Charge-leveling and proper treatment of long-range electrostatics in all-atom molecular dynamics at constant pH

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.

Targeting the conserved active site of splicing machines with specific and selective small molecule modulators

The self-splicing group II introns are bacterial and organellar ancestors of the nuclear spliceosome and retro-transposable elements of pharmacological and biotechnological importance. Integrating enzymatic, crystallographic, and simulation studies, we demonstrate how these introns recognize small molecules through their conserved active site. These RNA-binding small molecules selectively inhibit the two steps of splicing by adopting distinctive poses at different stages of catalysis, and by preventing crucial active site conformational changes that are essential for splicing progression. Our data exemplify the enormous power of RNA binders to mechanistically probe vital cellular pathways. Most importantly, by proving that the evolutionarily-conserved RNA core of splicing machines can recognize small molecules specifically, our work provides a solid basis for the rational design of splicing modulators not only against bacterial and organellar introns, but also against the human spliceosome, which is a validated drug target for the treatment of congenital diseases and cancers.

Constant-pH Simulations with the Polarizable Atomic Multipole AMOEBA Force Field

Accurately predicting protein behavior across diverse pH environments remains a significant challenge in biomolecular simulations. Existing constant-pH molecular dynamics (CpHMD) algorithms are limited to fixed-charge force fields, hindering their application to biomolecular systems described by permanent atomic multipoles or induced dipoles. This work overcomes these limitations by introducing the first polarizable CpHMD algorithm in the context of the Atomic Multipole Optimized Energetics for Biomolecular Applications (AMOEBA) force field. Additionally, our implementation in the open-source Force Field X (FFX) software has the unique ability to handle titration state changes for crystalline systems including flexible support for all 230 space groups. The evaluation of constant-pH molecular dynamics (CpHMD) with the AMOEBA force field was performed on 11 crystalline peptide systems that span the titrating amino acids (Asp, Glu, His, Lys, and Cys). Titration states were correctly predicted for 15 out of the 16 amino acids present in the 11 systems, including for the coordination of Zn2+ by cysteines. The lone exception was for a HIS-ALA peptide where CpHMD predicted both neutral histidine tautomers to be equally populated, whereas the experimental model did not consider multiple conformers and diffraction data are unavailable for rerefinement. This work demonstrates the promise polarizable CpHMD simulations for pKa predictions, the study of biochemical mechanisms such as the catalytic triad of proteases, and for improved protein-ligand binding affinity accuracy in the context of pharmaceutical lead optimization.

Why is the Omicron main protease of SARS-CoV-2 less stable than its wild-type counterpart? A crystallographic, biophysical, and theoretical study of the free enzyme and its complex with inhibitor 13b-K

During the continuing evolution of SARS-CoV-2, the Omicron variant of concern emerged in the second half of 2021 and has been dominant since November that year. Along with its sublineages, it has maintained a prominent role ever since. The Nsp5 main protease (Mpro) of the Omicron virus is characterized by a single dominant mutation, P132H. Here we determined the X-ray crystal structures of the P132H mutant (or O-Mpro) as free enzyme and in complex with the Mpro inhibitor, the alpha-ketoamide 13b-K, and we conducted enzymology, biophysical as well as theoretical studies to characterize the O-Mpro. We found that O-Mpro has a similar overall structure and binding with 13b-K; however, it displays lower enzymatic activity and lower thermal stability compared to the WT-Mpro (with "WT" referring to the original Wuhan-1 strain). Intriguingly, the imidazole ring of His132 and the carboxylate plane of Glu240 are in a stacked configuration in the X-ray structures determined here. The empirical folding free energy calculations suggest that the O-Mpro dimer is destabilized relative to the WT-Mpro due to the less favorable van der Waals interactions and backbone conformation in the individual protomers. The all-atom continuous constant pH molecular dynamics (MD) simulations reveal that His132 and Glu240 display coupled titration. At pH 7, His132 is predominantly neutral and in a stacked configuration with respect to Glu240 which is charged. In order to examine whether the Omicron mutation eases the emergence of further Mpro mutations, we also determined crystal structures of the relatively frequent P132H+T169S double mutant but found little evidence for a correlation between the two sites.

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.

Performance and Analysis of the Alchemical Transfer Method for Binding-Free-Energy Predictions of Diverse Ligands

The Alchemical Transfer Method (ATM) is herein validated against the relative binding-free energies (RBFEs) of a diverse set of protein-ligand complexes. We employed a streamlined setup workflow, a bespoke force field, and AToM-OpenMM software to compute the RBFEs of the benchmark set prepared by Schindler and collaborators at Merck KGaA. This benchmark set includes examples of standard small R-group ligand modifications as well as more challenging scenarios, such as large R-group changes, scaffold hopping, formal charge changes, and charge-shifting transformations. The novel coordinate perturbation scheme and a dual-topology approach of ATM address some of the challenges of single-topology alchemical RBFE methods. Specifically, ATM eliminates the need for splitting electrostatic and Lennard-Jones interactions, atom mapping, defining ligand regions, and postcorrections for charge-changing perturbations. Thus, ATM is simpler and more broadly applicable than conventional alchemical methods, especially for scaffold-hopping and charge-changing transformations. Here, we performed well over 500 RBFE calculations for eight protein targets and found that ATM achieves accuracy comparable to that of existing state-of-the-art methods, albeit with larger statistical fluctuations. We discuss insights into the specific strengths and weaknesses of the ATM method that will inform future deployments. This study confirms that ATM can be applied as a production tool for RBFE predictions across a wide range of perturbation types within a unified, open-source framework.

Stimuli-responsive viscosity modifiers

Stimuli responsive viscosity modifiers entail an important class of materials which allow for smart material formation utilizing various stimuli for switching such as pH, temperature, light and salinity. They have seen applications in the biomedical space including tissue engineering and drug delivery, wherein stimuli responsive hydrogels and polymeric vessels have been extensively applied. Applications have also been seen in other domains like the energy sector and automobile industry, in technologies such as enhanced oil recovery. The chemistry and microstructural arrangements of the aqueous morphologies of dissolved materials are usually sensitive to the aforementioned stimuli which subsequently results in rheological sensitivity as well. Herein, we overview different structures capable of viscosity modification as well as go over the rheological theory associated with classical systems studied in literature. A detailed analysis allows us to explore correlations between commonly discussed models such as molecular packing parameter, tube reptation and stress relaxation with structural and rheological changes. We then present five primary mechanisms corresponding to stimuli responsive viscosity modification: (i) packing parameter modification via functional group conditioning and (ii) via dynamic bond formation, (iii) mesh formation by interlinking of network nodes, (iv) viscosity modification by chain conformation changes and (v) viscosity modification by particle jamming. We also overview several recent examples from literature that employ the concepts discussed to create novel classes of intriguing stimuli responsive structures and their corresponding rheological properties. Furthermore, we also explore systems that are responsive to multiple stimuli which can provide enhanced functionality and versatility by providing multi-level and precise actuation. Such systems have been used for programmed site-specific drug delivery.

Anions and Cations Affect Amino Acid Dissociation Equilibria via Distinct Mechanisms

Salts reduce the pKa of weak acids by a mechanism sensitive to ion identity and concentration via charge screening of the deprotonated state. In this study, we utilize constant pH molecular dynamics simulations to understand the molecular mechanism behind the salt-dependent dissociation of aspartic acid (Asp). We calculate the pKa of Asp in the presence of a monovalent salt and investigate Hofmeister ion effects by systematically varying the ionic radii. We observe that increasing the anion size leads to a monotonic decrease in Asp pKa. Conversely, the cation size affects the pKa nonmonotonically, interpretable in the context of the law of matching water affinity. The net effect of salt on Asp acidity is governed by an interplay of solvation and competing ion interactions. The proposed mechanism is rather general and can be applicable to several problems in Hofmeister ion chemistry, such as pH effects on protein stability and soft matter interfaces.

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.

Computational Study of the pH-Dependent Ionic Environment around β-Lactoglobulin

Ions are involved in multiple biological processes and may exist bound to biomolecules or may be associated with their surface. Although the presence of ions in nucleic acids has traditionally gained more interest, ion-protein interactions, often with a marked dependency on pH, are beginning to gather attention. Here we present a detailed analysis on the binding and distribution of ions around β-lactoglobulin using a constant-pH MD (CpHMD) method, at a pH range 3-8, and compare it with the more traditional Poisson-Boltzmann (PB) model and the existing experimental data. Most analyses used ion concentration maps built around the protein, obtained from either the CpHMD simulations or PB calculations. The requirements of approximate charge neutrality and ionic strength equal to bulk, imposed on the MD box, imply that the absolute value of the ion excess should be half the protein charge, which is in agreement with experimental observation on other proteins ( Proc. Natl. Acad. Sci. U.S.A. 2021, 118, e2015879118) and lends support to this protocol. In addition, the protein total charge (including territorially bound ions) estimated with MD is in excellent agreement with electrophoretic measurements. Overall, the CpHMD simulations show good agreement with the nonlinear form of the PB (NLPB) model but not with its linear form, which involves a theoretical inconsistency in the calculation of the concentration maps. In several analyses, the observed pH-dependent trends for the counterions and co-ions are those generally expected, and the ion concentration maps correctly converge to the bulk ionic strength as one moves away from the protein. Despite the overall similarity, the CpHMD and NLPB approaches show some discrepancies when analyzed in more detail, which may be related to an apparent overestimation of counterion excess and underestimation of co-ion exclusion by the NLPB model, particularly at short distances from the protein.

Increasing the Realism of in Silico pHLIP Peptide Models with a Novel pH Gradient CpHMD Method

The pH-low insertion peptides (pHLIP) are pH-dependent membrane inserting peptides, whose function depends on the cell microenvironment acidity. Several peptide variants have been designed to improve upon the wt-sequence, particularly the state transition kinetics and the selectivity for tumor pH. The variant 3 (Var3) peptide is a 27 residue long peptide, with a key titrating residue (Asp-13) that, despite showing a modest performance in liposomes (pK^ins ∼ 5.0), excelled in tumor cell experiments. To help rationalize these results, we focused on the pH gradient in the cell membrane, which is one of the crucial properties that are not present in liposomes. We extended our CpHMD-L method and its pH replica-exchange (pHRE) implementation to include a pH gradient and mimic the pHLIP-membrane microenvironment in a cell where the internal pH is fixed (pH 7.2) and the external pH is allowed to change. We showed that, by properly modeling the pH-gradient, we can correctly predict the experimentally observed loss and gain of performance in tumor cells experiments by the wt and Var3 sequences, respectively. In sum, the pH gradient implementation allowed for more accurate and realistic pK_a estimations and was a pivotal step in bridging the in silico data and the in vivo cell experiments.

Extending the Stochastic Titration CpHMD to CHARMM36m

The impact of pH on proteins is significant but often neglected in molecular dynamics simulations. Constant-pH Molecular Dynamics (CpHMD) is the state-of-the-art methodology to deal with these effects. However, it still lacks widespread adoption by the scientific community. The stochastic titration CpHMD is one of such methods that, until now, only supported the GROMOS force field family. Here, we extend this method's implementation to include the CHARMM36m force field available in the GROMACS software package. We test this new implementation with a diverse group of proteins, namely, lysozyme, Staphylococcal nuclease, and human and E. coli thioredoxins. All proteins were conformationally stable in the simulations, even at extreme pH values. The RMSE values (pK_a prediction vs experimental) obtained were very encouraging, in particular for lysozyme and human thioredoxin. We have also identified a few residues that challenged the CpHMD simulations, highlighting scenarios where the method still needs improvement independently of the force field. The CHARMM36m all-atom implementation was more computationally efficient when compared with the GROMOS 54A7, taking advantage of a shorter nonbonded interaction cutoff and a less frequent neighboring list update. The new extension will allow the study of pH effects in many systems for which this force field is particularly suited, i.e., proteins, membrane proteins, lipid bilayers, and nucleic acids.

Best Practices in Constant pH MD Simulations: Accuracy and Sampling

Various approaches have been proposed to include the effect of pH in molecular dynamics (MD) simulations. Among these, the λ-dynamics approach proposed by Brooks and co-workers [Kong, X.; Brooks III, C. L. J. Chem. Phys.1996, 105, 2414−2423] can be performed with little computational overhead and hfor each typeence be used to routinely perform MD simulations at microsecond time scales, as shown in the accompanying paper [Aho, N. et al. J. Chem. Theory Comput.2022, DOI: 10.1021/acs.jctc.2c00516]. At such time scales, however, the accuracy of the molecular mechanics force field and the parametrization becomes critical. Here, we address these issues and provide the community with guidelines on how to set up and perform long time scale constant pH MD simulations. We found that barriers associated with the torsions of side chains in the CHARMM36m force field are too high for reaching convergence in constant pH MD simulations on microsecond time scales. To avoid the high computational cost of extending the sampling, we propose small modifications to the force field to selectively reduce the torsional barriers. We demonstrate that with such modifications we obtain converged distributions of both protonation and torsional degrees of freedom and hence consistent pK_a estimates, while the sampling of the overall configurational space accessible to proteins is unaffected as compared to normal MD simulations. We also show that the results of constant pH MD depend on the accuracy of the correction potentials. While these potentials are typically obtained by fitting a low-order polynomial to calculated free energy profiles, we find that higher order fits are essential to provide accurate and consistent results. By resolving problems in accuracy and sampling, the work described in this and the accompanying paper paves the way to the widespread application of constant pH MD beyond pK_a prediction.

Galvani Offset Potential and Constant-pH Simulations of Membrane Proteins

A central problem in computational biophysics is the treatment of titratable residues in molecular dynamics simulations of large biological macromolecular systems. Conventional simulation methods ascribe a fixed ionization state to titratable residues in accordance with their pK_a and the pH of the system, assuming that an effective average model will be able to capture the predominant behavior of the system. While this assumption may be justifiable in many cases, it is certainly limited, and it is important to design alternative methodologies allowing a more realistic treatment. Constant-pH simulation methods provide powerful approaches to handle titratable residues more realistically by allowing the ionization state to vary statistically during the simulation. Extending the molecular mechanical (MM) potential energy function to a family of potential functions accounting for different ionization states, constant-pH simulations are designed to sample all accessible configurations and ionization states, properly weighted according to their Boltzmann factor. Because protonation and deprotonation events correspond to a change in the total charge, difficulties arise when the long-range Coulomb interaction is treated on the basis of an idealized infinite simulation model and periodic boundary conditions with particle-mesh Ewald lattice sums. Charging free-energy calculations performed under these conditions in aqueous solution depend on the Galvani potential of the bulk water phase. This has important implications for the equilibrium and nonequilibrium constant-pH simulation methods grounded in the relative free-energy difference corresponding to the protonated and unprotonated residues. Here, the effect of the Galvani potential is clarified, and a simple practical solution is introduced to address this issue in constant-pH simulations of the acid-sensing ion channel (ASIC).

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.

Alchemical Free Energy Calculations to Investigate Protein-Protein Interactions: the Case of the CDC42/PAK1 Complex

Here, we show that alchemical free energy calculations can quantitatively compute the effect of mutations at the protein–protein interface. As a test case, we have used the protein complex formed by the small Rho-GTPase CDC42 and its downstream effector PAK1, a serine/threonine kinase. Notably, the CDC42/PAK1 complex offers a wealth of structural, mutagenesis, and binding affinity data because of its central role in cellular signaling and cancer progression. In this context, we have considered 16 mutations in the CDC42/PAK1 complex and obtained excellent agreement between computed and experimental data on binding affinity. Importantly, we also show that a careful analysis of the side-chain conformations in the mutated amino acids can considerably improve the computed estimates, solving issues related to sampling limitations. Overall, this study demonstrates that alchemical free energy calculations can conveniently be integrated into the design of experimental mutagenesis studies.

Novel US-CpHMD Protocol to Study the Protonation-Dependent Mechanism of the ATP/ADP Carrier

We have designed a protocol combining constant-pH molecular dynamics (CpHMD) simulations with an umbrella sampling (US) scheme (US-CpHMD) to study the mechanism of ADP/ATP transport (import and export) by their inner mitochondrial membrane carrier protein [ADP/ATP carrier (AAC)]. The US scheme helped overcome the limitations of sampling the slow kinetics involved in these substrates' transport, while CpHMD simulations provided an unprecedented realism by correctly capturing the associated protonation changes. The import of anionic substrates along the mitochondrial membrane has a strong energetic disadvantage due to a smaller substrate concentration and an unfavorable membrane potential. These limitations may have created an evolutionary pressure on AAC to develop specific features benefiting the import of ADP. In our work, the potential of mean force profiles showed a clear selectivity in the import of ADP compared to ATP, while in the export, no selectivity was observed. We also observed that AAC sequestered both substrates at longer distances in the import compared to the export process. Furthermore, only in the import process do we observe transient protonation of both substrates when going through the AAC cavity, which is an important advantage to counteract the unfavorable mitochondrial membrane potential. Finally, we observed a substrate-induced disruption of the matrix salt-bridge network, which can promote the conformational transition (from the C- to M-state) required to complete the import process. This work unraveled several important structural features where the complex electrostatic interactions were pivotal to interpreting the protein function and illustrated the potential of applying the US-CpHMD protocol to other transport processes involving membrane proteins.

Constant pH Coarse-Grained Molecular Dynamics with Stochastic Charge Neutralization

pH dependence abounds in biochemical systems; however, many simulation methods used to investigate these systems do not consider this property. Using a modified version of the hybrid non-equilibrium molecular dynamics (MD)/Monte Carlo algorithm, we include a stochastic charge neutralization method, which is particularly suited to the MARTINI force field and enables artifact-free Ewald summation methods in electrostatic calculations. We demonstrate the efficacy of this method by reproducing pH-dependent self-assembly and self-organization behavior previously reported in experimental literature. In addition, we have carried out experimental oleic acid titrations where we report the results in a more relevant way for the comparison with computational methods than has previously been done.

Addressing Intersite Coupling Unlocks Large Combinatorial Chemical Spaces for Alchemical Free Energy Methods

Alchemical free energy methods are playing a growing role in molecular design, both for computer-aided drug design of small molecules and for computational protein design. Multisite λ dynamics (MSλD) is a uniquely scalable alchemical free energy method that enables more efficient exploration of combinatorial alchemical spaces encountered in molecular design, but simulations have typically been limited to a few hundred ligands or sequences. Here, we focus on coupling between sites to enable scaling to larger alchemical spaces. We first discuss updates to the biasing potentials that facilitate MSλD sampling to include coupling terms and show that this can provide more thorough sampling of alchemical states. We then harness coupling between sites by developing a new free energy estimator based on the Potts models underlying direct coupling analysis, a method for predicting contacts from sequence coevolution, and find it yields more accurate free energies than previous estimators. The sampling requirements of the Potts model estimator scale with the square of the number of sites, a substantial improvement over the exponential scaling of the standard estimator. This opens up exploration of much larger alchemical spaces with MSλD for molecular design.

Approach to Study pH-Dependent Protein Association Using Constant-pH Molecular Dynamics: Application to the Dimerization of β-Lactoglobulin

Protein-protein association is often mediated by electrostatic interactions and modulated by pH. However, experimental and computational studies have often overlooked the effect of association on the protonation state of the protein. In this work, we present a methodological approach based on constant-pH molecular dynamics (MD), which aims to provide a detailed description of a pH-dependent protein-protein association, and apply it to the dimerization of β-lactoglobulin (BLG). A selection of analyses is performed using the data generated by constant-pH MD simulations of monomeric and dimeric forms of bovine BLG, in the pH range 3-8. First, we estimate free energies of dimerization using a computationally inexpensive approach based on the Wyman-Tanford linkage theory, calculated in a new way through the use of thermodynamically based splines. The individual free energy contribution of each titratable site is also calculated, allowing for identification of relevant residues. Second, the correlations between the proton occupancies of pairs of sites are calculated (using the Pearson coefficient), and extensive networks of correlated sites are observed at acidic pH values, sometimes involving distant pairs. In general, strongly correlated sites are also slow proton exchangers and contribute significantly to the pH-dependency of the dimerization free energy. Third, we use ionic density as a fingerprint of protein charge distribution and observe electrostatic complementarity between the monomer faces that form the dimer interface, more markedly at the isoionic point (where maximum dimerization occurs) than at other pH values, which might contribute to guide the association. Finally, the pH-dependent dimerization modes are inspected using PCA, among other analyses, and two states are identified: a relaxed state at pH 4-8 (with the typical alignment of the crystallographic structure) and a compact state at pH 3-4 (with a tighter association and rotated alignment). This work shows that an approach based on constant-pH MD simulations can produce rich detailed pictures of pH-dependent protein associations, as illustrated for BLG dimerization.

BLaDE: A Basic Lambda Dynamics Engine for GPU-Accelerated Molecular Dynamics Free Energy Calculations

There is an accelerating interest in practical applications of alchemical free energy methods to problems in protein design, constant pH simulations, and especially computer-aided drug design. In the present paper, we describe a basic lambda dynamics engine (BLaDE) that enables alchemical free energy simulations, including multisite λ dynamics (MSλD) simulations, on graphical processor units (GPUs). We find that BLaDE is 5 to 8 times faster than the current GPU implementation of MSλD-based free energy calculations in CHARMM. We also demonstrate that BLaDE running standard molecular dynamics attains a performance competitive with and sometimes exceeding that of the highly optimized OpenMM GPU code. BLaDE is available as a standalone program and through an API in CHARMM.

Recent Developments in Free Energy Calculations for Drug Discovery

The grand challenge in structure-based drug design is achieving accurate prediction of binding free energies. Molecular dynamics (MD) simulations enable modeling of conformational changes critical to the binding process, leading to calculation of thermodynamic quantities involved in estimation of binding affinities. With recent advancements in computing capability and predictive accuracy, MD based virtual screening has progressed from the domain of theoretical attempts to real application in drug development. Approaches including the Molecular Mechanics Poisson Boltzmann Surface Area (MM-PBSA), Linear Interaction Energy (LIE), and alchemical methods have been broadly applied to model molecular recognition for drug discovery and lead optimization. Here we review the varied methodology of these approaches, developments enhancing simulation efficiency and reliability, remaining challenges hindering predictive performance, and applications to problems in the fields of medicine and biochemistry.

PyAutoFEP: An Automated Free Energy Perturbation Workflow for GROMACS Integrating Enhanced Sampling Methods

Free energy perturbation (FEP) calculations are now routinely used in drug discovery to estimate the relative FEB (RFEB) of small molecules to a biomolecular target of interest. Using enhanced sampling can improve the correlation between predictions and experimental data, especially in systems with conformational changes. Due to the large number of perturbations required in drug discovery campaigns, the manual setup of FEP calculations is no longer viable. Here, we introduce PyAutoFEP, a flexible and open-source tool to aid the setup of RFEB FEP. PyAutoFEP is written in Python3, and automates the generation of perturbation maps, dual topologies, system building and molecular dynamics (MD), and analysis. PyAutoFEP supports multiple force fields, incorporates replica exchange with solute tempering (REST) and replica exchange with solute scaling (REST2) enhanced sampling methods, and allows flexible λ values along perturbation windows. To validate PyAutoFEP, it was applied to a set of 14 Farnesoid X receptor ligands, a system included in the drug design data resource grand challenge 2. An 88% mean correct sign prediction was achieved, and 75% of the predictions had an error below 1.5 kcal/mol. Results using Amber03/GAFF, CHARMM36m/CGenFF, and OPLS-AA/M/LigParGen had Pearson's r values of 0.71 ± 0.13, 0.30 ± 0.27, and 0.66 ± 0.20, respectively. The Amber03/GAFF and OPLS-AA/M/LigParGen results were on par with the top grand challenge 2 submissions. Applying REST2 improved the results using CHARMM36m/CGenFF (Pearson's r = 0.43 ± 0.21) but had little impact on the other force fields. CHARMM36-YF and CHARMM36-WYF modifications did not yield improved predictions compared to CHARMM36m. Finally, we estimated the probability of finding a molecule 1 pK_i better than a lead when using PyAutoFEP to screen 10 or 100 analogues. The probabilities, when compared to random sampling, increased up to sevenfold when 100 molecules were to be screened, suggesting that PyAutoFEP would likely be useful for lead optimization. PyAutoFEP is available on GitHub at https://github.com/lmmpf/PyAutoFEP.

A Constant-pH Hybrid Monte Carlo Method with a Configuration-Selection Scheme Using the Zero Energy Difference Condition: Elucidation of Molecular Diffusivity Correlated with a pH-Dependent Solvation Shell

We have proposed a new constant-pH (CpH) hybrid Monte Carlo (MC) method with a configuration-selection (CS) scheme, called the CS-CpH method, to obtain pH-dependent physical properties within a framework of atomistic molecular simulation. The CS-CpH method consists of carrying out a short equilibrium molecular dynamics (MD) and a searching MD coupled with thermostats and barostats to generate physically plausible configurations with changed protonation states (PSs) that are subsequently accepted or rejected according to the Metropolis MC procedure. As an example, we have applied it to glutamic acid in aqueous solution and have demonstrated that it can work to generate reasonably the pH-dependent microscopic configuration ensemble compatible with the experimental pK_a value and also to show interestingly the molecular diffusivity correlated with pH-dependent solvation shell. In conclusion, we believe that the present CS-CpH method becomes a quite useful tool to study the microscopic origin of various pH-dependent phenomena, interpreting them in the atomistic chemical processes.

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.

Exploring the pH-Dependent Structure-Dynamics-Function Relationship of Human Renin

Renin is a pepsin-like aspartyl protease and an important drug target for the treatment of hypertension; despite three decades' research, its pH-dependent structure-function relationship remains poorly understood. Here, we employed continuous constant pH molecular dynamics (CpHMD) simulations to decipher the acid/base roles of renin's catalytic dyad and the conformational dynamics of the flap, which is a common structural feature among aspartyl proteases. The calculated pK_a's suggest that catalytic Asp38 and Asp226 serve as the general base and acid, respectively, in agreement with experiment and supporting the hypothesis that renin's neutral optimum pH is due to the substrate-induced pK_a shifts of the aspartic dyad. The CpHMD data confirmed our previous hypothesis that hydrogen bond formation is the major determinant of the dyad pK_a order. Additionally, our simulations showed that renin's flap remains open regardless of pH, although a Tyr-inhibited state is occasionally formed above pH 5. These findings are discussed in comparison to the related aspartyl proteases, including β-secretases 1 and 2, cathepsin D, and plasmepsin II. Our work represents a first step toward a systematic understanding of the pH-dependent structure-dynamics-function relationships of pepsin-like aspartyl proteases that play important roles in biology and human disease states.

Charge-Changing Perturbations and Path Sampling via Classical Molecular Dynamic Simulations of Simple Guest-Host Systems

Currently, two different methods dominate the field of biomolecular free-energy calculations for the prediction of binding affinities. Pathway methods are frequently used for large ligands that bind on the surface of a host, such as protein-protein complexes. Alchemical methods, on the other hand, are preferably applied for small ligands that bind to deeply buried binding sites. The latter methods are also widely known to be heavily artifacted by the representation of electrostatic energies in periodic simulation boxes, in particular, when net-charge changes are involved. Different methods have been described to deal with these artifacts, including postsimulation correction schemes and instantaneous correction schemes (e.g., co-alchemical perturbation of ions). Here, we use very simple test systems to show that instantaneous correction schemes with no change in the system net charge lower the artifacts but do not eliminate them. Furthermore, we show that free energies from pathway methods suffer from the same artifacts.

Mutant thermal proteome profiling for characterization of missense protein variants and their associated phenotypes within the proteome

Temperature-sensitive (TS) missense mutants have been foundational for characterization of essential gene function. However, an unbiased approach for analysis of biochemical and biophysical changes in TS missense mutants within the context of their functional proteomes is lacking. We applied MS-based thermal proteome profiling (TPP) to investigate the proteome-wide effects of missense mutations in an application that we refer to as mutant thermal proteome profiling (mTPP). This study characterized global impacts of temperature sensitivity-inducing missense mutations in two different subunits of the 26S proteasome. The majority of alterations identified by RNA-Seq and global proteomics were similar between the mutants, which could suggest that a similar functional disruption is occurring in both missense variants. Results from mTPP, however, provide unique insights into the mechanisms that contribute to the TS phenotype in each mutant, revealing distinct changes that were not obtained using only steady-state transcriptome and proteome analyses. Computationally, multisite λ-dynamics simulations add clear support for mTPP experimental findings. This work shows that mTPP is a precise approach to measure changes in missense mutant-containing proteomes without the requirement for large amounts of starting material, specific antibodies against proteins of interest, and/or genetic manipulation of the biological system. Although experiments were performed under permissive conditions, mTPP provided insights into the underlying protein stability changes that cause dramatic cellular phenotypes observed at nonpermissive temperatures. Overall, mTPP provides unique mechanistic insights into missense mutation dysfunction and connection of genotype to phenotype in a rapid, nonbiased fashion.

Improved GROMOS 54A7 Charge Sets for Phosphorylated Tyr, Ser, and Thr to Deal with pH-Dependent Binding Phenomena

Phosphorylation is a ubiquitous post-translational modification in proteins, and the phosphate group is present constitutively or transiently in most biological building blocks. These phosphorylated biomolecules are involved in many high-affinity binding/unbinding events that rely predominantly on electrostatic interactions. To build accurate models of these molecules, we need an improved description of the atomic partial charges for all relevant protonation states. In this work, we showed that the commonly used protocols to derive atomic partial charges using well-solvated molecules are inadequate to model the protonation equilibria in binding events. We introduced a protocol based on PB/MC calculations with a single representative conformation (of both protonation states) and used the resulting pK_a estimations to help manually curate the atomic partial charges. The final charge set, which is fully compatible with the GROMOS 54A7 force field, proved to be very effective in modeling the protonation equilibrium in different phosphorylated peptides in the free (tetrapeptides, pentapeptides, and pY1021) and protein-complexed forms (pY1021/PLC-γ1 complex). This was particularly important in the case of the pY1021 bound to the SH2 domain of PLC-γ1, where only our curated charge set captured the correct protonation equilibrium at the neutral to slightly acidic pH range. The binding/unbinding phenomena in that pH range are biologically relevant, and to improve our models, we need to go beyond the commonly used protocols and obtain revised force field parameters for these molecules.

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.

Titratable Martini model for constant pH simulations

In this work, we deliver a proof of concept for a fast method that introduces pH effects into classical coarse-grained (CG) molecular dynamics simulations. Our approach is based upon the latest version of the popular Martini CG model to which explicit proton mimicking particles are added. We verify our approach against experimental data involving several different molecules and different environmental conditions. In particular, we compute titration curves, pH dependent free energies of transfer, and lipid bilayer membrane affinities as a function of pH. Using oleic acid as an example compound, we further illustrate that our method can be used to study passive translocation in lipid bilayers via protonation. Finally, our model reproduces qualitatively the expansion of the macromolecule dendrimer poly(propylene imine) as well as the associated pKa shift of its different generations. This example demonstrates that our model is able to pick up collective interactions between titratable sites in large molecules comprising many titratable functional groups.

Combining Alchemical Transformation with a Physical Pathway to Accelerate Absolute Binding Free Energy Calculations of Charged Ligands to Enclosed Binding Sites

We present a new approach to more accurately and efficiently compute the absolute binding free energy for receptor-ligand complexes. Currently, the double decoupling method (DDM) and the potential of mean force method (PMF) are widely used to compute the absolute binding free energy of biomolecular complexes. DDM relies on alchemically decoupling the ligand from its environments, which can be computationally challenging for large ligands and charged ligands because of the large magnitude of the decoupling free energies involved. In contrast, the PMF method uses a physical pathway to directly transfer the ligand from solution to the receptor binding pocket and thus avoids some of the aforementioned problems in DDM. However, the PMF method has its own drawbacks: because of its reliance on a ligand binding/unbinding pathway that is free of steric obstructions from the receptor atoms, the method has difficulty treating ligands with buried atoms. To overcome the limitation in the standard PMF approach and enable buried ligands to be treated, here we develop a new method called AlchemPMF in which steric obstructions along the physical pathway for binding are alchemically removed. We have tested the new approach on two important drug targets involving charged ligands. One is HIV-1 integrase bound to an allosteric inhibitor; the other is the human telomeric DNA G-quadruplex in complex with a natural product protoberberine buried in the binding pocket. For both systems, the new approach leads to more reliable estimates of absolute binding free energies with smaller error bars and closer agreements with experiments compared with those obtained from the existing methods, demonstrating the effectiveness of the new method in overcoming the hysteresis often encountered in PMF binding free energy calculations of such systems. The new approach could also be used to improve the sampling of water equilibration and resolvation of the binding pocket as the ligand is extracted.

Correcting electrostatic artifacts due to net-charge changes in the calculation of ligand binding free energies

Alchemically derived free energies are artifacted when the perturbed moiety has a nonzero net charge. The source of the artifacts lies in the effective treatment of the electrostatic interactions within and between the perturbed atoms and remaining (partial) charges in the simulated system. To treat the electrostatic interactions effectively, lattice-summation (LS) methods or cutoff schemes in combination with a reaction-field contribution are usually employed. Both methods render the charging component of the calculated free energies sensitive to essential parameters of the system like the cutoff radius or the box side lengths. Here, we discuss the results of three previously published studies of ligand binding. These studies presented estimates of binding free energies that were artifacted due to the charged nature of the ligands. We show that the size of the artifacts can be efficiently calculated and raw simulation data can be corrected. We compare the corrected results with experimental estimates and nonartifacted estimates from path-sampling methods. Although the employed correction scheme involves computationally demanding continuum-electrostatics calculations, we show that the correction estimate can be deduced from a small sample of configurations rather than from the entire ensemble. This observation makes the calculations of correction terms feasible for complex biological systems. To show the general applicability of the proposed procedure, we also present results where the correction scheme was used to correct independent free energies obtained from simulations employing a cutoff scheme or LS electrostatics. In this work, we give practical guidelines on how to apply the appropriate corrections easily.

Approaching protein design with multisite λ dynamics: Accurate and scalable mutational folding free energies in T4 lysozyme

The estimation of changes in free energy upon mutation is central to the problem of protein design. Modern protein design methods have had remarkable success over a wide range of design targets, but are reaching their limits in ligand binding and enzyme design due to insufficient accuracy in mutational free energies. Alchemical free energy calculations have the potential to supplement modern design methods through more accurate molecular dynamics based prediction of free energy changes, but suffer from high computational cost. Multisite λ dynamics (MSλD) is a particularly efficient and scalable free energy method with potential to explore combinatorially large sequence spaces inaccessible with other free energy methods. This work aims to quantify the accuracy of MSλD and demonstrate its scalability. We apply MSλD to the classic problem of calculating folding free energies in T4 lysozyme, a system with a wealth of experimental measurements. Single site mutants considering 32 mutations show remarkable agreement with experiment with a Pearson correlation of 0.914 and mean unsigned error of 1.19 kcal/mol. Multisite mutants in systems with up to five concurrent mutations spanning 240 different sequences show comparable agreement with experiment. These results demonstrate the promise of MSλD in exploring large sequence spaces for protein design.

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

We present a GPU implementation of the continuous constant pH molecular dynamics (CpHMD) based on the most recent generalized Born implicit-solvent model in the pmemd engine of the Amber molecular dynamics package. To test the accuracy of the tool for rapid pK_a predictions, a series of 2 ns single-pH simulations were performed for over 120 titratable residues in 10 benchmark proteins that were previously used to test the various continuous CpHMD methods. The calculated pK_a's showed a root-mean-square deviation of 0.80 and correlation coefficient of 0.83 with respect to experiment. Also, 90% of the pK_a's were converged with estimated errors below 0.1 pH units. Surprisingly, this level of accuracy is similar to our previous replica-exchange simulations with 2 ns per replica and an exchange attempt frequency of 2 ps^-1 (Huang, Harris, and Shen J. Chem. Inf. Model. 2018 , 58 , 1372 - 1383 ). Interestingly, for the linked titration sites in two enzymes, although residue-specific protonation state sampling in the single-pH simulations was not converged within 2 ns, the protonation fraction of the linked residues appeared to be largely converged, and the experimental macroscopic pK_a values were reproduced to within 1 pH unit. Comparison with replica-exchange simulations with different exchange attempt frequencies showed that the splitting between the two macroscopic pK_a's is underestimated with frequent exchange attempts such as 2 ps^-1, while single-pH simulations overestimate the splitting. The same trend is seen for the single-pH vs replica-exchange simulations of a hydrogen-bonded aspartyl dyad in a much larger protein. A 2 ns single-pH simulation of a 400-residue protein takes about 1 h on a single NVIDIA GeForce RTX 2080 graphics card, which is over 1000 times faster than a CpHMD run on a single CPU core of a high-performance computing cluster node. Thus, we envision that GPU-accelerated continuous CpHMD may be used in routine pK_a predictions for a variety of applications, from assisting MD simulations with protonation state assignment to offering pH-dependent corrections of binding free energies and identifying reactive hot spots for covalent drug design.

Relative Binding Affinity Prediction of Charge-Changing Sequence Mutations with FEP in Protein-Protein Interfaces

Building on the substantial progress that has been made in using free energy perturbation (FEP) methods to predict the relative binding affinities of small molecule ligands to proteins, we have previously shown that results of similar quality can be obtained in predicting the effect of mutations on the binding affinity of protein–protein complexes. However, these results were restricted to mutations which did not change the net charge of the side chains due to known difficulties with modeling perturbations involving a change in charge in FEP. Various methods have been proposed to address this problem. Here we apply the co-alchemical water approach to study the efficacy of FEP calculations of charge changing mutations at the protein–protein interface for the antibody–gp120 system investigated previously and three additional complexes. We achieve an overall root mean square error of 1.2 kcal/mol on a set of 106 cases involving a change in net charge selected by a simple suitability filter using side-chain predictions and solvent accessible surface area to be relevant to a biologic optimization project. Reasonable, although less precise, results are also obtained for the 44 more challenging mutations that involve buried residues, which may in some cases require substantial reorganization of the local protein structure, which can extend beyond the scope of a typical FEP simulation. We believe that the proposed prediction protocol will be of sufficient efficiency and accuracy to guide protein engineering projects for which optimization and/or maintenance of a high degree of binding affinity is a key objective.

Generalized Born Based Continuous Constant pH Molecular Dynamics in Amber: Implementation, Benchmarking and Analysis

Solution pH plays an important role in structure and dynamics of biomolecular systems; however, pH effects cannot be accurately accounted for in conventional molecular dynamics simulations based on fixed protonation states. Continuous constant pH molecular dynamics (CpHMD) based on the λ-dynamics framework calculates protonation states on the fly during dynamical simulation at a specified pH condition. Here we report the CPU-based implementation of the CpHMD method based on the GBNeck2 generalized Born (GB) implicit-solvent model in the pmemd engine of the Amber molecular dynamics package. The performance of the method was tested using pH replica-exchange titration simulations of Asp, Glu and His side chains in 4 miniproteins and 7 enzymes with experimentally known p K_a's, some of which are significantly shifted from the model values. The added computational cost due to CpHMD titration ranges from 11 to 33% for the data set and scales roughly linearly as the ratio between the titrable sites and number of solute atoms. Comparison of the experimental and calculated p K_a's using 2 ns per replica sampling yielded a mean unsigned error of 0.70, a root-mean-squared error of 0.91, and a linear correlation coefficient of 0.79. Though this level of accuracy is similar to the GBSW-based CpHMD in CHARMM, in contrast to the latter, the current implementation was able to reproduce the experimental orders of the p K_a's of the coupled carboxylic dyads. We quantified the sampling errors, which revealed that prolonged simulation is needed to converge p K_a's of several titratable groups involved in salt-bridge-like interactions or deeply buried in the protein interior. Our benchmark data demonstrate that GBNeck2-CpHMD is an attractive tool for protein p K_a predictions.

Membrane-Induced p Ka Shifts in wt-pHLIP and Its L16H Variant

The pH (low) insertion peptides (pHLIPs) is a family of peptides that are able to insert into a lipid bilayer at acidic pH. The molecular mechanism of pHLIPs insertion, folding, and stability in the membrane at low pH is based on multiple protonation events, which are challenging to study at the molecular level. More specifically, the relation between the experimental p K of insertion (p K^exp) of pHLIPs and the p K_a of the key residues is yet to be clarified. We carried out a computational study, complemented with new experimental data, and established the influence of (de)protonation of titrable residues on the stability of the peptide membrane-inserted state. Constant-pH molecular dynamics simulations were employed to calculate the p K_a values of these residues along the membrane normal. In the wt-pHLIP, we identified Asp14 as the key residue for the stability of the membrane-inserted state, and its p K_a value is strongly correlated with the experimental p K^exp measured in thermodynamics studies. Also, in order to narrow down the pH range at which pHLIP is stable in the membrane, we designed a new pHLIP variant, L16H, where Leu in the 16th position was replaced by a titrable His residue. Our results showed that the L16H variant undergoes two transitions. The calculated p K_a and experimentally observed p K^exp values are in good agreement. Two distinct p K^exp values delimit a pH range where the L16H peptide is stably inserted in the membrane, while, outside this range, the membrane-inserted state is destabilized and the peptide exits from the bilayer. pHLIP peptides have been successfully used to target cancer cells for the delivery of diagnostics and therapeutic agents to acidic tumors. The fine-tuning of the stability of the pHLIP inserted state and its restriction to a narrow well-defined pH range might allow the design of new peptides, able to discriminate between tissues with different extracellular pH values.

Predicting Catalytic Proton Donors and Nucleophiles in Enzymes: How Adding Dynamics Helps Elucidate the Structure-Function Relationships

Despite the relevance of understanding structure-function relationships, robust prediction of proton donors and nucleophiles in enzyme active sites remains challenging. Here we tested three types of state-of-the-art computational methods to calculate the p K_a's of the buried and hydrogen bonded catalytic dyads in five enzymes. We asked the question what determines the p K_a order, i.e., what makes a residue proton donor vs a nucleophile. The continuous constant pH molecular dynamics simulations captured the experimental p K_a orders and revealed that the negative nucleophile is stabilized by increased hydrogen bonding and solvent exposure as compared to the proton donor. Surprisingly, this simple trend is not apparent from crystal structures and the static structure-based calculations. While the generality of the findings awaits further testing via a larger set of data, they underscore the role of dynamics in bridging enzyme structures and functions.

Role of Counterions in Constant-pH Molecular Dynamics Simulations of PAMAM Dendrimers

Electrostatic interactions play a pivotal role in the structure and mechanism of action of most biomolecules. There are several conceptually different methods to deal with electrostatics in molecular dynamics simulations. Ionic strength effects are usually introduced using such methodologies and can have a significant impact on the quality of the final conformation space obtained. We have previously shown that full system neutralization can lead to wrong lipidic phases in the 25% PA/PC bilayer (J. Chem. Theory Comput. 2014,10, 5483-5492). In this work, we investigate how two limit approaches to the ionic strength treatment (implicitly with GRF or using full system neutralization with either GRF or PME) can influence the conformational space of the second-generation PAMAM dendrimer. Constant-pH MD simulations were used to map PAMAM's conformational space at its full pH range (from 2.5 to 12.5). Our simulations clearly captured the coupling between protonation and conformation in PAMAM. Interestingly, the dendrimer conformational distribution was almost independent of the ionic strength treatment methods, which is in contrast to what we have observed in charged lipid bilayers. Overall, our results confirm that both GRF with implicit ionic strength and a fully neutralized system with PME are valid approaches to model charged globular systems, using the GROMOS 54A7 force field.

Constant pH Molecular Dynamics Reveals How Proton Release Drives the Conformational Transition of a Transmembrane Efflux Pump

AcrB is the inner-membrane transporter of an E. coli AcrAB-TolC tripartite efflux complex, which plays a major role in the intrinsic resistance to clinically important antibiotics. AcrB pumps a wide range of toxic substrates by utilizing the proton gradient between periplasm and cytoplasm. Crystal structures of AcrB revealed three distinct conformational states of the transport cycle, substrate access, binding, and extrusion or loose (L), tight (T), and open (O) states. However, the specific residue(s) responsible for proton binding/release and the mechanism of proton-coupled conformational cycling remain controversial. Here we use the newly developed membrane hybrid-solvent continuous constant pH molecular dynamics technique to explore the protonation states and conformational dynamics of the transmembrane domain of AcrB. Simulations show that both Asp407 and Asp408 are deprotonated in the L/T states, while only Asp408 is protonated in the O state. Remarkably, release of a proton from Asp408 in the O state results in large conformational changes, such as the lateral and vertical movement of transmembrane helices as well as the salt-bridge formation between Asp408 and Lys940 and other side chain rearrangements among essential residues. Consistent with the crystallographic differences between the O and L protomers, simulations offer dynamic details of how proton release drives the O-to-L transition in AcrB and address the controversy regarding the proton/drug stoichiometry. This work offers a significant step toward characterizing the complete cycle of proton-coupled drug transport in AcrB and further validates the membrane hybrid-solvent CpHMD technique for studies of proton-coupled transmembrane proteins which are currently poorly understood.

CDOCKER and λ-dynamics for prospective prediction in D₃R Grand Challenge 2

The opportunity to prospectively predict ligand bound poses and free energies of binding to the Farnesoid X Receptor in the D3R Grand Challenge 2 provided a useful exercise to evaluate CHARMM based docking (CDOCKER) and [Formula: see text]-dynamics methodologies for use in "real-world" applications in computer aided drug design. In addition to measuring their current performance, several recent methodological developments have been analyzed retrospectively to highlight best procedural practices in future applications. For pose prediction with CDOCKER, when the protein structure used for rigid receptor docking was close to the crystallographic holo structure, reliable poses were obtained. Benzimidazoles, with a known holo receptor structure, were successfully docked with an average RMSD of 0.97 [Formula: see text]. Other non-benzimidazole ligands displayed less accuracy largely because the receptor structures we chose for docking were too different from the experimental holo structures. However, retrospective analysis has shown that when these ligands were re-docked into their holo structures, the average RMSD dropped to 1.18 [Formula: see text] for all ligands. When sulfonamides and spiros were docked with the apo structure, which agrees more with their holo structure than the structures we chose, five out of six ligands were correctly docked. These docking results emphasize the need for flexible receptor docking approaches. For [Formula: see text]-dynamics techniques, including multisite [Formula: see text]-dynamics (MS[Formula: see text]D), reasonable agreement with experiment was observed for the 33 ligands investigated; root mean square errors of 2.08 and 1.67 kcal/mol were obtained for free energy sets 1 and 2, respectively. Retrospectively, soft-core potentials, adaptive landscape flattening, and biasing potential replica exchange (BP-REX) algorithms were critical to model large substituent perturbations with sufficient precision and within restrictive timeframes, such as was required with participation in Grand Challenge 2. These developments, their associated benefits, and proposed procedures for their use in future applications are discussed.

Conformational dynamics of cathepsin D and binding to a small-molecule BACE1 inhibitor

BACE1 is a major therapeutic target for prevention and treatment of Alzheimer's disease. Developing inhibitors that can selectively target BACE1 in favor of other proteases, especially cathepsin D (CatD), has presented significant challenges. Here, we investigate the conformational dynamics and protonation states of BACE1 and CatD using continuous constant pH molecular dynamics with pH replica-exchange sampling protocol. Despite similar structure, BACE1 and CatD exhibit markedly different active site dynamics. BACE1 displays pH-dependent flap dynamics that controls substrate accessibility, while the CatD flap is relatively rigid and remains open in the pH range 2.5-6. Interestingly, although each protease hydrolyzes peptide bonds, the protonation states of the catalytic dyads are different within the active pH range. The acidic and basic components of the BACE1 catalytic dyad are clear, while either aspartic acid of the CatD catalytic dyad could play the role of acid or base. Finally, we investigate binding of the inhibitor LY2811376 developed by Eli Lilly to BACE1 and CatD. Surprisingly, in the enzyme active pH range, LY2811376 forms a stronger salt bridge with the catalytic dyad in CatD than in BACE1, which might explain the retinal toxicity of the inhibitor related to off-target inhibition of CatD. This work highlights the complexity and challenge in structure-based drug design where receptor-ligand binding induces protonation state change in both the protein and the inhibitor. © 2017 Wiley Periodicals, Inc.

Accurate Three States Model for Amino Acids with Two Chemically Coupled Titrating Sites in Explicit Solvent Atomistic Constant pH Simulations and pK(a) Calculations

Correct protonation of titratable groups in biomolecules is crucial for their accurate description by molecular dynamics simulations. In the context of constant pH simulations, an additional protonation degree of freedom is introduced for each titratable site, allowing the protonation state to change dynamically with changing structure or electrostatics. Here, we extend previous approaches for an accurate description of chemically coupled titrating sites. A second reaction coordinate is used to switch between two tautomeric states of an amino acid with chemically coupled titratable sites, such as aspartate (Asp), glutamate (Glu), and histidine (His). To this aim, we test a scheme involving three protonation states. To facilitate charge neutrality as required for periodic boundary conditions and Particle Mesh Ewald (PME) electrostatics, titration of each respective amino acid is coupled to a "water" molecule that is charged in the opposite direction. Additionally, a force field modification for Amber99sb is introduced and tested for the description of carboxyl group protonation. Our three states model is tested by titration simulations of Asp, Glu, and His, yielding a good agreement, reproducing the correct geometry of the groups in their different protonation forms. We further show that the ion concentration change due to the neutralizing "water" molecules does not significantly affect the protonation free energies of the titratable groups, suggesting that the three states model provides a good description of biomolecular dynamics at constant pH.

Probing the Structure of the Escherichia coli Periplasmic Proteins HdeA and YmgD by Molecular Dynamics Simulations

HdeA and YmgD are structurally homologous proteins in the periplasm of Escherichia coli. HdeA has been shown to represent an acid-activated chaperone, whereas the function of YmgD has not yet been characterized. We performed pH-titrating molecular dynamics simulations (pHtMD) to investigate the structural changes of both proteins and to assess whether YmgD may also exhibit an unfolding behavior similar to that of HdeA. The unfolding pathway of HdeA includes partially unfolded dimer structures, which represent a prerequisite for subsequent dissociation. In contrast to the coupled unfolding and dissociation of HdeA, YmgD displays dissociation of the folded subunits, and the subunits do not undergo significant unfolding even at low pH values. The differences in subunit stability between HdeA and YmgD may be explained by the structural features of helix D, which represents the starting point of unfolding in HdeA. In summary, the present study suggests that YmgD either is not an acid-activated chaperone or, at least, does not require unfolding for activation.