so that the system matches experimental data. This can be done while minimally changing the underlying free energy of the molecular simulation. Current minimal biasing methods require replicas, which can lead to unphysical dynamics and introduces new complexity: the choice of replica number and their properties. Here, we describe a new method, called experiment directed simulation that does not require replicas, converges rapidly, can match many data simultaneously, and minimally modifies the potential. The experiment directed simulation method is demonstrated on model systems and a three-component electrolyte simulation. The theory used to derive the method also provides insight into how changing a molecular force-field impacts the expected value of observables in simulation.

Molecular mechanism of a hotdog-fold acyl-CoA thioesterase

Thioesterases are enzymes that hydrolyze thioester bonds between a carbonyl group and a sulfur atom. They catalyze key steps in fatty acid biosynthesis and metabolism, as well as polyketide biosynthesis. The reaction molecular mechanism of most hotdog-fold acyl-CoA thioesterases remains unknown, but several hypotheses have been put forward in structural and biochemical investigations. The reaction of a human thioesterase (hTHEM2), representing a thioesterase family with a hotdog fold where a coenzyme A moiety is cleaved, was simulated by quantum mechanics/molecular mechanics metadynamics techniques to elucidate atomic and electronic details of its mechanism, its transition-state conformation, and the free energy landscape of the process. A single-displacement acid-base-like mechanism, in which a nucleophilic water molecule is activated by an aspartate residue acting as a base, was found, confirming previous experimental proposals. The results provide unambiguous evidence of the formation of a tetrahedral-like transition state. They also explain the roles of other conserved active-site residues during the reaction, especially that of a nearby histidine/serine pair that protonates the thioester sulfur atom, the participation of which could not be elucidated from mutation analyses alone.

Using multiscale preconditioning to accelerate the convergence of iterative molecular calculations

Iterative procedures for optimizing properties of molecular models often converge slowly owing to the computational cost of accurately representing features of interest. Here, we introduce a preconditioning scheme that allows one to use a less expensive model to guide exploration of the energy landscape of a more expensive model and thus speed the discovery of locally stable states of the latter. We illustrate our approach in the contexts of energy minimization and the string method for finding transition pathways. The relation of the method to other multilevel simulation techniques and possible extensions are discussed.