Constant pH molecular dynamics simulations: Current status and recent applications

Force Field Limitations of All-Atom Continuous Constant pH Molecular Dynamics

All-atom constant pH molecular dynamics simulations offer a powerful tool for understanding pH-mediated and proton-coupled biological processes. As the protonation equilibria of protein sidechains are shifted by electrostatic interactions and desolvation energies, pK a values calculated from the constant pH simulations may be sensitive to the underlying protein force field and water model. Here we investigated the force field dependence of the all-atom particle mesh Ewald (PME) continuous constant pH (PME-CpHMD) simulations of a mini-protein BBL. The replica-exchange titration simulations based on the Amber ff19sb and ff14sb force fields with the respective water models showed significantly overestimated pK a downshifts for a buried histidine (His166) and for two glutamic acids (Glu141 and Glu161) that are involved in salt-bridge interactions. These errors (due to undersolvation of neutral histidines and overstabilization of salt bridges) are consistent with the previously reported pK a's based on the CHARMM c22/CMAP force field, albeit in larger magnitudes. The pK a calculations also demonstrated that ff19sb with OPC water is significantly more accurate than ff14sb with TIP3P water, and the salt-bridge related pK a downshifts can be partially alleviated by the atom-pair specific Lennard-Jones corrections (NBFIX). Together, these data suggest that the accuracies of the protonation equilibria of proteins from constant pH simulations can significantly benefit from improvements of force fields.

CHARMM at 45: Enhancements in Accessibility, Functionality, and Speed

Since its inception nearly a half century ago, CHARMM has been playing a central role in computational biochemistry and biophysics. Commensurate with the developments in experimental research and advances in computer hardware, the range of methods and applicability of CHARMM have also grown. This review summarizes major developments that occurred after 2009 when the last review of CHARMM was published. They include the following: new faster simulation engines, accessible user interfaces for convenient workflows, and a vast array of simulation and analysis methods that encompass quantum mechanical, atomistic, and coarse-grained levels, as well as extensive coverage of force fields. In addition to providing the current snapshot of the CHARMM development, this review may serve as a starting point for exploring relevant theories and computational methods for tackling contemporary and emerging problems in biomolecular systems. CHARMM is freely available for academic and nonprofit research at https://academiccharmm.org/program.

Assessment of amino acid charge states based on cryo-electron microscopy and molecular dynamics simulations of respiratory complex I

The charge states of titratable amino acid residues play a key role in the function of membrane-bound bioenergetic proteins. However, determination of these charge states both through experimental and computational approaches is extremely challenging. Cryo-EM density maps can provide insights on the charge states of titratable amino acid residues. By performing classical atomistic molecular dynamics simulations on the high resolution cryo-EM structures of respiratory complex I from Yarrowia lipolytica, we analyze the conformational and charge states of a key acidic residue in its ND1 subunit, aspartic acid D203, which is also a mitochondrial disease mutation locus. We suggest that in the native state of respiratory complex I, D203 is negatively charged and maintains a stable hydrogen bond to a conserved arginine residue. Alternatively, upon conformational change in the turnover state of the enzyme, its sidechain attains a charge-neutral status. We discuss the implications of this analysis on the molecular mechanism of respiratory complex I.

Quantifying Induced Dipole Effects in Small Molecule Permeation in a Model Phospholipid Bilayer

The cell membrane functions as a semipermeable barrier that governs the transport of materials into and out of cells. The bilayer features a distinct dielectric gradient due to the amphiphilic nature of its lipid components. This gradient influences various aspects of small molecule permeation and the folding and functioning of membrane proteins. Here, we employ polarizable molecular dynamics simulations to elucidate the impact of the electronic environment on the permeation process. We simulated eight distinct amino-acid side chain analogs within a 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine bilayer using the Drude polarizable force field (FF). Our approach includes both unbiased and umbrella sampling simulations. By using a polarizable FF, we sought to investigate explicit dipole responses in relation to local electric fields along the membrane normal. We evaluate molecular dipole moments, which exhibit variation based on their localization within the membrane, and compare the outcomes with analogous simulations using the nonpolarizable CHARMM36 FF. This comparative analysis aims to discern characteristic differences in the free energy surfaces of permeation for the various amino-acid analogs. Our results provide the first systematic quantification of the impact of employing an explicitly polarizable FF in this context compared to the fixed-charge convention inherent to nonpolarizable FFs, which may not fully capture the influence of the membrane dielectric gradient.

Simulating the Skin Permeation Process of Ionizable Molecules

It is commonly assumed that ionizable molecules, such as drugs, permeate through the skin barrier in their neutral form. By using molecular dynamics simulations of the charged and neutral states separately, we can study the dynamic protonation behavior during the permeation process. We have studied three weak acids and three weak bases and conclude that the acids are ionized to a larger extent than the bases, when passing through the headgroup region of the lipid barrier structure, at pH values close to their pKa. It can also be observed that even if these dynamic protonation simulations are informative, in the cases studied herein they are not necessary for the calculation of permeability coefficients. It is sufficient to base the calculations only on the neutral form, as is commonly done.

Resolving coupled pH titrations using alchemical free energy calculations

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

In Silico Study of the Early Stages of Aggregation of β-Sheet Forming Antimicrobial Peptide GL13K

Antimicrobial peptides (AMPs) are of growing interest as potential candidates that may offer more resilience against antimicrobial resistance than traditional antibiotic agents. In this article, we perform the first in silico study of the synthetic ß sheet-forming AMP GL13K. Through atomistic simulations of single and multi-peptide systems under different conditions, we are able to shine a light on the short timescales of early aggregation. We find that isolated peptide conformations are primarily dictated by sequence rather than charge, whereas changing charge has a significant impact on the conformational free energy landscape of multi-peptide systems. We demonstrate that the loss of charge-charge repulsion is a sufficient minimal model for experimentally observed aggregation. Overall, our work explores the molecular biophysical underpinnings of the first stages of aggregation of a unique AMP, laying necessary groundwork for its further development as an antibiotic candidate.

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

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

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

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

High Charge Density in Peptide Dendrimers is Required to Destabilize Membranes: Insights into Endosome Evasion

Peptide dendrimers are a type of branched, symmetric, and topologically well-defined molecule that have already been used as delivery systems for nucleic acid transfection. Several of the most promising sequences showed high efficiency in many key steps of transfection, namely, binding siRNA, entering cells, and evading the endosome. However, small changes to the peptide dendrimers, such as in the hydrophobic core, the amino acid chirality, or the total available charges, led to significantly different experimental results with unclear mechanistic insights. In this work, we built a computational model of several of those peptide dendrimers (MH18, MH13, and MH47) and some of their variants to study the molecular details of the structure and function of these molecules. We performed CpHMD simulations in the aqueous phase and in interaction with a lipid bilayer to assess how conformation and protonation are affected by pH in different environments. We found that while the different peptide dendrimer sequences lead to no substantial structural differences in the aqueous phase, the total charge and, more importantly, the total charge density are key for the capacity of the dendrimer to interact and destabilize the membrane. These dendrimers become highly charged when the pH changes from 7.5 to 4.5, and the presence of a high charge density, which is decreased for MH47 that has four fewer titratable lysines, is essential to trigger membrane destabilization. These findings are in excellent agreement with the experimental data and help us to understand the high efficiency of some dendrimers and why the dendrimer MH47 is unable to complete the transfection process. This evidence provides further understanding of the mode of action of these peptide dendrimers and will be pivotal for the future design of new sequences with improved transfection capabilities.

Perspective on Integrative Simulations of Bioenergetic Domains

Bioenergetic processes in cells, such as photosynthesis or respiration, integrate many time and length scales, which makes the simulation of energy conversion with a mere single level of theory impossible. Just like the myriad of experimental techniques required to examine each level of organization, an array of overlapping computational techniques is necessary to model energy conversion. Here, a perspective is presented on recent efforts for modeling bioenergetic phenomena with a focus on molecular dynamics simulations and its variants as a primary method. An overview of the various classical, quantum mechanical, enhanced sampling, coarse-grained, Brownian dynamics, and Monte Carlo methods is presented. Example applications discussed include multiscale simulations of membrane-wide electron transport, rate kinetics of ATP turnover from electrochemical gradients, and finally, integrative modeling of the chromatophore, a photosynthetic pseudo-organelle.

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

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

Role of Protonation States in the Stability of Molecular Dynamics Simulations of High-Resolution Membrane Protein Structures

Classical molecular dynamics (MD) simulations provide unmatched spatial and time resolution of protein structure and function. However, the accuracy of MD simulations often depends on the quality of force field parameters and the time scale of sampling. Another limitation of conventional MD simulations is that the protonation states of titratable amino acid residues remain fixed during simulations, even though protonation state changes coupled to conformational dynamics are central to protein function. Due to the uncertainty in selecting protonation states, classical MD simulations are sometimes performed with all amino acids modeled in their standard charged states at pH 7. Here, we performed and analyzed classical MD simulations on high-resolution cryo-EM structures of two large membrane proteins that transfer protons by catalyzing protonation/deprotonation reactions. In simulations performed with titratable amino acids modeled in their standard protonation (charged) states, the structure diverges far from its starting conformation. In comparison, MD simulations performed with predetermined protonation states of amino acid residues reproduce the structural conformation, protein hydration, and protein-water and protein-protein interactions of the structure much better. The results support the notion that it is crucial to perform basic protonation state calculations, especially on structures where protonation changes play an important functional role, prior to the launch of any conventional MD simulations. Furthermore, the combined approach of fast protonation state prediction and MD simulations can provide valuable information about the charge states of amino acids in the cryo-EM sample. Even though accurate prediction of protonation states in proteinaceous environments currently remains a challenge, we introduce an approach of combining pKa prediction with cryo-EM density map analysis that helps in improving not only the protonation state predictions but also the atomic modeling of density data.

Perspectives on Computational Enzyme Modeling: From Mechanisms to Design and Drug Development

Understanding enzyme mechanisms is essential for unraveling the complex molecular machinery of life. In this review, we survey the field of computational enzymology, highlighting key principles governing enzyme mechanisms and discussing ongoing challenges and promising advances. Over the years, computer simulations have become indispensable in the study of enzyme mechanisms, with the integration of experimental and computational exploration now established as a holistic approach to gain deep insights into enzymatic catalysis. Numerous studies have demonstrated the power of computer simulations in characterizing reaction pathways, transition states, substrate selectivity, product distribution, and dynamic conformational changes for various enzymes. Nevertheless, significant challenges remain in investigating the mechanisms of complex multistep reactions, large-scale conformational changes, and allosteric regulation. Beyond mechanistic studies, computational enzyme modeling has emerged as an essential tool for computer-aided enzyme design and the rational discovery of covalent drugs for targeted therapies. Overall, enzyme design/engineering and covalent drug development can greatly benefit from our understanding of the detailed mechanisms of enzymes, such as protein dynamics, entropy contributions, and allostery, as revealed by computational studies. Such a convergence of different research approaches is expected to continue, creating synergies in enzyme research. This review, by outlining the ever-expanding field of enzyme research, aims to provide guidance for future research directions and facilitate new developments in this important and evolving field.

Electrostatic interactions between charge regulated spherical macroions

We study the interaction between two charge regulating spherical macroions with dielectric interior and dissociable surface groups immersed in a monovalent electrolyte solution. The charge dissociation is modelled via the Frumkin-Fowler-Guggenheim isotherm, which allows for multiple adsorption equilibrium states. The interactions are derived from the solutions of the mean-field Poisson-Boltzmann type theory with charge regulation boundary conditions. For a range of conditions we find symmetry breaking transitions from symmetric to asymmetric charge distribution exhibiting annealed charge patchiness, which results in like-charge attraction even in a univalent electrolyte-thus fundamentally modifying the nature of electrostatic interactions in charge-stabilized colloidal suspensions.

Anions and Cations Affect Amino Acid Dissociation Equilibria via Distinct Mechanisms

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

Advantages of Multidimensional Biasing in Accelerated Dynamics: Application to the Calculation of the Acid pKa for Acetic Acid

The use of accelerated sampling methods such as metadynamics has shown a significant advantage in calculations that involve infrequent events, which would otherwise require sampling a prohibitive number of configurations to determine the difference in free energies between two or more chemically distinct states such as in the calculation of acid dissociation constants Ka. In this case, the most common method is to bias the system via a single collective variable (CV) representing the coordination number of the proton donor group, which yields results in reasonable agreement with experiments. Here we study the deprotonation of acetic acid using the reactive force field ReaxFF and observe a significant dependence of Ka on the simulation box size when biasing only the coordination number CV, which is due to incomplete sampling of the deprotonated state for small simulation systems and inefficient sampling for larger ones. Incorporating a second CV representing the distance between the H3O+ cation and the acetate anion results in substantially more efficient sampling, both accelerating the dynamics and virtually eliminating the computational box size dependence.

Structure and dynamics of pteridine reductase 1: the key phenomena relevant to enzyme function and drug design

Pteridine reductase 1 (PTR1) is a folate and pterin pathway enzyme unique for pathogenic trypanosomatids. As a validated drug target, PTR1 has been the focus of recent research efforts aimed at finding more effective treatments against human parasitic diseases such as leishmaniasis or sleeping sickness. Previous PTR1-centered structural studies highlighted the enzyme characteristics, such as flexible regions around the active site, highly conserved structural waters, and species-specific differences in pocket properties and dynamics, which likely impacts the binding of natural substrates and inhibitors. Furthermore, several aspects of the PTR1 function, such as the substrate inhibition phenomenon and the level of ligand binding cooperativity in the enzyme homotetramer, likely related to the global enzyme dynamics, are poorly known at the molecular level. We postulate that future drug design efforts could greatly benefit from a better understanding of these phenomena through studying both the local and global PTR1 dynamics. This review highlights the key aspects of the PTR1 structure and dynamics relevant to structure-based drug design that could be effectively investigated by modeling approaches. Particular emphasis is given to the perspective of molecular dynamics, what has been accomplished in this area to date, and how modeling could impact the PTR1-targeted drug design in the future.

PKAD-2: New entries and expansion of functionalities of the database of experimentally measured pKa's of proteins

Almost all biological reactions are pH dependent and understanding the origin of pH dependence requires knowledge of the pKa's of ionizable groups. Here we report a new edition of PKAD, the PKAD-2, which is a database of experimentally measured pKa's of proteins, both wild type and mutant proteins. The new additions include 117 wild type and 54 mutant pKa values, resulting in total 1742 experimentally measured pKa's. The new edition of PKAD-2 includes 8 new wild type and 12 new mutant proteins, resulting in total of 220 proteins. This new edition incorporates a visual 3D image of the highlighted residue of interest within the corresponding protein or protein complex. Hydrogen bonds were identified, counted, and implemented as a search feature. Other new search features include the number of neighboring residues <4A from the heaviest atom of the side chain of a given amino acid. Here, we present PKAD-2 with the intention to continuously incorporate novel features and current data with the goal to be used as benchmark for computational methods.

Unusual Aspects of Charge Regulation in Flexible Weak Polyelectrolytes

This article reviews the state of the art of the studies on charge regulation (CR) effects in flexible weak polyelectrolytes (FWPE). The characteristic of FWPE is the strong coupling of ionization and conformational degrees of freedom. After introducing the necessary fundamental concepts, some unconventional aspects of the the physical chemistry of FWPE are discussed. These aspects are: (i) the extension of statistical mechanics techniques to include ionization equilibria and, in particular, the use of the recently proposed Site Binding-Rotational Isomeric State (SBRIS) model, which allows the calculation of ionization and conformational properties on the same foot; (ii) the recent progresses in the inclusion of proton equilibria in computer simulations; (iii) the possibility of mechanically induced CR in the stretching of FWPE; (iv) the non-trivial adsorption of FWPE on ionized surfaces with the same charge sign as the PE (the so-called "wrong side" of the isoelectric point); (v) the influence of macromolecular crowding on CR.

Basis for Accurate Protein pKa Prediction with Machine Learning

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

Molecular mechanism underlying desensitization of the proton-activated chloride channel PAC

Desensitization is a common property of membrane receptors, including ion channels. The newly identified proton-activated chloride (PAC) channel plays an important role in regulating the pH and size of organelles in the endocytic pathway, and is also involved in acid-induced cell death. However, how the PAC channel desensitizes is largely unknown. Here, we show by patch-clamp electrophysiological studies that PAC (also known as TMEM206/ASOR) undergoes pH-dependent desensitization upon prolonged acid exposure. Through structure-guided and comprehensive mutagenesis, we identified several residues critical for PAC desensitization, including histidine (H) 98, glutamic acid (E) 94, and aspartic acid (D) 91 at the extracellular extension of the transmembrane helix 1 (TM1), as well as E107, D109, and E250 at the extracellular domain (ECD)-transmembrane domain (TMD) interface. Structural analysis and molecular dynamic simulations revealed extensive interactions between residues at the TM1 extension and those at the ECD-TMD interface. These interactions likely facilitate PAC desensitization by stabilizing the desensitized conformation of TM1, which undergoes a characteristic rotational movement from the resting and activated states to the desensitized state. Our studies establish a new paradigm of channel desensitization in this ubiquitously expressed ion channel and pave the way for future investigation of its relevance in cellular physiology and disease.