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

Toward Accurate pH-Dependent Binding Constant Predictions Using Molecular Docking and Constant-pH MD Calculations

pH is an important physicochemical property that modulates proteins' structure and interaction patterns. A simple change in a site's protonation state in an enzyme's catalytic pocket can strongly alter its activity and its affinity to substrate, products, or inhibitors. We addressed this pH effect issue by evaluating its impact on donepezil binding to acetylcholinesterase (AChE). We compared the binding affinities obtained from molecular docking (weighted from the protonation states sampled by constant-pH MD) with those from molecular mechanics/Poisson-Boltzmann surface area and isothermal titration calorimetry data. The computational methods showed a clear trend where donepezil binding to the catalytic cavity is improved with the drug protonation (lowering pH). However, the loss of binding affinity observed experimentally at pH 6.0 indicates that other phenomena eluding our computational approaches are occurring. Possible factors include the shape of the access tunnel to the AChE catalytic pocket (which is captured in our MD time scale) or an entropic penalty difference between neutral and protonated donepezil. Altogether, this work highlighted the need to improve our computational methods to capture the pH effects in protein/drug binding, while also exposing the limitations that will inevitably arise from these new advances.

Accurate Protein pKa Prediction with Physical Organic Chemistry Guided 3D Protein Representation

Protein pKa is a fundamental physicochemical parameter that dictates protein structure and function. However, accurately determining protein site-pKa values remains a substantial challenge, both experimentally and theoretically. In this study, we introduce a physical organic approach, leveraging a protein structural and physical-organic-parameter-based representation (P-SPOC), to develop a rapid and intuitive model for protein pKa prediction. Our P-SPOC model achieves state-of-the-art predictive accuracy, with a mean absolute error (MAE) of 0.33 pKa units. Furthermore, we have incorporated advanced protein structure prediction models, like AlphaFold2, to approximate structures for proteins lacking three-dimensional representations, which enhances the applicability of our model in the context of structure-undetermined protein research. To promote broader accessibility within the research community, an online prediction interface was also established at isyn.luoszgroup.com.

Tools for analyzing protonation states and for tracing proton transfer pathways with examples from the Rb. sphaeroides photosynthetic reaction centers

Protons participate in many reactions. In proteins, protons need paths to move in and out of buried active sites. The vectorial movement of protons coupled to electron transfer reactions establishes the transmembrane electrochemical gradient used for many reactions, including ATP synthesis. Protons move through hydrogen bonded chains of waters and hydroxy side chains via the Grotthuss mechanism and by proton binding and release from acidic and basic residues. MCCE analysis shows that proteins exist in a large number of protonation states. Knowledge of the equilibrium ensemble can provide a rational basis for setting protonation states in simulations that fix them, such as molecular dynamics (MD). The proton path into the Q_B site in the bacterial reaction centers (RCs) of Rb. sphaeroides is analyzed by MD to provide an example of the benefits of using protonation states found by the MCCE program. A tangled web of side chains and waters link the cytoplasm to Q_B. MCCE analysis of snapshots from multiple trajectories shows that changing the input protonation state of a residue in MD biases the trajectory shifting the proton affinity of that residue. However, the proton affinity of some residues is more sensitive to the input structure. The proton transfer networks derived from different trajectories are quite robust. There are some changes in connectivity that are largely restricted to the specific residues whose protonation state is changed. Trajectories with Q_B^•- are compared with earlier results obtained with Q_B [Wei et. al Photosynthesis Research volume 152, pages153-165 (2022)] showing only modest changes. While introducing new methods the study highlights the difficulty of establishing the connections between protein conformation.

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.

Electrostatics in Computational Biophysics and Its Implications for Disease Effects

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

A Fast and Interpretable Deep Learning Approach for Accurate Electrostatics-Driven pKa Predictions in Proteins

Existing computational methods for estimating pK_a values in proteins rely on theoretical approximations and lengthy computations. In this work, we use a data set of 6 million theoretically determined pK_a shifts to train deep learning models, which are shown to rival the physics-based predictors. These neural networks managed to infer the electrostatic contributions of different chemical groups and learned the importance of solvent exposure and close interactions, including hydrogen bonds. Although trained only using theoretical data, our pKAI+ model displayed the best accuracy in a test set of ∼750 experimental values. Inference times allow speedups of more than 1000× compared to physics-based methods. By combining speed, accuracy, and a reasonable understanding of the underlying physics, our models provide a game-changing solution for fast estimations of macroscopic pK_a values from ensembles of microscopic values as well as for many downstream applications such as molecular docking and constant-pH molecular dynamics simulations.

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.

How much can physics do for protein design?

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

Poor Person's pH Simulation of Membrane Proteins

pH conditions are central to the functioning of all biomolecules. However, implications of pH changes are nontrivial on a molecular scale. Though a rigorous microscopic definition of pH exists, its implementation in classical molecular dynamics (MD) simulations is cumbersome, and more so in large integral membrane systems. In this chapter, an integrative pipeline is described that combines Multi-Conformation Continuum Electrostatics (MCCE) computations with MD simulations to capture the effect of transient protonation states on the coupled conformational changes in transmembrane proteins. The core methodologies are explained, and all the software required to set up this pipeline are outlined with their key parameters. All associated analyses of structure and function are provided using two case studies, namely those of bioenergetic complexes: NADH dehydrogenase (complex I) and V_o domain of V-type ATPase. The hybrid MCCE-MD pipeline has allowed the discovery of hydrogen bond networks, ligand binding pathways, and disease-causing mutations.

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.

Improved Protocol to Tackle the pH Effects on Membrane-Inserting Peptides

Many important biological pathways rely on membrane-interacting peptides or proteins, which can alter the biophysical properties of the cell membrane by simply adsorbing to its surface to undergo a full insertion process. To study these phenomena with atomistic detail, model peptides have been used to refine the current computational methodologies. Improvements have been made with force-field parameters, enhanced sampling techniques to obtain faster sampling, and the addition of chemical-physical properties, such as pH, whose influence dramatically increases at the water/membrane interface. The pH (low) insertion peptide (pHLIP) is a peptide that inserts across a membrane bilayer depending on the pH due to the presence of a key residue (Asp14) whose acidity-induced protonation triggers the whole process. The complex nature of these peptide/membrane interactions resulted in sampling limitations of the protonation and configurational space albeit using state-of-the-art methods such as the constant-pH molecular dynamics. To address this issue and circumvent those limitations, new simulations were performed with our newly developed pH-replica exchange method using wild-type (wt)-pHLIP in different 2-oleoyl-1-palmitoyl-sn-glycero-3-phosphocholine membrane sizes. This technique provided enhanced sampling and allowed for the calculation of more complete Asp14 pK_a profiles. The conformational heterogeneity derived from strong electrostatic interactions between Asp14 and the lipid phosphate groups was identified as the source of most pK_a variability. In spite of these persistent and harder-to-equilibrate phosphate interactions, the pK_a values at deeper regions (6.0-6.2) still predicted the experimental pK of insertion (6.0) since the electrostatic perturbation decays as the residue inserts further into the membrane. We also observed that reducing the system size leads to membrane deformations where it increasingly loses the ability to accommodate the pHLIP-induced perturbations. This indicates that large membrane patches, such as 256 or even 352 lipids, are needed to obtain stable and more realistic pHLIP/membrane systems. These results strengthen our method pK_a predictive and analytical capabilities to study the intricate play of electrostatic effects of the peptide/membrane interface, granting confidence for future applications in similar systems.

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.

The Lysosomotropic Activity of Hydrophobic Weak Base Drugs is Mediated via Their Intercalation into the Lysosomal Membrane

Lipophilic weak base therapeutic agents, termed lysosomotropic drugs (LDs), undergo marked sequestration and concentration within lysosomes, hence altering lysosomal functions. This lysosomal drug entrapment has been described as luminal drug compartmentalization. Consistent with our recent finding that LDs inflict a pH-dependent membrane fluidization, we herein demonstrate that LDs undergo intercalation and concentration within lysosomal membranes. The latter was revealed experimentally and computationally by (a) confocal microscopy of fluorescent compounds and drugs within lysosomal membranes, and (b) molecular dynamics modeling of the pH-dependent membrane insertion and accumulation of an assortment of LDs, including anticancer drugs. Based on the multiple functions of the lysosome as a central nutrient sensory hub and a degradation center, we discuss the molecular mechanisms underlying the alteration of morphology and impairment of lysosomal functions as consequences of LDs’ intercalation into lysosomes. Our findings bear important implications for drug design, drug induced lysosomal damage, diseases and pertaining therapeutics.

q-Canonical Monte Carlo Sampling for Modeling the Linkage between Charge Regulation and Conformational Equilibria of Peptides

The overall charge content and the patterning of charged residues have a profound impact on the conformational ensembles adopted by intrinsically disordered proteins. These parameters can be altered by charge regulation, which refers to the effects of post-translational modifications, pH-dependent changes to charge, and conformational fluctuations that modify the pKa values of ionizable residues. Although atomistic simulations have played a prominent role in uncovering the major sequence-ensemble relationships of IDPs, most simulations assume fixed charge states for ionizable residues. This may lead to erroneous estimates for conformational equilibria if they are linked to charge regulation. Here, we report the development of a new method we term q-canonical Monte Carlo sampling for modeling the linkage between charge regulation and conformational equilibria. The method, which is designed to be interoperable with the ABSINTH implicit solvation model, operates as follows: For a protein sequence with n ionizable residues, we start with all 2n charge microstates and use a criterion based on model compound pKa values to prune down to a subset of thermodynamically relevant charge microstates. This subset is then grouped into mesostates, where all microstates that belong to a mesostate have the same net charge. Conformational distributions, drawn from a canonical ensemble, are generated for each of the charge microstates that make up a mesostate using a method we designate as proton walk sampling. This method combines Metropolis Monte Carlo sampling in conformational space with an auxiliary Markov process that enables interconversions between charge microstates along a mesostate. Proton walk sampling helps identify the most likely charge microstate per mesostate. We then use thermodynamic integration aided by the multistate Bennett acceptance ratio method to estimate the free energies for converting between mesostates. These free energies are then combined with the per-microstate weights along each mesostate to estimate standard state free energies and pH-dependent free energies for all thermodynamically relevant charge microstates. The results provide quantitative estimates of the probabilities and preferred conformations associated with every thermodynamically accessible charge microstate. We showcase the application of q-canonical sampling using two model systems. The results establish the soundness of the method and the importance of charge regulation in systems characterized by conformational heterogeneity.