Benchmark Study of the SCC-DFTB Approach for a Biomolecular Proton Channel

Understanding the Multifaceted Mechanism of Compound I Formation in Unspecific Peroxygenases through Multiscale Simulations

Unspecific peroxygenases (UPOs) can selectively oxyfunctionalize unactivated hydrocarbons by using peroxides under mild conditions. They circumvent the oxygen dilemma faced by cytochrome P450s and exhibit greater stability than the latter. As such, they hold great potential for industrial applications. A thorough understanding of their catalysis is needed to improve their catalytic performance. However, it remains elusive how UPOs effectively convert peroxide to Compound I (CpdI), the principal oxidizing intermediate in the catalytic cycle. Previous computational studies of this process primarily focused on heme peroxidases and P450s, which have significant differences in the active site from UPOs. Additionally, the roles of peroxide unbinding in the kinetics of CpdI formation, which is essential for interpreting existing experiments, have been understudied. Moreover, there has been a lack of free energy characterizations with explicit sampling of protein and hydration dynamics, which is critical for understanding the thermodynamics of the proton transport (PT) events involved in CpdI formation. To bridge these gaps, we employed multiscale simulations to comprehensively characterize the CpdI formation in wild-type UPO from Agrocybe aegerita (AaeUPO). Extensive free energy and potential energy calculations were performed in a quantum mechanics/molecular mechanics setting. Our results indicate that substrate-binding dehydrates the active site, impeding the PT from H2O2 to a nearby catalytic base (Glu196). Furthermore, the PT is coupled with considerable hydrogen bond network rearrangements near the active site, facilitating subsequent O-O bond cleavage. Finally, large unbinding free energy barriers kinetically stabilize H2O2 at the active site. These findings reveal a delicate balance among PT, hydration dynamics, hydrogen bond rearrangement, and cosubstrate unbinding, which collectively enable efficient CpdI formation. Our simulation results are consistent with kinetic measurements and offer new insights into the CpdI formation mechanism at atomic-level details, which can potentially aid the design of next-generation biocatalysts for sustainable chemical transformations of feedstocks.

Using Machine Learning to Greatly Accelerate Path Integral Ab Initio Molecular Dynamics

Ab initio molecular dynamics (AIMD) has become one of the most popular and robust approaches for modeling complicated chemical, liquid, and material systems. However, the formidable computational cost often limits its widespread application in simulations of the largest-scale systems. The situation becomes even more severe in cases where the hydrogen nuclei may be better described as quantized particles using a path integral representation. Here, we present a computational approach that combines machine learning with recent advances in path integral contraction schemes, and we achieve a 2 orders of magnitude acceleration over direct path integral AIMD simulation while at the same time maintaining its accuracy.

Multiscale Simulation of an Influenza A M2 Channel Mutant Reveals Key Features of Its Markedly Different Proton Transport Behavior

The influenza A M2 channel, a prototype for viroporins, is an acid-activated viroporin that conducts protons across the viral membrane, a critical step in the viral life cycle. Four central His37 residues control channel activation by binding subsequent protons from the viral exterior, which opens the Trp41 gate and allows proton flux to the interior. Asp44 is essential for maintaining the Trp41 gate in a closed state at high pH, resulting in asymmetric conduction. The prevalent D44N mutant disrupts this gate and opens the C-terminal end of the channel, resulting in increased conduction and a loss of this asymmetric conduction. Here, we use extensive Multiscale Reactive Molecular Dynamics (MS-RMD) and quantum mechanics/molecular mechanics (QM/MM) molecular dynamics simulations with an explicit, reactive excess proton to calculate the free energy of proton transport in this M2 mutant and to study the dynamic molecular-level behavior of D44N M2. We find that this mutation significantly lowers the barrier of His37 deprotonation in the activated state and shifts the barrier for entry to the Val27 tetrad. These free energy changes are reflected in structural shifts. Additionally, we show that the increased hydration around the His37 tetrad diminishes the effect of the His37 charge on the channel's water structure, facilitating proton transport and enabling activation from the viral interior. Altogether, this work provides key insight into the fundamental characteristics of PT in WT M2 and how the D44N mutation alters this PT mechanism, and it expands understanding of the role of emergent mutations in viroporins.

Quantum chemical investigation of the effect of alkali metal ions on the dynamic structure of water in aqueous solutions

Cation size primarily governs dynamic correlations in aqueous solutions. However, drawing a clear line between chaotropic and cosmotrope ions is complicated by the fact that all cations delay dynamic correlation decay.

Understanding and Tracking the Excess Proton in Ab Initio Simulations; Insights from IR Spectra

Proton transport in aqueous media is ubiquitously important in chemical and biological processes. Although ab initio molecular dynamics (AIMD) simulations have made great progress in characterizing proton transport, there has been a long-standing challenge in defining and tracking the excess proton, or more properly, the center of excess charge (CEC) created when a hydrogen nucleus distorts the electron distributions of water molecules in a delocalized and highly dynamic nature. Yet, defining (and biasing) such a CEC is essential when combining AIMD with enhanced sampling methods to calculate the relevant macroscopic properties via free-energy landscapes, which is the standard practice for most processes of interest. Several CEC formulas have been proposed and used, but none have yet been systematically tested or rigorously derived. In this paper, we show that the CEC can be used as a computational tool to disentangle IR features of the solvated excess proton from its surrounding solvent, and in turn, how correlating the features in the excess charge spectrum with the behavior of CEC in simulations enables a systematic evaluation of various CEC definitions. We present a new definition of CEC and show how it overcomes the limitations of those currently available both from a spectroscopic point of view and from a practical perspective of performance in enhanced sampling simulations.

Density-Functional Tight-Binding Study of Carbonaceous Species Diffusion on the (100)-γ-Al2O3 Surface

Carbonaceous or oxy-carbon species are intermediates formed during C _x H _y combustion on a Pt _n /Al₂O₃ catalyst, which contain carbon, hydrogen, and oxygen atoms. The accumulation of the carbonaceous species, arguably, leads to catalytic deactivation; therefore, their removal is of importance. As the diffusion process is occasionally the rate-determining step in the growth of carbonaceous species, the present study aims to reveal the diffusion mechanisms. The free energy barriers of acetate, formate, and methoxy diffusion on the (100)-γ-Al₂O₃ surface were evaluated through extensive metadynamics simulations at the density-functional tight-binding level. The present work deduces that each adopted carbonaceous species exhibits different diffusion mechanisms and supports experimental evidence that the acetate species exhibits the slowest diffusivity among the adopted carbonaceous species.

Quantum Phonon Transport in Nanomaterials: Combining Atomistic with Non-Equilibrium Green's Function Techniques

A crucial goal for increasing thermal energy harvesting will be to progress towards atomistic design strategies for smart nanodevices and nanomaterials. This requires the combination of computationally efficient atomistic methodologies with quantum transport based approaches. Here, we review our recent work on this problem, by presenting selected applications of the PHONON tool to the description of phonon transport in nanostructured materials. The PHONON tool is a module developed as part of the Density-Functional Tight-Binding (DFTB) software platform. We discuss the anisotropic phonon band structure of selected puckered two-dimensional materials, helical and horizontal doping effects in the phonon thermal conductivity of boron nitride-carbon heteronanotubes, phonon filtering in molecular junctions, and a novel computational methodology to investigate time-dependent phonon transport at the atomistic level. These examples illustrate the versatility of our implementation of phonon transport in combination with density functional-based methods to address specific nanoscale functionalities, thus potentially allowing for designing novel thermal devices.

Benchmarking density functional tight binding models for barrier heights and reaction energetics of organic molecules

Density Functional Tight Binding (DFTB) models are two to three orders of magnitude faster than ab initio and Density Functional Theory (DFT) methods and therefore are particularly attractive in applications to large molecules and condensed phase systems. To establish the applicability of DFTB models to general chemical reactions, we conduct benchmark calculations for barrier heights and reaction energetics of organic molecules using existing databases and several new ones compiled in this study. Structures for the transition states and stable species have been fully optimized at the DFTB level, making it possible to characterize the reliability of DFTB models in a more thorough fashion compared to conducting single point energy calculations as done in previous benchmark studies. The encouraging results for the diverse sets of reactions studied here suggest that DFTB models, especially the most recent third-order version (DFTB3/3OB augmented with dispersion correction), in most cases provide satisfactory description of organic chemical reactions with accuracy almost comparable to popular DFT methods with large basis sets, although larger errors are also seen for certain cases. Therefore, DFTB models can be effective for mechanistic analysis (e.g., transition state search) of large (bio)molecules, especially when coupled with single point energy calculations at higher levels of theory. © 2017 Wiley Periodicals, Inc.

Water Multilayers on TiO2 (101) Anatase Surface: Assessment of a DFTB-Based Method

A water/(101) anatase TiO₂ interface has been investigated with the DFT-based self-consistent-charge density functional tight-binding theory (SCC-DFTB). By comparison of the computed structural, energetic, and dynamical properties with standard DFT-GGA and experimental data, we assess the accuracy of SCC-DFTB for this prototypical solid–liquid interface. We tested different available SCC-DFTB parameters for Ti-containing compounds and, accordingly, combined them to improve the reliability of the method. To better describe water energetics, we have also introduced a modified hydrogen-bond-damping function (HBD). With this correction, equilibrium structures and adsorption energies of water on (101) anatase both for low (0.25 ML) and full (1 ML) coverages are in excellent agreement with those obtained with a higher level of theory (DFT-GGA). Furthermore, Born–Oppenheimer molecular dynamics (MD) simulations for mono-, bi-, and trilayers of water on the surface, as computed with SCC-DFTB, evidence similar ordering and energetics as DFT-GGA Car–Parrinello MD results. Finally, we have evaluated the energy barrier for the dissociation of a water molecule on the anatase (101) surface. Overall, the combined set of parameters with the HBD correction (SCC-DFTB+HBD) is shown to provide a description of the water/water/titania interface, which is very close to that obtained by standard DFT-GGA, with a remarkably reduced computational cost. Hence, this study opens the way to the future investigations on much more extended and realistic TiO₂/liquid water systems, which are extremely relevant for many modern technological applications.

Acid activation mechanism of the influenza A M2 proton channel

The homotetrameric influenza A M2 channel (AM2) is an acid-activated proton channel responsible for the acidification of the influenza virus interior, an important step in the viral lifecycle. Four histidine residues (His37) in the center of the channel act as a pH sensor and proton selectivity filter. Despite intense study, the pH-dependent activation mechanism of the AM2 channel has to date not been completely understood at a molecular level. Herein we have used multiscale computer simulations to characterize (with explicit proton transport free energy profiles and their associated calculated conductances) the activation mechanism of AM2. All proton transfer steps involved in proton diffusion through the channel, including the protonation/deprotonation of His37, are explicitly considered using classical, quantum, and reactive molecular dynamics methods. The asymmetry of the proton transport free energy profile under high-pH conditions qualitatively explains the rectification behavior of AM2 (i.e., why the inward proton flux is allowed when the pH is low in viral exterior and high in viral interior, but outward proton flux is prohibited when the pH gradient is reversed). Also, in agreement with electrophysiological results, our simulations indicate that the C-terminal amphipathic helix does not significantly change the proton conduction mechanism in the AM2 transmembrane domain; the four transmembrane helices flanking the channel lumen alone seem to determine the proton conduction mechanism.

Computationally Efficient Multiscale Reactive Molecular Dynamics to Describe Amino Acid Deprotonation in Proteins

An important challenge in the simulation of biomolecular systems is a quantitative description of the protonation and deprotonation process of amino acid residues. Despite the seeming simplicity of adding or removing a positively charged hydrogen nucleus, simulating the actual protonation/deprotonation process is inherently difficult. It requires both the explicit treatment of the excess proton, including its charge defect delocalization and Grotthuss shuttling through inhomogeneous moieties (water and amino residues), and extensive sampling of coupled condensed phase motions. In a recent paper (J. Chem. Theory Comput. 2014, 10, 2729-2737), a multiscale approach was developed to map high-level quantum mechanics/molecular mechanics (QM/MM) data into a multiscale reactive molecular dynamics (MS-RMD) model in order to describe amino acid deprotonation in bulk water. In this article, we extend the fitting approach (called FitRMD) to create MS-RMD models for ionizable amino acids within proteins. The resulting models are shown to faithfully reproduce the free energy profiles of the reference QM/MM Hamiltonian for PT inside an example protein, the ClC-ec1 H(+)/Cl(-) antiporter. Moreover, we show that the resulting MS-RMD models are computationally efficient enough to then characterize more complex 2-dimensional free energy surfaces due to slow degrees of freedom such as water hydration of internal protein cavities that can be inherently coupled to the excess proton charge translocation. The FitRMD method is thus shown to be an effective way to map ab initio level accuracy into a much more computationally efficient reactive MD method in order to explicitly simulate and quantitatively describe amino acid protonation/deprotonation in proteins.

An adaptive quantum mechanics/molecular mechanics method for the infrared spectrum of water: incorporation of the quantum effect between solute and solvent

Quantum effects in solute–solvent interactions, such as the many-body effect and the dipole-induced dipole, are known to be critical factors influencing the infrared spectra of species in the liquid phase.

Modeling reactivation of the phosphorylated human butyrylcholinesterase by QM(DFTB)/MM calculations

Human butyrylcholinesterase (BChE) is a bioscavenger that protects the enzyme which is critical for the central nerve system, acetylcholinesterase, from poisoning by organophosphorus agents. Elucidating the details of the hydrolysis reaction mechanism is important to understand how the phosphorylated BChE can be reactivated. Application of the QM(DFTB)/MM(AMBER) method to construct the minimum energy pathways for the hydrolysis reaction of the diethylphosphorylated BChE allowed us to suggest a mechanism of reactivation of the wild-type and the G117H mutated enzyme. Unlike previous approaches assuming that either His438 or His117 serves as a general base in the catalysis, in our proposal the Glu197 residue is responsible for activation of the nucleophilic water molecule (Wat) leading to the chemical transformations that restore the catalytic Ser198 residue in BChE. In agreement with the experimental data, it is shown that the G117H mutation facilitates the reactivation of the inhibited enzyme.

A delocalized proton-binding site within a membrane protein

The role of protein-bound water molecules in protein function and catalysis is an emerging topic. Here, we studied the solvation of an excess proton by protein-bound water molecules and the contribution of the surrounding amino acid residues at the proton release site of the membrane protein bacteriorhodopsin. It hosts an excess proton within a protein-bound water cluster, which is hydrogen bonded to several surrounding amino acids. Indicative of delocalization is a broad continuum absorbance experimentally observed by time-resolved Fourier transform infrared spectroscopy. In combination with site-directed mutagenesis, the involvement of several amino acids (especially Glu-194 and Glu-204) in the delocalization was elaborated. Details regarding the contributions of the glutamates and water molecules to the delocalization mode in biomolecular simulations are controversial. We carried out quantum mechanics/molecular mechanics (QM/MM) self-consistent charge density functional tight-binding simulations for all amino acids that have been experimentally shown to be involved in solvation of the excess proton, and systematically investigated the influence of the quantum box size. We compared calculated theoretical infrared spectra with experimental ones as a measure for the correct description of excess proton delocalization. A continuum absorbance can only be observed for small quantum boxes containing few amino acids and/or water molecules. Larger quantum boxes, including all experimentally shown involved amino acids, resulted in narrow absorbance bands, indicating protonation of a single binding site in contradiction to experimental results. We conclude that small quantum boxes seem to reproduce representative extreme cases of proton delocalization modes: proton delocalization only on water molecules or only between Glu-194 and Glu-204. Extending the experimental spectral region to lower wave numbers, a water-delocalized proton reproduces the observed continuum absorbance better than a glutamate-shared delocalized proton. However, a full agreement between QM simulations and experimental results on the delocalized excess proton will require a larger quantum box as well as more sophisticated QM/MM methods.

Hydrated Excess Protons Can Create Their Own Water Wires

Grotthuss shuttling of an excess proton charge defect through hydrogen bonded water networks has long been the focus of theoretical and experimental studies. In this work we show that there is a related process in which water molecules move ("shuttle") through a hydrated excess proton charge defect in order to wet the path ahead for subsequent proton charge migration. This process is illustrated through reactive molecular dynamics simulations of proton transport through a hydrophobic nanotube, which penetrates through a hydrophobic region. Surprisingly, before the proton enters the nanotube, it starts "shooting" water molecules into the otherwise dry space via Grotthuss shuttling, effectively creating its own water wire where none existed before. As the proton enters the nanotube (by 2-3 Å), it completes the solvation process, transitioning the nanotube to the fully wet state. By contrast, other monatomic cations (e.g., K(+)) have just the opposite effect, by blocking the wetting process and making the nanotube even drier. As the dry nanotube gradually becomes wet when the proton charge defect enters it, the free energy barrier of proton permeation through the tube via Grotthuss shuttling drops significantly. This finding suggests that an important wetting mechanism may influence proton translocation in biological systems, i.e., one in which protons "create" their own water structures (water "wires") in hydrophobic spaces (e.g., protein pores) before migrating through them. An existing water wire, e.g., one seen in an X-ray crystal structure or MD simulations without an explicit excess proton, is therefore not a requirement for protons to transport through hydrophobic spaces.

Accurate hydrogen bond energies within the density functional tight binding method

The density-functional-based tight-binding (DFTB) approach has been recently extended by incorporating one-center exchange-like terms in the expansion of the multicenter integrals. This goes beyond the Mulliken approximation and leads to a scheme which treats in a self-consistent way the fluctuations of the whole dual density matrix and not only its diagonal elements (Mulliken charges). To date, only the performance of this new formalism to reproduce excited-state properties has been assessed (Domínguez et al. J. Chem. Theory Comput., 2013, 9, 4901-4914). Here we study the effect of our corrections on the computation of hydrogen bond energies for water clusters and water-containing systems. The limitations of traditional DFTB to reproduce hydrogen bonds has been acknowledged often. We compare our results for a set of 22 small water clusters and water-containing systems as well as for five water hexadecamers to those obtained with the DFTB3 method. Additionally, we combine our extension with a third-order energy expansion in the charge fluctuations. Our results show that the new formalisms significantly improve upon original DFTB.

Impact of distributions and mixtures on the charge transfer properties of graphene nanoflakes

Many of the promising new applications of graphene nanoflakes are moderated by charge transfer reactions occurring between defects, such as edges, and the surrounding environment. In this context the sign and value of properties such as the ionization potential, electron affinity, electronegativity and chemical hardness can be useful indicators of the efficiency of graphene nanoflakes for different reactions, and can help identify new application areas. However, as samples of graphene nanoflakes cannot necessarily be perfectly monodispersed, it is necessary to predict these properties for polydispersed ensembles of flakes, and provide a statistical solution. In this study we use some simple statistical methods, in combination with electronic structure simulations, to predict the charge transfer properties of different types of ensembles where restrictions have been placed on the diversity of the structures. By predicting quality factors for a variety of cases, we find that there is a clear motivation for restricting the sizes and suppressing certain morphologies to increase the selectivity and efficiency of charge transfer reactions; even if samples cannot be completely purified.

Microscopic basis for kinetic gating in Cytochrome c oxidase: insights from QM/MM analysis

Understanding the mechanism of vectorial proton pumping in biomolecules requires establishing the microscopic basis for the regulation of both thermodynamic and kinetic features of the relevant proton transfer steps.

Understanding the mechanism of vectorial proton pumping in biomolecules requires establishing the microscopic basis for the regulation of both thermodynamic and kinetic features of the relevant proton transfer steps. For the proton pump cytochrome c oxidase, while the regulation of thermodynamic driving force for key proton transfers has been discussed in great detail, the microscopic basis for the control of proton transfer kinetics has been poorly understood. Here we carry out extensive QM/MM free energy simulations to probe the kinetics of relevant proton transfer steps and analyze the effects of local structure and hydration level. We show that protonation of the proton loading site (PLS, taken to be a propionate of heme a₃) requires a concerted process in which a key glutamic acid (Glu286H) delivers the proton to the PLS while being reprotonated by an excess proton coming from the D-channel. The concerted nature of the mechanism is a crucial feature that enables the loading of the PLS before the cavity containing Glu286 is better hydrated to lower its pK_a to experimentally measured range; the charged rather than dipolar nature of the process also ensures a tight coupling with heme a reduction, as emphasized by Siegbahn and Blomberg. In addition, we find that rotational flexibility of the PLS allows its protonation before that of the binuclear center (the site where oxygen gets reduced to water). Together with our recent study (P. Goyal, et al., Proc. Natl. Acad. Sci. U. S. A., 2013, 110, 18886–18891) that focused on the modulation of Glu286 pK_a, the current work suggests a mechanism that builds in a natural sequence for the protonation of the PLS prior to that of the binuclear center. This provides microscopic support to the kinetic constraints revealed by kinetic network analysis as essential elements that ensure an efficient vectorial proton transport in cytochrome c oxidase.

Molecular simulation of water and hydration effects in different environments: challenges and developments for DFTB based models

We discuss the description of water and hydration effects that employs an approximate density functional theory, DFTB3, in either a full QM or QM/MM framework. The goal is to explore, with the current formulation of DFTB3, the performance of this method for treating water in different chemical environments, the magnitude and nature of changes required to improve its performance, and factors that dictate its applicability to reactions in the condensed phase in a QM/MM framework. A relatively minor change (on the scale of kBT) in the O-H repulsive potential is observed to substantially improve the structural properties of bulk water under ambient conditions; modest improvements are also seen in dynamic properties of bulk water. This simple change also improves the description of protonated water clusters, a solvated proton, and to a more limited degree, a solvated hydroxide. By comparing results from DFTB3 models that differ in the description of water, we confirm that proton transfer energetics are adequately described by the standard DFTB3/3OB model for meaningful mechanistic analyses. For QM/MM applications, a robust parametrization of QM-MM interactions requires an explicit consideration of condensed phase properties, for which an efficient sampling technique was developed recently and is reviewed here. The discussions help make clear the value and limitations of DFTB3 based simulations, as well as the developments needed to further improve the accuracy and transferability of the methodology.

Density functional tight binding: values of semi-empirical methods in an ab initio era

Semi-empirical (SE) methods are derived from Hartree-Fock (HF) or Density Functional Theory (DFT) by neglect and approximation of electronic integrals. Thereby, parameters are introduced which have to be determined from reference calculations and/or by fitting to available experimental data. This leads to computational methods that are about 2-3 orders of magnitude faster than the standard HF/DFT methods using medium sized basis sets while being about 3 orders of magnitude slower than empirical force field methods (Molecular Mechanics: MM). Therefore, SE methods are most appropriate for a specific range of applications. These include the study of systems that contain a large number of atoms and therefore being too large for ab initio or DFT methods and also problems where dynamic or entropic effects are particularly important. In the latter case, the errors made by considering a very limited number of molecular structures or neglecting entropic contributions can be much larger than the accuracy lost due to the use of SE methods. Another area where SE methods are attractive concerns the analysis of systems for which reliable MM models are not readily available. Therefore, even in an era when rapid progress is being made in ab initio methods, there is considerable interest in further developing SE methods. We illustrate this point by focusing on the discussion of recent development and application of the Density Functional Tight Binding method.

Multiscale Reactive Molecular Dynamics for Absolute pKa Predictions and Amino Acid Deprotonation

Accurately calculating a weak acid's pK_a from simulations remains a challenging task. We report a multiscale theoretical approach to calculate the free energy profile for acid ionization, resulting in accurate absolute pK_a values in addition to insights into the underlying mechanism. Importantly, our approach minimizes empiricism by mapping electronic structure data (QM/MM forces) into a reactive molecular dynamics model capable of extensive sampling. Consequently, the bulk property of interest (the absolute pK_a) is the natural consequence of the model, not a parameter used to fit it. This approach is applied to create reactive models of aspartic and glutamic acids. We show that these models predict the correct pK_a values and provide ample statistics to probe the molecular mechanism of dissociation. This analysis shows changes in the solvation structure and Zundel-dominated transitions between the protonated acid, contact ion pair, and bulk solvated excess proton.