Towards accurate ab initio QM/MM calculations of free-energy profiles of enzymatic reactions

Machine Learning-Driven Multiscale Modeling: Bridging the Scales with a Next-Generation Simulation Infrastructure

Interdependence across time and length scales is common in biology, where atomic interactions can impact larger-scale phenomenon. Such dependence is especially true for a well-known cancer signaling pathway, where the membrane-bound RAS protein binds an effector protein called RAF. To capture the driving forces that bring RAS and RAF (represented as two domains, RBD and CRD) together on the plasma membrane, simulations with the ability to calculate atomic detail while having long time and large length- scales are needed. The Multiscale Machine-Learned Modeling Infrastructure (MuMMI) is able to resolve RAS/RAF protein-membrane interactions that identify specific lipid-protein fingerprints that enhance protein orientations viable for effector binding. MuMMI is a fully automated, ensemble-based multiscale approach connecting three resolution scales: (1) the coarsest scale is a continuum model able to simulate milliseconds of time for a 1 μm2 membrane, (2) the middle scale is a coarse-grained (CG) Martini bead model to explore protein-lipid interactions, and (3) the finest scale is an all-atom (AA) model capturing specific interactions between lipids and proteins. MuMMI dynamically couples adjacent scales in a pairwise manner using machine learning (ML). The dynamic coupling allows for better sampling of the refined scale from the adjacent coarse scale (forward) and on-the-fly feedback to improve the fidelity of the coarser scale from the adjacent refined scale (backward). MuMMI operates efficiently at any scale, from a few compute nodes to the largest supercomputers in the world, and is generalizable to simulate different systems. As computing resources continue to increase and multiscale methods continue to advance, fully automated multiscale simulations (like MuMMI) will be commonly used to address complex science questions.

Factors That Determine the Variation of Equilibrium and Kinetic Properties of QM/MM Enzyme Simulations: QM Region, Conformation, and Boundary Condition

To analyze the impact of various technical details on the results of quantum mechanical (QM)/molecular mechanical (MM) enzyme simulations, including the QM region size, catechol-O-methyltransferase (COMT) is studied as a model system using an approximate QM/MM method (DFTB3/CHARMM). The results show that key equilibrium and kinetic properties for methyl transfer in COMT exhibit limited variations with respect to the size of the QM region, which ranges from ∼100 to ∼500 atoms in this study. With extensive sampling, local and global structural characteristics of the enzyme are largely conserved across the studied QM regions, while the nature of the transition state (e.g., secondary kinetic isotope effect) and reaction exergonicity are largely maintained. Deviations in the free energy profile with different QM region sizes are similar in magnitude to those observed with changes in other simulation protocols, such as different initial enzyme conformations and boundary conditions. Electronic structural properties, such as the covariance matrix of residual charge fluctuations, appear to exhibit rather long-range correlations, especially when the peptide backbone is included in the QM region; this observation holds when a range-separated DFT approach is used as the QM region, suggesting that delocalization error is unlikely the origin. Overall, the analyses suggest that multiple simulation details determine the results of QM/MM enzyme simulations with comparable contributions.

Quantum-Mechanical/Molecular-Mechanical (QM/MM) Simulations for Understanding Enzyme Dynamics

Quantum mechanics/molecular mechanics (QM/MM) methods have become widely used for computational modeling of enzyme structure and mechanism. In these approaches, a portion of the enzyme of great interest (e.g., where a chemical reaction is occurring) is treated with QM, whereas the surrounding region is treated with MM. A critical challenge with these methods is the choice of the region to partition into QM and which to treat with MM along with numerous practical choices that must be made at each step of the modeling procedure. Here, we attempt to simplify this process by describing the steps involved in preparing protein structures, choosing the appropriate QM region size and electronic structure methods, preparing all necessary input files, and troubleshooting common errors for QM/MM simulations of enzymes.

Catalytic Descriptors to Investigate Catalytic Power in the Reaction of Haloalkane Dehalogenase Enzyme with 1,2-Dichloroethane

Enzymes play a fundamental role in many biological processes. We present a theoretical approach to investigate the catalytic power of the haloalkane dehalogenase reaction with 1,2-dichloroethane. By removing the three main active-site residues one by one from haloalkane dehalogenase, we found two reactive descriptors: one descriptor is the distance difference between the breaking bond and the forming bond, and the other is the charge difference between the transition state and the reactant complex. Both descriptors scale linearly with the reactive barriers, with the three-residue case having the smallest barrier and the zero-residue case having the largest. The results demonstrate that, as the number of residues increases, the catalytic power increases. The predicted free energy barriers using the two descriptors of this reaction in water are 23.1 and 24.2 kcal/mol, both larger than the ones with any residues, indicating that the water solvent hinders the reactivity. Both predicted barrier heights agree well with the calculated one at 25.2 kcal/mol using a quantum mechanics and molecular dynamics approach, and also agree well with the experimental result at 26.0 kcal/mol. This study shows that reactive descriptors can also be used to describe and predict the catalytic performance for enzyme catalysis.

Mechanisms of Proteolytic Enzymes and Their Inhibition in QM/MM Studies

Experimental evidence for enzymatic mechanisms is often scarce, and in many cases inadvertently biased by the employed methods. Thus, apparently contradictory model mechanisms can result in decade long discussions about the correct interpretation of data and the true theory behind it. However, often such opposing views turn out to be special cases of a more comprehensive and superior concept. Molecular dynamics (MD) and the more advanced molecular mechanical and quantum mechanical approach (QM/MM) provide a relatively consistent framework to treat enzymatic mechanisms, in particular, the activity of proteolytic enzymes. In line with this, computational chemistry based on experimental structures came up with studies on all major protease classes in recent years; examples of aspartic, metallo-, cysteine, serine, and threonine protease mechanisms are well founded on corresponding standards. In addition, experimental evidence from enzyme kinetics, structural research, and various other methods supports the described calculated mechanisms. One step beyond is the application of this information to the design of new and powerful inhibitors of disease-related enzymes, such as the HIV protease. In this overview, a few examples demonstrate the high potential of the QM/MM approach for sophisticated pharmaceutical compound design and supporting functions in the analysis of biomolecular structures.

Dopamine-Decorated TiO2 Nanoparticles in Water: A QM/MM vs an MM Description

Nanoparticle functionalization is a modern strategy in nanotechnology to build up devices for several applications. Modeling fully decorated metal oxide nanoparticles of realistic size (few nanometers) in an aqueous environment is a challenging task. In this work, we present a case study relevant for solar-light exploitation and for biomedical applications, i.e., a dopamine-functionalized TiO₂ nanoparticle (1700 atoms) in bulk water, for which we have performed an extensive comparative investigation with both MM and QM/MM approaches of the structural properties and of the conformational dynamics. We have used a combined multiscale protocol for a more efficient exploration of the complex conformational space. On the basis of the results of this study and of some QM and experimental data, we have defined strengths and limitations of the existing force field parameters. Our findings will be useful for an improved modeling and simulation of many other similar hybrid bioinorganic nanosystems in an aqueous environment that are pivotal in a broad range of nanotechnological applications.

Multi-level free energy simulation with a staged transformation approach

Combining multiple levels of theory in free energy simulations to balance computational accuracy and efficiency is a promising approach for studying processes in the condensed phase. While the basic idea has been proposed and explored for quite some time, it remains challenging to achieve convergence for such multi-level free energy simulations as it requires a favorable distribution overlap between different levels of theory. Previous efforts focused on improving the distribution overlap by either altering the low-level of theory for the specific system of interest or ignoring certain degrees of freedom. Here, we propose an alternative strategy that first identifies the degrees of freedom that lead to gaps in the distributions of different levels of theory and then treats them separately with either constraints or restraints or by introducing an intermediate model that better connects the low and high levels of theory. As a result, the conversion from the low level to the high level model is done in a staged fashion that ensures a favorable distribution overlap along the way. Free energy components associated with different steps are mostly evaluated explicitly, and thus, the final result can be meaningfully compared to the rigorous free energy difference between the two levels of theory with limited and well-defined approximations. The additional free energy component calculations involve simulations at the low level of theory and therefore do not incur high computational costs. The approach is illustrated with two simple but non-trivial solution examples, and factors that dictate the reliability of the result are discussed.

Both Configuration and QM Region Size Matter: Zinc Stability in QM/MM Models of DNA Methyltransferase

Quantum-mechanical/molecular-mechanical (QM/MM) methods are essential to the study of metalloproteins, but the relative importance of sampling and degree of QM treatment in achieving quantitative predictions is poorly understood. We study the relative magnitude of configurational and QM-region sensitivity of energetic and electronic properties in a representative Zn²⁺ metal binding site of a DNA methyltransferase. To quantify property variations, we analyze snapshots extracted from 250 ns of molecular dynamics simulation. To understand the degree of QM-region sensitivity, we perform analysis using QM regions ranging from a minimal 49-atom region consisting only of the Zn²⁺ metal and its four coordinating Cys residues up to a 628-atom QM region that includes residues within 12 Å of the metal center. Over the configurations sampled, we observe that illustrative properties (e.g., rigid Zn²⁺ removal energy) exhibit large fluctuations that are well captured with even minimal QM regions. Nevertheless, for both energetic and electronic properties, we observe a slow approach to asymptotic limits with similarly large changes in absolute values that converge only with larger (ca. 300-atom) QM region sizes. For the smaller QM regions, the electronic description of Zn²⁺ binding is incomplete: the metal binds too tightly and is too stabilized by the strong electrostatic potential of MM point charges, and the Zn-S bond covalency is overestimated. Overall, this work suggests that efficient sampling with QM/MM in small QM regions is an effective method to explore the influence of enzyme structure on target properties. At the same time, accurate descriptions of electronic and energetic properties require a larger QM region than the minimal metal-coordinating residues in order to converge treatment of both metal-local bonding and the overall electrostatic environment.

Molecular Dynamics model of peptide-protein conjugation: case study of covalent complex between Sos1 peptide and N-terminal SH3 domain from Grb2

We have investigated covalent conjugation of VPPPVPPRRRX′ peptide (where X′ denotes N^ε-chloroacetyl lysine) to N-terminal SH3 domain from adapter protein Grb2. Our experimental results confirmed that the peptide first binds to the SH3 domain noncovalently before establishing a covalent linkage through reaction of X′ with the target cysteine residue C32. We have also confirmed that this reaction involves a thiolate-anion form of C32 and follows the S_N2 mechanism. For this system, we have developed a new MD-based protocol to model the formation of covalent conjugate. The simulation starts with the known coordinates of the noncovalent complex. When two reactive groups come into contact during the course of the simulation, the reaction is initiated. The reaction is modeled via gradual interpolation between the two sets of force field parameters that are representative of the noncovalent and covalent complexes. The simulation proceeds smoothly, with no appreciable perturbations to temperature, pressure or volume, and results in a high-quality MD model of the covalent complex. The validity of this model is confirmed using the experimental chemical shift data. The new MD-based approach offers a valuable tool to explore the mechanics of protein-peptide conjugation and build accurate models of covalent complexes.

Quantum Mechanical Description of Electrostatics Provides a Unified Picture of Catalytic Action Across Methyltransferases

Methyl transferases (MTases) are a well-studied class of enzymes for which competing enzymatic enhancement mechanisms have been suggested, ranging from structural methyl group CH···X hydrogen bonds (HBs) to electrostatic- and charge-transfer-driven stabilization of the transition state (TS). We identified all Class I MTases for which reasonable resolution (<2.0 Å) crystal structures could be used to form catalytically competent ternary complexes for multiscale (i.e., quantum-mechanical/molecular-mechanical or QM/MM) simulation of the S_N2 methyl transfer reaction coordinate. The four Class I MTases studied have both distinct functions (e.g., protein repair or biosynthesis) and substrate nucleophiles (i.e., C, N, or O). While CH···X HBs stabilize all reactant complexes, no universal TS stabilization role is found for these interactions in MTases. A consistent picture is instead obtained through analysis of charge transfer and electrostatics, wherein much of cofactor-substrate charge separation is maintained in the TS region, and electrostatic potential is correlated with substrate nucleophilicity (i.e., intrinsic reactivity).

Revealing quantum mechanical effects in enzyme catalysis with large-scale electronic structure simulation

Enzymes have evolved to facilitate challenging reactions at ambient conditions with specificity seldom matched by other catalysts. Computational modeling provides valuable insight into catalytic mechanism, and the large size of enzymes mandates multi-scale, quantum mechanical-molecular mechanical (QM/MM) simulations. Although QM/MM plays an essential role in balancing simulation cost to enable sampling with full QM treatment needed to understand electronic structure in enzyme active sites, the relative importance of these two strategies for understanding enzyme mechanism is not well known. We explore challenges in QM/MM for studying the reactivity and stability of three diverse enzymes: i) Mg2+-dependent catechol O-methyltransferase (COMT), ii) radical enzyme choline trimethylamine lyase (CutC), and iii) DNA methyltransferase (DNMT1), which has structural Zn2+ binding sites. In COMT, strong non-covalent interactions lead to long range coupling of electronic structure properties across the active site, but the more isolated nature of the metallocofactor in DNMT1 leads to faster convergence of some properties. We quantify these effects in COMT by computing covariance matrices of by-residue electronic structure properties during dynamics and along the reaction coordinate. In CutC, we observe spontaneous bond cleavage following initiation events, highlighting the importance of sampling and dynamics. We use electronic structure analysis to quantify the relative importance of CHO and OHO non-covalent interactions in imparting reactivity. These three diverse cases enable us to provide some general recommendations regarding QM/MM simulation of enzymes.

Large-scale QM/MM free energy simulations of enzyme catalysis reveal the influence of charge transfer

Hybrid quantum mechanical-molecular mechanical (QM/MM) simulations provide key insights into enzyme structure-function relationships. Numerous studies have demonstrated that large QM regions are needed to systematically converge ground state, zero temperature properties with electrostatic embedding QM/MM. However, it is not well known if ab initio QM/MM free energy simulations have this same dependence, in part due to the hundreds of thousands of energy evaluations required for free energy estimations that in turn limit QM region size. Here, we leverage recent advances in electronic structure efficiency and accuracy to carry out range-separated hybrid density functional theory free energy simulations in a representative methyltransferase. By studying 200 ps of ab initio QM/MM dynamics for each of five QM regions from minimal (64 atoms) to one-sixth of the protein (544 atoms), we identify critical differences between large and small QM region QM/MM in charge transfer between substrates and active site residues as well as in geometric structure and dynamics that coincide with differences in predicted free energy barriers. Distinct geometric and electronic structure features in the largest QM region indicate that important aspects of enzymatic rate enhancement in methyltransferases are identified with large-scale electronic structure.

Mechanistic Insight on the Activity and Substrate Selectivity of Nonheme Iron Dioxygenases

Nonheme iron dioxygenases catalyze vital reactions for human health particularly related to aging processes. They are involved in the biosynthesis of amino acids, but also the biodegradation of toxic compounds. Typically they react with their substrate(s) through oxygen atom transfer, although often with the assistance of a co-substrate like α-ketoglutarate that is converted to succinate and CO₂ . Many reaction processes catalyzed by the nonheme iron dioxygenases are stereoselective or regiospecific and hence understanding the mechanism and protein involvement in the selectivity is important for the design of biotechnological applications of these enzymes. To this end, I will review recent work of our group on nonheme iron dioxygenases and include background information on their general structure and catalytic cycle. Examples of stereoselective and regiospecific reaction mechanisms we elucidated are for the AlkB repair enzyme, prolyl-4-hydroxylase and the ergothioneine biosynthesis enzyme. Finally, I cover an example where we bioengineered S-p-hydroxymandelate synthase into the R-p-hydroxymandelate synthase.

BAR-based optimum adaptive sampling regime for variance minimization in alchemical transformation: the nonequilibrium stratification

Following the previously proposed equilibrate-state sampling based adaptive sampling regime Optimum Bennett Acceptance Ratio (OBAR), we introduce its nonequilibrium extension, the Optimum Crooks' Equation (OCE) in the current work. The efficiency of the NonEquilibrium Work (NEW) stratification is improved by adaptively manipulating the significance of each nonequilibrium realization followed by importance sampling. As is exhibited in the equilibrium case, the nonequilibrium extension outperforms the simple equal time rule used in nonequilibrium stratification in the sense of minimizing the total variance of the free energy estimate. The speedup of this non-equal time rule is more than 1-fold. The Time Derivative of total Variance (TDV) proposed for the OBAR criterion is extended to determine the importance of each nonequilibrium transformation, which is linearly dependent on the variance. The TDV in the nonequilibrium case gives a totally different importance rank from the standard errors of the free energy differences and OBAR TDV due to the duration of nonequilibrium pulling being added into the OCE equation. The performance of the OCE workflow is demonstrated in the solvation of several small molecules with a series of lambda increments and relaxation times between successive perturbations. To the best of our knowledge, such a nonequilibrium adaptive sampling regime in alchemical transformation is unprecedented.

QM/MM methods for free energies and photochemistry

Hybrid computational methods describing a small region of a biomolecular system with quantum mechanics and the bulk with molecular mechanics, referred to as QM/MM methods, are now a central part of computational biochemistry. This review considers developments in the QM/MM approach that make it easier to calculate free energies using accurate QM-based potential energy expressions. We also describe techniques to treat electronic coupling between the core region and the MM environment. Polarizability of the protein matrix is important but so is electronic coupling. Applications of these new methods, especially to photochemistry, are discussed.

Importance of an Orchestrate Participation of each Individual Residue Present at a Catalytic Site

GTP hydrolysis is indispensable to keep a living cell healthy. Nature has evolved so many enzymes to enhance the slow GTP hydrolysis. Rab GTPases are evolved to regulate vesicle trafficking. GTPase activating proteins (GAPs) accelerates their intrinsic slow GTP hydrolysis in order to maintain the sustainability between cellular events. Any malfunction/interference in this hydrolysis disrupts normal cellular events and causes severe diseases. In this study, GTP hydrolysis mechanism of Rab33B catalyzed by TBC-domain GAP protein Gyp1p has been decoded using extensive ab initio QM/MM metadynamics simulations. An organized coupled movement of individual residues present at the catalytic site is found to be the key factor for this reaction. An unorganized coupled movement leads the hydrolysis through very high energy pathways. This also reveals that the chemical transformations occurring at a catalytic site are residue specific.

Extensive Assessment of Various Computational Methods for Aspartate's pKa Shift

A series of computational methods for pK_a shift prediction are extensively tested on a set of benchmark protein systems, aiming at identifying pitfalls and evaluating their performance on high variants. Including 19 ASP residues in 10 protein systems, the benchmark set consists of both residues with highly shifted pK_a values as well as those varying little from the reference value, with an experimental RMS free energy differences of 2.49 kcal/mol with respect to blocked amino acid, namely the RMS pK_a shift being 1.82 pK_a units. The constant pH molecular dynamics (MD), alchemical methods, PROPKA3.1, and multiconformation continuum electrostatics give RMSDs of 1.52, 2.58, 1.37, and 3.52 pK_a units, respectively, on the benchmark set. The empirical scoring method is the most accurate one with extremely low computational cost, and the pH-dependent model is also able to provide accurate results, while the accuracy of MD sampling incorporating alchemical free energy simulation is prohibited by convergence achievement and the performance of conformational search incorporating multiconformation continuum electrostatics is bad. Former research works did not define statistical uncertainty with care and yielded the questionable conclusion that alchemical methods perform well in most benchmarks. In this work the traditional alchemical methods are thoroughly tested for high variants. We also performed the first application of nonequilibrium alchemical methods to the pK_a cases.

Computing converged free energy differences between levels of theory via nonequilibrium work methods: Challenges and opportunities

We demonstrate that Jarzynski's equation can be used to reliably compute free energy differences between low and high level representations of systems. The need for such a calculation arises when employing the so-called "indirect" approach to free energy simulations with mixed quantum mechanical/molecular mechanical (QM/MM) Hamiltonians; a popular technique for circumventing extensive simulations involving quantum chemical computations. We have applied this methodology to several small and medium sized organic molecules, both in the gas phase and explicit solvent. Test cases include several systems for which the standard approach; that is, free energy perturbation between low and high level description, fails to converge. Finally, we identify three major areas in which the difference between low and high level representations make the calculation of ΔAlow→high difficult: bond stretching and angle bending, different preferred conformations, and the response of the MM region to the charge distribution of the QM region. © 2016 Wiley Periodicals, Inc.

Perspective: Defining and quantifying the role of dynamics in enzyme catalysis

Enzymes control chemical reactions that are key to life processes, and allow them to take place on the time scale needed for synchronization between the relevant reaction cycles. In addition to general interest in their biological roles, these proteins present a fundamental scientific puzzle, since the origin of their tremendous catalytic power is still unclear. While many different hypotheses have been put forward to rationalize this, one of the proposals that has become particularly popular in recent years is the idea that dynamical effects contribute to catalysis. Here, we present a critical review of the dynamical idea, considering all reasonable definitions of what does and does not qualify as a dynamical effect. We demonstrate that no dynamical effect (according to these definitions) has ever been experimentally shown to contribute to catalysis. Furthermore, the existence of non-negligible dynamical contributions to catalysis is not supported by consistent theoretical studies. Our review is aimed, in part, at readers with a background in chemical physics and biophysics, and illustrates that despite a substantial body of experimental effort, there has not yet been any study that consistently established a connection between an enzyme's conformational dynamics and a significant increase in the catalytic contribution of the chemical step. We also make the point that the dynamical proposal is not a semantic issue but a well-defined scientific hypothesis with well-defined conclusions.

BAR-based optimum adaptive sampling regime for variance minimization in alchemical transformation

The efficiency of alchemical free energy simulations with a staging strategy is improved by adaptively manipulating the significance of each ensemble followed by importance sampling.

How Large Should the QM Region Be in QM/MM Calculations? The Case of Catechol O-Methyltransferase

Hybrid quantum mechanical-molecular mechanical (QM/MM) simulations are widely used in studies of enzymatic catalysis. Until recently, it has been cost prohibitive to determine the asymptotic limit of key energetic and structural properties with respect to increasingly large QM regions. Leveraging recent advances in electronic structure efficiency and accuracy, we investigate catalytic properties in catechol O-methyltransferase, a prototypical methyltransferase critical to human health. Using QM regions ranging in size from reactants-only (64 atoms) to nearly one-third of the entire protein (940 atoms), we show that properties such as the activation energy approach within chemical accuracy of the large-QM asymptotic limits rather slowly, requiring approximately 500-600 atoms if the QM residues are chosen simply by distance from the substrate. This slow approach to asymptotic limit is due to charge transfer from protein residues to the reacting substrates. Our large QM/MM calculations enable identification of charge separation for fragments in the transition state as a key component of enzymatic methyl transfer rate enhancement. We introduce charge shift analysis that reveals the minimum number of protein residues (approximately 11-16 residues or 200-300 atoms for COMT) needed for quantitative agreement with large-QM simulations. The identified residues are not those that would be typically selected using criteria such as chemical intuition or proximity. These results provide a recipe for a more careful determination of QM region sizes in future QM/MM studies of enzymes.

Comparison of Methods To Reweight from Classical Molecular Simulations to QM/MM Potentials

We examine methods to reweight classical molecular mechanics solvation calculations to more expensive QM/MM energy functions. We first consider the solvation free energy difference between ethane and methanol in a QM/MM Hamiltonian from configurations generated in a cheaper MM potential. The solute molecules in the QM/MM Hamiltonian are treated with B3LYP/6-31G*, and the solvent water molecules are treated classically. The free energy difference in the QM/MM Hamiltonian is estimated using Boltzmann reweighting with both the non-Boltzmann Bennett method (NBB) and the multistate Bennett acceptance ratio (MBAR), and the variance of each method is directly compared for an identical data set. For this system, MBAR-derived methods are found to produce smaller overall uncertainties than NBB-based methods. Additionally, we show that to reduce the variance in the overall free energy difference estimate in this system for a fixed amount of QM/MM calculations, the energy re-evaluations in the Boltzmann reweighting step should be concentrated on the physical MM states with the highest overlap to the QM/MM states, rather than allocated equally over all sampled MM states. We also show that reallocating the QM/MM re-evaluations can be used to diagnose poor overlap between the sampled and target state. The solvation free energies for molecules in the SAMPL4 solvation data set are also calculated in the QM/MM Hamiltonian with NBB and MBAR, and the variances are marginally smaller for MBAR. Overall, NBB and MBAR produce similar variances for systems with poor sampling efficiency, and MBAR provides smaller variances than NBB in systems with high sampling efficiency. Both NBB and MBAR converge to identical solvation free energy estimates in the QM/MM Hamiltonian, and the RMSD to experimental values for molecules in the SAMPL4 solvation data set decreases by approximately 28% when switching from the MM Hamiltonian to the QM/MM Hamiltonian.

Enhancing Paradynamics for QM/MM Sampling of Enzymatic Reactions

Despite the enormous increase in computer power, it is still extremely challenging to obtain computationally converging sampling of ab initio QM/MM (QM(ai)/MM) free energy surfaces in condensed phases. The sampling problem can be significantly reduced by the use of the reference potential paradynamics (PD) approach, but even this approach still requires major computer time in studies of enzymatic reactions. To further reduce the sampling problem we developed here a new PD version where we use an empirical valence bond reference potential that has a minimum rather than a maximum at the transition state region of the target potential (this is accomplished conveniently by shifting the EVB of the product state). Hence, we can map the TS region in a more efficient way. Here, we introduce and validate the inverted EVB PD approach. The validation involves the study of the S(N)2 step of the reaction catalyzed by haloakene dehalogenase (DhlA) and the GTP hydrolysis in the RasGAP system. In addition, we have also studied the corresponding reaction in water for each of the systems described here and the reaction involving trimethylsulfonium and dimethylamine in solution. The results are encouraging and the new strategy appears to provide a powerful way of evaluating QM(ai)/MM activation free energies.

Structure and dynamics of the fibronectin-III domains of Aplysia californica cell adhesion molecules

Due to their homophilic and heterophilic binding properties, cell adhesion molecules (CAMs) such as integrin, cadherin and the immunoglobulin superfamily CAMs are of primary importance in cell-cell and cell-substrate interactions, signalling pathways and other crucial biological processes. We study the molecular structures and conformational dynamics of the two fibronectin type III (Fn-III) extracellular domains of the Aplysia californica CAM (apCAM) protein, by constructing and probing an atomically-detailed structural model based on apCAM's homology with other CAMs. The stability and dynamic properties of the Fn-III domains, individually and in tandem, are probed and analysed using all-atom explicit-solvent molecular dynamics (MD) simulations and normal mode analysis of their corresponding elastic network models. The refined structural model of the Fn-III tandem of apCAM reveals a specific pattern of amino acid interactions that controls the stability of the β-sheet rich structure and could affect apCAM's response to physical or chemical changes of its environment. It also exposes the important role of several specific charged residues in modulating the structural properties of the linker segment connecting the two Fn-III domains, as well as of the inter-domain interface.

Quantum Mechanics/Molecular Mechanics Modeling of Enzymatic Processes: Caveats and Breakthroughs

Nature has developed large groups of enzymatic catalysts with the aim to transfer substrates into useful products, which enables biosystems to perform all their natural functions. As such, all biochemical processes in our body (we drink, we eat, we breath, we sleep, etc.) are governed by enzymes. One of the problems associated with research on biocatalysts is that they react so fast that details of their reaction mechanisms cannot be obtained with experimental work. In recent years, major advances in computational hardware and software have been made and now large (bio)chemical systems can be studied using accurate computational techniques. One such technique is the quantum mechanics/molecular mechanics (QM/MM) technique, which has gained major momentum in recent years. Unfortunately, it is not a black-box method that is easily applied, but requires careful set-up procedures. In this work we give an overview on the technical difficulties and caveats of QM/MM and discuss work-protocols developed in our groups for running successful QM/MM calculations.

Use of Nonequilibrium Work Methods to Compute Free Energy Differences Between Molecular Mechanical and Quantum Mechanical Representations of Molecular Systems

Carrying out free energy simulations (FES) using quantum mechanical (QM) Hamiltonians remains an attractive, albeit elusive goal. Renewed efforts in this area have focused on using "indirect" thermodynamic cycles to connect "low level" simulation results to "high level" free energies. The main obstacle to computing converged free energy results between molecular mechanical (MM) and QM (ΔA(MM→QM)), as recently demonstrated by us and others, is differences in the so-called "stiff" degrees of freedom (e.g., bond stretching) between the respective energy surfaces. Herein, we demonstrate that this problem can be efficiently circumvented using nonequilibrium work (NEW) techniques, i.e., Jarzynski's and Crooks' equations. Initial applications of computing ΔA(NEW)(MM→QM), for blocked amino acids alanine and serine as well as to generate butane's potentials of mean force via the indirect QM/MM FES method, showed marked improvement over traditional FES approaches.

A Multiscale Treatment of Angeli's Salt Decomposition

Sodium trioxodinitrate's (Na2N2O3, Angeli's salt) unique cardiovascular effects have been associated with its ability to yield HNO upon dissociation under physiological conditions. Due to its potential applications in new therapies for heart failure, the dissociation of Angeli's salt has recently received increased attention. The decomposition mechanism has been previously studied by quantum mechanical methods using a continuum approximation (PCM) for the solvent effects. In this work we use our recently developed interface of the Amber and Gaussian packages via the PUPIL package to study Angeli's salt dissociation in a hybrid QM/MM scheme where the water solvent molecules are treated explicitly with classical mechanics while the solute is treated with full quantum mechanics (UB3LYP/6-31+G(d) and UMP2/6-31+G(d)) level. Multiple steered molecular dynamics was used with the Jarzynski relationship to extract the free energy profile for the process. We obtain 4.8 kcal mol(-1) and 6.4 kcal mol(-1) free energy barriers for the N-N bond breaking for UB3LYP and UMP2, respectively. The geometries and Mulliken charges for reactant, transition state, and products have been characterized through a number of hybrid QM/MM molecular dynamics runs with the N-N distance restrained to representative values of each species. The results highlight the role of individual solvent molecules for the reaction energetics and provide a comparison point against implicit solvation methods.

Insights into the mechanism of oxidation of dihydroorotate to orotate catalysed by human class 2 dihydroorotate dehydrogenase: a QM/MM free energy study

The dihydroorotate dehydrogenase (DHOD) enzyme catalyzes the unique redox reaction in the de novo pyrimidine biosynthesis pathway. In this reaction, the oxidation of dihydroorotate (DHO) to orotate (OA) and reduction of the flavin mononucleotide (FMN) cofactor is catalysed by DHOD. The class 2 DHOD, to which the human enzyme belongs, was experimentally shown to follow a stepwise mechanism but the data did not allow the determination of the order of bond-breaking in a stepwise oxidation of DHO. The goal of this study is to understand the reaction mechanism at the molecular level of class 2 DHOD, which may aid in the design of inhibitors that selectively impact the activity of only certain members of the enzyme family. In this paper, the catalytic mechanism of oxidation of DHO to OA in human DHOD was studied using a hybrid Quantum Mechanical/Molecular Mechanical (QM/MM) approach and Molecular Dynamics (MD) simulations. The free energy barriers calculated reveal that the mechanism in human DHOD occurs via a stepwise reaction pathway. In the first step, a proton is abstracted from the C5 of DHO to the deprotonated Ser215 side chain. Whereas, in the second step, the transfer of the hydride or hydride equivalent from the C6 of DHO to the N5 of FMN, where free energy barrier calculated by the DFT/MM level is 10.84 kcal mol(-1). Finally, a residual decomposition analysis was carried out in order to elucidate the influence of the catalytic region residues during DHO oxidation.

A QM/MM free energy study of the oxidation mechanism of dihydroorotate dehydrogenase (class 1A) from Lactococcus lactis

The dihydroorotate dehydrogenase (DHOD) class 1A enzyme catalyzes is the only redox enzyme in the biosynthetic pathway (de novo) of pyrimidines where dihydroorotate (DHO) is oxidized to orotate (OA) coupled to reduction of a flavin mononucleotide (FMN) cofactor. The rupture of two DHO C-H bonds can proceed in a concerted or stepwise way. Herein, the catalytic mechanism of DHOD from Lactococcus lactis involving DHO oxidation (first half-reaction) was described using a hybrid quantum mechanics/molecular mechanics (QM/MM) approach and molecular dynamics simulations. The free energy profile obtained from self-consistent charge-density functional tight binding/molecular mechanics calculations (corrected by DFT/MM) reveals that this occurs with the proton abstraction from DHO C5 to Cys130 deprotonated and DHO H6 is transferred to FMN N5 in a concerted mechanism with a very low barrier of 5.64 kcal/mol. Finally, through a residual decomposition analysis, the residues that have the main influence on the redox reaction were identified.

Predicting the functions and specificity of triterpenoid synthases: a mechanism-based multi-intermediate docking approach

Terpenoid synthases construct the carbon skeletons of tens of thousands of natural products. To predict functions and specificity of triterpenoid synthases, a mechanism-based, multi-intermediate docking approach is proposed. In addition to enzyme function prediction, other potential applications of the current approach, such as enzyme mechanistic studies and enzyme redesign by mutagenesis, are discussed.

The rapid growth in the number of protein sequences presents challenges for enzyme function assignment. Computational methods, such as bioinformatics, homology modeling and docking, are becoming increasingly important for predicting of enzyme functions from protein sequences. Terpenoids are one of largest classes of natural products, and many drugs (e.g. taxol) consist of terpenoids or terpenoid derivatives. Understanding the biosynthesis of the terpenoids is of great interest. Terpenoid synthases catalyze the key cyclization steps of the biosynthesis of terpenoids via carbocation rearrangements, generating numerous multiple-ring carbon skeletons. Triterpenoid synthases, as an important class of terpenoid synthases, catalyze the cyclization of either squalene or oxido-squalene into cyclized products such as sterols (e.g. lanosterol). In this work, we propose a computational approach that can be used to predict product specificity of the triterpenoid synthases. Our approach provides insight into the ‘design principles’ of these fascinating enzymes, and may become a practical approach for function prediction and enzyme engineering.

Quantum mechanics/molecular mechanics dual Hamiltonian free energy perturbation

The dual Hamiltonian free energy perturbation (DH-FEP) method is designed for accurate and efficient evaluation of the free energy profile of chemical reactions in quantum mechanical/molecular mechanical (QM/MM) calculations. In contrast to existing QM/MM FEP variants, the QM region is not kept frozen during sampling, but all degrees of freedom except for the reaction coordinate are sampled. In the DH-FEP scheme, the sampling is done by semiempirical QM/MM molecular dynamics (MD), while the perturbation energy differences are evaluated from high-level QM/MM single-point calculations at regular intervals, skipping a pre-defined number of MD sampling steps. After validating our method using an analytic model potential with an exactly known solution, we report a QM/MM DH-FEP study of the enzymatic reaction catalyzed by chorismate mutase. We suggest guidelines for QM/MM DH-FEP calculations and default values for the required computational parameters. In the case of chorismate mutase, we apply the DH-FEP approach in combination with a single one-dimensional reaction coordinate and with a two-dimensional collective coordinate (two individual distances), with superior results for the latter choice.

Computational insights into function and inhibition of fatty acid amide hydrolase

The Fatty Acid Amide Hydrolase (FAAH) enzyme is a membrane-bound serine hydrolase responsible for the deactivating hydrolysis of a family of naturally occurring fatty acid amides. FAAH is a critical enzyme of the endocannabinoid system, being mainly responsible for regulating the level of its main cannabinoid substrate anandamide. For this reason, pharmacological inhibition of FAAH, which increases the level of endogenous anandamide, is a promising strategy to cure a variety of diseases including pain, inflammation, and cancer. Much structural, mutagenesis, and kinetic data on FAAH has been generated over the last couple of decades. This has prompted several informative computational investigations to elucidate, at the atomic-level, mechanistic details on catalysis and inhibition of this pharmaceutically relevant enzyme. Here, we review how these computational studies - based on classical molecular dynamics, full quantum mechanics, and hybrid QM/MM methods - have clarified the binding and reactivity of some relevant substrates and inhibitors of FAAH. We also discuss the experimental implications of these computational insights, which have provided a thoughtful elucidation of the complex physical and chemical steps of the enzymatic mechanism of FAAH. Finally, we discuss how computations have been helpful for building structure-activity relationships of potent FAAH inhibitors.

Catalytic mechanism of L,D-transpeptidase 2 from Mycobacterium tuberculosis described by a computational approach: insights for the design of new antibiotics drugs

Tuberculosis is perhaps the most persistent human disease caused by an infections bacterium, Mycobacterium tuberculosis. The L,D-transpeptidase enzyme catalyzes the formation of 3 → 3 peptidoglycan cross-links of the Mtb cell wall and facilitates resistance against classical β-lactams. Herein, the experimentally proposed mechanism for LdtMt2 was studied by performing QM/MM MD simulations. The whole mechanistic process includes two stages: acylation and deacylation. During the acylation step, two steps were observed: the first step is a thiolate/imidazole ion-pair in the zwitterionic form, and the second step is the nucleophilic attack on the carboxyl carbon of the natural substrate accompanied by the breaking of the peptide bond on substrate. In the deacylation step the acyl-enzyme suffers a nucleophilic attack on the carboxyl carbon by the amine group of the second substrate. Our free energy results obtained by PMF analysis reveal that the first step (acylation) is the rate-limiting step in the whole catalytic mechanism in accordance with the experimental proposal. Also, the residues responsible for binding of the substrate and transition state stabilization were identified by energy decomposition methods.

Recent advances in QM/MM free energy calculations using reference potentials

Background

Recent years have seen enormous progress in the development of methods for modeling (bio)molecular systems. This has allowed for the simulation of ever larger and more complex systems. However, as such complexity increases, the requirements needed for these models to be accurate and physically meaningful become more and more difficult to fulfill. The use of simplified models to describe complex biological systems has long been shown to be an effective way to overcome some of the limitations associated with this computational cost in a rational way.

Scope of review

Hybrid QM/MM approaches have rapidly become one of the most popular computational tools for studying chemical reactivity in biomolecular systems. However, the high cost involved in performing high-level QM calculations has limited the applicability of these approaches when calculating free energies of chemical processes. In this review, we present some of the advances in using reference potentials and mean field approximations to accelerate high-level QM/MM calculations. We present illustrative applications of these approaches and discuss challenges and future perspectives for the field.

Major conclusions

The use of physically-based simplifications has shown to effectively reduce the cost of high-level QM/MM calculations. In particular, lower-level reference potentials enable one to reduce the cost of expensive free energy calculations, thus expanding the scope of problems that can be addressed.

General significance

As was already demonstrated 40 years ago, the usage of simplified models still allows one to obtain cutting edge results with substantially reduced computational cost. This article is part of a Special Issue entitled Recent developments of molecular dynamics.

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We present some of the advances to accelerate high-level QM/MM calculations.

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Quantitative limitations of low-level methods can be overcome by these approaches.

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Reference potentials make free energy simulations feasible for large systems.

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Automated fitting reduces the need of expensive sampling of high-level approaches.

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Application of reference potentials can be extended to a wide range of processes.

Effect of Anharmonicity on Adsorption Thermodynamics

The effect of anharmonic corrections to the vibrational energies of extended systems is explored. Particular attention is paid to the thermodynamics of adsorption of small molecules on catalytically relevant systems typically affected by anharmonicity. The implemented scheme obtains one-dimensional anharmonic model potentials by distorting the equilibrium structure along the normal modes using both rectilinear (Cartesian) or curvilinear (internal) representations. Only in the latter case, the modes are decoupled also at higher order of the potential and the thermodynamic functions change in the expected directions. The method is applied to calculate ab initio enthalpies, entropies, and Gibbs free energies for the adsorption of methane in acidic chabazite (H-CHA) and on MgO(001) surface. The values obtained for the adsorption of methane in H-CHA (273.15 K, 0.1 MPa, θ = 0.5) are ΔH = -19.3, -TΔS = 11.9, and ΔG = -7.5 kJ/mol. For methane on the MgO(001) (47 K, 1.3 × 10(-14) MPa, θ = 1) ΔH = -14.4, -TΔS = 16.6, and ΔG = 2.1 kJ/mol are obtained. The calculated desorption temperature is 44 K, and the desorption prefactor is 4.26 × 10(12) s(-1). All calculated results agree within chemical accuracy limits with experimental data.

Computing the Free Energy Barriers for Less by Sampling with a Coarse Reference Potential while Retaining Accuracy of the Target Fine Model

Proposed in this contribution is a protocol for calculating fine-physics (e.g., ab initio QM/MM) free-energy surfaces at a high level of accuracy locally (e.g., only at reactants and at the transition state for computing the activation barrier) from targeted fine-physics sampling and extensive exploratory coarse-physics sampling. The full free-energy surface is still computed but at a lower level of accuracy from coarse-physics sampling. The method is analytically derived in terms of the umbrella sampling and the free-energy perturbation methods which are combined with the thermodynamic cycle and the targeted sampling strategy of the paradynamics approach. The algorithm starts by computing low-accuracy fine-physics free-energy surfaces from the coarse-physics sampling in order to identify the reaction path and to select regions for targeted sampling. Thus, the algorithm does not rely on the coarse-physics minimum free-energy reaction path. Next, segments of high-accuracy free-energy surface are computed locally at selected regions from the targeted fine-physics sampling and are positioned relative to the coarse-physics free-energy shifts. The positioning is done by averaging the free-energy perturbations computed with multistep linear response approximation method. This method is analytically shown to provide results of the thermodynamic integration and the free-energy interpolation methods, while being extremely simple in implementation. Incorporating the metadynamics sampling to the algorithm is also briefly outlined. The application is demonstrated by calculating the B3LYP//6-31G*/MM free-energy barrier for an enzymatic reaction using a semiempirical PM6/MM reference potential. These modifications allow computing the activation free energies at a significantly reduced computational cost but at the same level of accuracy compared to computing full potential of mean force.

Multiscale Free Energy Simulations: An Efficient Method for Connecting Classical MD Simulations to QM or QM/MM Free Energies Using Non-Boltzmann Bennett Reweighting Schemes

The reliability of free energy simulations (FES) is limited by two factors: (a) the need for correct sampling and (b) the accuracy of the computational method employed. Classical methods (e.g., force fields) are typically used for FES and present a myriad of challenges, with parametrization being a principle one. On the other hand, parameter-free quantum mechanical (QM) methods tend to be too computationally expensive for adequate sampling. One widely used approach is a combination of methods, where the free energy difference between the two end states is computed by, e.g., molecular mechanics (MM), and the end states are corrected by more accurate methods, such as QM or hybrid QM/MM techniques. Here we report two new approaches that significantly improve the aforementioned scheme; with a focus on how to compute corrections between, e.g., the MM and the more accurate QM calculations. First, a molecular dynamics trajectory that properly samples relevant conformational degrees of freedom is generated. Next, potential energies of each trajectory frame are generated with a QM or QM/MM Hamiltonian. Free energy differences are then calculated based on the QM or QM/MM energies using either a non-Boltzmann Bennett approach (QM-NBB) or non-Boltzmann free energy perturbation (NB-FEP). Both approaches are applied to calculate relative and absolute solvation free energies in explicit and implicit solvent environments. Solvation free energy differences (relative and absolute) between ethane and methanol in explicit solvent are used as the initial test case for QM-NBB. Next, implicit solvent methods are employed in conjunction with both QM-NBB and NB-FEP to compute absolute solvation free energies for 21 compounds. These compounds range from small molecules such as ethane and methanol to fairly large, flexible solutes, such as triacetyl glycerol. Several technical aspects were investigated. Ultimately some best practices are suggested for improving methods that seek to connect MM to QM (or QM/MM) levels of theory in FES.