Constant pH Molecular Dynamics Method Research Articles

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.

Unravelling Constant pH Molecular Dynamics in Oligopeptides with Explicit Solvation Model.

An accurate description of the protonation state of amino acids is essential to correctly simulate the conformational space and the mechanisms of action of proteins or other biochemical systems. The pH and the electrochemical environments are decisive factors to define the effective pKa of amino acids and, therefore, the protonation state. However, they are poorly considered in Molecular Dynamics (MD) simulations. To deal with this problem, constant pH Molecular Dynamics (cpHMD) methods have been developed in recent decades, demonstrating a great ability to consider the effective pKa of amino acids within complex structures. Nonetheless, there are very few studies that assess the effect of these approaches in the conformational sampling. In a previous work of our research group, we detected strengths and weaknesses of the discrete cpHMD method implemented in AMBER when simulating capped tripeptides in implicit solvent. Now, we progressed this assessment by including explicit solvation in these peptides. To analyze more in depth the scope of the reported limitations, we also carried out simulations of oligopeptides with distinct positions of the titratable amino acids. Our study showed that the explicit solvation model does not improve the previously noted weaknesses and, furthermore, the separation of the titratable amino acids in oligopeptides can minimize them, thus providing guidelines to improve the conformational sampling in the cpHMD simulations.

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.

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.

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.

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.

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 pKa 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 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 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.

Computing pKa Shifts Using Traditional Molecular Dynamics: Example of Acid-Base Indicator Dyes in Organized Solutions.

A compound's acidity constant (Ka) in a given medium determines its protonation state and, thus, its behavior and physicochemical properties. Therefore, it is among the key characteristics considered during the design of new compounds for the needs of advanced technology, medicine, and biological research, a notable example being pH sensors. The computational prediction of Ka for weak acids and bases in homogeneous solvents is presently rather well developed. However, it is not the case for more complex media, such as microheterogeneous solutions. The constant-pH molecular dynamics (MD) method is a notable contribution to the solution of the problem, but it is not commonly used. Here, we develop an approach for predicting Ka changes of weak small-molecule acids upon transfer from water to colloid solutions by means of traditional classical molecular dynamics. The approach is based on free energy (ΔG) computations and requires limited experiment data input during calibration. It was successfully tested on a series of pH-sensitive acid-base indicator dyes in micellar solutions of surfactants. The difficulty of finite-size effects affecting ΔG computation between states with different total charges is taken into account by evaluating relevant corrections; their impact on the results is discussed, and it is found non-negligible (0.1-0.4 pKa units). A marked bias is found in the ΔG values of acid deprotonation, as computed from MD, which is apparently caused by force-field issues. It is hypothesized to affect the constant-pH MD and reaction ensemble MD methods as well. Consequently, for these methods, a preliminary calibration is suggested.

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.

A pH Replica Exchange Scheme in the Stochastic Titration Constant-pH MD Method.

Solution pH is a physicochemical property that has a key role in cellular regulation, and its impact at the molecular level is often difficult to study by experimental methods. In this context, several theoretical methods were developed to study pH effects in macromolecules. The stochastic titration constant-pH molecular dynamics method (CpHMD) was developed by coupling molecular sampling methods, which are appropriate to study the conformational ensemble of biomolecules, with continuum electrostatics approaches, which properly describe pH-dependent protonation states. However, in difficult cases, the protonation sampling can be too slow for the commonly accessible computational times. In this work, we combined a pH replica exchange scheme with this CpHMD method and explored several optimization strategies and possible limitations.

All-Atom Continuous Constant pH Molecular Dynamics With Particle Mesh Ewald and Titratable Water.

Development of a pH stat to properly control solution pH in biomolecular simulations has been a long-standing goal in the community. Toward this goal recent years have witnessed the emergence of the so-called constant pH molecular dynamics methods. However, the accuracy and generality of these methods have been hampered by the use of implicit-solvent models or truncation-based electrostatic schemes. Here we report the implementation of the particle mesh Ewald (PME) scheme into the all-atom continuous constant pH molecular dynamics (CpHMD) method, enabling CpHMD to be performed with a standard MD engine at a fractional added computational cost. We demonstrate the performance using pH replica-exchange CpHMD simulations with titratable water for a stringent test set of proteins, HP36, BBL, HEWL, and SNase. With the sampling time of 10 ns per replica, most pKa's are converged, yielding the average absolute and root-mean-square deviations of 0.61 and 0.77, respectively, from experiment. Linear regression of the calculated vs experimental pKa shifts gives a correlation coefficient of 0.79, a slope of 1, and an intercept near 0. Analysis reveals inadequate sampling of structure relaxation accompanying a protonation-state switch as a major source of the remaining errors, which are reduced as simulation prolongs. These data suggest PME-based CpHMD can be used as a general tool for pH-controlled simulations of macromolecular systems in various environments, enabling atomic insights into pH-dependent phenomena involving not only soluble proteins but also transmembrane proteins, nucleic acids, surfactants, and polysaccharides.

Constant-pH MD Simulations Portray the Protonation and Structural Behavior of Four Decapeptides Designed to Coordinate Cu(2+).

The cyclic decapeptide C-Asp, containing one Asp residue and three His residues, was designed by Fragoso et al. (Chem. Eur. J. 2013, 19, 2076) to bind Cu(2+) exclusively through the side chain groups and mimic copper coordination in metalloproteins. A variant of the cyclodecapeptide where Asp is substituted by Asn (C-Asn) has also been synthesized in addition to the linear ("open") counterparts of both forms (O-Asp and O-Asn), testing the importance of cyclization and the presence of Asp in Cu(2+) coordination (Chem. Eur. J. 2013, 19, 2076; Dalton Trans. 2013, 42, 6182). All peptides formed a major species at neutral pH that was able to coordinate Cu(2+) exclusively through the neutral imidazole groups and the Asp side chain, when present, with C-Asp being the most effective. A detailed description of the protonation behavior of each histidine could help understanding the coordination species being formed in the pH range and eventually further optimizing the peptide's design. However, the standard current methods (NMR titrations) are not very suited for proximal groups titrating in the same pH range. In this work, we used the stochastic titration constant-pH molecular dynamics method to calculate the protonation curves and pKa of each titrable residue in the four decapeptides, in the absence of Cu(2+) ions. The global protonation curves obtained in our simulations are in very good agreement with the existing potentiometric titration curves. The histidines are titrating very closely, and the Asp forms abundant salt bridges with the basic residues, displaying an unusually low pKa value. In addition, we could observe that the four peptides are very unstructured in the absence of copper, and not even the cyclic forms exhibit a significant β-sheet, unlike what could be expected from the presence of β-turn inducer units in this type of scaffold.

Mechanism of Proton Transport of the M2 Proton Channel Studied by Constant pH Molecular Dynamics

The M2 protein of the influenza virus is a proton-selective homotetrameric channel. During virus entry, M2 is activated by the low pH of the endosome and transports protons into the virion, initiating viral uncoating. A histidine tetrad in the pore of the M2 transmembrane domain is responsible for pH activation and proton selectivity. A number of different mechanisms have been proposed for proton transport of M2 based on experimental and computational studies. To test these hypotheses, we applied the explicit-solvent continuous constant pH molecular dynamics method to study the pH-dependent conformational dynamics of M2 in explicit membrane. The calculated pKa values of the histidine tetrad are comparable to experimental values. The C-terminal openning of M2 became wider when pH was lowered. This work provides novel insight into the coupled protonation and conformational dynamics of the M2 proton channel.

Effects of system net charge and electrostatic truncation on all-atom constant pH molecular dynamics.

Constant pH molecular dynamics offers a means to rigorously study the effects of solution pH on dynamical processes. Here, we address two critical questions arising from the most recent developments of the all-atom continuous constant pH molecular dynamics (CpHMD) method: (1) What is the effect of spatial electrostatic truncation on the sampling of protonation states? (2) Is the enforcement of electrical neutrality necessary for constant pH simulations? We first examined how the generalized reaction field and force-shifting schemes modify the electrostatic forces on the titration coordinates. Free energy simulations of model compounds were then carried out to delineate the errors in the deprotonation free energy and salt-bridge stability due to electrostatic truncation and system net charge. Finally, CpHMD titration of a mini-protein HP36 was used to understand the manifestation of the two types of errors in the calculated pK(a) values. The major finding is that enforcing charge neutrality under all pH conditions and at all time via cotitrating ions significantly improves the accuracy of protonation-state sampling. We suggest that such finding is also relevant for simulations with particle mesh Ewald, considering the known artifacts due to charge-compensating background plasma.

Why a diaminopyrrolic tripodal receptor binds mannosides in acetonitrile but not in water?

Intermolecular interactions involving carbohydrates and their natural receptors play important roles in several biological processes. The development of synthetic receptors is very useful to study these recognition processes. Recently, it was synthetized a diaminopyrrolic tripodal receptor that is selective for mannosides, which are obtained from mannose, a sugar with significant relevance in living systems. However, this receptor is significantly more active in acetonitrile than in water. In this work, we performed several molecular dynamics and constant-pH molecular dynamics simulations in acetonitrile and water to evaluate the conformational space of the receptor and to understand the molecular detail of the receptor–mannoside interaction. The protonation states sampled by the receptor show that the positive charges are always as distant as possible in order to avoid large intramolecular repulsions. Moreover, the conformational space of the receptor is very similar in water above pH 4.0 and in acetonitrile. From the simulations with the mannoside, we observe that the interactions are more specific in acetonitrile (mainly hydrogen bonds) than in water (mainly hydrophobic). Our results suggest that the readiness of the receptor to bind mannoside is not significantly affected in water (above pH 4.0). Probably, the hydrogen bond network that is formed in acetonitrile (which is weaker in water) is the main reason for the higher activity in this solvent. This work also presents a new implementation of the stochastic titration constant-pH molecular dynamics method to a synthetic receptor of sugars and attests its ability to describe the protonation/conformation coupling in these molecules.

Exploring pKa Values for Buried Residues in Membrane Bilayers using Constant pH Molecular Dynamics Simulations

Environmental conditions such as pH are considered to play profound roles in determining proteins' structures and functions. In recent years, several experimental and computational techniques have been developed to improve our understanding of the effects of pH on proteins. However, the implicit representation of solvents in the current constant pH molecular dynamics (CpHMD) methods can lead to undesirable side effects in calculating pKa values of titratable side chains. These effects can be even more pronounced for membrane proteins where the rigid nature of the current implicit membrane models causes unrealistic pKa shifts in favor of neutral states. Inspired by recently published pKa values for Lys residues in model transmembrane peptides (Gleason NJ et al. (2013) PNAS 110:1692-1695), here we explore a newly developed CpHMD technique based on an all-atom representation of solvent/lipid molecules and proteins for simple transmembrane peptide models with a titratable side chain. The pKa values of the side chains along with the pH dependent configuration of these peptides in the membrane bilayer are investigated and compared with the available experimental values. Motivated by the excellent agreement between the calculated pKa values and the experiment for model peptides, the purely explicit CpHMD is also applied to study the pKa values of titratable side chains of influenza A proton channel (M2) and its pH dependent structural change in the membrane bilayer.

Protonation States in Molecular Dynamics Simulations of Peptide Folding and Binding

Peptides are important signaling modules, acting both as individual hormones and as parts of larger molecules, mediating their protein-protein interactions. Many peptidic and peptidomimetic drugs have reached the marketplace and opportunities for peptide-based drug discovery are on the rise. pH-dependent behavior of peptides is well documented in the context of misfolding diseases and peptide translocation. Changes in the protonation states of peptide residues often have a crucial effect on a peptide's structure, dynamics and function, which may be exploited for biotechnological applications. The current review surveys the increasing levels of sophistication in the treatment of protonation states in computational studies involving peptides. Specifically we describe I) the common practice of assigning a single protonation state and using it throughout the dynamic simulation, II) approaches that consider multiple protonation states and compare computed observables to experimental ones, III) constant pH molecular dynamics methods that couple changes in protonation states with conformational dynamics "on the fly". Applications of conformational dynamics treatment of peptides in the context of binding, folding and interactions with the membrane are presented, illustrating the growing body of work in this field and highlighting the importance of careful handling of protonation states of peptidic residues.

Computational Investigation of the pH Dependence of Loop Flexibility and Catalytic Function in Glycoside Hydrolases

Cellulase enzymes cleave glycosidic bonds in cellulose to produce cellobiose via either retaining or inverting hydrolysis mechanisms, which are significantly pH-dependent. Many fungal cellulases function optimally at pH ~5, and their activities decrease dramatically at higher or lower pH. To understand the molecular-level implications of pH in cellulase structure, we use a hybrid, solvent-based, constant pH molecular dynamics method combined with pH-based replica exchange to determine the pK(a) values of titratable residues of a glycoside hydrolase (GH) family 6 cellobiohydrolase (Cel6A) and a GH family 7 cellobiohydrolase (Cel7A) from the fungus Hypocrea jecorina. For both enzymes, we demonstrate that a bound substrate significantly affects the pKa values of the acid residues at the catalytic center. The calculated pK(a) values of catalytic residues confirm their proposed roles from structural studies and are consistent with the experimentally measured apparent pKa values. Additionally, GHs are known to impart a strained pucker conformation in carbohydrate substrates in active sites for catalysis, and results from free energy calculations combined with constant pH molecular dynamics suggest that the correct ring pucker is stable near the optimal pH for both Cel6A and Cel7A. Much longer molecular dynamics simulations of Cel6A and Cel7A with fixed protonation states based on the calculated pK(a) values suggest that pH affects the flexibility of tunnel loops, which likely affects processivity and substrate complexation. Taken together, this work demonstrates several molecular-level effects of pH on GH enzymes important for cellulose turnover in the biosphere and relevant to biomass conversion processes.

Application of Explicit-Solvent Constant ph Molecular Dynamics to Proteins

Solution pH is a critical factor in biological and chemical processes. To enable molecular simulations of proton-coupled dynamics in these processes, the continuous constant pH molecular dynamics (CpHMD) method has been developed. Recently, we extended the CpHMD framework to explicit-solvent simulations and tested on the titration of a series of aliphatic dicarboxylic acids. Here we applied the method to several proteins including 36-residue HP36, 45-residue BBL, 56-residue NTL9, and 129-residue HEWL. The calculated pKa's have a root mean square deviation below one pH unit from experiment. This accuracy is comparable to the hybrid-solvent CpHMD, where the Generalized-Born (GB) implicit-solvent model is used to propagate titration coordinates while explicit-solvent is used to propagate conformational degrees of freedom. However, the explicit-solvent method avoids the artifacts and limitations of the GB model. This work demonstrates that the explicit-solvent CpHMD method paves the way for realizing pH-controlled all-atom MD simulations.

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

Recent development of constant pH molecular dynamics (CpHMD) methods has offered promise for adding pH-stat in molecular dynamics simulations. However, until now the working pH molecular dynamics (pHMD) implementations are dependent in part or whole on implicit-solvent models. Here we show that proper treatment of long-range electrostatics and maintaining charge neutrality of the system are critical for extending the continuous pHMD framework to the all-atom representation. The former is achieved here by adding forces to titration coordinates due to long-range electrostatics based on the generalized reaction field method, while the latter is made possible by a charge-leveling technique that couples proton titration with simultaneous ionization or neutralization of a co-ion in solution. We test the new method using the pH-replica-exchange CpHMD simulations of a series of aliphatic dicarboxylic acids with varying carbon chain length. The average absolute deviation from the experimental pK(a) values is merely 0.18 units. The results show that accounting for the forces due to extended electrostatics removes the large random noise in propagating titration coordinates, while maintaining charge neutrality of the system improves the accuracy in the calculated electrostatic interaction between ionizable sites. Thus, we believe that the way is paved for realizing pH-controlled all-atom molecular dynamics in the near future.