Sampling free energy surfaces as slices by combining umbrella sampling and metadynamics

Parameter Optimization Method in Multidimensional Umbrella Sampling

Umbrella sampling (US) is an effective method for calculating free-energy landscapes (FELs). However, the complexity of controlling the sampling positions complicates multidimensional FEL calculations. In this study, we proposed a method for controlling sampling by optimizing the US parameters. This method comprises the introduction of a target point and the optimization of the parameters to sample a window around this point. We approximated each window to normal distributions using an umbrella integration method and calculated the divergences between the window distributions and the state distributed at the target position by a variationally enhanced sampling method. Thus, the minimization of the divergence facilitated sampling around the target point, after which the parameters could be optimized on the fly while performing equilibration simulation. In practice, our method employs bias potentials with off-diagonal terms, ensuring a more efficient calculation of multidimensional FEL. Additionally, we developed an algorithm for determining the target point for automated FEL search; the algorithm samples in a specified direction while controlling the overlap of distributions. We performed three different FEL calculations as examples: (1) the calculation of the permeation of a water molecule through a lipid bilayer (one-dimensional FEL), (2) the calculation of the internal structural changes in alanine dipeptide in water (two-dimensional FEL), and (3) the calculation of the internal structural changes from a β-strand structure to an α-helix structure in alanine decapeptide (Ala10, 16-dimensional FEL). These results confirmed that our method could control the number of US windows and calculate the high-dimensional FELs that could not be evaluated by the conventional US method.

Estimating Free-Energy Surfaces and Their Convergence from Multiple, Independent Static and History-Dependent Biased Molecular-Dynamics Simulations with Mean Force Integration

Addressing the sampling problem is central to obtaining quantitative insight from molecular dynamics simulations. Adaptive biased sampling methods, such as metadynamics, tackle this issue by perturbing the Hamiltonian of a system with a history-dependent bias potential, enhancing the exploration of the ensemble of configurations and estimating the corresponding free energy surface (FES). Nevertheless, efficiently assessing and systematically improving their convergence remains an open problem. Here, building on mean force integration (MFI), we develop and test a metric for estimating the convergence of FESs obtained by combining asynchronous, independent simulations subject to diverse biasing protocols, including static biases, different variants of metadynamics, and various combinations of static and history-dependent biases. The developed metric and the ability to combine independent simulations granted by MFI enable us to devise strategies to systematically improve the quality of FES estimates. We demonstrate our approach by computing FES and assessing the convergence of a range of systems of increasing complexity, including one- and two-dimensional analytical FESs, alanine dipeptide, a Lennard-Jones supersaturated vapor undergoing liquid droplet nucleation, and the model of a colloidal system crystallizing via a two-step mechanism. The methods presented here can be generally applied to biased simulations and are implemented in pyMFI, a publicly accessible, open-source Python library.

Speeding-up Hybrid Functional-Based Ab Initio Molecular Dynamics Using Multiple Time-stepping and Resonance-Free Thermostat

Ab initio molecular dynamics (AIMD) based on density functional theory (DFT) has become a workhorse for studying the structure, dynamics, and reactions in condensed matter systems. Currently, AIMD simulations are primarily carried out at the level of generalized gradient approximation (GGA), which is at the second rung of DFT functionals in terms of accuracy. Hybrid DFT functionals, which form the fourth rung in the accuracy ladder, are not commonly used in AIMD simulations as the computational cost involved is 100 times or higher. To facilitate AIMD simulations with hybrid functionals, we propose here an approach using multiple time stepping with adaptively compressed exchange operator and resonance-free thermostat, that could speed up the calculations by ∼30 times or more for systems with a few hundred of atoms. We demonstrate that by achieving this significant speed up and making the compute time of hybrid functional-based AIMD simulations at par with that of GGA functionals, we are able to study several complex condensed matter systems and model chemical reactions in solution with hybrid functionals that were earlier unthinkable to be performed.

An interoperable implementation of collective-variable based enhanced sampling methods in extended phase space within the OpenMM package

Collective variable (CV)-based enhanced sampling techniques are widely used today for accelerating barrier-crossing events in molecular simulations. A class of these methods, which includes temperature accelerated molecular dynamics (TAMD)/driven-adiabatic free energy dynamics (d-AFED), unified free energy dynamics (UFED), and temperature accelerated sliced sampling (TASS), uses an extended variable formalism to achieve quick exploration of conformational space. These techniques are powerful, as they enhance the sampling of a large number of CVs simultaneously compared to other techniques. Extended variables are kept at a much higher temperature than the physical temperature by ensuring adiabatic separation between the extended and physical subsystems and employing rigorous thermostatting. In this work, we present a computational platform to perform extended phase space enhanced sampling simulations using the open-source molecular dynamics engine OpenMM. The implementation allows users to have interoperability of sampling techniques, as well as employ state-of-the-art thermostats and multiple time-stepping. This work also presents protocols for determining the critical parameters and procedures for reconstructing high-dimensional free energy surfaces. As a demonstration, we present simulation results on the high dimensional conformational landscapes of the alanine tripeptide in vacuo, tetra-N-methylglycine (tetra-sarcosine) peptoid in implicit solvent, and the Trp-cage mini protein in explicit water.

Kinetic reconstruction of free energies as a function of multiple order parameters

A vast array of phenomena, ranging from chemical reactions to phase transformations, are analyzed in terms of a free energy surface defined with respect to a single or multiple order parameters. Enhanced sampling methods are typically used, especially in the presence of large free energy barriers, to estimate free energies using biasing protocols and sampling of transition paths. Kinetic reconstructions of free energy barriers of intermediate height have been performed, with respect to a single order parameter, employing the steady state properties of unconstrained simulation trajectories when barrier crossing is achievable with reasonable computational effort. Considering such cases, we describe a method to estimate free energy surfaces with respect to multiple order parameters from a steady state ensemble of trajectories. The approach applies to cases where the transition rates between pairs of order parameter values considered is not affected by the presence of an absorbing boundary, whereas the macroscopic fluxes and sampling probabilities are. We demonstrate the applicability of our prescription on different test cases of random walkers executing Brownian motion in order parameter space with an underlying (free) energy landscape and discuss strategies to improve numerical estimates of the fluxes and sampling. We next use this approach to reconstruct the free energy surface for supercooled liquid silicon with respect to the degree of crystallinity and density, from unconstrained molecular dynamics simulations, and obtain results quantitatively consistent with earlier results from umbrella sampling.

A Multiple Proton Transfer Mechanism for the Charging Step of the Aminoacylation Reaction at the Active Site of Aspartyl tRNA Synthetase

Aspartyl-tRNA synthetase catalyzes the attachment of aspartic acid to its cognate tRNA by the aminoacylation reaction during the initiation of the protein biosynthesis process. In the second step of the aminoacylation reaction, known as the charging step, the aspartate moiety is transferred from aspartyl-adenylate to the 3'-OH of A76 of tRNA through a proton transfer process. We have investigated different pathways for the charging step through three separate QM/MM simulations combined with the enhanced sampling method of well-sliced metadynamics and found out the most feasible pathway for the reaction at the active site of the enzyme. In the charging reaction, both the phosphate group and the ammonium group after deprotonation can potentially act as a base for proton transfer in the substrate-assisted mechanism. We have considered three possible mechanisms involving different pathways of proton transfer, and only one of them is determined to be enzymatically feasible. The free energy landscape along reaction coordinates where the phosphate group acts as the general base showed that, in the absence of water, the barrier height is 52.6 kcal/mol. The free energy barrier is reduced to 39.7 kcal/mol when the active site water molecules are also treated quantum mechanically, thus allowing a water mediated proton transfer. The charging reaction involving the ammonium group of the aspartyl adenylate is found to follow a path where first a proton from the ammonium group moves to a water in the vicinity forming a hydronium ion (H₃O⁺) and NH₂ group. The hydronium ion subsequently passes the proton to the Asp233 residue, thus minimizing the chance of back proton transfer from hydronium to the NH₂ group. The neutral NH₂ group subsequently takes the proton from the O3' of A76 with a free energy barrier of 10.7 kcal/mol. In the next step, the deprotonated O3' makes a nucleophilic attack to the carbonyl carbon forming a tetrahedral transition state with a free energy barrier of 24.8 kcal/mol. Thus, the present work shows that the charging step proceeds through a multiple proton transfer mechanism where the amino group formed after deprotonation acts as the base to capture a proton from O3' of A76 rather than the phosphate group. The current study also shows the important role played by Asp233 in the proton transfer process.

Hierarchical Materials from High Information Content Macromolecular Building Blocks: Construction, Dynamic Interventions, and Prediction

Hierarchical materials that exhibit order over multiple length scales are ubiquitous in nature. Because hierarchy gives rise to unique properties and functions, many have sought inspiration from nature when designing and fabricating hierarchical matter. More and more, however, nature's own high-information content building blocks, proteins, peptides, and peptidomimetics, are being coopted to build hierarchy because the information that determines structure, function, and interfacial interactions can be readily encoded in these versatile macromolecules. Here, we take stock of recent progress in the rational design and characterization of hierarchical materials produced from high-information content blocks with a focus on stimuli-responsive and "smart" architectures. We also review advances in the use of computational simulations and data-driven predictions to shed light on how the side chain chemistry and conformational flexibility of macromolecular blocks drive the emergence of order and the acquisition of hierarchy and also on how ionic, solvent, and surface effects influence the outcomes of assembly. Continued progress in the above areas will ultimately usher in an era where an understanding of designed interactions, surface effects, and solution conditions can be harnessed to achieve predictive materials synthesis across scale and drive emergent phenomena in the self-assembly and reconfiguration of high-information content building blocks.

Free Energy Landscape of the Adenylation Reaction of the Aminoacylation Process at the Active Site of Aspartyl tRNA Synthetase

The process of protein biosynthesis is initiated by the aminoacylation process where a transfer ribonucleic acid (tRNA) is charged by the attachment of its cognate amino acid at the active site of the corresponding aminoacyl tRNA synthetase enzyme. The first step of the aminoacylation process, known as the adenylation reaction, involves activation of the cognate amino acid where it reacts with a molecule of adenosine triphosphate (ATP) at the active site of the enzyme to form the aminoacyl adenylate and inorganic pyrophosphate. In the current work, we have investigated the adenylation reaction between aspartic acid and ATP at the active site of the fully solvated aspartyl tRNA synthetase (AspRS) from Escherichia coli in aqueous medium at room temperature through hybrid quantum mechanical/molecular mechanical (QM/MM) simulations combined with enhanced sampling methods of well-tempered and well-sliced metadynamics. The objective of the present work is to study the associated free energy landscape and reaction barrier and also to explore the effects of active site mutation on the free energy surface of the reaction. The current calculations include finite temperature effects on free energy profiles. In particular, apart from contributions of interaction energies, the current calculations also include contributions of conformational, vibrational, and translational entropy of active site residues, substrates, and also the rest of the solvated protein and surrounding water into the free energy calculations. The present QM/MM metadynamics simulations predict a free energy barrier of 23.35 and 23.5 kcal/mol for two different metadynamics methods used to perform the reaction at the active site of the wild type enzyme. The free energy barrier increases to 30.6 kcal/mol when Arg217, which is an important conserved residue of the wild type enzyme at its active site, is mutated by alanine. These free energy results including the effect of mutation compare reasonably well with those of kinetic experiments that are available in the literature. The current work also provides molecular details of structural changes of the reactants and surroundings as the system dynamically evolves along the reaction pathway from reactant to the product state through QM/MM metadynamics simulations.

Exploration of high dimensional free energy landscapes by a combination of temperature-accelerated sliced sampling and parallel biasing

Temperature-accelerated sliced sampling (TASS) is an enhanced sampling method for achieving accelerated and controlled exploration of high-dimensional free energy landscapes in molecular dynamics simulations. With the aid of umbrella bias potentials, the TASS method realizes a controlled exploration and divide-and-conquer strategy for computing high-dimensional free energy surfaces. In TASS, diffusion of the system in the collective variable (CV) space is enhanced with the help of metadynamics bias and elevated-temperature of the auxiliary degrees of freedom (DOF) that are coupled to the CVs. Usually, a low-dimensional metadynamics bias is applied in TASS. In order to further improve the performance of TASS, we propose here to use a highdimensional metadynamics bias, in the same form as in a parallel bias metadynamics scheme. Here, a modified reweighting scheme, in combination with artificial neural network is used for computing unbiased probability distribution of CVs and projections of high-dimensional free energy surfaces. We first validate the accuracy and efficiency of our method in computing the four-dimensional free energy landscape for alanine tripeptide in vacuo. Subsequently, we employ the approach to calculate the eight-dimensional free energy landscape of alanine pentapeptide in vacuo. Finally, the method is applied to a more realistic problem wherein we compute the broad four-dimensional free energy surface corresponding to the deacylation of a drug molecule which is covalently complexed with a β-lactamase enzyme. We demonstrate that using parallel bias in TASS improves the efficiency of exploration of high-dimensional free energy landscapes.

Boosting the conformational sampling by combining replica exchange with solute tempering and well-sliced metadynamics

Methods that combine collective variable (CV) based enhanced sampling and global tempering approaches are used in speeding-up the conformational sampling and free energy calculation of large and soft systems with a plethora of energy minima. In this paper, a new method of this kind is proposed in which the well-sliced metadynamics approach (WSMTD) is united with replica exchange with solute tempering (REST2) method. WSMTD employs a divide-and-conquer strategy wherein high-dimensional slices of a free energy surface are independently sampled and combined. The method enables one to accomplish a controlled exploration of the CV-space with a restraining bias as in umbrella sampling, and enhance-sampling of one or more orthogonal CVs using a metadynamics like bias. The new hybrid method proposed here enables boosting the sampling of more slow degrees of freedom in WSMTD simulations, without the need to specify associated CVs, through a replica exchange scheme within the framework of REST2. The high-dimensional slices of the probability distributions of CVs computed from the united WSMTD and REST2 simulations are subsequently combined using the weighted histogram analysis method to obtain the free energy surface. We show that the new method proposed here is accurate, improves the conformational sampling, and achieves quick convergence in free energy estimates. We demonstrate this by computing the conformational free energy landscapes of solvated alanine tripeptide and Trp-cage mini protein in explicit water.

Free Energy Landscape and Proton Transfer Pathways of the Transimination Reaction at the Active site of the Serine Hydroxymethyltransferase Enzyme in Aqueous Medium

Serine hydroxymethyltransferase (SHMT) is a ubiquitous enzyme belonging to the fold type I or aspartate aminotransferase (AspAT) family of the pyridoxal 5'-phosphate (PLP)-dependent enzymes. Like other PLP-dependent enzymes, SHMT also undergoes the so-called transimination reaction before exhibiting its enzymatic activity. The transimination process constitutes an important pre-step for all PLP-dependent enzymes, where an internal aldimine of the PLP-enzyme complex gets converted to an external aldimine of the substrate-PLP complex at the active site of the enzyme. In case of the transimination reaction involving SHMT, the PLP molecule bound to the active site lysine residue of SHMT (internal aldimine) gets detached from the enzyme by a serine substrate to produce an external aldimine complex, where the PLP is now bound to the serine substrate. In the current study, the free energy surfaces and reaction pathways of different steps of the transimination reaction at the active site of SHMT are investigated by employing hybrid quantum mechanical/molecular mechanical (QM/MM) simulations combined with metadynamics methods of rare event sampling. It is found that the process of transimination involving serine and PLP at the active site of the SHMT enzyme takes place through different elementary steps such as the formation of the first geminal diamine intermediate (GDI1), transfer of a proton from the substrate serine to the phenolic oxygen of PLP, followed by another proton transfer from PLP to the amine nitrogen of lysine with the formation of the second geminal diamine intermediate (GDI2), and finally, detachment of the active site lysine residue from PLP to produce the external aldimine.

Effects of Salts on the Solvation of Hydrophobic Objects in Water

The solvation of large, hydrophobic objects in water is facilitated by the formation of a low-density region surrounding the solute that is separated from the bulk liquid by an interface, which has a structure that resembles that between a liquid and its vapor. We study the effect of dissolved sodium chloride on the thermodynamics of solvation and on the solvent structure surrounding hydrophobic solutes in the size regime where this interface is not yet fully formed. Using biased Molecular Dynamics computer simulations, we calculate solvation free energies and orientational distributions of water molecules at different salt concentrations and solute sizes. We find that while the effects of sodium chloride on thermodynamic properties are small, the ions' response to the presence of a hydrophobic solute differs significantly from that of the water. Our findings provide mechanistic insight into how our understanding of hydrophobic solvation in water can be extended to electrolyte solutions.

Achieving an Order of Magnitude Speedup in Hybrid-Functional- and Plane-Wave-Based Ab Initio Molecular Dynamics: Applications to Proton-Transfer Reactions in Enzymes and in Solution

Ab initio molecular dynamics (MD) with hybrid density functionals and a plane wave basis is computationally expensive due to the high computational cost of exact exchange energy evaluation. Recently, we proposed a strategy to combine adaptively compressed exchange (ACE) operator formulation and a multiple time step integration scheme to reduce the computational cost significantly [J. Chem. Phys. 2019, 151, 151102 ]. However, it was found that the construction of the ACE operator, which has to be done at least once in every MD time step, is computationally expensive. In the present work, systematic improvements are introduced to further speed up by employing localized orbitals for the construction of the ACE operator. By this, we could achieve a computational speedup of an order of magnitude for a periodic system containing 32 water molecules. Benchmark calculations were carried out to show the accuracy and efficiency of the method in predicting the structural and dynamical properties of bulk water. To demonstrate the applicability, computationally intensive free-energy computations at the level of hybrid density functional theory were performed to investigate (a) methyl formate hydrolysis reaction in neutral aqueous media and (b) proton-transfer reaction within the active-site residues of the class C β-lactamase enzyme.

Wettability of cellulose surfaces under the influence of an external electric field

HYPOTHESIS

Interfacial tensions play an important role in dewatering of hydrophilic materials like nanofibrillated cellulose, and are affected by the molecular organization of water at the interface. Application of an electric field influences the orientation of water molecules along the field direction. Hence, it should be possible to alter the interfacial free energies to tune the wettability of cellulose surface through application of an external electric field thus, aiding the dewatering process.

SIMULATIONS

Molecular dynamics simulations of cellulose surface in contact with water under the influence of an external electric field have been conducted with GLYCAM-06 forcefield. The effect of variation in electric field intensity and directions on the spreading coefficient has been addressed via orientational preference of water molecules and interfacial free energy analyses.

FINDINGS

The application of electric field influences the interfacial free energy difference at the cellulose-water interface. The spreading coefficient increases with the electric field directed parallel to the cellulose-water interface while it decreases in the perpendicular electric field. Variation in interfacial free energies seems to explain the change in contact angle adequately in presence of an electric field. The wettability of cellulose surface can be tuned by the application of an external electric field.

Collective variable-based enhanced sampling and machine learning

ABSTRACT

Collective variable-based enhanced sampling methods have been widely used to study thermodynamic properties of complex systems. Efficiency and accuracy of these enhanced sampling methods are affected by two factors: constructing appropriate collective variables for enhanced sampling and generating accurate free energy surfaces. Recently, many machine learning techniques have been developed to improve the quality of collective variables and the accuracy of free energy surfaces. Although machine learning has achieved great successes in improving enhanced sampling methods, there are still many challenges and open questions. In this perspective, we shall review recent developments on integrating machine learning techniques and collective variable-based enhanced sampling approaches. We also discuss challenges and future research directions including generating kinetic information, exploring high-dimensional free energy surfaces, and efficiently sampling all-atom configurations.

Refined metadynamics through canonical sampling using time-invariant bias potential: A study of polyalcohol dehydration in hot acidic solutions

We propose a canonical sampling method to refine metadynamics simulations a posteriori, where the hills obtained from metadynamics are used as a time-invariant bias potential. In this way, the statistical error in the computed reaction barriers is reduced by an efficient sampling of the collective variable space at the free energy level of interest. This simple approach could be useful particularly when two or more free energy barriers are to be compared among chemical reactions in different or competing conditions. The method was then applied to study the acid dependence of polyalcohol dehydration reactions in high-temperature aqueous solutions. It was found that the reaction proceeds consistently via an S_N 2 mechanism, whereby the free energy of protonation of the hydroxyl group created as an intermediate is affected significantly by the acidic species. Although demonstration is shown for a specific problem, the computational method suggested herein could be generally used for simulations of complex reactions in the condensed phase.

Accessing slow diffusion in solids by employing metadynamics simulation

Molecular dynamics (MD) is a powerful tool to investigate microscopic transport of atoms and molecules in condensed matter. However, there lies a large class of systems wherein atomic diffusion is too slow a process relative to the feasible time scales of typical atomistic simulations. Here, we demonstrate that with judicial implementation of a metadynamics (MTD) technique, the microscopic mechanism of atomic transport in solids can be accessed within a reasonable computational time. The calculations are carried out on the two end members of the true NASICON solid solutions, namely NaZr2(PO4)3 and Na4Zr2(SiO4)3, wherein Na+ diffusion is too slow to be accessed through standard MD simulations. The study also provides fresh insights on correlated ion hops and their implications on the effective diffusion barrier. The results are compared with climbing image nudged elastic band (CI-NEB) calculation, and available experimental results.

Efficient computation of free energy surfaces of chemical reactions using ab initio molecular dynamics with hybrid functionals and plane waves

Ab initio molecular dynamics (AIMD) simulations employing density functional theory (DFT) and plane waves are routinely carried out using density functionals at the level of generalized gradient approximation (GGA). AIMD simulations employing hybrid density functionals are of great interest as it offers a more accurate description of structural and dynamic properties than the GGA functionals. However, the computational cost for carrying out calculations using hybrid functionals and plane wave basis set is at least two orders of magnitude higher than that using GGA functionals. Recently, we proposed a strategy that combined the adaptively compressed exchange operator formulation and the multiple time step integration scheme to reduce the computational cost by an order of magnitude [J. Chem. Phys. 151, 151102 (2019)]. In this work, we demonstrate the application of this method to study chemical reactions, in particular, formamide hydrolysis in an alkaline aqueous medium. By actuating our implementation with the well-sliced metadynamics scheme, we can compute the two-dimensional free energy surface of this reaction at the level of hybrid-DFT. This work also investigates the accuracy of the PBE0 (hybrid) and the PBE (GGA) functionals in predicting the free energetics of this chemical reaction.

Analytical Method Using a Scaled Hypersphere Search for High-Dimensional Metadynamics Simulations

Metadynamics (MTD) is one of the most effective methods for calculating the free energy surface and finding rare events. Nevertheless, numerous studies using MTD have been carried out using 3D or lower dimensional collective variables (CVs), as higher dimensional CVs require costly computational resources and the obtained results are too complex to understand the important events. The latter issue can be conveniently solved by utilizing the free energy reaction network (FERN), which is a graph structure consisting of edges of minimum free energy paths (MFEPs), nodes of equation (EQ) points, and transition state (TS) points. In the present article, a new method for exploring FERNs on high-dimensional CVs using MTD and the scaled hypersphere search (SHS) method is described. A test calculation based on the MTD-SHS simulation of met-enkephalin in explicit water with 7 CVs was conducted. As a result, 889 EQ points and 1805 TS points were found. The MTD-SHS approach can find MFEPs exhaustively; therefore, the FERNs can be estimated without any a priori knowledge of the EQ and TS points.

Transient States and Barriers from Molecular Simulations and the Milestoning Theory: Kinetics in Ligand-Protein Recognition and Compound Design

This study presents a novel computational approach to study molecular recognition and binding kinetics for drug-like compounds dissociating from a flexible protein system. The intermediates and their free energy profile during ligand association and dissociation processes control ligand-protein binding kinetics and bring a more complete picture of ligand-protein binding. The method applied the milestoning theory to extract kinetics and thermodynamics information from running short classical molecular dynamics (MD) simulations for frames from a given dissociation path. High-dimensional ligand-protein motions (3N-6 degrees of freedom) during ligand dissociation were reduced by use of principal component modes for assigning more than 100 milestones, and classical MD runs were allowed to travel multiple milestones to efficiently obtain ensemble distribution of initial structures for MD simulations and estimate the transition time and rate during ligand traveling between milestones. We used five pyrazolourea ligands and cyclin-dependent kinase 8 with cyclin C (CDK8/CycC) as our model system as well as metadynamics and a pathway search method to sample dissociation pathways. With our strategy, we constructed the free energy profile for highly mobile biomolecular systems. The computed binding free energy and residence time correctly ranked the pyrazolourea ligand series, in agreement with experimental data. Guided by a barrier of a ligand passing an αC helix and activation loop, we introduced one hydroxyl group to parent compounds to design our ligands with increased residence time and validated our prediction by experiments. This work provides a novel and robust approach to investigate dissociation kinetics of large and flexible systems for understanding unbinding mechanisms and designing new small-molecule drugs with desired binding kinetics.

Hydrolysis of cephalexin and meropenem by New Delhi metallo-β-lactamase: the substrate protonation mechanism is drug dependent

Emergence of antibiotic resistance due to New Delhi metallo-β-lactamase (NDM-1) bacterial enzymes is of great concern due to their ability to hydrolyze a wide range of antibiotics. There are ongoing efforts to obtain the atomistic details of the hydrolysis mechanism in order to develop inhibitors for NDM-1. In particular, it remains elusive how drug molecules of different families of antibiotics are hydrolyzed by NDM-1 in an efficient manner. Here we report the detailed molecular mechanism of NDM-1 catalyzed hydrolysis of cephalexin, a cephalosporin family drug, and meropenem, a carbapenem family drug. This study employs molecular dynamics (MD) simulations using hybrid quantum mechanical/molecular mechanical (QM/MM) methods at the density functional theory (DFT) level, based on which reaction pathways and the associated free energies are obtained. We find that the mechanism and the free energy barrier for the ring-opening step are the same for both the drug molecules, while the subsequent protonation step differs. In particular, we observe that the mechanism of the protonation step depends on the R2 group of the drug molecule. Our simulations show that allylic carbon protonation occurs in the case of the cephalexin drug molecule where Lys211 is the proton donor, and the proton transfer occurs via a water chain formed (only) at the ring-opened intermediate structure. Based on the free energy profiles, the overall kinetics of drug hydrolysis is discussed. Finally, we show that the proposed mechanisms and free energy profiles could explain various experimental observations.

Molecular insights into avibactam mediated class C β-lactamase inhibition: competition between reverse acylation and hydrolysis through desulfation

The spatial water probability density plots show that the axial –NHOSO₃ group of avibactam impedes the deacylating water molecule(s) to enter the active site, while the –NHSO₃ group in aztreonam is unable to prevent the water molecule(s) to diffuse into the active site.

Product Release Pathways in Human and Plasmodium falciparum Phosphoribosyltransferase

Atomistic molecular dynamics (MD) simulations coupled with the metadynamics technique were carried out to delineate the product (PPi.2Mg and IMP) release mechanisms from the active site of both human (Hs) and Plasmodium falciparum (Pf) hypoxanthine-guanine-(xanthine) phosphoribosyltransferase (HG(X)PRT). An early movement of PPi.2Mg from its binding site has been observed. The swinging motion of the Asp side chain (D134/D145) in the binding pocket facilitates the detachment of IMP, which triggers the opening of flexible loop II, the gateway to the bulk solvent. In PfHGXPRT, PPi.2Mg and IMP are seen to be released via the same path in all of the biased MD simulations. In HsHGPRT too, the product molecules follow similar routes from the active site; however, an alternate but minor escape route for PPi.2Mg has been observed in the human enzyme. Tyr 104 and Phe 186 in HsHGPRT and Tyr 116 and Phe 197 in PfHGXPRT are the key residues that mediate the release of IMP, whereas the motion of PPi.2Mg away from the reaction center is guided by the negatively charged Asp and Glu and a few positively charged residues (Lys and Arg) that line the product release channels. Mutations of a few key residues present in loop II of Trypanosoma cruzi (Tc) HGPRT have been shown to reduce the catalytic efficiency of the enzyme. Herein, in silico mutation of corresponding residues in loop II of HsHGPRT and PfHGXPRT resulted in partial opening of the flexible loop (loop II), thus exposing the active site to bulk water, which offers a rationale for the reduced catalytic activity of these two mutant enzymes. Investigations of the product release from these HsHGPRT and PfHGXPRT mutants delineate the role of these important residues in the enzymatic turnover.