Empirical Valence Bond Approach Research Articles

Q-RepEx: A Python pipeline to increase the sampling of empirical valence bond simulations

The exploration of chemical systems occurs on complex energy landscapes. Comprehensively sampling rugged energy landscapes with many local minima is a common problem for molecular dynamics simulations. These multiple local minima trap the dynamic system, preventing efficient sampling. This is a particular challenge for large biochemical systems with many degrees of freedom. Replica exchange molecular dynamics (REMD) is an approach that accelerates the exploration of the conformational space of a system, and thus can be used to enhance the sampling of complex biomolecular processes. In parallel, the empirical valence bond (EVB) approach is a powerful approach for modeling chemical reactivity in biomolecular systems. Here, we present an open-source Python-based tool that interfaces with the Q simulation package, and increases the sampling efficiency of the EVB free energy perturbation/umbrella sampling approach by means of REMD. This approach, Q-RepEx, both decreases the computational cost of the associated REMD-EVB simulations, and opens the door to more efficient studies of biochemical reactivity in systems with significant conformational fluctuations along the chemical reaction coordinate.

Exploiting the quantum mechanically derived force field for functional materials simulations

The computational design of functional materials relies heavily on large-scale atomistic simulations. Such simulations are often problematic for conventional classical force fields, which require tedious and time-consuming parameterization of interaction parameters. The problem can be solved using a quantum mechanically derived force field (QMDFF)—a system-specific force field derived directly from the first-principles calculations. We present a computational approach for atomistic simulations of complex molecular systems, which include the treatment of chemical reactions with the empirical valence bond approach. The accuracy of the QMDFF is verified by comparison with the experimental properties of liquid solvents. We illustrate the capabilities of our methodology to simulate functional materials in several case studies: chemical degradation of material in organic light-emitting diode (OLED), polymer chain packing, material morphology of organometallic photoresists. The presented methodology is fast, accurate, and highly automated, which allows its application in diverse areas of materials science.

Histidine protonation states are key in the LigI catalytic reaction mechanism.

Lignin is one of the world's most abundant organic polymers, and 2-pyrone-4,6-dicarboxylate lactonase (LigI) catalyzes the hydrolysis of 2-pyrone-4,6-dicarboxylate (PDC) in the degradation of lignin. The pH has profound effects on enzyme catalysis and therefore we studied this in the context of LigI. We found that changes of the pH mostly affects surface residues, while the residues at the active site are more subject to changes of the surrounding microenvironment. In accordance with this, a high pH facilitates the deprotonation of the substrate. Detailed free energy calculations by the empirical valence bond (EVB) approach revealed that the overall hydrolysis reaction is more likely when the three active site histidines (His31, His33 and His180) are protonated at the ɛ site, however, protonation at the δ site may be favored during specific steps of the reaction. Our studies have uncovered the determinant role of the protonation state of the active site residues His31, His33 and His180 in the hydrolysis of PDC.

Empirical Valence Bond Simulations of Organophosphate Hydrolysis: Theory and Practice.

Recent years have seen an explosion of interest in understanding the mechanisms of phosphate ester hydrolysis in biological systems, using a range of computational approaches, each with different advantages and limitations. In this contribution, we present the empirical valence bond (EVB) approach as a powerful tool for modeling biochemical reactivity, using the example of organophosphate hydrolysis by diisopropyl fluorophosphatase as our model reaction. We walk the reader through the protocol for setting up and performing EVB simulations, as well as key technical considerations that need to be taken into account. Finally, we provide examples of the applications of the EVB approach to understanding different experimental observables.

Why does the Y326I mutant of monoamine oxidase B decompose an endogenous amphetamine at a slower rate than the wild type enzyme? Reaction step elucidated by multiscale molecular simulations.

This work investigates the Y326I point mutation effect on the kinetics of oxidative deamination of phenylethylamine (PEA) catalyzed by the monoamine oxidase B (MAO B) enzyme. PEA is a neuromodulator capable of affecting the plasticity of the brain and is responsible for the mood enhancing effect caused by physical exercise. Due to a similar functionality, PEA is often regarded as an endogenous amphetamine. The rate limiting step of the deamination was simulated at the multiscale level, employing the Empirical Valence Bond approach for the quantum treatment of the involved valence states, whereas the environment (solvated protein) was represented with a classical force field. A comparison of the reaction free energy profiles delivered by simulation of the reaction in the wild type MAO B and its Y326I mutant yields an increase in the barrier by 1.06 kcal mol-1 upon mutation, corresponding to a roughly 6-fold decrease in the reaction rate. This is in excellent agreement with the experimental kinetic studies. Inspection of simulation trajectories reveals possible sources of the point mutation effect, namely vanishing favorable electrostatic interactions between PEA and a Tyr326 side chain and an increased amount of water molecules at the active site due to the replacement of tyrosine by a less spacious isoleucine residue, thereby increasing the dielectric shielding of the catalytic environment provided by the enzyme.

SN2 Reaction Rate Enhancement by β-Cyclodextrin at the Liquid/Liquid Interface

An inverse phase transfer catalyst typically enhances the rate of biphasic reaction by bringing the water-insoluble reactant from the organic to the aqueous phase. We use the empirical valence bond (EVB) approach to obtain reaction free energy profiles for a model SN2 reaction inside the β-cyclodextrin (β-CD) cavity at the water/1-bromooctane interface and in bulk water to show that a significant rate enhancement is taking place at the liquid/liquid interface rather than in the bulk. By examining several solvent–solute structural and energetic properties, we demonstrate that the rate enhancement when the reaction takes place inside the cavity at the interface is primarily due to limited accessibility of interfacial water molecules, which results in destabilization of the reactants. Greater accessibility of water molecules when the catalyst is in the bulk stabilizes the reactants and does not lead to rate enhancement despite the significant hydrophobicity of the cavity’s interior.

Theory and Applications of the Empirical Valence Bond Approach: From Physical Chemistry to Chemical Biology

Theory and Applications of the Empirical Valence Bond Approach: From Physical Chemistry to Chemical Biology

Comparing hydroxide and hydronium at the instantaneous air-water interface using polarizable multi-state empirical valence bond models

A new molecular model for the hydroxide anion was developed and its propensity for the air-water interface was compared with that of the hydronium ion. The multi-state empirical valence bond approach with polarizable potentials was used for both of these, allowing them to share their charge with adjacent water molecules. The hydroxide anion appeared to have a lower propensity for the air-water interface than that of hydronium when comparing its potential of mean force with respect to the Gibbs dividing surface. However, upon further inspection it was found that the hydroxide and hydronium ions had similar free energies at the instantaneous air-water interface. The reason for this discrepancy is that the hydroxide anion has a greater free energy when it was partially solvated. Or in other words, when the hydroxide anion is one molecular layer from the instantaneous air-water interface, but potentially still near the Gibbs dividing surface, it is less stable than the hydronium in a similar configuration. This shows that using the instantaneous interface can provide additional important insights.

The empirical valence bond model: theory and applications

AbstractRecent years have seen an explosion in computer power, allowing for the examination of ever more challenging problems. For instance, a recent simulation study, which was the first of its kind, was able to actually explore the dynamical nature of enzyme catalysis on a millisecond timescale (Pisliakov AV, Cao J, Kamerlin SCL, Warshel A. Proc Natl Acad Sci U S A 2009, 106:17359.), something that as recently as a year or two ago would have been considered impossible. However, the questions that need addressing are nevertheless very complex, and experimental approaches can unfortunately often be inconclusive (Åqvist J, Kolmodin K, Florián J, Warshel A, Chem Biol 1999, 6:R71.) in answering them. Therefore, it is essential to have an approach that is both reliable and able to capture complex systems in order to resolve long‐standing controversies [particularly with regards to questions such as the origin of enzyme catalysis, where the relevant energy contributions cannot be separated without some computational models (Warshel A, Sharma PK, Kato M, Xiang Y, Liu H, Olsson MHM, Chem Rev 2006, 106:3210.)]. Herein, we will present the empirical valence bond (EVB) approach, which, at present, is arguably the most powerful tool for examining chemical reactivity in the condensed phase. We will illustrate the effectiveness of the EVB method when evaluating, for instance, catalytic effects and demonstrate that it is currently the optimal tool for elucidating challenging problems such as understanding the catalytic power of enzymes. Finally, the increasing appreciation of this approach can maybe best illustrated not only by its proliferation but also by attempts to capture its basic chemistry under a different name, as will be discussed in this work. © 2011 John Wiley & Sons, Ltd. WIREs Comput Mol Sci 2011 1 30–45 DOI: 10.1002/wcms.10This article is categorized under: Electronic Structure Theory > Combined QM/MM Methods

The EVB as a quantitative tool for formulating simulations and analyzing biological and chemical reactions.

Recent years have seen dramatic improvements in computer power, allowing ever more challenging problems to be approached. In light of this, it is imperative to have a quantitative model for examining chemical reactivity, both in the condensed phase and in solution, as well as to accurately quantify physical organic chemistry (particularly as experimental approaches can often be inconclusive). Similarly, computational approaches allow for great progress in studying enzyme catalysis, as they allow for the separation of the relevant energy contributions to catalysis. Due to the complexity of the problems that need addressing, there is a need for an approach that can combine reliability with an ability to capture complex systems in order to resolve long-standing controversies in a unique way. Herein, we will demonstrate that the empirical valence bond (EVB) approach provides a powerful way to connect the classical concepts of physical organic chemistry to the actual energies of enzymatic reactions by means of computation. Additionally, we will discuss the proliferation of this approach, as well as attempts to capture its basic chemistry and repackage it under different names. We believe that the EVB approach is the most powerful tool that is currently available for studies of chemical processes in the condensed phase in general and enzymes in particular, particularly when trying to explore the different proposals about the origin of the catalytic power of enzymes.

Electrostatic Contribution to the Transition States Binding Free Energy Using Simplified Coarse Grained Model

Simplified coarse-grained (CG) models (of the type originally developed by Levitt and Warshel (1)) can provide an effective way of evaluating the free energies of explicit protein models (2). Here we use such a reference potential strategy in evaluating the transition state electrostatic binding free energies calculations, which are essential for the rational enzyme design. The method is examined and demonstrated in studies of the effects of mutation on the transition state binding free energies of the esterase catalytic substrates (p-nitrophenyl acetate, 1-and 2-naphthyl acetates) of human carbonic anhydrase II (hCAII) and dienelactone hydrolase (DLH). These have been computed using empirical valence bond (EVB) approach in MOLARIS program (3) with and without the use of the CG model as a reference potential. The calculated electrostatic contributions to the transition state binding free energies reproduce the experimental trends (4, 5). This indicates that the method should provide a powerful tool for exploring the esterase activities of hCAII and DLH for understanding the promiscuity of these enzymes.(1) Levitt, M. and Warshel, A., Nature, 1975, vol. 253, no. 5495, pp. 694-698.(2) Messer, M. M., Roca, M., Chu, Z. T., Vicatos, S., Vardi-Kilshtain, A. and Warshel, A., Proteins, 2009, in press.(3) Lee, F. S., Chu, Z. T. and Warshel, A., J. Comp. Chem., 1993, vol. 14 p. 161.(4) Gould, S. M. and Tawfik, D. S., Biochemistry, 2005, vol. 44, no. 14, pp. 5444-5452.(5) Kim, H.-K., Liu, J.-W., Carr, P.D., Ollis, D.L., Acta Cryst., 2005, vol. D61, pp. 920-031.

On the origin of the catalytic power of carboxypeptidase A and other metalloenzymes

Zinc metalloenzymes play a major role in key biological processes and carboxypeptidase-A (CPA) is a major prototype of such enzymes. The present work quantifies the energetics of the catalytic reaction of CPA and its mutants using the empirical valence bond (EVB) approach. The simulations allow us to quantify the origin of the catalytic power of this enzyme and to examine different mechanistic alternatives. The first step of the analysis used experimental information to determine the activation energy of each assumed mechanism of the reference reaction without the enzyme. The next step of the analysis involved EVB simulations of the reference reaction and then a calibration of the simulations by forcing them to reproduce the energetics of the reference reaction, in each assumed mechanism. The calibrated EVB was then used in systematic simulations of the catalytic reaction in the protein environment, without changing any parameter. The simulations reproduced the observed rate enhancement in two feasible general acid-general base mechanisms (GAGB-1 and GAGB-2), although the calculations with the GAGB-2 mechanism underestimated the catalytic effect in some treatments. We also reproduced the catalytic effect in the R127A mutant. The mutation calculations indicate that the GAGB-2 mechanism is significantly less likely than the GAGB-1 mechanism. It is also found, that the enzyme loses all its catalytic effect without the metal. This and earlier studies show that the catalytic effect of the metal is not some constant electrostatic effect, that can be assessed from gas phase studies, but a reflection of the dielectric effect of the specific environment.

Implementation of umbrella integration within the framework of the empirical valence bond approach.

The umbrella integration method for calculating the potential of mean force (PMF) for a chemical reaction is implemented within the empirical valence bond (EVB) framework. In this implementation, the PMF is generated along the energy gap reaction coordinate, and the biasing potential is the difference between the mapping potential, which is defined to be a linear combination of the valence bond state energies, and the EVB ground state energy. The umbrella integration method is based on the derivative of the PMF with respect to the reaction coordinate. An analytical expression for this derivative applicable to certain types of EVB potentials is presented. The advantages of the umbrella integration method are illustrated by the application of both umbrella integration and the weighted histogram analysis method to the hydride transfer reaction catalyzed by the enzyme dihydrofolate reductase. This application demonstrates that the umbrella integration method reduces the statistical errors, converges efficiently, and does not require significantly overlapping windows. A modified version of the weighted histogram analysis method that shares these advantages is also proposed and implemented.

Proton Transfer 200 Years after von Grotthuss: Insights from Ab Initio Simulations

Figure 8 in ref. 1 is reproduced from Figure 1 in ref. 2. Panels (a)–(c) thereof, reprinted as Figure 1 1in this Addendum, illustrate schematically the essential steps of the proton diffusion mechanism in liquid water 3–12 as illustrated in Figure 2 in ref. 6 and Figure 1 in the review ref. 13. It should be noted that Figure 1 in ref. 2 and thus Figure 8 in ref. 1 is only a very schematic sketch of the structural diffusion process that has been previously sampled from actual ab initio molecular dynamics trajectories based on selected snapshot configurations such as those depicted in Figures 1 and 3 in ref. 3, Figure 3 in ref. 2, and, in particular, in Figure 1 in ref. 10. Reproduction of Figure 8 in ref. 1: 'Schematic representaion of the mechanism of structural diffusion of a)–c) H+ and d–f) OH− charge defects in liquid water.’; for panels a)–c) see also Figure 2 in ref. 6 and Figure 1 in the review ref. 13. The quotation marks in the sentence 'Shortly after, and independently from the first ab initio molecular dynamics simulation,[62] a molecular mechanism was “suggested”[76] that is “qualitatively consistent with the above mechanism”.' were used in ref. 1 in order to highlight explicit quotes from the following two sentences of ref. 6 (which is ref. [76] in ref. 1): 'It is suggested that the molecular mechanism behind prototropic mobility involves a periodic series of isomerizations between H9O4+ and H5O2+, the first triggered by hydrogen-bond cleavage of a second-shell water molecule and the second by the reverse, hydrogen-bond formation process.' and 'The animated trajectories are qualitatively consistent with the above mechanism.' whereby the specific mechanism referred to in the latter sentence is the one described in the former sentence and the animated trajectories are those published in ref. 3 (which is ref. [62] in ref. 1). The publication chronology of refs. 3, 6 collected in [76] in ref. 1 is provided in order to substantiate the conclusion drawn by the reviewer that both publications report results from independent research (see also the two publications refs. 14 and 5 that precede refs. 3 and 6, respectively), which is explicitly stated in the review 1. In particular, the quotation marks in the above-mentioned sentence from ref. 1 are not intended to be connected to or indicative of this chronology. Finally, it is added that proton transfer between two specified water molecules embedded in liquid water was investigated in ref. 15 using the empirical valence bond (EVB) approach in terms of a two-state model (see also ref. 16 in relation to the parameterization of this particular model) and, by construction, the simulation refers necessarily to a localized protonic defect that is confined to a particular hydrogen bond. Shortly later, so-called extended 17 or multi-state 9 EVB models were successful in simulating actual proton transport within the three-dimensional hydrogen-bonded water network and thus charge migration and Grotthuss structural diffusion in liquid water 7–9, 11, 12 as reviewed in ref. 18. I am grateful to Noam Agmon for bringing ref. [5] to my attention and to Greg Voth for commenting on the two-state EVB model 15.

Catalysis and Linear Free Energy Relationships in Aspartic Proteases

Aspartic proteases are receiving considerable attention as potential drug targets in several serious diseases, such as AIDS, malaria, and Alzheimer's disease. These enzymes cleave polypeptide chains, often between specific amino acid residues, but despite the common reaction mechanism, they exhibit large structural differences. Here, the catalytic mechanism of aspartic proteases plasmepsin II, cathepsin D, and HIV-1 protease is examined by computer simulations utilizing the empirical valence bond approach in combination with molecular dynamics and free energy perturbation calculations. Free energy profiles are established for four different substrates, each six amino acids long and containing hydrophobic side chains in the P1 and P1' positions. Our simulations reproduce the catalytic effect of these enzymes, which accelerate the reaction rate by a factor of approximately 10(10) compared to that of the corresponding uncatalyzed reaction in water. The calculations elucidate the origin of the catalytic effect and allow a rationalization of the fact that, despite large structural differences between plasmepsin II/cathepsin D and HIV-1 protease, the magnitude of their rate enhancement is very similar. Amino acid residues surrounding the active site together with structurally conserved water molecules are found to play an important role in catalysis, mainly through dipolar (electrostatic) stabilization. A linear free energy relationship for the reactions in the different enzymes is established that also demonstrates the reduced reorganization energy in the enzymes compared to that in the uncatalyzed water reaction.

Computer Simulation of Proton Solvation and Transport in Aqueous and Biomolecular Systems

The excess proton in aqueous media is critical to many aspects of chemistry, biology, and materials science. This species is at the heart of the most elementary of chemical (e.g., acid-base) and biological (e.g., bioenergetics) concepts, yet to this day, it remains mysterious, surprising, and often misunderstood. In this Account, our efforts to describe excess proton solvation and transport through computer modeling and simulation will be described. Results will be summarized for several important systems, as obtained from the multistate empirical valence bond (MS-EVB) approach, which allows for the explicit treatment of (Grotthuss) proton shuttling and charge delocalization.

Polarizable Solute in Polarizable and Flexible Solvents: Simulation Study of Electron Transfer Reaction Systems

A polarizable solute model, based on the empirical valence bond approach, is developed and applied to electron transfer (ET) reactions in polarizable and flexible water solvents. The polarization effect is investigated in comparison with a nonpolarizable solute and solvent model. With free energy curves constructed by a molecular dynamics simulation, the activation energy barrier and the reorganization energy related to ET processes are investigated. The present simulation results show that the activation energy barrier becomes larger in the polarizable model than in the nonpolarizable model and that this makes the ET rate slower than that with the nonpolarizable model. It is shown that the effect of the electronic energy difference of solute molecule on free energy profiles is remarkable and that, corresponding to this effect, the reorganization energy is significantly modified. These results indicate that the process of solvent polarization by the polarized solute to enhance the solute-solvent interaction is a key factor and that treating the polarization of both solute and solvent at the same time is essential. Also, the polarization effect on the diffusive motion of the solute molecule in the polarization solvent is studied. The polarized solute molecule shows slower diffusive motion compared with that in the nonpolarizable model.

Nucleophilic Substitution Reactions at Liquid/Liquid Interfaces: Molecular Dynamics Simulation of a Model SN1 Dissociation Reaction at the Water/Carbon Tetrachloride Interface

The ionic dissociation step of the nucleophilic substitution reaction t-BuCl --> t-Bu(+) + Cl(-) is studied at the water/carbon tetrachloride interface using molecular dynamics computer simulations. The empirical valence bond approach is used to couple two diabatic states, covalent and ionic, in the electronically adiabatic limit. The umbrella sampling technique is used to calculate the potential of mean force along the reaction coordinate (defined as the t-Bu to Cl distance) at several interface regions of varying distances from the Gibbs dividing surface. We find a significant increase of the ionic dissociation barrier height and of the reaction free energy at the interface relative to bulk water. This is shown to be due to the reduced polarity of the interface which causes a destabilization of the pure ionic state. However, deformation to the neat interface structure in the form of water protrusions into the organic phase may provide partial stabilization of the ionic species. The importance of these structural effects is examined by repeating the calculations with an artificially smooth interface. The destabilization of the ionic state at the interface also manifests itself with a rapid (picosecond time scale) recombination dynamics of the ions to form the parent molecule followed by a slow vibrational relaxation.

A molecular-dynamics study of a model SN1 dissociation reaction at the water liquid/vapor interface

The thermodynamics and dynamics of a model S(N)1 reaction: t-BuCl --> t-Bu+ + Cl- is studied at the water liquid/vapor interface using molecular-dynamics computer simulations. The empirical valence bond approach is used to couple two diabatic states, covalent and ionic, in the electronically adiabatic limit. Umbrella sampling calculations are used to calculate the potential of mean force along the reaction coordinate (defined as the t-Bu to Cl distance) in bulk water and in several locations at the interface. We find a significant increase of the dissociation barrier height and of the reaction free energy at the interface relative to the bulk. This is shown to be due to the reduced polarity of the interface. Reactive flux correlation function calculations show significant deviation of the rate constant from the transition-state theory: The transmission coefficients range from 0.49 in the bulk to 0.05 above the Gibbs surface. The low transmission coefficient at the interface despite the lower friction is shown to be due to slow vibrational relaxation.

Scattering, Trapping, and Ionization of HCl at the Surface of Liquid Glycerol

A model for the interactions between HCl and liquid glycerol, based on the Empirical Valence Bond (EVB) approach, is developed and used to investigate by molecular dynamics computer simulations the early events following the collision of an HCl molecule with the glycerol surface. The calculated trapping probability at 2.4 and 22 kcal/mol collision energies and the fractional energy loss of scattered HCl molecules agree well with experiments. The potential of mean force for HCl in the bulk and at the glycerol surface exhibits a low barrier to the formation of the contact ion pair, suggesting the possibility of proton transfer at the interface. Trapped HCl molecules undergo rapid relaxation and solvation and begin to form contact ion pairs on the picosecond time scale, which is consistent with the low barrier to the formation of the ion pair derived from the equilibrium potential of mean force calculations.