Enhancing Paradynamics for QM/MM Sampling of Enzymatic Reactions

Navigating the landscape of enzyme design: from molecular simulations to machine learning

Global environmental issues and sustainable development call for new technologies for fine chemical synthesis and waste valorization. Biocatalysis has attracted great attention as the alternative to the traditional organic synthesis. However, it is challenging to navigate the vast sequence space to identify those proteins with admirable biocatalytic functions. The recent development of deep-learning based structure prediction methods such as AlphaFold2 reinforced by different computational simulations or multiscale calculations has largely expanded the 3D structure databases and enabled structure-based design. While structure-based approaches shed light on site-specific enzyme engineering, they are not suitable for large-scale screening of potential biocatalysts. Effective utilization of big data using machine learning techniques opens up a new era for accelerated predictions. Here, we review the approaches and applications of structure-based and machine-learning guided enzyme design. We also provide our view on the challenges and perspectives on effectively employing enzyme design approaches integrating traditional molecular simulations and machine learning, and the importance of database construction and algorithm development in attaining predictive ML models to explore the sequence fitness landscape for the design of admirable biocatalysts.

Seeding the multi-dimensional nonequilibrium pulling for Hamiltonian variation: indirect nonequilibrium free energy simulations at QM levels

The combination of free energy simulations in the alchemical and configurational spaces provides a feasible route to access the thermodynamic profiles under a computationally demanding target Hamiltonian. Normally, due to the significant differences between the computational cost of ab initio quantum mechanics (QM) calculations and those of semi-empirical quantum mechanics (SQM) and molecular mechanics (MM), this indirect method could be used to obtain the QM thermodynamics by combining the SQM or MM results and the SQM-to-QM or MM-to-QM corrections. In our previous work, a multi-dimensional nonequilibrium pulling framework for Hamiltonian variations was introduced based on bidirectional pulling and bidirectional reweighting. The method performs nonequilibrium free energy simulations in the configurational space to obtain the thermodynamic profile along the conformational change pathway under a selected computationally efficient Hamiltonian, and uses the nonequilibrium alchemical method to correct or perturb the thermodynamic profile to that under the target Hamiltonian. The BAR-based method is designed to achieve the best generality and transferability and thus leads to modest (∼20 fold) speedup. In this work, we explore the possibility of further accelerating the nonequilibrium free energy simulation by employing unidirectional pulling and using the selection criterion to obtain the initial configurations used to initiate nonequilibrium trajectories following the idea of adaptive steered molecular dynamics (ASMD). A single initial condition is used to seed the whole multi-dimensional nonequilibrium free energy simulation and the sampling is performed fully in the nonequilibrium ensemble. Introducing very short ps-length equilibrium sampling to grab more initial seeds could also be helpful. The ASMD scheme estimates the free energy difference with the unidirectional exponential average (EXP), but it does not follow exactly the requirements of the EXP estimator. Another deficiency of the seeding simulation is the inherently sequential or serial pulling due to the inter-segment dependency, which triggers some problems in the parallelizability of the simulation. Numerical tests are performed to grasp some insights and guidelines for using this selection-criterion-based ASMD scheme. The presented selection-criterion-based multi-dimensional ASMD scheme follows the same perturbation network of the BAR-based method, and thus could be used in various Hamiltonian-variation cases.

A General Picture of Cucurbit[8]uril Host-Guest Binding

Describing, understanding, and designing complex interaction networks within macromolecular systems remain challenging in modern chemical research. Host-guest systems, despite their relative simplicity in both the structural feature and interaction patterns, still pose problems in theoretical modeling. The barrel-shaped supramolecular container cucurbit[8]uril (CB8) shows promising functionalities in various areas, e.g., catalysis and molecular recognition. It can stably coordinate a series of structurally diverse guests with high affinities. In this work, we examine the binding of seven commonly abused drugs to the CB8 host, aiming at providing a general picture of CB8-guest binding. Extensive sampling of the configurational space of these host-guest systems is performed, and the binding pathway and interaction patterns of CB8-guest complexes are investigated. A thorough comparison of widely used fixed-charge models for drug-like molecules is presented. Iterative refitting of the atomic charges suggests significant conformation dependence of charge generation. The initial model generated at the original conformation could be inaccurate for new conformations explored during conformational search, and the newly fitted charge set improves the prediction-experiment correlation significantly. Our investigations of the configurational space of CB8-drug complexes suggest that the host-guest interactions are more complex than expected. Despite the structural simplicities of these molecules, the conformational fluctuations of the host and the guest molecules and orientations of functional groups lead to the existence of an ensemble of binding modes. The insights of the binding thermodynamics, performance of fixed-charge models, and binding patterns of the CB8-guest systems are useful for studying and elucidating the binding mechanism of other host-guest complexes.

Evaluating QM/MM Free Energy Surfaces for Ranking Cysteine Protease Covalent Inhibitors

One tactic for cysteine protease inhibition is to form a covalent bond between an electrophilic atom of the inhibitor and the thiol of the catalytic cysteine. In this study, we evaluate the reaction free energy obtained from a hybrid quantum mechanical/molecular mechanical (QM/MM) free energy profile as a predictor of affinity for reversible, covalent inhibitors of rhodesain. We demonstrate that the reaction free energy calculated with the PM6/MM potential is in agreement with the experimental data and suggest that the free energy profile for covalent bond formation in a protein environment may be a useful tool for the inhibitor design.

Theoretical understanding of the thermodynamics and interactions in transcriptional regulator TtgR-ligand binding

The transcriptional regulator TtgR belongs to the TetR family of transcriptional repressors. It depresses the transcription of the TtgABC operon and itself and thus regulates the extrusion of noxious chemicals with efflux pumps in bacterial cells. As the ligand-binding domain of TtgR is rather flexible, it can bind with a number of structurally diverse ligands, such as antibiotics, flavonoids and aromatic solvents. In the current work, we perform equilibrium and nonequilibrium alchemical free energy simulation to predict the binding affinities of a series of ligands targeting the TtgR protein and an agreement between the theoretical prediction and the experimental result is observed. End-point methods MM/PBSA and MM/GBSA are also employed for comparison. We further study the interaction maps and contacts between the protein and the ligand and identify important interactions in the protein-ligand binding cases. The dynamics fluctuation and secondary structures are also investigated. The current work sheds light on atomic and thermodynamic understanding of the TtgR-ligand interactions.

BAR-based multi-dimensional nonequilibrium pulling for indirect construction of QM/MM free energy landscapes: from semi-empirical to ab initio

The indirect method for the construction of quantum mechanics (QM)/molecular mechanics (MM) free energy landscapes provides a cheaper alternative for free energy simulations at the QM level. The indirect method features a direct calculation of the free energy profile with a computationally efficient but less accurate Hamiltonian (i.e. low-level Hamiltonian) and a low-level-to-high-level correction. In the thermodynamic cycle, the direct low-level calculation along the physically meaningful reaction coordinate is corrected via the alchemical method, which is often achieved with perturbation-based techniques. In our previous work, a multi-dimensional nonequilibrium pulling framework is proposed for the indirect construction of QM/MM free energy landscapes. Previously, we focused on obtaining semi-empirical QM (SQM) results indirectly from direct MM simulations and MM to SQM corrections. In this work, we apply this method to obtain results under ab initio QM Hamiltonians by combining direct SQM results and SQM to QM corrections. A series of SQM and QM Hamiltonians are benchmarked. It is observed that PM6 achieves the best performance among the low-level Hamiltonians. Therefore, we recommend using PM6 as the low-level theory in the indirect free energy simulation. Considering its higher similarity to the high-level Hamiltonians, PM6 corrected with the bond charge correction could be more accurate than the existing AM1-BCC model. Another central result in the current work is a basic protocol of choosing the strength of restraints and an appropriate time step in nonequilibrium free energy simulation at the stiff spring limit. We provide theoretical derivations to emphasize the importance of using a sufficiently large force constant and choosing an appropriate time step. It is worth noting that a general rule of thumb for choosing the time step, according to our derivation, is that a time step of 1 fs or smaller should be used, as long as the stiff spring approximation is employed, even in simulations with constraints on bonds involving hydrogen atoms.

BAR-based multi-dimensional nonequilibrium pulling for indirect construction of a QM/MM free energy landscape

Construction of free energy landscapes at the quantum mechanics (QM) level is computationally demanding. As shown in previous studies, by employing an indirect scheme (i.e. constructing a thermodynamic cycle connecting QM states via an alchemical pathway), simulations are converged with much less computational burden. The indirect scheme makes QM/molecular mechanics (MM) free energy simulation orders of magnitude faster than the direct QM/MM schemes. However, the indirect QM/MM simulations were mostly equilibrium sampling based and the nonequilibrium methods were merely exploited in one-dimensional alchemical QM/MM end-state correction at two end states. In this work, we represent a multi-dimensional nonequilibrium pulling scheme for indirect QM/MM free energy simulations, where the whole free energy simulation is performed only with nonequilibrium methods. The collective variable (CV) space we explore is a combination of one alchemical CV and one physically meaningful CV. The current nonequilibrium indirect QM/MM simulation method can be seen as the generalization of equilibrium perturbation based indirect QM/MM methods. The test systems include one backbone dihedral case and one distance case. The two cases are significantly different in size, enabling us to investigate the dependence of the speedup of the indirect scheme on the size of the system. It is shown that the speedup becomes larger when the size of the system becomes larger, which is consistent with the scaling behavior of QM Hamiltonians.

Experimental study and computational modelling of cruzain cysteine protease inhibition by dipeptidyl nitriles

Chagas disease affects millions of people in Latin America. This disease is caused by the protozoan parasite Trypanossoma cruzi. The cysteine protease cruzain is a key enzyme for the survival and propagation of this parasite lifecycle. Nitrile-based inhibitors are efficient inhibitors of cruzain that bind by forming a covalent bond with this enzyme. Here, three nitrile-based inhibitors dubbed Neq0409, Neq0410 and Neq0570 were synthesized, and the thermodynamic profile of the bimolecular interaction with cruzain was determined using isothermal titration calorimetry (ITC). The result suggests the inhibition process is enthalpy driven, with a detrimental contribution of entropy. In addition, we have used hybrid Quantum Mechanical/Molecular Mechanical (QM/MM) and Molecular Dynamics (MD) simulations to investigate the reaction mechanism of reversible covalent modification of cruzain by Neq0409, Neq0410 and Neq0570. The computed free energy profile shows that the nucleophilic attack of Cys25 on the carbon C1 of inhibitiors and the proton transfer from His162 to N1 of the dipeptidyl nitrile inhibitor take place in a single step. The calculated free energy of the inhibiton reaction is in agreement with covalent experimental binding. Altogether, the results reported here suggests that nitrile-based inhibitors are good candidates for the development of reversible covalent inhibitors of cruzain and other cysteine proteases.

Efficient Computation of Free Energy Surfaces of Diels⁻Alder Reactions in Explicit Solvent at Ab Initio QM/MM Level

For Diels–Alder (DA) reactions in solution, an accurate and converged free energy (FE) surface at ab initio (ai) quantum mechanical/molecular mechanical (QM/MM) level is imperative for the understanding of reaction mechanism. However, this computation is still far too expensive. In a previous work, we proposed a new method termed MBAR+wTP, with which the computation of the ai FE profile can be accelerated by several orders of magnitude via a three-step procedure: (I) an umbrella sampling (US) using a semi-empirical (SE) QM/MM Hamiltonian is performed; (II) the FE profile is generated using the Multistate Bennett Acceptance Ratio (MBAR) analysis; and (III) a weighted Thermodynamic Perturbation (wTP) from the SE Hamiltonian to the ai Hamiltonian is performed to obtain the ai QM/MM FE profile using weight factors from the MBAR analysis. In this work, this method is extended to the calculations of two-dimensional FE surfaces of two Diels–Alder reactions of cyclopentadiene with either acrylonitrile or 1-4-naphthoquinone at ai QM/MM level. The accurate activation free energies at the ai QM/MM level, which are much closer to the experimental measurements than those calculated by other methods, indicate that this MBAR+wTP method can be applied in the studies of complex reactions in condensed phase with much-enhanced efficiency.

Relative Ligand-Binding Free Energies Calculated from Multiple Short QM/MM MD Simulations

We have devised a new efficient approach to compute combined quantum mechanical (QM) and molecular mechanical (MM, i.e. QM/MM) ligand-binding relative free energies. Our method employs the reference-potential approach with free-energy perturbation both at the MM level (between the two ligands) and from MM to QM/MM (for each ligand). To ensure that converged results are obtained for the MM → QM/MM perturbations, explicit QM/MM molecular dynamics (MD) simulations are performed with two intermediate mixed states. To speed up the calculations, we utilize the fact that the phase space can be extensively sampled at the MM level. Therefore, we run many short QM/MM MD simulations started from snapshots of the MM simulations, instead of a single long simulation. As a test case, we study the binding of nine cyclic carboxylate ligands to the octa-acid deep cavitand. Only the ligand is in the QM system, treated with the semiempirical PM6-DH+ method. We show that for eight of the ligands, we obtain well converged results with short MD simulations (1-15 ps). However, in one case, the convergence is slower (∼50 ps) owing to a mismatch between the conformational preferences of the MM and QM/MM potentials. We test the effect of initial minimization, the need of equilibration, and how many independent simulations are needed to reach a certain precision. The results show that the present approach is about four times faster than using standard MM → QM/MM free-energy perturbations with the same accuracy and precision.

An adaptive bias - hybrid MD/kMC algorithm for protein folding and aggregation

In this paper, we present a novel hybrid Molecular Dynamics/kinetic Monte Carlo (MD/kMC) algorithm and apply it to protein folding and aggregation in explicit solvent. The new algorithm uses a dynamical definition of biases throughout the MD component of the simulation, normalized in relation to the unbiased forces. The algorithm guarantees sampling of the underlying ensemble in dependency of one average linear coupling factor 〈α〉_τ. We test the validity of the kinetics in simulations of dialanine and compare dihedral transition kinetics with long-time MD-simulations. We find that for low 〈α〉_τ values, kinetics are in good quantitative agreement. In folding simulations of TrpCage and TrpZip4 in explicit solvent, we also find good quantitative agreement with experimental results and prior MD/kMC simulations. Finally, we apply our algorithm to study growth of the Alzheimer Amyloid Aβ 16-22 fibril by monomer addition. We observe two possible binding modes, one at the extremity of the fibril (elongation) and one on the surface of the fibril (lateral growth), on timescales ranging from ns to 8 μs.

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.

Unraveling the Addition-Elimination Mechanism of EPSP Synthase through Computer Modeling

Enolpyruvyl transfer from phosphoenolpyruvate (PEP) to the hydroxyl group of shikimate-5-OH-3-phosphate (S3P) is catalyzed by 5-enolpyruvylshikimate 3-phosphate (EPSP) synthase in a reaction that involves breaking the C-O bond of PEP. Catalysis involves an addition-elimination mechanism with the formation of a tetrahedral intermediate (THI). Experiments have elucidated the mechanism of THI formation and breakdown. However, the catalytic action of EPSP synthase and the individual roles of catalytic residues Asp313 and Glu341 remains unclear. We have used a hybrid quantum mechanical/molecular mechanical (QM/MM) approach to explore the free energy surface in a reaction catalyzed by EPSP synthase. The Glu341 was the most favorable acid/base catalyst. Our results indicate that the protonation of PEP C3 precedes the nucleophilic attack on PEP C2 in the addition mechanism. Also, the breaking of the C-O bond of THI to form an EPSP cation intermediate must occur before proton transfer from PEP C3 to Glu341 in the elimination mechanism. Analysis of the FES supports cationic intermediate formation during the reaction catalyzed by EPSP synthase. Finally, the computational model indicates a proton transfer shift (Hammond shift) from Glu341 to C3 for an enzyme-based reaction with the shifted transition state, earlier than in the reference reaction in water.

Coupled Valence-Bond State Molecular Dynamics Description of an Enzyme-Catalyzed Reaction in a Non-Aqueous Organic Solvent

Enzymes are widely used in nonaqueous solvents to catalyze non-natural reactions. While experimental measurements showed that the solvent nature has a strong effect on the reaction kinetics, the molecular details of the catalytic mechanism in nonaqueous solvents have remained largely elusive. Here we study the transesterification reaction catalyzed by the paradigm subtilisin Carlsberg serine protease in an organic apolar solvent. The rate-limiting acylation step involves a proton transfer between active-site residues and the nucleophilic attack of the substrate to form a tetrahedral intermediate. We design the first coupled valence-bond state model that simultaneously describes both reactions in the enzymatic active site. We develop a new systematic procedure to parametrize this model on high-level ab initio QM/MM free energy calculations that account for the molecular details of the active site and for both substrate and protein conformational fluctuations. Our calculations show that the reaction energy barrier changes dramatically with the solvent and protein conformational fluctuations. We find that the mechanism of the tetrahedral intermediate formation during the acylation step is similar to that determined under aqueous conditions, and that the proton transfer and nucleophilic attack reactions occur concertedly. We identify the reaction coordinate to be mostly due to the rearrangement of some residual water molecules close to the active site.

Catalysis by solvation rather than the desolvation effect: exploring the catalytic efficiency of SAM-dependent chlorinase

Chlorinase SalL active sites provide electrostatic stabilization of the transition state which is the origin of its catalytic effect.