GPU-Accelerated Implementation of Continuous Constant pH Molecular Dynamics in Amber: pKa Predictions with Single-pH Simulations

Resolving coupled pH titrations using alchemical free energy calculations

In a protein, nearby titratable sites can be coupled: the (de)protonation of one may affect the other. The degree of this interaction depends on several factors and can influence the measured p K a . Here, we derive a formalism based on double free energy differences ( Δ Δ G ) for quantifying the individual site p K a values of coupled residues. As Δ Δ G values can be obtained by means of alchemical free energy calculations, the presented approach allows for a convenient estimation of coupled residue p K a s in practice. We demonstrate that our approach and a previously proposed microscopic p K a formalism, can be combined with alchemical free energy calculations to resolve pH-dependent protein p K a values. Toy models and both, regular and constant-pH molecular dynamics simulations, alongside experimental data, are used to validate this approach. Our results highlight the insights gleaned when coupling and microstate probabilities are analyzed and suggest extensions to more complex enzymatic contexts. Furthermore, we find that naïvely computed p K a values that ignore coupling, can be significantly improved when coupling is accounted for, in some cases reducing the error by half. In short, alchemical free energy methods can resolve the p K a values of both uncoupled and coupled residues.

Multistate Method to Efficiently Account for Tautomerism and Protonation in Alchemical Free-Energy Calculations

The majority of drug-like molecules contain at least one ionizable group, and many common drug scaffolds are subject to tautomeric equilibria. Thus, these compounds are found in a mixture of protonation and/or tautomeric states at physiological pH. Intrinsically, standard classical molecular dynamics (MD) simulations cannot describe such equilibria between states, which negatively impacts the prediction of key molecular properties in silico. Following the formalism described by de Oliveira and co-workers (J. Chem. Theory Comput. 2019, 15, 424-435) to consider the influence of all states on the binding process based on alchemical free-energy calculations, we demonstrate in this work that the multistate method replica-exchange enveloping distribution sampling (RE-EDS) is well suited to describe molecules with multiple protonation and/or tautomeric states in a single simulation. We apply our methodology to a series of eight inhibitors of factor Xa with two protonation states and a series of eight inhibitors of glycogen synthase kinase 3β (GSK3β) with two tautomeric states. In particular, we show that given a sufficient phase-space overlap between the states, RE-EDS is computationally more efficient than standard pairwise free-energy methods.

Exploring Structural Insights of Aβ42 and α-Synuclein Monomers and Heterodimer: A Comparative Study Using Implicit and Explicit Solvent Simulations

Protein misfolding, aggregation, and fibril formation play a central role in the development of severe neurological disorders, including Alzheimer's and Parkinson's diseases. The structural stability of mature fibrils in these diseases is of great importance, as organisms struggle to effectively eliminate amyloid plaques. To address this issue, it is crucial to investigate the early stages of fibril formation when monomers aggregate into small, toxic, and soluble oligomers. However, these structures are inherently disordered, making them challenging to study through experimental approaches. Recently, it has been shown experimentally that amyloid-β 42 (Aβ42) and α-synuclein (α-Syn) can coassemble. This has motivated us to investigate the interaction between their monomers as a first step toward exploring the possibility of forming heterodimeric complexes. In particular, our study involves the utilization of various Amber and CHARMM force-fields, employing both implicit and explicit solvent models in replica exchange and conventional simulation modes. This comprehensive approach allowed us to assess the strengths and weaknesses of these solvent models and force fields in comparison to experimental and theoretical findings, ensuring the highest level of robustness. Our investigations revealed that Aβ42 and α-Syn monomers can indeed form stable heterodimers, and the resulting heterodimeric model exhibits stronger interactions compared to the Aβ42 dimer. The binding of α-Syn to Aβ42 reduces the propensity of Aβ42 to adopt fibril-prone conformations and induces significant changes in its conformational properties. Notably, in AMBER-FB15 and CHARMM36m force fields with the use of explicit solvent, the presence of Aβ42 significantly increases the β-content of α-Syn, consistent with the experiments showing that Aβ42 triggers α-Syn aggregation. Our analysis clearly shows that although the use of implicit solvent resulted in too large compactness of monomeric α-Syn, structural properties of monomeric Aβ42 and the heterodimer were preserved in explicit-solvent simulations. We anticipate that our study sheds light on the interaction between α-Syn and Aβ42 proteins, thus providing the atom-level model required to assess the initial stage of aggregation mechanisms related to Alzheimer's and Parkinson's diseases.

Identification of histidine residues that affect the T/R-state conformations of human hemoglobin using constant pH molecular dynamics simulations

Human hemoglobin (Hb) is a tetrameric protein consisting of two α and two β subunits that can adopt a low-affinity T- and high-affinity R-state conformations. Under physiological pH conditions, histidine (His) residues are the main sites for proton binding or release, and their protonation states can affect the T/R-state conformation of Hb. However, it remains unclear which His residues can effectively affect the Hb conformation. Herein, the impact of the 38 His residues of Hb on its T/R-state conformations was evaluated using constant-pH molecular dynamics (CpHMD) simulations at physiological pH while focusing on the His protonation states. Overall, the protonation states of some His residues were found to be correlated with the Hb conformation state. These residues were mainly located in the proximity of the heme (α87 and β92), and at the α1β2 and α2β1 interfaces (α89 and β97). This correlation may be partly explained by how easily hydrogen bonds can be formed, which depends on the protonation states of the His residues. Taken together, these CpHMD-based findings provide new insights into the identification of titratable His residues α87, α89, β92, and β97 that can affect Hb conformational switching under physiological pH conditions.

phbuilder: A Tool for Efficiently Setting up Constant pH Molecular Dynamics Simulations in GROMACS

Constant pH molecular dynamics (MD) is a powerful technique that allows the protonation state of residues to change dynamically, thereby enabling the study of pH dependence in a manner that has not been possible before. Recently, a constant pH implementation was incorporated into the GROMACS MD package. Although this implementation provides good accuracy and performance, manual modification and the preparation of simulation input files are required, which can be complicated, tedious, and prone to errors. To simplify and automate the setup process, we present phbuilder, a tool that automatically prepares constant pH MD simulations for GROMACS by modifying the input structure and topology as well as generating the necessary parameter files. phbuilder can prepare constant pH simulations from both initial structures and existing simulation systems, and it also provides functionality for performing titrations and single-site parametrizations of new titratable group types. The tool is freely available at www.gitlab.com/gromacs-constantph. We anticipate that phbuilder will make constant pH simulations easier to set up, thereby making them more accessible to the GROMACS user community.

Advances in Computational Approaches for Estimating Passive Permeability in Drug Discovery

Passive permeation of cellular membranes is a key feature of many therapeutics. The relevance of passive permeability spans all biological systems as they all employ biomembranes for compartmentalization. A variety of computational techniques are currently utilized and under active development to facilitate the characterization of passive permeability. These methods include lipophilicity relations, molecular dynamics simulations, and machine learning, which vary in accuracy, complexity, and computational cost. This review briefly introduces the underlying theories, such as the prominent inhomogeneous solubility diffusion model, and covers a number of recent applications. Various machine-learning applications, which have demonstrated good potential for high-volume, data-driven permeability predictions, are also discussed. Due to the confluence of novel computational methods and next-generation exascale computers, we anticipate an exciting future for computationally driven permeability predictions.

Comparative Performance of High-Throughput Methods for Protein pKa Predictions

The medically relevant field of protein-based therapeutics has triggered a demand for protein engineering in different pH environments of biological relevance. In silico engineering workflows typically employ high-throughput screening campaigns that require evaluating large sets of protein residues and point mutations by fast yet accurate computational algorithms. While several high-throughput pKa prediction methods exist, their accuracies are unclear due to the lack of a current comprehensive benchmarking. Here, seven fast, efficient, and accessible approaches including PROPKA3, DeepKa, PKAI, PKAI+, DelPhiPKa, MCCE2, and H++ were systematically tested on a nonredundant subset of 408 measured protein residue pKa shifts from the pKa database (PKAD). While no method outperformed the null hypotheses with confidence, as illustrated by statistical bootstrapping, DeepKa, PKAI+, PROPKA3, and H++ had utility. More specifically, DeepKa consistently performed well in tests across multiple and individual amino acid residue types, as reflected by lower errors, higher correlations, and improved classifications. Arithmetic averaging of the best empirical predictors into simple consensuses improved overall transferability and accuracy up to a root-mean-square error of 0.76 pKa units and a correlation coefficient (R2) of 0.45 to experimental pKa shifts. This analysis should provide a basis for further methodological developments and guide future applications, which require embedding of computationally inexpensive pKa prediction methods, such as the optimization of antibodies for pH-dependent antigen binding.

Multiway Analysis Reveals Hydrophobicity as the Sole Determinant of Dynamic Peptide-Acetonitrile-Water Association Behavior

Multiway analysis, a class of techniques developed for the purpose of studying multi-dimensional multivariate data, has been applied to study the dynamical structure of the first solvation layer of Ace-Gly-X-Gly-Nme peptides (where X is any amino acid) perturbed with the increase in concentrations of acetonitrile. Separate MD simulations of each peptide were carried out in five different concentrations of acetonitrile. Association of peptide, water, and acetonitrile atoms was quantified in terms of the relative abundance of Delaunay tetrahedra whose vertices could be centered on either the peptide, acetonitrile, or water atoms. A three-way data set comprising nine types of Delaunay tetrahedra in the first dimension, five concentrations of acetonitrile in the second dimension, and 26 different peptides in the third dimension was subjected to two different multiway methods viz., the constrained PARAFAC and the unconstrained Tucker3 analysis. The results unequivocally show that the dynamic peptide-acetonitrile-water association behavior could be solely explained by the hydrophobicity of the central amino acid. The study also demonstrates the utility of multiway analysis for the integration and interpretation of large number of separate MD simulations.

Integrative Approach to Dissect the Drug Resistance Mechanism of the H172Y Mutation of SARS-CoV-2 Main Protease

Nirmatrelvir is an orally available inhibitor of SARS-CoV-2 main protease (Mpro) and the main ingredient of Paxlovid, a drug approved by the U.S. Food and Drug Administration for high-risk COVID-19 patients. Recently, a rare natural mutation, H172Y, was found to significantly reduce nirmatrelvir's inhibitory activity. As the COVID-19 cases skyrocket in China and the selective pressure of antiviral therapy builds in the US, there is an urgent need to characterize and understand how the H172Y mutation confers drug resistance. Here, we investigated the H172Y Mpro's conformational dynamics, folding stability, catalytic efficiency, and inhibitory activity using all-atom constant pH and fixed-charge molecular dynamics simulations, alchemical and empirical free energy calculations, artificial neural networks, and biochemical experiments. Our data suggest that the mutation significantly weakens the S1 pocket interactions with the N-terminus and perturbs the conformation of the oxyanion loop, leading to a decrease in the thermal stability and catalytic efficiency. Importantly, the perturbed S1 pocket dynamics weaken the nirmatrelvir binding in the P1 position, which explains the decreased inhibitory activity of nirmatrelvir. Our work demonstrates the predictive power of the combined simulation and artificial intelligence approaches, and together with biochemical experiments, they can be used to actively surveil continually emerging mutations of SARS-CoV-2 Mpro and assist the optimization of antiviral drugs. The presented approach, in general, can be applied to characterize mutation effects on any protein drug targets.

Basis for Accurate Protein pKa Prediction with Machine Learning

pH regulates protein structures and the associated functions in many biological processes via protonation and deprotonation of ionizable side chains where the titration equilibria are determined by pK_a's. To accelerate pH-dependent molecular mechanism research in the life sciences or industrial protein and drug designs, fast and accurate pK_a prediction is crucial. Here we present a theoretical pK_a data set PHMD549, which was successfully applied to four distinct machine learning methods, including DeepKa, which was proposed in our previous work. To reach a valid comparison, EXP67S was selected as the test set. Encouragingly, DeepKa was improved significantly and outperforms other state-of-the-art methods, except for the constant-pH molecular dynamics, which was utilized to create PHMD549. More importantly, DeepKa reproduced experimental pK_a orders of acidic dyads in five enzyme catalytic sites. Apart from structural proteins, DeepKa was found applicable to intrinsically disordered peptides. Further, in combination with solvent exposures, it is revealed that DeepKa offers the most accurate prediction under the challenging circumstance that hydrogen bonding or salt bridge interaction is partly compensated by desolvation for a buried side chain. Finally, our benchmark data qualify PHMD549 and EXP67S as the basis for future developments of protein pK_a prediction tools driven by artificial intelligence. In addition, DeepKa built on PHMD549 has been proven an efficient protein pK_a predictor and thus can be applied immediately to, for example, pK_a database construction, protein design, drug discovery, and so on.

An Integrative Approach to Dissect the Drug Resistance Mechanism of the H172Y Mutation of SARS-CoV-2 Main Protease

Nirmatrelvir is an orally available inhibitor of SARS-CoV-2 main protease (Mpro) and the main ingredient of PAXLOVID, a drug approved by FDA for high-risk COVID-19 patients. Recently, a rare natural mutation, H172Y, was found to significantly reduce nirmatrelvir's inhibitory activity. As the COVID-19 cases skyrocket in China and the selective pressure of antiviral therapy builds up in the US, there is an urgent need to characterize and understand how the H172Y mutation confers drug resistance. Here we investigated the H172Y Mpro's conformational dynamics, folding stability, catalytic efficiency, and inhibitory activity using all-atom constant pH and fixed-charge molecular dynamics simulations, alchemical and empirical free energy calculations, artificial neural networks, and biochemical experiments. Our data suggests that the mutation significantly weakens the S1 pocket interactions with the N-terminus and perturbs the conformation of the oxyanion loop, leading to a decrease in the thermal stability and catalytic efficiency. Importantly, the perturbed S1 pocket dynamics weakens the nirma-trelvir binding in the P1 position, which explains the decreased inhibitory activity of nirmatrelvir. Our work demonstrates the predictive power of the combined simulation and artificial intel-ligence approaches, and together with biochemical experiments they can be used to actively surveil continually emerging mutations of SARS-CoV-2 Mpro and assist the discovery of new antiviral drugs. The presented workflow can be applicable to characterize mutation effects on any protein drug targets.

Understanding the Key Roles of pH Buffer in Accelerating Lignin Degradation by Lignin Peroxidase

pH buffer plays versatile roles in both biology and chemistry. In this study, we unravel the critical role of pH buffer in accelerating degradation of the lignin substrate in lignin peroxidase (LiP) using QM/MM MD simulations and the nonadiabatic electron transfer (ET) and proton-coupled electron transfer (PCET) theories. As a key enzyme involved in lignin degradation, LiP accomplishes the oxidation of lignin via two consecutive ET reactions and the subsequent C-C cleavage of the lignin cation radical. The first one involves ET from Trp171 to the active species of Compound I, while the second one involves ET from the lignin substrate to the Trp171 radical. Differing from the common view that pH = 3 may enhance the oxidizing power of Cpd I via protonation of the protein environment, our study shows that the intrinsic electric fields have minor effects on the first ET step. Instead, our study shows that the pH buffer of tartaric acid plays key roles during the second ET step. Our study shows that the pH buffer of tartaric acid can form a strong H-bond with Glu250, which can prevent the proton transfer from the Trp171-H^•+ cation radical to Glu250, thereby stabilizing the Trp171-H^•+ cation radical for the lignin oxidation. In addition, the pH buffer of tartaric acid can enhance the oxidizing power of the Trp171-H^•+ cation radical via both the protonation of the proximal Asp264 and the second-sphere H-bond with Glu250. Such synergistic effects of pH buffer facilitate the thermodynamics of the second ET step and reduce the overall barrier of lignin degradation by ∼4.3 kcal/mol, which corresponds to a rate acceleration of 10³-fold that agrees with experiments. These findings not only expand our understanding on pH-dependent redox reactions in both biology and chemistry but also provide valuable insights into tryptophan-mediated biological ET reactions.

Molecular determinants of acrylamide neurotoxicity through covalent docking

Acrylamide (ACR) is formed during food processing by Maillard reaction between sugars and proteins at high temperatures. It is also used in many industries, from water waste treatment to manufacture of paper, fabrics, dyes and cosmetics. Unfortunately, cumulative exposure to acrylamide, either from diet or at the workplace, may result in neurotoxicity. Such adverse effects arise from covalent adducts formed between acrylamide and cysteine residues of several neuronal proteins via a Michael addition reaction. The molecular determinants of acrylamide reactivity and its impact on protein function are not completely understood. Here we have compiled a list of acrylamide protein targets reported so far in the literature in connection with neurotoxicity and performed a systematic covalent docking study. Our results indicate that acrylamide binding to cysteine is favored in the presence of nearby positively charged amino acids, such as lysines and arginines. For proteins with more than one reactive Cys, docking scores were able to discriminate between the primary ACR modification site and secondary sites modified only at high ACR concentrations. Therefore, docking scores emerge as a potential filter to predict Cys reactivity against acrylamide. Inspection of the ACR-protein complex structures provides insights into the putative functional consequences of ACR modification, especially for non-enzyme proteins. Based on our study, covalent docking is a promising computational tool to predict other potential protein targets mediating acrylamide neurotoxicity.

Reliable and Accurate Prediction of Single-Residue pKa Values through Free Energy Perturbation Calculations

Accurate prediction of the pK_a's of protein residues is crucial to many applications in biological simulation and drug discovery. Here, we present the use of free energy perturbation (FEP) calculations for the prediction of single-protein residue pK_a values. We begin with an initial set of 191 residues with experimentally determined pK_a values. To isolate sampling limitations from force field inaccuracies, we develop an algorithm to classify residues whose environments are significantly affected by crystal packing effects. We then report an approach to identify buried histidines that require significant sampling beyond what is achieved in typical FEP calculations. We therefore define a clean data set not requiring algorithms capable of predicting major conformational changes on which other pK_a prediction methods can be tested. On this data set, we report an RMSE of 0.76 pK_a units for 35 ASP residues, 0.51 pK_a units for 44 GLU residues, and 0.67 pK_a units for 76 HIS residues.

GPU-Accelerated All-Atom Particle-Mesh Ewald Continuous Constant pH Molecular Dynamics in Amber

Constant pH molecular dynamics (MD) simulations sample protonation states on the fly according to the conformational environment and user specified pH conditions; however, the current accuracy is limited due to the use of implicit-solvent models or a hybrid solvent scheme. Here, we report the first GPU-accelerated implementation, parametrization, and validation of the all-atom continuous constant pH MD (CpHMD) method with particle-mesh Ewald (PME) electrostatics in the Amber22 pmemd.cuda engine. The titration parameters for Asp, Glu, His, Cys, and Lys were derived for the CHARMM c22 and Amber ff14sb and ff19sb force fields. We then evaluated the PME-CpHMD method using the asynchronous pH replica-exchange titration simulations with the c22 force field for six benchmark proteins, including BBL, hen egg white lysozyme (HEWL), staphylococcal nuclease (SNase), thioredoxin, ribonuclease A (RNaseA), and human muscle creatine kinase (HMCK). The root-mean-square deviation from the experimental pK_a's of Asp, Glu, His, and Cys is 0.76 pH units, and the Pearson's correlation coefficient for the pK_a shifts with respect to model values is 0.80. We demonstrated that a finite-size correction or much enlarged simulation box size can remove a systematic error of the calculated pK_a's and improve agreement with experiment. Importantly, the simulations captured the relevant biology in several challenging cases, e.g., the titration order of the catalytic dyad Glu35/Asp52 in HEWL and the coupled residues Asp19/Asp21 in SNase, the large pK_a upshift of the deeply buried catalytic Asp26 in thioredoxin, and the large pK_a downshift of the deeply buried catalytic Cys283 in HMCK. We anticipate that PME-CpHMD will offer proper pH control to improve the accuracies of MD simulations and enable mechanistic studies of proton-coupled dynamical processes that are ubiquitous in biology but remain poorly understood due to the lack of experimental tools and limitation of current MD simulations.

Constant pH molecular dynamics simulations: Current status and recent applications

Many important protein functions are carried out through proton-coupled conformational dynamics. Thus, the ability to accurately model protonation states dynamically has wide-ranging implications. Over the past two decades, two main types of constant pH methods (discrete and continuous) have been developed to enable proton-coupled molecular dynamics (MD) simulations. In this short review, we discuss the current status of the development and highlight recent applications that have advanced our understanding of protein structure-function relationships. We conclude the review by outlining the remaining challenges in the method development and projecting important areas for future applications.

Electrostatics in Computational Biophysics and Its Implications for Disease Effects

This review outlines the role of electrostatics in computational molecular biophysics and its implication in altering wild-type characteristics of biological macromolecules, and thus the contribution of electrostatics to disease mechanisms. The work is not intended to review existing computational approaches or to propose further developments. Instead, it summarizes the outcomes of relevant studies and provides a generalized classification of major mechanisms that involve electrostatic effects in both wild-type and mutant biological macromolecules. It emphasizes the complex role of electrostatics in molecular biophysics, such that the long range of electrostatic interactions causes them to dominate all other forces at distances larger than several Angstroms, while at the same time, the alteration of short-range wild-type electrostatic pairwise interactions can have pronounced effects as well. Because of this dual nature of electrostatic interactions, being dominant at long-range and being very specific at short-range, their implications for wild-type structure and function are quite pronounced. Therefore, any disruption of the complex electrostatic network of interactions may abolish wild-type functionality and could be the dominant factor contributing to pathogenicity. However, we also outline that due to the plasticity of biological macromolecules, the effect of amino acid mutation may be reduced, and thus a charge deletion or insertion may not necessarily be deleterious.

A Guide to the Continuous Constant pH Molecular Dynamics Methods in Amber and CHARMM [Article v1.0]

Like temperature and pressure, solution pH is an important environmental variable in biomolecular simulations. Virtually all proteins depend on pH to maintain their structure and function. In conventional molecular dynamics (MD) simulations of proteins, pH is implicitly accounted for by assigning and fixing protonation states of titratable sidechains. This is a significant limitation, as the assigned protonation states may be wrong and they may change during dynamics. In this tutorial, we guide the reader in learning and using the various continuous constant pH MD methods in Amber and CHARMM packages, which have been applied to predict pK a values and elucidate proton-coupled conformational dynamics of a variety of proteins including enzymes and membrane transporters.

Profiling MAP kinase cysteines for targeted covalent inhibitor design

Mitogen-activated protein kinases (MAPK) are important therapeutic targets, and yet no inhibitors have advanced to the market. Here we applied the GPU-accelerated continuous constant pH molecular dynamics (CpHMD) to calculate the pK a's and profile the cysteine reactivities of all 14 MAPKs for assisting the targeted covalent inhibitor design. The simulations not only recapitulated but also rationalized the reactive cysteines in the front pocket of JNK1/2/3 and the extended front pocket of p38α. Interestingly, the DFG - 1 cysteine in the DFG-in conformation of ERK1/ERK2 was found somewhat reactive or unreactive; however, simulations of MKK7 showed that switching to the DFG-out conformation makes the DFG - 1 cysteine reactive, suggesting the advantage of type II covalent inhibitors. Additionally, the simulations prospectively predicted several druggable cysteine and lysine sites, including the αH head cysteine in JNK1/3 and DFG + 6 cysteine in JNK2, corroborating the chemical proteomic screening data. Given the low cost and the ability to offer physics-based rationales, we envision CpHMD simulations to complement the chemo-proteomic platform for systematic profiling cysteine reactivities for targeted covalent drug discovery.

Protein pK a Prediction with Machine Learning

Protein pK _a prediction is essential for the investigation of the pH-associated relationship between protein structure and function. In this work, we introduce a deep learning-based protein pK _a predictor DeepKa, which is trained and validated with the pK _a values derived from continuous constant-pH molecular dynamics (CpHMD) simulations of 279 soluble proteins. Here, the CpHMD implemented in the Amber molecular dynamics package has been employed (Huang Y.J. Chem. Inf. Model.2018, 58, 1372-1383). Notably, to avoid discontinuities at the boundary, grid charges are proposed to represent protein electrostatics. We show that the prediction accuracy by DeepKa is close to that by CpHMD benchmarking simulations, validating DeepKa as an efficient protein pK _a predictor. In addition, the training and validation sets created in this study can be applied to the development of machine learning-based protein pK _a predictors in the future. Finally, the grid charge representation is general and applicable to other topics, such as the protein-ligand binding affinity prediction.

Reactivities of the Front Pocket N-Terminal Cap Cysteines in Human Kinases

The front pocket (FP) N-terminal cap (Ncap) cysteine is the most popular site of covalent modification in kinases. A long-standing hypothesis associates the Ncap position with cysteine hyper-reactivity; however, traditional computational predictions suggest that the FP Ncap cysteines are predominantly unreactive. Here we applied the state-of-the-art continuous constant pH molecular dynamics (CpHMD) to test the Ncap hypothesis. Simulations found that the Ncap cysteines of BTK/BMX/TEC/ITK/TXK, JAK3, and MKK7 are reactive to varying degrees; however, those of BLK and EGFR/ERBB2/ERBB4 possessing a Ncap+3 aspartate are unreactive. Analysis suggested that hydrogen bonding and electrostatic interactions drive the reactivity, and their absence renders the Ncap cysteine unreactive. To further test the Ncap hypothesis, we examined the FP Ncap+2 cysteines in JNK1/JNK2/JNK3 and CASK. Our work offers a systematic understanding of the cysteine structure-reactivity relationship and illustrates the use of CpHMD to differentiate cysteines toward the design of targeted covalent inhibitors with reduced chemical reactivities.

How much can physics do for protein design?

Physics and physical chemistry are an important thread in computational protein design, complementary to knowledge-based tools. They provide molecular mechanics scoring functions that need little or no ad hoc parameter readjustment, methods to thoroughly sample equilibrium ensembles, and different levels of approximation for conformational flexibility. They led recently to the successful redesign of a small protein using a physics-based folded state energy. Adaptive Monte Carlo or molecular dynamics schemes were discovered where protein variants are populated as per their ligand-binding free energy or catalytic efficiency. Molecular dynamics have been used for backbone flexibility. Implicit solvent models have been refined, polarizable force fields applied, and many physical insights obtained.

Advances in optimizing enzyme electrostatic preorganization

Utilizing electric fields to catalyze chemical reactions is not a new idea, but in enzymology it undergoes a renaissance, inspired by Warhsel's concept of electrostatic preorganization. According to this concept, the source of the immense catalytic efficiency of enzymes is the intramolecular electric field that permanently favors the reaction transition state over the reactants. Within enzyme design, computational efforts have fallen short in designing enzymes with natural-like efficacy. The outcome could improve if long-range electrostatics (often omitted in current protocols) would be optimized. Here, we highlight the major developments in methods for analyzing and designing electric fields generated by the protein scaffolds, in order to both better understand how natural enzymes function, and aid artificial enzyme design.

Titr-DMD-A Rapid, Coarse-Grained Quasi-All-Atom Constant pH Molecular Dynamics Framework

The pH-dependence of enzyme fold stability and catalytic activity is a fundamentally dynamic, structural property which is difficult to study. The challenges and expense of investigating dynamic, atomic scale behavior experimentally means that computational methods, particularly constant pH molecular dynamics (CpHMD), are well situated tools for this. However, these methods often struggle with affordable sampling of sufficiently long time scales while also obtaining accurate pKa prediction and verifying the structures they generate. We introduce Titr-DMD, an affordable CpHMD method that combines the quasi-all-atom coarse-grained discrete molecular dynamics (DMD) method for conformational sampling with Propka for pKa prediction, to circumvent these issues. The combination enables rapid sampling on limited computational resources, while simulations are still performed on the atomic scale. We benchmark the method on a set of proteins with experimentally attested pKa and on the pH triggered conformational change in a staphylococcal nuclease mutant, a rare experimental study of such behavior. Our results show Titr-DMD to be an effective and inexpensive method to study pH-coupled protein dynamics.

Anti-TNF Alpha Antibody Humira with pH-dependent Binding Characteristics: A constant-pH Molecular Dynamics, Gaussian Accelerated Molecular Dynamics, and In Vitro Study

Humira is a monoclonal antibody that binds to TNF alpha, inactivates TNF alpha receptors, and inhibits inflammation. Neonatal Fc receptors can mediate the transcytosis of Humira-TNF alpha complex structures and process them toward degradation pathways, which reduces the therapeutic effect of Humira. Allowing the Humira-TNF alpha complex structures to dissociate to Humira and soluble TNF alpha in the early endosome to enable Humira recycling is crucial. We used the cytoplasmic pH (7.4), the early endosomal pH (6.0), and pKa of histidine side chains (6.0-6.4) to mutate the residues of complementarity-determining regions with histidine. Our engineered Humira (W1-Humira) can bind to TNF alpha in plasma at neutral pH and dissociate from the TNF alpha in the endosome at acidic pH. We used the constant-pH molecular dynamics, Gaussian accelerated molecular dynamics, two-dimensional potential mean force profiles, and in vitro methods to investigate the characteristics of W1-Humira. Our results revealed that the proposed Humira can bind TNF alpha with pH-dependent affinity in vitro. The W1-Humira was weaker than wild-type Humira at neutral pH in vitro, and our prediction results were close to the in vitro results. Furthermore, our approach displayed a high accuracy in antibody pH-dependent binding characteristics prediction, which may facilitate antibody drug design. Advancements in computational methods and computing power may further aid in addressing the challenges in antibody drug design.

Continuous Constant pH Molecular Dynamics Simulations of Transmembrane Proteins

Many membrane channels, transporters, and receptors utilize a pH gradient or proton coupling to drive functionally relevant conformational transitions. Conventional molecular dynamics simulations employ fixed protonation states, thus neglecting the coupling between protonation and conformational equilibria. Here we describe the membrane-enabled hybrid-solvent continuous constant pH molecular dynamics method for capturing atomic details of proton-coupled conformational dynamics of transmembrane proteins. Example protocols from our recent application studies of proton channels and ion/substrate transporters are discussed.

Proton-Coupled Conformational Activation of SARS Coronavirus Main Proteases and Opportunity for Designing Small-Molecule Broad-Spectrum Targeted Covalent Inhibitors

The SARS coronavirus 2 (SARS-CoV-2) main protease (Mpro) is an attractive broad-spectrum antiviral drug target. Despite the enormous progress in structure elucidation, the Mpro's structure-function relationship remains poorly understood. Recently, a peptidomimetic inhibitor has entered clinical trial; however, small-molecule orally available antiviral drugs have yet to be developed. Intrigued by a long-standing controversy regarding the existence of an inactive state, we explored the proton-coupled dynamics of the Mpros of SARS-CoV-2 and the closely related SARS-CoV using a newly developed continuous constant pH molecular dynamics (MD) method and microsecond fixed-charge all-atom MD simulations. Our data supports a general base mechanism for Mpro's proteolytic function. The simulations revealed that protonation of His172 alters a conserved interaction network that upholds the oxyanion loop, leading to a partial collapse of the conserved S1 pocket, consistent with the first and controversial crystal structure of SARS-CoV Mpro determined at pH 6. Interestingly, a natural flavonoid binds SARS-CoV-2 Mpro in the close proximity to a conserved cysteine (Cys44), which is hyper-reactive according to the CpHMD titration. This finding offers an exciting new opportunity for small-molecule targeted covalent inhibitor design. Our work represents a first step toward the mechanistic understanding of the proton-coupled structure-dynamics-function relationship of CoV Mpros; the proposed strategy of designing small-molecule covalent inhibitors may help accelerate the development of orally available broad-spectrum antiviral drugs to stop the current pandemic and prevent future outbreaks.

On the Use of the Discrete Constant pH Molecular Dynamics to Describe the Conformational Space of Peptides

Solvent pH is an important property that defines the protonation state of the amino acids and, therefore, modulates the interactions and the conformational space of the biochemical systems. Generally, this thermodynamic variable is poorly considered in Molecular Dynamics (MD) simulations. Fortunately, this lack has been overcome by means of the Constant pH Molecular Dynamics (CPHMD) methods in the recent decades. Several studies have reported promising results from these approaches that include pH in simulations but focus on the prediction of the effective pKa of the amino acids. In this work, we want to shed some light on the CPHMD method and its implementation in the AMBER suitcase from a conformational point of view. To achieve this goal, we performed CPHMD and conventional MD (CMD) simulations of six protonatable amino acids in a blocked tripeptide structure to compare the conformational sampling and energy distributions of both methods. The results reveal strengths and weaknesses of the CPHMD method in the implementation of AMBER18 version. The change of the protonation state according to the chemical environment is presumably an improvement in the accuracy of the simulations. However, the simulations of the deprotonated forms are not consistent, which is related to an inaccurate assignment of the partial charges of the backbone atoms in the CPHMD residues. Therefore, we recommend the CPHMD methods of AMBER program but pointing out the need to compare structural properties with experimental data to bring reliability to the conformational sampling of the simulations.

Assessment of proton-coupled conformational dynamics of SARS and MERS coronavirus papain-like proteases: Implication for designing broad-spectrum antiviral inhibitors

Broad-spectrum antiviral drugs are urgently needed to stop the Coronavirus Disease 2019 pandemic and prevent future ones. The novel severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is related to the SARS-CoV and Middle East respiratory syndrome coronavirus (MERS-CoV), which have caused the previous outbreaks. The papain-like protease (PLpro) is an attractive drug target due to its essential roles in the viral life cycle. As a cysteine protease, PLpro is rich in cysteines and histidines, and their protonation/deprotonation modulates catalysis and conformational plasticity. Here, we report the pK_a calculations and assessment of the proton-coupled conformational dynamics of SARS-CoV-2 in comparison to SARS-CoV and MERS-CoV PLpros using the recently developed graphical processing unit (GPU)-accelerated implicit-solvent continuous constant pH molecular dynamics method with a new asynchronous replica-exchange scheme, which allows computation on a single GPU card. The calculated pK_a's support the catalytic roles of the Cys-His-Asp triad. We also found that several residues can switch protonation states at physiological pH among which is C270/271 located on the flexible blocking loop 2 (BL2) of SARS-CoV-2/CoV PLpro. Simulations revealed that the BL2 can open and close depending on the protonation state of C271/270, consistent with the most recent crystal structure evidence. Interestingly, despite the lack of an analogous cysteine, BL2 in MERS-CoV PLpro is also very flexible, challenging a current hypothesis. These findings are supported by the all-atom fixed-charge simulations and provide a starting point for more detailed studies to assist the structure-based design of broad-spectrum inhibitors against CoV PLpros.

Alternative proton-binding site and long-distance coupling in Escherichia coli sodium-proton antiporter NhaA

Escherichia coli NhaA is a prototypical sodium-proton antiporter responsible for maintaining cellular ion and volume homeostasis by exchanging two protons for one sodium ion; despite two decades of research, the transport mechanism of NhaA remains poorly understood. Recent crystal structure and computational studies suggested Lys300 as a second proton-binding site; however, functional measurements of several K300 mutants demonstrated electrogenic transport, thereby casting doubt on the role of Lys300. To address the controversy, we carried out state-of-the-art continuous constant pH molecular dynamics simulations of NhaA mutants K300A, K300R, K300Q/D163N, and K300Q/D163N/D133A. Simulations suggested that K300 mutants maintain the electrogenic transport by utilizing an alternative proton-binding residue Asp133. Surprisingly, while Asp133 is solely responsible for binding the second proton in K300R, Asp133 and Asp163 jointly bind the second proton in K300A, and Asp133 and Asp164 jointly bind two protons in K300Q/D163N. Intriguingly, the coupling between Asp133 and Asp163 or Asp164 is enabled through the proton-coupled hydrogen-bonding network at the flexible intersection of two disrupted helices. These data resolve the controversy and highlight the intricacy of the compensatory transport mechanism of NhaA mutants. Alternative proton-binding site and proton sharing between distant aspartates may represent important general mechanisms of proton-coupled transport in secondary active transporters.

Accurate Prediction of GPCR Ligand Binding Affinity with Free Energy Perturbation

The computational prediction of relative binding free energies is a crucial goal for drug discovery, and G protein-coupled receptors (GPCRs) are arguably the most important drug target class. However, they present increased complexity to model compared to soluble globular proteins. Despite breakthroughs, experimental X-ray crystal and cryo-EM structures are challenging to attain, meaning computational models of the receptor and ligand binding mode are sometimes necessary. This leads to uncertainty in understanding ligand-protein binding induced changes such as, water positioning and displacement, side chain positioning, hydrogen bond networks, and the overall structure of the hydration shell around the ligand and protein. In other words, the very elements that define structure activity relationships (SARs) and are crucial for accurate binding free energy calculations are typically more uncertain for GPCRs. In this work we use free energy perturbation (FEP) to predict the relative binding free energies for ligands of two different GPCRs. We pinpoint the key aspects for success such as the important role of key water molecules, amino acid ionization states, and the benefit of equilibration with specific ligands. Initial calculations following typical FEP setup and execution protocols delivered no correlation with experiment, but we show how results are improved in a logical and systematic way. This approach gave, in the best cases, a coefficient of determination (R²) compared with experiment in the range of 0.6-0.9 and mean unsigned errors compared to experiment of 0.6-0.7 kcal/mol. We anticipate that our findings will be applicable to other difficult-to-model protein ligand data sets and be of wide interest for the community to continue improving FE binding energy predictions.

Assessment of Proton-Coupled Conformational Dynamics of SARS and MERS Coronavirus Papain-like Proteases: Implication for Designing Broad-Spectrum Antiviral Inhibitors

Broad-spectrum antiviral drugs are urgently needed to stop the COVID-19 pandemic and prevent future ones. The novel severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is related to SARS-CoV and Middle East respiratory syndrome coronavirus (MERS-CoV), which have caused the previous outbreaks. The papain-like protease (PLpro) is an attractive drug target due to its essential roles in the viral life cycle. As a cysteine protease, PLpro is rich in cysteines and histidines and their protonation/deprotonation modulates catalysis and conformational plasticity. Here we report the pKa calculations and assessment of the proton-coupled conformational dynamics of SARS-CoV-2 in comparison to SARS-CoV and MERS-CoV PLpros using a newly developed GPU-accelerated implicit-solvent continuous constant pH molecular dynamics method with an asynchronous replica-exchange scheme. The calculated pKa's support the catalytic roles of the Cys-His-Asp triad. We also found that several residues can switch protonation states at physiological pH, among which is C270/271 located on the flexible blocking loop 2 (BL2) of SARS-CoV-2/CoV PLpro. Simulations revealed that the BL2 conformational dynamics is coupled to the titration of C271/270, in agreement with the crystal structures of SARS-CoV-2 PLpro. Simulations also revealed that BL2 in MERS-CoV PLpro is very flexible, sampling both open and closed states despite the lack of an analogous cysteine. Our work provides a starting point for more detailed mechanistic studies to assist structure-based design of broad-spectrum inhibitors against CoV PLpros.

Predicting Reactive Cysteines with Implicit-Solvent-Based Continuous Constant pH Molecular Dynamics in Amber

Cysteines existing in the deprotonated thiolate form or having a tendency to become deprotonated are important players in enzymatic and cellular redox functions and frequently exploited in covalent drug design; however, most computational studies assume cysteines as protonated. Thus, developing an efficient tool that can make accurate and reliable predictions of cysteine protonation states is timely needed. We recently implemented a generalized Born (GB) based continuous constant pH molecular dynamics (CpHMD) method in Amber for protein pKa calculations on CPUs and GPUs. Here we benchmark the performance of GB-CpHMD for predictions of cysteine pKa's and reactivities using a data set of 24 proteins with both down- and upshifted cysteine pKa's. We found that 10 ns single-pH or 4 ns replica-exchange CpHMD titrations gave root-mean-square errors of 1.2-1.3 and correlation coefficients of 0.8-0.9 with respect to experiment. The accuracy of predicting thiolates or reactive cysteines at physiological pH with single-pH titrations is 86 or 81% with a precision of 100 or 90%, respectively. This performance well surpasses the traditional structure-based methods, particularly a widely used empirical pKa tool that gives an accuracy less than 50%. We discuss simulation convergence, dependence on starting structures, common determinants of the pKa downshifts and upshifts, and the origin of the discrepancies from the structure-based calculations. Our work suggests that CpHMD titrations can be performed on a desktop computer equipped with a single GPU card to predict cysteine protonation states for a variety of applications, from understanding biological functions to covalent drug design.

Catalytic Site pKa Values of Aspartic, Cysteine, and Serine Proteases: Constant pH MD Simulations

Enzymatic function and activity of proteases is closely controlled by the pH value. The protonation states of titratable residues in the active site react to changes in the pH value, according to their pK_a, and thereby determine the functionality of the enzyme. Knowledge of the titration behavior of these residues is crucial for the development of drugs targeting the active site residues. However, experimental pK_a data are scarce, since the systems’ size and complexity make determination of these pK_a values inherently difficult. In this study, we use single pH constant pH MD simulations as a fast and robust tool to estimate the active site pK_a values of a set of aspartic, cysteine, and serine proteases. We capture characteristic pK_a shifts of the active site residues, which dictate the experimentally determined activity profiles of the respective protease family. We find clear differences of active site pK_a values within the respective families, which closely match the experimentally determined pH preferences of the respective proteases. These shifts are caused by a distinct network of electrostatic interactions characteristic for each protease family. While we find convincing agreement with experimental data for serine and aspartic proteases, we observe clear deficiencies in the description of the titration behavior of cysteines within the constant pH MD framework and highlight opportunities for improvement. Consequently, with this work, we provide a concise set of active site pK_a values of aspartic and serine proteases, which could serve as reference for future theoretical as well as experimental studies.

Analysis of Glycosyl-Enzyme Intermediate Formation in the Catalytic Mechanism of Influenza Virus Neuraminidase Using Molecular Modeling

Using classical molecular dynamics, constant-pH molecular dynamics simulation, metadynamics, and combined quantum mechanical and molecular mechanical approach, we identified an alternative pathway of glycosyl-enzyme intermediate formation during oligosaccharide substrate conversion by the influenza H5N1 neuraminidase. The Asp151 residue located in the enzyme mobile loop plays a key role in catalysis within a wide pH range due to the formation of a network of interactions with water molecules. Considering that propagation of influenza virus takes place in the digestive tract of birds at low pH values and in the human respiratory tract at pH values close to neutral, the existence of alternative reaction pathways functioning at different medium pH can explain the dual tropism of the virus and circulation of H5N1 viral strains capable of transmission from birds to humans.

Accurate Estimation of pKb Values for Amino Groups from Surface Electrostatic Potential (VS,min) Calculations: The Isoelectric Points of Amino Acids as a Case Study

Theoretical calculation of equilibrium dissociation constants is a very computationally demanding and time-consuming process since it requires an extremely accurate computation of the solvation free energy changes for each of the species involved. By correlating the minimum surface electrostatic potential (V_S,min) on the nitrogen atom of several aliphatic amino groups-calculated at the density functional theory (DFT) ωB97X-D/cc-pVDZ level of theory-we obtained regression models for each kind of substitution pattern from which we interpolate their corresponding pK_b values with remarkable accuracy: primary R² = 0.9519; secondary R² = 0.9112; and tertiary R² = 0.8172 (N = 20 for each family). These models were validated with tests sets (N = 5) with mean absolute error (MAE) values of 0.1213 (primary), 0.4407 (secondary), and 0.3057 (tertiary). Combining this ansatz with another previously reported by our group to estimate pK_a values [Caballero-García, G.; et al. Molecules 2019, 24(1), 79] we are able to reproduce the isoelectric points of 13 amino acids with no titrable side chains with MAE = 0.4636 pI units.