Constant-pH molecular dynamics simulations: a test case of succinic acid

Constant pH molecular dynamics simulations: Current status and recent applications

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

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.

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.

Protein pKa Prediction by Tree-Based Machine Learning

Protonation states of ionizable protein residues modulate many essential biological processes. For correct modeling and understanding of these processes, it is crucial to accurately determine their pKa values. Here, we present four tree-based machine learning models for protein pKa prediction. The four models, Random Forest, Extra Trees, eXtreme Gradient Boosting (XGBoost), and Light Gradient Boosting Machine (LightGBM), were trained on three experimental PDB and pKa datasets, two of which included a notable portion of internal residues. We observed similar performance among the four machine learning algorithms. The best model trained on the largest dataset performs 37% better than the widely used empirical pKa prediction tool PROPKA and 15% better than the published result from the pKa prediction method DelPhiPKa. The overall root-mean-square error (RMSE) for this model is 0.69, with surface and buried RMSE values being 0.56 and 0.78, respectively, considering six residue types (Asp, Glu, His, Lys, Cys, and Tyr), and 0.63 when considering Asp, Glu, His, and Lys only. We provide pKa predictions for proteins in human proteome from the AlphaFold Protein Structure Database and observed that 1% of Asp/Glu/Lys residues have highly shifted pKa values close to the physiological pH.

Titration of Adenine in a GA Mismatch with Grand Canonical Simulations

Computational prediction of the pKa of ionizable groups remains a central challenge in biomolecular modeling. Although all-atom fixed-charge force fields could be accurate to describe the interaction network within the biomolecules, proper sampling techniques are required to obtain the thermodynamic information in the (de)protonation event. Sufficient sampling requires an ensemble of structures from simulations with proper treatments of the acid-base equilibria, and the grand canonical simulation technique could be used to model the growth/annihilation of hydrogen atoms by merging Hamiltonians of different protonation states into one simulation ensemble. The electrostatic feature of nucleotide systems is especially difficult to model, and the situation becomes more challenging when the ionizable site is highly perturbed. Although there are many successful predictions obtained from the grand canonical constant pH simulations, few reports focus on highly perturbed nucleotide systems with unconventional base-pair features. In this work, with the discrete constant pH method, we investigate the titration thermodynamics of an adenine in the catalytic triad in a 35-nucleotide single-stranded RNA hairpin, featuring an unconventional GA mismatch and a substantially shifted pKa value. Validation tests are performed with two system setups, both of which provide pKa predictions in good agreement with the experimental value. A single-configuration-based technique is used to calculate the pKa for comparison. The current success indicates the predictive power of the current nucleotide modeling framework.

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.

Reservoir pH replica exchange

We present the reservoir pH replica exchange (R-pH-REM) method for constant pH simulations. The R-pH-REM method consists of a two-step procedure; the first step involves generation of one or more reservoirs of conformations. Each reservoir is obtained from a standard or enhanced molecular dynamics simulation with a constrained (fixed) protonation state. In the second step, fixed charge constraints are relaxed, as the structures from one or more reservoirs are periodically injected into a constant pH or a pH-replica exchange (pH-REM) simulation. The benefit of this two-step process is that the computationally intensive part of conformational search can be decoupled from constant pH simulations, and various techniques for enhanced conformational sampling can be applied without the need to integrate such techniques into the pH-REM framework. Simulations on blocked Lys, KK, and KAAE peptides were used to demonstrate an agreement between pH-REM and R-pH-REM simulations. While the reservoir simulations are not needed for these small test systems, the real need arises in cases when ionizable molecules can sample two or more conformations separated by a large energy barrier, such that adequate sampling is not achieved on a time scale of standard constant pH simulations. Such problems might be encountered in protein systems that exploit conformational transitions for function. A hypothetical case is studied, a small molecule with a large torsional barrier; while results of pH-REM simulations depend on the starting structure, R-pH-REM calculations on this model system are in excellent agreement with a theoretical model.

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.

Effect of pH on the hinge region of influenza viral protein: a combined constant pH and well-tempered molecular dynamics study

Despite the knowledge that the influenza protein, hemagglutinin, undergoes a large conformational change at low pH during the process of fusion with the host cell, its molecular mechanism remains elusive. The present constant pH molecular dynamics (CpHMD) study identifies the residues responsible for large conformational change in acidic condition. Based on the pKa calculations, it is predicted that His-106 is much more responsible for the large conformational change than any other residues in the hinge region of hemagglutinin protein. Potential of mean force profile from well-tempered meta-dynamics (WT-MtD) simulation is also generated along the folding pathway by considering radius of gyration (R _gyr) as a collective variable (CV). It is very clear from the present WT-MtD study, that the initial bending starts at that hinge region, which may trigger other conformational changes. Both the protein-protein and protein-water HB time correlation functions are monitored along the folding pathway. The protein-protein (full or hinge region) HB time correlation functions are always found to be stronger than those of the protein-water time correlation functions. The dynamical balance between protein-protein and protein-water HB interactions favors the stabilization of the folded state.

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.

Free energy landscape of siRNA-polycation complexation: Elucidating the effect of molecular geometry, polymer flexibility, and charge neutralization

The success of medical threatments with DNA and silencing interference RNA is strongly related to the design of efficient delivery technologies. Cationic polymers represent an attractive strategy to serve as nucleic-acid carriers with the envisioned advantages of efficient complexation, low cost, ease of production, well-defined size, and low polydispersity index. However, the balance between efficacy and toxicity (safety) of these polymers is a challenge and in need of improvement. With the aim of designing more effective polycationic-based gene carriers, many parameters such as carrier morphology, size, molecular weight, surface chemistry, and flexibility/rigidity ratio need to be taken into consideration. In the present work, the binding mechanism of three cationic polymers (polyarginine, polylysine and polyethyleneimine) to a model siRNA target is computationally investigated at the atomistic level. In order to better understand the polycationic carrier-siRNA interactions, replica exchange molecular dynamic simulations were carried out to provide an exhaustive exploration of all the possible binding sites, taking fully into account the siRNA flexibility together with the presence of explicit solvent and ions. Moreover, well-tempered metadynamics simulations were employed to elucidate how molecular geometry, polycation flexibility, and charge neutralization affect the siRNA-polycations free energy landscape in term of low-energy binding modes and unbinding free energy barriers. Significant differences among polymer binding modes have been detected, revealing the advantageous binding properties of polyarginine and polylysine compared to polyethyleneimine.

Extensive Assessment of Various Computational Methods for Aspartate's pKa Shift

A series of computational methods for pK_a shift prediction are extensively tested on a set of benchmark protein systems, aiming at identifying pitfalls and evaluating their performance on high variants. Including 19 ASP residues in 10 protein systems, the benchmark set consists of both residues with highly shifted pK_a values as well as those varying little from the reference value, with an experimental RMS free energy differences of 2.49 kcal/mol with respect to blocked amino acid, namely the RMS pK_a shift being 1.82 pK_a units. The constant pH molecular dynamics (MD), alchemical methods, PROPKA3.1, and multiconformation continuum electrostatics give RMSDs of 1.52, 2.58, 1.37, and 3.52 pK_a units, respectively, on the benchmark set. The empirical scoring method is the most accurate one with extremely low computational cost, and the pH-dependent model is also able to provide accurate results, while the accuracy of MD sampling incorporating alchemical free energy simulation is prohibited by convergence achievement and the performance of conformational search incorporating multiconformation continuum electrostatics is bad. Former research works did not define statistical uncertainty with care and yielded the questionable conclusion that alchemical methods perform well in most benchmarks. In this work the traditional alchemical methods are thoroughly tested for high variants. We also performed the first application of nonequilibrium alchemical methods to the pK_a cases.

Control of the hierarchical assembly of π-conjugated optoelectronic peptides by pH and flow

Coarse-grained molecular simulations reveal the influence of pH and flow on the self-assembly of DFAG-OPV3-GAFD optoelectronic peptides.

Effect of a buried ion pair in the hydrophobic core of a protein: An insight from constant pH molecular dynamics study

Constant pH molecular dynamics (CpHMD) is a commonly used sampling method, which incorporates the coupling of conformational flexibility and protonation state of a protein during the simulation by using pH as an external parameter. The effects on the structure and stability of a hyperstable variant of staphylococcal nuclease (Δ+PHS) protein of an artificial charge pair buried in its hydrophobic core are investigated by applying both CpHMD and accelerated molecular dynamics coupled with constant pH (CpHaMD) methods. Generalized Born electrostatics is used to model the solvent water. Two sets of starting coordinates of V23E/L36K variant of Δ+PHS, namely, Maestro generated coordinates from Δ+PHS and crystal structure coordinates of the same are considered for detail investigations. On the basis of root mean square displacement (RMSD) and root mean square fluctuations (RMSF) calculations, it is observed that this variant is stable over a wide range of pH. The calculated pKa values for aspartate and glutamate residues based on both CpHMD and CpHaMD simulations are consistent with the reported experimental values (within ± 0.5 to ± 1.5 pH unit), which clearly indicates that the local chemical environment of the carboxylic acids in V23E/L36K variant are comparable to the parent form. The strong salt bridge interaction between the mutated pair, E23/K36 and additional hydrogen bonds formed in the V23E/L36K variant, may help to compensate for the unfavorable self-energy experienced by the burial of these residues in the hydrophobic core. However, from RMSD, RMSF, and pKa analysis, no significant change in the global conformation of V23E/L36K variant with respect to the parent form, Δ+PHS is noticed.

Coarse-grained modeling of RNA 3D structure

Functional RNA molecules depend on three-dimensional (3D) structures to carry out their tasks within the cell. Understanding how these molecules interact to carry out their biological roles requires a detailed knowledge of RNA 3D structure and dynamics as well as thermodynamics, which strongly governs the folding of RNA and RNA-RNA interactions as well as a host of other interactions within the cellular environment. Experimental determination of these properties is difficult, and various computational methods have been developed to model the folding of RNA 3D structures and their interactions with other molecules. However, computational methods also have their limitations, especially when the biological effects demand computation of the dynamics beyond a few hundred nanoseconds. For the researcher confronted with such challenges, a more amenable approach is to resort to coarse-grained modeling to reduce the number of data points and computational demand to a more tractable size, while sacrificing as little critical information as possible. This review presents an introduction to the topic of coarse-grained modeling of RNA 3D structures and dynamics, covering both high- and low-resolution strategies. We discuss how physics-based approaches compare with knowledge based methods that rely on databases of information. In the course of this review, we discuss important aspects in the reasoning process behind building different models and the goals and pitfalls that can result.

Charge-Neutral Constant pH Molecular Dynamics Simulations Using a Parsimonious Proton Buffer

In constant pH molecular dynamics simulations, the protonation states of titratable sites can respond to changes of the pH and of their electrostatic environment. Consequently, the number of protons bound to the biomolecule, and therefore the overall charge of the system, fluctuates during the simulation. To avoid artifacts associated with a non-neutral simulation system, we introduce an approach to maintain neutrality of the simulation box in constant pH molecular dynamics simulations, while maintaining an accurate description of all protonation fluctuations. Specifically, we introduce a proton buffer that, like a buffer in experiment, can exchange protons with the biomolecule enabling its charge to fluctuate. To keep the total charge of the system constant, the uptake and release of protons by the buffer are coupled to the titration of the biomolecule with a constraint. We find that, because the fluctuation of the total charge (number of protons) of a typical biomolecule is much smaller than the number of titratable sites of the biomolecule, the number of buffer sites required to maintain overall charge neutrality without compromising the charge fluctuations of the biomolecule, is typically much smaller than the number of titratable sites, implying markedly enhanced simulation and sampling efficiency.

Computation of pH-dependent binding free energies

Protein-ligand binding accompanies changes in the surrounding electrostatic environments of the two binding partners and may lead to changes in protonation upon binding. In cases where the complex formation results in a net transfer of protons, the binding process is pH-dependent. However, conventional free energy computations or molecular docking protocols typically employ fixed protonation states for the titratable groups in both binding partners set a priori, which are identical for the free and bound states. In this review, we draw attention to these important yet largely ignored binding-induced protonation changes in protein-ligand association by outlining physical origins and prevalence of the protonation changes upon binding. Following a summary of various theoretical methods for pKa prediction, we discuss the theoretical framework to examine the pH dependence of protein-ligand binding processes.

pKa predictions for proteins, RNAs, and DNAs with the Gaussian dielectric function using DelPhi pKa

We developed a Poisson-Boltzmann based approach to calculate the pKa values of protein ionizable residues (Glu, Asp, His, Lys and Arg), nucleotides of RNA and single stranded DNA. Two novel features were utilized: the dielectric properties of the macromolecules and water phase were modeled via the smooth Gaussian-based dielectric function in DelPhi and the corresponding electrostatic energies were calculated without defining the molecular surface. We tested the algorithm by calculating pKa values for more than 300 residues from 32 proteins from the PPD dataset and achieved an overall RMSD of 0.77. Particularly, the RMSD of 0.55 was achieved for surface residues, while the RMSD of 1.1 for buried residues. The approach was also found capable of capturing the large pKa shifts of various single point mutations in staphylococcal nuclease (SNase) from pKa-cooperative dataset, resulting in an overall RMSD of 1.6 for this set of pKa's. Investigations showed that predictions for most of buried mutant residues of SNase could be improved by using higher dielectric constant values. Furthermore, an option to generate different hydrogen positions also improves pKa predictions for buried carboxyl residues. Finally, the pKa calculations on two RNAs demonstrated the capability of this approach for other types of biomolecules.

Computational scheme for pH-dependent binding free energy calculation with explicit solvent

We present a computational scheme to compute the pH‐dependence of binding free energy with explicit solvent. Despite the importance of pH, the effect of pH has been generally neglected in binding free energy calculations because of a lack of accurate methods to model it. To address this limitation, we use a constant‐pH methodology to obtain a true ensemble of multiple protonation states of a titratable system at a given pH and analyze the ensemble using the Bennett acceptance ratio (BAR) method. The constant pH method is based on the combination of enveloping distribution sampling (EDS) with the Hamiltonian replica exchange method (HREM), which yields an accurate semi‐grand canonical ensemble of a titratable system. By considering the free energy change of constraining multiple protonation states to a single state or releasing a single protonation state to multiple states, the pH dependent binding free energy profile can be obtained. We perform benchmark simulations of a host‐guest system: cucurbit[7]uril (CB[7]) and benzimidazole (BZ). BZ experiences a large pK_a shift upon complex formation. The pH‐dependent binding free energy profiles of the benchmark system are obtained with three different long‐range interaction calculation schemes: a cutoff, the particle mesh Ewald (PME), and the isotropic periodic sum (IPS) method. Our scheme captures the pH‐dependent behavior of binding free energy successfully. Absolute binding free energy values obtained with the PME and IPS methods are consistent, while cutoff method results are off by 2 kcal mol⁻¹. We also discuss the characteristics of three long‐range interaction calculation methods for constant‐pH simulations.

Short-time dynamics of pH-dependent conformation and substrate binding in the active site of beta-glucosidases: A computational study

The complete degradation of cellulose to glucose is essential to carbon turnover in terrestrial ecosystems and to engineered biofuel production. A rate-limiting step in this pathway is catalyzed by beta-glucosidase (BG) enzymes, which convert cellulobiose into two glucose molecules. The activity of these enzymes has been shown to vary with solution pH. However, it is not well understood how pH influences the enzyme conformation required for catalytic action on the substrate. A structural understanding of this pH effect is important for predicting shifts in BG activity in bioreactors and environmental matrices, in addition to informing targeted protein engineering. Here we applied molecular dynamics simulations to explore conformational and substrate binding dynamics in two well-characterized BGs of bacterial (Clostridium cellulovorans) and fungal (Trichoderma reesei) origins as a function of pH. The enzymes were simulated in an explicit solvated environment, with NaCl as electrolytes, at their prominent ionization states obtained at pH 5, 6, 7, and 7.5. Our findings indicated that pH-dependent changes in the ionization states of non-catalytic residues localized outside of the immediate active site led to pH-dependent disruption of the active site conformation. This disruption interferes with favorable H-bonding interactions with catalytic residues required to initiate catalysis on the substrate. We also identified specific non-catalytic residues that are involved in stabilizing the substrate at the optimal pH for enzyme activity. The simulations further revealed the dynamics of water-bridging interactions both outside and inside the substrate binding cleft during structural changes in the enzyme-substrate complex. These findings provide new structural insights into the pH-dependent substrate binding specificity in BGs.

Constant pH molecular dynamics study on the doubly mutated staphylococcal nuclease: capturing the microenvironment

Small rearrangements of residues in the microenvironment of V23E/L36K variant of staphylococcal nuclease can effectively be captured by CpHMD method.

Constant pH Molecular Dynamics in Explicit Solvent with Enveloping Distribution Sampling and Hamiltonian Exchange

We present a new computational approach for constant pH simulations in explicit solvent based on the combination of the enveloping distribution sampling (EDS) and Hamiltonian replica exchange (HREX) methods. Unlike constant pH methods based on variable and continuous charge models, our method is based on discrete protonation states. EDS generates a hybrid Hamiltonian of different protonation states. A smoothness parameter s is used to control the heights of energy barriers of the hybrid-state energy landscape. A small s value facilitates state transitions by lowering energy barriers. Replica exchange between EDS potentials with different s values allows us to readily obtain a thermodynamically accurate ensemble of multiple protonation states with frequent state transitions. The analysis is performed with an ensemble obtained from an EDS Hamiltonian without smoothing, s = ∞, which strictly follows the minimum energy surface of the end states. The accuracy and efficiency of this method is tested on aspartic acid, lysine, and glutamic acid, which have two protonation states, a histidine with three states, a four-residue peptide with four states, and snake cardiotoxin with eight states. The pKa values estimated with the EDS-HREX method agree well with the experimental pKa values. The mean absolute errors of small benchmark systems range from 0.03 to 0.17 pKa units, and those of three titratable groups of snake cardiotoxin range from 0.2 to 1.6 pKa units. This study demonstrates that EDS-HREX is a potent theoretical framework, which gives the correct description of multiple protonation states and good calculated pKa values.

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.

Constant pH molecular dynamics of proteins in explicit solvent with proton tautomerism

pH is a ubiquitous regulator of biological activity, including protein-folding, protein-protein interactions, and enzymatic activity. Existing constant pH molecular dynamics (CPHMD) models that were developed to address questions related to the pH-dependent properties of proteins are largely based on implicit solvent models. However, implicit solvent models are known to underestimate the desolvation energy of buried charged residues, increasing the error associated with predictions that involve internal ionizable residue that are important in processes like hydrogen transport and electron transfer. Furthermore, discrete water and ions cannot be modeled in implicit solvent, which are important in systems like membrane proteins and ion channels. We report on an explicit solvent constant pH molecular dynamics framework based on multi-site λ-dynamics (CPHMD(MSλD)). In the CPHMD(MSλD) framework, we performed seamless alchemical transitions between protonation and tautomeric states using multi-site λ-dynamics, and designed novel biasing potentials to ensure that the physical end-states are predominantly sampled. We show that explicit solvent CPHMD(MSλD) simulations model realistic pH-dependent properties of proteins such as the Hen-Egg White Lysozyme (HEWL), binding domain of 2-oxoglutarate dehydrogenase (BBL) and N-terminal domain of ribosomal protein L9 (NTL9), and the pKa predictions are in excellent agreement with experimental values, with a RMSE ranging from 0.72 to 0.84 pKa units. With the recent development of the explicit solvent CPHMD(MSλD) framework for nucleic acids, accurate modeling of pH-dependent properties of both major class of biomolecules-proteins and nucleic acids is now possible.

Capturing molten globule state of α-lactalbumin through constant pH molecular dynamics simulations

The recently developed methods of constant pH molecular dynamics directly captures the correlation between protonation and conformation to probe protein structure, function, and dynamics. In this work, we investigate the effect of pH on the conformational properties of the protein human α-lactalbumin. Constant pH simulations at both acidic and alkaline medium indicate the formation of the molten globule state, which is in accordance with the previous experimental observations (especially, in acidic medium). The size of the protein measured by its radius of gyration (RG) exhibits a marked increase in both acidic and alkaline medium, which matches with the corresponding experimentally observed value of RG found in the molten globule. The probability of native contacts is also considerably reduced at acidic and basic pH as compared to that of native structure crystallized at neutral pH. The mean fractal dimension D2 of the protein records a sharp increase in basic medium as compared to those in neutral and acidic solutions implying a significant pH induced conformational change. The mean square fluctuations of all residues of the entire protein are found to increase by several folds in both acidic and basic medium, which may be correlated with the normalized solvent accessibility of the residues indicating role of solvent accessible surface area on protein internal dynamics. The helices comprising the α-domain of the protein are moderately preserved in the acidic and alkaline pH. However, the β-sheet structures present in the β-domain are completely disrupted in both acidic as well as basic pH.

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.

pH-sensitive residues in the p19 RNA silencing suppressor protein from carnation Italian ringspot virus affect siRNA binding stability

Tombusviruses, such as Carnation Italian ringspot virus (CIRV), encode a protein homodimer called p19 that is capable of suppressing RNA silencing in their infected hosts by binding to and sequestering short-interfering RNA (siRNA) away from the RNA silencing pathway. P19 binding stability has been shown to be sensitive to changes in pH but the specific amino acid residues involved have remained unclear. Using constant pH molecular dynamics simulations, we have identified key pH-dependent residues that affect CIRV p19-siRNA binding stability at various pH ranges based on calculated changes in the free energy contribution from each titratable residue. At high pH, the deprotonation of Lys60, Lys67, Lys71, and Cys134 has the largest effect on the binding stability. Similarly, deprotonation of several acidic residues (Asp9, Glu12, Asp20, Glu35, and/or Glu41) at low pH results in a decrease in binding stability. At neutral pH, residues Glu17 and His132 provide a small increase in the binding stability and we find that the optimal pH range for siRNA binding is between 7.0 and 10.0. Overall, our findings further inform recent experiments and are in excellent agreement with data on the pH-dependent binding profile.

pH-dependent dynamics of complex RNA macromolecules

The role of pH-dependent protonation equilibrium in modulating RNA dynamics and function is one of the key unanswered questions in RNA biology. Molecular dynamics (MD) simulations can provide insight into the mechanistic roles of protonated nucleotides, but it is only capable of modeling fixed protonation states and requires prior knowledge of the key residue's protonation state. Recently, we developed a framework for constant pH molecular dynamics simulations (CPHMDMSλD) of nucleic acids, where the nucleotides' protonation states are modeled as dynamic variables that are coupled to the structural dynamics of the RNA. In the present study, we demonstrate the application of CPHMDMSλD to the lead-dependent ribozyme; establishing the validity of this approach for modeling complex RNA structures. We show that CPHMDMSλD accurately predicts the direction of the pKa shifts and reproduces experimentally-measured microscopic pKa values with an average unsigned error of 1.3 pKa units. The effects of coupled titration states in RNA structures are modeled, and the importance of conformation sampling is highlighted. The general accuracy of CPHMDMSλD simulations in reproducing pH-dependent observables reported in this work demonstrates that constant pH simulations provides a powerful tool to investigate pH-dependent processes in nucleic acids.

Simulation studies of the mechanism of membrane transporters

Membrane transporters facilitate active transport of their specific substrates, often against their electrochemical gradients across the membrane, through coupling the process to various sources of cellular energy, for example, ATP binding and hydrolysis in primary transporters, and pre-established electrochemical gradient of molecular species other than the substrate in the case of secondary transporters. In order to provide efficient energy-coupling mechanisms, membrane transporters have evolved into molecular machines in which stepwise binding, translocation, and transformation of various molecular species are closely coupled to protein conformational changes that take the transporter from one functional state to another during the transport cycle. Furthermore, in order to prevent the formation of leaky states and to be able to pump the substrate against its electrochemical gradient, all membrane transporters use the widely-accepted "alternating access mechanism," which ensures that the substrate is only accessible from one side of the membrane at a given time, but relies on complex and usually global protein conformational changes that differ for each family of membrane transporters. Describing the protein conformational changes of different natures and magnitudes is therefore at the heart of mechanistic studies of membrane transporters. Here, using a number of membrane transporters from diverse families, we present common protocols used in setting up and performing molecular dynamics simulations of membrane transporters and in analyzing the results, in order to characterize relevant motions of the system. The emphasis will be on highlighting how optimal design of molecular dynamics simulations combined with mechanistically oriented analysis can shed light onto key functionally relevant protein conformational changes in this family of membrane proteins.

Charge parametrization of the DvH-c3 heme group: validation using constant-(pH,E) molecular dynamics simulations

We studied the effect of using different heme group charge parametrization methods and schemes (Merz-Kollman, CHELPG, and single- and multiconformational RESP) on the quality of the results produced by the constant-(pH,E) MD method, applied to the redox titration of Desulfovibrio vulgaris Hildenborough cytochrome c(3). These new and more accurate charge sets enabled us to overcome the previously reported dependence of the method's performance on the dielectric constant, ε, assigned to the protein region. In particular, we found a systematic, clear shift of the E(mod) toward more negative values than those previously reported, in agreement with an electrostatics based reasoning. The simulations showed strong coupling between protonating/redox sites. We were also able to capture significant direct and, especially, indirect interactions between hemes, such as those mediated by histidine 67. Our results highlight the importance of having a good quantum description of the system before deriving atomic partial charges for classic force fields.

pH-replica exchange molecular dynamics in proteins using a discrete protonation method

Protonation equilibria in biological molecules modulates structure, dynamics, and function. A pH-replica exchange molecular dynamics (pH-REMD) method is described here to improve the coupling between conformational and protonation sampling. Under a Hamiltonian replica exchange setup, conformations are swapped between two neighboring replicas, which themselves are at different pHs. The method has been validated on a series of biological systems. We applied pH-REMD to a series of model compounds, to an terminally charged ADFDA pentapeptide, and to a heptapeptide derived from the ovomucoid third domain (OMTKY3). In all of those systems, the predicted pK(a) by pH-REMD is very close to the experimental value and almost identical to the ones obtained by constant pH molecular dynamics (CpH MD). The method presented here, pH-REMD, has the advantage of faster convergence properties due to enhanced sampling of both conformation and protonation spaces.

Potential of mean force of water-proton bath and molecular dynamic simulation of proteins at constant pH

An advanced implicit solvent model of water-proton bath for protein simulations at constant pH is presented. The implicit water-proton bath model approximates the potential of mean force of a protein in water solvent in a presence of hydrogen ions. Accurate and fast computational implementation of the implicit water-proton bath model is developed using the continuum electrostatic Poisson equation model for calculation of ionization equilibrium and the corrected MSR6 generalized Born model for calculation of the electrostatic atom-atom interactions and forces. Molecular dynamics (MD) method for protein simulation in the potential of mean force of water-proton bath is developed and tested on three proteins. The model allows to run MD simulations of proteins at constant pH, to calculate pH-dependent properties and free energies of protein conformations. The obtained results indicate that the developed implicit model of water-proton bath provides an efficient way to study thermodynamics of biomolecular systems as a function of pH, pH-dependent ionization-conformation coupling, and proton transfer events.

Constant pH Molecular Dynamics Simulations of Nucleic Acids in Explicit Solvent

The nucleosides of adenine and cytosine have pKa values of 3.50 and 4.08, respectively, and are assumed to be unprotonated under physiological conditions. However, evidence from recent NMR and X-Ray crystallography studies has revealed the prevalence of protonated adenine and cytosine in RNA macromolecules. Such nucleotides with elevated pKa values may play a role in stabilizing RNA structure and participate in the mechanism of ribozyme catalysis. With the work presented here, we establish the framework and demonstrate the first constant pH MD simulations (CPHMD) for nucleic acids in explicit solvent in which the protonation state is coupled to the dynamical evolution of the RNA system via λ-dynamics. We adopt the new functional form λ(Nexp) for λ that was recently developed for Multi-Site λ-Dynamics (MSλD) and demonstrate good sampling characteristics in which rapid and frequent transitions between the protonated and unprotonated states at pH = pKa are achieved. Our calculated pKa values of simple nucleotides are in a good agreement with experimentally measured values, with a mean absolute error of 0.24 pKa units. This work demonstrates that CPHMD can be used as a powerful tool to investigate pH-dependent biological properties of RNA macromolecules.

Probing pH-dependent dissociation of HdeA dimers

HdeA protein is a small, ATP-independent, acid stress chaperone that undergoes a dimer-to-monomer transition in acidic environments. The HdeA monomer binds a broad range of proteins to prevent their acid-induced aggregation. To understand better HdeA's function and mechanism, we perform constant-pH molecular dynamics simulations (CPHMD) to elucidate the details of the HdeA dimer dissociation process. First the pK(a) values of all the acidic titratable groups in HdeA are obtained and reveal a large pK(a) shift only for Glu(37). However, the pH-dependent monomer charge exhibits a large shift from -4 at pH > 6 to +6 at pH = 2.5, suggesting that the dramatic change in charge on each monomer may drive dissociation. By combining the CPHMD approach with umbrella sampling, we demonstrate a significant stability decrease of the HdeA dimer when the environmental pH changes from 4.0 to 3.5 and identify the key acidic residue-lysine interactions responsible for the observed pH sensing in HdeA chaperon activity function.

pH replica-exchange method based on discrete protonation states

We propose a new algorithm for obtaining proton titration curves of ionizable residues. The algorithm is a pH replica-exchange method (PHREM), which is based on the constant pH algorithm of Mongan et al. (J Comput Chem 2004;25:2038-2048). In the original replica-exchange method, simulations of different replicas are performed at different temperatures, and the temperatures are exchanged between the replicas. In our PHREM, simulations of different replicas are performed at different pH values, and the pHs are exchanged between the replicas. The PHREM was applied to a blocked amino acid and to two protein systems (snake cardiotoxin and turkey ovomucoid third domain), in conjunction with a generalized Born implicit solvent. The performance and accuracy of this algorithm and the original constant pH method (PHMD) were compared. For a single set of simulations at different pHs, the use of PHREM yields more accurate Hill coefficients of titratable residues. By performing multiple sets of constant pH simulations started with different initial states, the accuracy of predicted pK(a) values and Hill coefficients obtained with PHREM and PHMD methods becomes comparable. However, the PHREM algorithm exhibits better samplings of the protonation states of titratable residues and less scatter of the titration points and thus better precision of measured pK(a) values and Hill coefficients. In addition, PHREM exhibits faster convergence of individual simulations than the original constant pH algorithm.

Predicting pKa values with continuous constant pH molecular dynamics

Knowledge of pK(a) values is important for understanding structure and function relationships in proteins. Over the past two decades, theoretical methods for pK(a) calculations have been mainly based on macroscopic models, in which the protein is considered as a low-dielectric cavity embedded in a high-dielectric continuum. In recent years, constant pH molecular dynamics methods have been developed based on a microscopic description of the protein. We describe here the methodology of continuous constant pH molecular dynamics (CPHMD), which has emerged as one of the most robust and accurate tools for predicting protein pK(a)s and for the study of pH-modulated conformational dynamics. We illustrate the utility of CPHMD by the calculation of pK(a)s for surface residues in ribonuclease A, buried residues in staphylococcal nuclease, and titratable groups in the intrinsically flexible protein α-lactalbumin. We will compare the CPHMD results with experimental data as well as calculations from PB-based and empirical methods. These examples demonstrate the accuracy and robustness of the CPHMD method and its ability to capture the correlation between ionization equilibria and conformational dynamics as well as the local dielectric response to structural rearrangement. Finally, we discuss future improvement of the CPHMD method.

Measuring the successes and deficiencies of constant pH molecular dynamics: a blind prediction study

A constant pH molecular dynamics method has been used in the blind prediction of pK_a values of titratable residues in wild type and mutated structures of the Staphylococcal nuclease (SNase) protein. The predicted values have been subsequently compared to experimental values provided by the laboratory of García-Moreno. CpHMD performs well in predicting the pK_a of solvent-exposed residues. For residues in the protein interior, the CpHMD method encounters some difficulties in reaching convergence and predicting the pK_a values for residues having strong interactions with neighboring residues. These results show the need to accurately and sufficiently sample conformational space in order to obtain pK_a values consistent with experimental results.

Electrostatics in proteins and protein-ligand complexes

Accurate computational methods for predicting electrostatic energies are of major importance for our understanding of protein energetics in general for computer-aided drug design as well as for the design of novel biocatalysts and protein therapeutics. Electrostatic energies are of particular importance in such applications as virtual screening, drug design and protein-protein docking due to the high charge density of protein ligands and small-molecule drugs, and the frequent protonation state changes observed when drugs bind to their protein targets. Therefore, the development of a reliable and fast algorithm for the evaluation of electrostatic free energies, as an important contributor to the overall protein energy function, has been the focus for many scientists over the past three decades. In this review we describe the current state-of-the-art in modeling electrostatic effects in proteins and protein-ligand complexes. We focus mainly on the merits and drawbacks of the continuum methodology, and speculate on future directions in refining algorithms for calculating electrostatic energies in proteins using experimental data.

Constant pH Molecular Dynamics in Explicit Solvent with λ-Dynamics

pH is an important parameter in condensed-phase systems, because it determines the protonation state of titratable groups and thus influences the structure, dynamics, and function of molecules in solution. In most force field simulation protocols, however, the protonation state of a system (rather than its pH) is kept fixed and cannot adapt to changes of the local environment. Here, we present a method, implemented within the MD package GROMACS, for constant pH molecular dynamics simulations in explicit solvent that is based on the λ-dynamics approach. In the latter, the dynamics of the titration coordinate λ, which interpolates between the protonated and deprotonated states, is driven by generalized forces between the protonated and deprotonated states. The hydration free energy, as a function of pH, is included to facilitate constant pH simulations. The protonation states of titratable groups are allowed to change dynamically during a simulation, thus reproducing average protonation probabilities at a certain pH. The accuracy of the method is tested against titration curves of single amino acids and a dipeptide in explicit solvent.

Histidine-mediated pH-sensitive regulation of M-ficolin:GlcNAc binding activity in innate immunity examined by molecular dynamics simulations

BACKGROUND

M-ficolin, a pathogen recognition molecule in the innate immune system, binds sugar residues including N-acetyl-D-glucosamine (GlcNAc), which is displayed on invading microbes and on apoptotic cells. The cis and trans Asp282-Cys283 peptide bond in the M-ficolin, which was found to occur at neutral and acidic pH in crystal structures, has been suggested to represent binding and non-binding activity, respectively. A detailed understanding of the pH-dependent conformational changes in M-ficolin and pH-mediated discrimination mechanism of GlcNAc-binding activity are crucial to both immune-surveillance and clearance of apoptotic cells.

METHODOLOGY/PRINCIPAL FINDINGS

By immunodetection analysis, we found that the pH-sensitive binding of GlcNAc is regulated by a conformational equilibrium between the active and inactive states of M-ficolin. We performed constant pH molecular dynamics (MD) simulation at a series of pH values to explore the pH effect on the cis-trans isomerization of the Asp282-Cys283 peptide bond in the M-ficolin fibrinogen-like domain (FBG). Analysis of the hydrogen bond occupancy of wild type FBG compared with three His mutants (H251A, H284A and H297A) corroborates that His284 is indispensible for pH-dependent binding. H251A formed new but weaker hydrogen bonds with GlcNAc. His297, unlike the other two His mutants, is more dependent on the solution pH and also contributes to cis-trans isomerization of the Asp282-Cys283 peptide bond in weak basic solution.

CONCLUSIONS/SIGNIFICANCE

Constant pH MD simulation indicated that the cis active isomer of Asp282-Cys283 peptide bond was predominant around neutral pH while the trans bond gradually prevailed towards acidic environment. The protonation of His284 was found to be associated with the trans-to-cis isomerization of Asp282-Cys283 peptide bond which dominantly regulates the GlcNAc binding. Our MD simulation approach provides an insight into the pH-sensitive proteins and hence, ligand binding activity.

Conformational relaxation and water penetration coupled to ionization of internal groups in proteins

Molecular dynamics simulations were used to examine the effects of ionization of internal groups on the structures of eighteen variants of staphylococcal nuclease (SNase) with internal Lys, Asp, or Glu. In most cases the RMSD values of internal ionizable side chains were larger when the ionizable moieties were charged than when they were neutral. Calculations of solvent-accessible surface area showed that the internal ionizable side chains were buried in the protein interior when they were neutral and moved toward crevices and toward the protein-water interface when they were charged. The only exceptions are Lys-36, Lys-62, and Lys-103, which remained buried even after charging. With the exception of Lys-38, the number of internal water molecules surrounding the ionizable group increased upon charging: the average number of water oxygen atoms within the first hydration shell increased by 1.7 for Lys residues, by 5.2 for Asp residues, and by 3.2 for Glu residues. The polarity of the microenvironment of the ionizable group also increased when the groups were charged: the average number of polar atoms of any kind within the first hydration shell increased by 2.7 for Lys residues, by 4.8 for Asp residues, and by 4.0 for Glu residues. An unexpected correlation was observed between the absolute value of the shifts in pK(a) values measured experimentally, and several parameters of structural relaxation: the net difference in the polarity of the microenvironment of the charged and neutral forms of the ionizable groups, the net difference in hydration of the charged and neutral forms of the ionizable groups, and the difference in RMSD values of the charged and neutral forms of the ionizable groups. The effects of ionization of internal groups on the conformation of the backbone were noticeable but mostly small and localized to the area immediately next to the internal ionizable moiety. Some variants did exhibit local unfolding.

Constant pH replica exchange molecular dynamics in biomolecules using a discrete protonation model

A constant pH replica exchange molecular dynamics (REMD) method is proposed and implemented to improve coupled protonation and conformational state sampling. By mixing conformational sampling at constant pH (with discrete protonation states) with a temperature ladder, this method avoids conformational trapping. Our method was tested and applied to seven different biological systems. The constant pH REMD not only predicted pKa correctly for small, model compounds but also converged faster than constant pH molecular dynamics (MD). We further tested our constant pH REMD on a heptapeptide from ovomucoid third domain (OMTKY3). Although constant pH REMD and MD produced very close pKa values, the constant pH REMD showed its advantage in the efficiency of conformational and protonation state samplings.