Computation of pH-dependent binding free energies

Methods for Theoretical Treatment of Local Fields in Proteins and Enzymes

Electric fields generated by protein scaffolds are crucial in enzymatic catalysis. This review surveys theoretical approaches for detecting, analyzing, and comparing electric fields, electrostatic potentials, and their effects on the charge density within enzyme active sites. Pioneering methods like the empirical valence bond approach rely on evaluating ionic and covalent resonance forms influenced by the field. Strategies employing polarizable force fields also facilitate field detection. The vibrational Stark effect connects computational simulations to experimental Stark spectroscopy, enabling direct comparisons. We highlight how protein dynamics induce fluctuations in local fields, influencing enzyme activity. Recent techniques assess electric fields throughout the active site volume rather than only at specific bonds, and machine learning helps relate these global fields to reactivity. Quantum theory of atoms in molecules captures the entire electron density landscape, providing a chemically intuitive perspective on field-driven catalysis. Overall, these methodologies show protein-generated fields are highly dynamic and heterogeneous, and understanding both aspects is critical for elucidating enzyme mechanisms. This holistic view empowers rational enzyme engineering by tuning electric fields, promising new avenues in drug design, biocatalysis, and industrial applications. Future directions include incorporating electric fields as explicit design targets to enhance catalytic performance and biochemical functionalities.

Enhanced and Efficient Predictions of Dynamic Ionization through Constant-pH Adiabatic Free Energy Dynamics

Dynamic or structurally induced ionization is a critical aspect of many physical, chemical, and biological processes. Molecular dynamics (MD) based simulation approaches, specifically constant pH MD methods, have been developed to simulate ionization states of molecules or proteins under experimentally or physiologically relevant conditions. While such approaches are now widely utilized to predict ionization sites of macromolecules or to study physical or biological phenomena, they are often computationally expensive and require long simulation times to converge. In this article, using the principles of adiabatic free energy dynamics, we introduce an efficient technique for performing constant pH MD simulations within the framework of the adiabatic free energy dynamics (AFED) approach. We call the new approach pH-AFED. We show that pH-AFED provides highly accurate predictions of protein residue pKa values, with a MUE of 0.5 pKa units when coupled with driven adiabatic free energy dynamics (d-AFED), while reducing the required simulation times by more than an order of magnitude. In addition, pH-AFED can be easily integrated into most constant pH MD codes or implementations and flexibly adapted to work in conjunction with enhanced sampling algorithms that target collective variables. We demonstrate that our approaches, with both pH-AFED standalone as well as pH-AFED combined with collective variable based enhanced sampling, provide promising predictive accuracy, with a MUE of 0.6 and 0.5 pKa units respectively, on a diverse range of proteins and enzymes, ranging up to 186 residues and 21 titratable sites. Lastly, we demonstrate how this approach can be utilized to understand the in vivo performance engineered antibodies for immunotherapy.

Accurately Predicting Protein pKa Values Using Nonequilibrium Alchemy

The stability, solubility, and function of a protein depend on both its net charge and the protonation states of its individual residues. pKa is a measure of the tendency for a given residue to (de)protonate at a specific pH. Although pKa values can be resolved experimentally, theory and computation provide a compelling alternative. To this end, we assess the applicability of a nonequilibrium (NEQ) alchemical free energy method to the problem of pKa prediction. On a data set of 144 residues that span 13 proteins, we report an average unsigned error of 0.77 ± 0.09, 0.69 ± 0.09, and 0.52 ± 0.04 pK for aspartate, glutamate, and lysine, respectively. This is comparable to current state-of-the-art predictors and the accuracy recently reached using free energy perturbation methods (e.g., FEP+). Moreover, we demonstrate that our open-source, pmx-based approach can accurately resolve the pKa values of coupled residues and observe a substantial performance disparity associated with the lysine partial charges in Amber14SB/Amber99SB*-ILDN, for which an underused fix already exists.

pH and non-covalent ligand binding modulate Zika virus NS2B/NS3 protease binding site residues: Discoveries from MD and constant pH MD simulations

Zika virus (ZIKV) is a global health concern and has been linked to severe neurological pathologies. Although no medication is available yet, many efforts to develop antivirals and host cell binding inhibitors led to attractive drug-like scaffolds, mainly targeting the nonstructural NS2B/NS3 protease (NS2B/NS3pro). NS2B/NS3pro active site has several titratable residues susceptible to pH changes and ligand binding; hence, understanding these residues' protonation is essential to drug design efforts targeting the active site. Here we use in silico methods to probe non-covalent binding and its effect on pKa shifts of the active site residues on a ligand-free protease and with a non-peptidic competitive inhibitor (K_i=13.5 µM). By applying constant pH molecular dynamics, we found that the catalytic residues of the unbound NS2B/NS3pro achieved the protonation needed for the serine protease mechanism over the pH value of 8.5. Nevertheless, the protease in the holo state achieved this same scenario at lower pH values. Also, non-covalent binding affected the catalytic triad (H51, D75, and S135) by stabilizing their distances and interaction network. Thus, NS2B/NS3pro residues configuration for activity might be both pH-dependent and influenced by ligand binding. However, compound presence within the binding site destabilized the NS2B, interfering with the closed and active conformation necessary for substrate binding and catalysis. Our outcomes provide valuable insights into non-covalent inhibitor behavior and its effect on protease active site residues, impacting optimization and design of novel compounds. Communicated by Ramaswamy H. Sarma.

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

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

The Molecular Effects of Dietary Acid Load on Metabolic Disease (The Cellular PasaDoble: The Fast-Paced Dance of pH Regulation)

Metabolic diseases are becoming more common and more severe in populations adhering to western lifestyle. Since metabolic conditions are highly diet and lifestyle dependent, it is suggested that certain diets are the cause for a wide range of metabolic dysfunctions. Oxidative stress, excess calcium excretion, inflammation, and metabolic acidosis are common features in the origins of most metabolic disease. These primary manifestations of "metabolic syndrome" can lead to insulin resistance, diabetes, obesity, and hypertension. Further complications of the conditions involve kidney disease, cardiovascular disease, osteoporosis, and cancers. Dietary analysis shows that a modern "Western-style" diet may facilitate a disruption in pH homeostasis and drive disease progression through high consumption of exogenous acids. Because so many physiological and cellular functions rely on acid-base reactions and pH equilibrium, prolonged exposure of the body to more acids than can effectively be buffered, by chronic adherence to poor diet, may result in metabolic stress followed by disease. This review addresses relevant molecular pathways in mammalian cells discovered to be sensitive to acid - base equilibria, their cellular effects, and how they can cascade into an organism-level manifestation of Metabolic Syndromes. We will also discuss potential ways to help mitigate this digestive disruption of pH and metabolic homeostasis through dietary change.

Benchmark of Popular Free Energy Approaches Revealing the Inhibitors Binding to SARS-CoV-2 Mpro

The COVID-19 pandemic has killed millions of people worldwide since its outbreak in December 2019. The pandemic is caused by the SARS-CoV-2 virus whose main protease (Mpro) is a promising drug target since it plays a key role in viral proliferation and replication. Currently, developing an effective therapy is an urgent task, which requires accurately estimating the ligand-binding free energy to SARS-CoV-2 Mpro. However, it should be noted that the accuracy of a free energy method probably depends on the protein target. A highly accurate approach for some targets may fail to produce a reasonable correlation with the experiment when a novel enzyme is considered as a drug target. Therefore, in this context, the ligand-binding affinity to SARS-CoV-2 Mpro was calculated via various approaches. The molecular docking approach was manipulated using Autodock Vina (Vina) and Autodock4 (AD4) protocols to preliminarily investigate the ligand-binding affinity and pose to SARS-CoV-2 Mpro. The binding free energy was then refined using the fast pulling of ligand (FPL), linear interaction energy (LIE), molecular mechanics-Poisson-Boltzmann surface area (MM-PBSA), and free energy perturbation (FEP) methods. The benchmark results indicated that for docking calculations, Vina is more accurate than AD4, and for free energy methods, FEP is the most accurate method, followed by LIE, FPL, and MM-PBSA (FEP > LIE ≈ FPL > MM-PBSA). Moreover, atomistic simulations revealed that the van der Waals interaction is the dominant factor. The residues Thr26, His41, Ser46, Asn142, Gly143, Cys145, His164, Glu166, and Gln189 are essential elements affecting the binding process. Our benchmark provides guidelines for further investigations using computational approaches.

MHCBI: a pipeline for calculating peptide-MHC binding energy using semi-empirical quantum mechanical methods with explicit/implicit solvent models

Experimentally estimating peptide-major histocompatibility complex (pMHC) binding affinity has been quite challenging due to the many receptors and the many potential ligands implicated in it. We have thus proposed a straightforward computational methodology considering the different mechanisms involved in pMHC binding to facilitate studying such receptor-ligand interactions. We have developed a pipeline using semi-empirical quantum mechanical methods for calculating pMHC class I and II molecules' binding energy (BE). This pipeline can systematize the methodology for calculating pMHC system BE, enabling the rational design of T-cell epitopes to be used as pharmaceuticals and vaccines.

Estimating the Roles of Protonation and Electronic Polarization in Absolute Binding Affinity Simulations

Accurate prediction of binding free energies is critical to streamlining the drug development and protein design process. With the advent of GPU acceleration, absolute alchemical methods, which simulate the removal of ligand electrostatics and van der Waals interactions with the protein, have become routinely accessible and provide a physically rigorous approach that enables full consideration of flexibility and solvent interaction. However, standard explicit solvent simulations are unable to model protonation or electronic polarization changes upon ligand transfer from water to the protein interior, leading to inaccurate prediction of binding affinities for charged molecules. Here, we perform extensive simulation totaling ∼540 μs to benchmark the impact of modeling conditions on predictive accuracy for absolute alchemical simulations. Binding to urokinase plasminogen activator (UPA), a protein frequently overexpressed in metastatic tumors, is evaluated for a set of 10 inhibitors with extended flexibility, highly charged character, and titratable properties. We demonstrate that the alchemical simulations can be adapted to utilize the MBAR/PBSA method to improve the accuracy upon incorporating electronic polarization, highlighting the importance of polarization in alchemical simulations of binding affinities. Comparison of binding energy prediction at various protonation states indicates that proper electrostatic setup is also crucial in binding affinity prediction of charged systems, prompting us to propose an alternative binding mode with protonated ligand phenol and Hid-46 at the binding site, a testable hypothesis for future experimental validation.

Activation of Caspase-3 by Terpenoids and Flavonoids in Different Types of Cancer Cells

BACKGROUND

Caspase-3 is accountable for the execution of apoptosis. Recently, it has gained attention as a promising target for the discovery of natural products as anticancer agents.

METHODS

We examined the efficacy of two different sets of natural products (terpenoids and flavonoids) towards caspase-3 activity adopting in silico, cell-free and cell-based activity and real-time gene expression analysis.

RESULTS

It was observed that terpenes activate caspase-3 activity in both the cell-free and cell-based systems, which was supported by the gene expression analysis, binding energy and activation constant. Flavonoids' action, however, was limited to the cell-based system and transcriptional regulation suggesting their indirect association, which enhanced the enzyme activity and up-regulated the expression of mRNA levels in the cells. Among the tested natural products, (+) carvone was observed to be the best activator of caspase-3 in K562 (34.4 μM), WRL-68 (22.3 μM), HeLa (18.7 μM), MCF-7 (39.4 μM) and MDA-MB-231 cell lines (45.1 μM).

CONCLUSION

Overall, terpenoids have a persistent activation of caspase-3 in all the investigated systems, while flavonoids circuitously affect the enzyme activity.

Calculation of VS,max and Its Use as a Descriptor for the Theoretical Calculation of pKa Values for Carboxylic Acids

The theoretical calculation of pKa values for Brønsted acids is a challenging task that involves sophisticated and time-consuming methods. Therefore, heuristic approaches are efficient and appealing methodologies to approximate these values. Herein, we used the maximum surface electrostatic potential (V_S,max) on the acidic hydrogen atoms of carboxylic acids to describe the H-bond interaction with water (the same descriptor that is used to characterize σ-bonded complexes) and correlate the results with experimental pKa values to obtain a predictive model for other carboxylic acids. We benchmarked six different methods, all including an implicit solvation model (water): Five density functionals and the Møller–Plesset second order perturbation theory in combination with six different basis sets for a total of thirty-six levels of theory. The ωB97X-D/cc-pVDZ level of theory stood out as the best one for consistently reproducing the reported pKa values, with a predictive power of 98% correlation in a test set of ten other carboxylic acids.

Molecular mechanism of substrate selectivity of the arginine-agmatine Antiporter AdiC

The arginine-agmatine antiporter (AdiC) is a component of an acid resistance system developed by enteric bacteria to resist gastric acidity. In order to avoid neutral proton antiport, the monovalent form of arginine, about as abundant as its divalent form under acidic conditions, should be selectively bound by AdiC for transport into the cytosol. In this study, we shed light on the mechanism through which AdiC distinguishes Arg⁺ from Arg²⁺ of arginine by investigating the binding of both forms in addition to that of divalent agmatine, using a combination of molecular dynamics simulations with molecular and quantum mechanics calculations. We show that AdiC indeed preferentially binds Arg⁺. The weaker binding of divalent compounds results mostly from their greater tendency to remain hydrated than Arg⁺. Our data suggests that the binding of Arg⁺ promotes the deprotonation of Glu208, a gating residue, which in turn reinforces its interactions with AdiC, leading to longer residence times of Arg⁺ in the binding site. Although the total electric charge of the ligand appears to be the determinant factor in the discrimination process, two local interactions formed with Trp293, another gating residue of the binding site, also contribute to the selection mechanism: a cation-π interaction with the guanidinium group of Arg⁺ and an anion-π interaction involving Glu208.

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.

Characterization of Ionizable Groups' Environments in Proteins and Protein-Ligand Complexes through a Statistical Analysis of the Protein Data Bank

We conduct a statistical analysis of the molecular environment of common ionizable functional groups in both protein-ligand complexes and inside proteins from the Protein Data Bank (PDB). In particular, we characterize the frequency, type, and density of the interacting atoms as well as the presence of a potential counterion. We found that for ligands, most guanidinium groups, half of primary and secondary amines, and one-fourth of imidazole neighbor a carboxylate group. Tertiary amines bind more rarely near carboxylate groups, which may be explained by a crowded neighborhood and hydrophobic character. In comparison to the environment seen by the ligands, inside proteins, an environment enriched in main-chain atoms is found, and the prevalence of direct charge neutralization by carboxylate groups is different. When the ionizable character of water molecules and phenolic or hydroxyl groups is accounted, considering a high-resolution dataset (less than 1.5 Å), charge neutralization could occur for well above 80% of the ligand functional groups considered, but for tertiary amines.

Development of constant-pH simulation methods in implicit solvent and applications in biomolecular systems

pH is a critical parameter for biological and technological systems directly related with electrical charges. It can give rise to peculiar electrostatic phenomena, which also makes them more challenging. Due to the quantum nature of the process, involving the forming and breaking of chemical bonds, quantum methods should ideally by employed. Nevertheless, due to the very large number of ionizable sites, different macromolecular conformations, salt conditions, and all other charged species, the CPU time cost simply becomes prohibitive for computer simulations, making this a quite complex problem. Simplified methods based on Monte Carlo sampling have been devised and will be reviewed here, highlighting the updated state-of-the-art of this field, advantages, and limitations of different theoretical protocols for biomolecular systems (proteins and nucleic acids). Following a historical perspective, the discussion will be associated with the applications to protein interactions with other proteins, polyelectrolytes, and nanoparticles.

Investigation of the bindings of a class of inhibitors with GSK3β kinase using thermodynamic integration MD simulation and kinase assay

GSK3β kinase is a noteworthy target for discovery of the drugs that will be used to treat several diseases. In the effort to identify a new inhibitor lead compound, we utilized thermodynamic integration (TI)-molecular dynamics (MD) simulation and kinase assay to investigate the bindings between GSK3β kinase and five compounds that were analogous to a known inhibitor with an available crystal structure. TI-MD simulations of the first two compounds (analogs 1 and 2) were used for calibration. The computed binding affinities of analogs 1 and 2 agreed well with the experimental results. The rest three compounds (analogs 3-5) were newly obtained from a database search, and their affinity data were newly measured in our labs. TI-MD simulations predicted the binding modes and the computed ΔΔG values have a reasonably good correlation with the experimental affinity data. These newly identified inhibitors appear to be new leads according to our survey of GSK3β inhibitors listed in recent review articles. The predicted binding modes of these compounds should aid in designing new derivatives of these compounds in the future.

Docking Screens for Novel Ligands Conferring New Biology

It is now plausible to dock libraries of 10 million molecules against targets over several days or weeks. When the molecules screened are commercially available, they may be rapidly tested to find new leads. Although docking retains important liabilities (it cannot calculate affinities accurately nor even reliably rank order high-scoring molecules), it can often can distinguish likely from unlikely ligands, often with hit rates above 10%. Here we summarize the improvements in libraries, target quality, and methods that have supported these advances, and the open access resources that make docking accessible. Recent docking screens for new ligands are sketched, as are the binding, crystallographic, and in vivo assays that support them. Like any technique, controls are crucial, and key experimental ones are reviewed. With such controls, docking campaigns can find ligands with new chemotypes, often revealing the new biology that may be docking's greatest impact over the next few years.

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.