Predicting protein pK(a) by environment similarity

Evidence for a high pKa of an aspartic acid residue in the active site of CALB by a fully atomistic multiscale approach

Candida antarctica Lipase B (CALB) is a paradigm for the family of lipases. At pH 7, the optimal pH for catalysis, the protonation state of an aspartic acid of the active site (Asp134) could not be conclusively assigned. In fact, the pK_a estimate provided by a widely used computational tool, namely PropKa, that predicts pKa values of ionizable groups in proteins based on the crystallographic structure, is only slightly above 7 (pKa = 7.25). This, along with the lack of an experimental evaluation, makes the assignment of its protonation state at neutral pH challenging. Here, we calculate the pK_a of Asp134 by means of a fully atomistic multiscale computational approach based on classical molecular dynamics (MD) simulation and the perturbed matrix method (PMM), namely the MD-PMM approach. MD-PMM is able to take into account the dynamics of the system and, at the same time, to treat the deprotonation step at the quantum level. The calculations provide a pK_a value of 8.9 ± 1.1, hence suggesting that Asp134 in CALB should be protonated at neutral, and even at slightly basic, pH.

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.

Prediction of protein pK a with representation learning

The behavior of proteins is closely related to the protonation states of the residues. Therefore, prediction and measurement of pK a are essential to understand the basic functions of proteins. In this work, we develop a new empirical scheme for protein pK a prediction that is based on deep representation learning. It combines machine learning with atomic environment vector (AEV) and learned quantum mechanical representation from ANI-2x neural network potential (J. Chem. Theory Comput. 2020, 16, 4192). The scheme requires only the coordinate information of a protein as the input and separately estimates the pK a for all five titratable amino acid types. The accuracy of the approach was analyzed with both cross-validation and an external test set of proteins. Obtained results were compared with the widely used empirical approach PROPKA. The new empirical model provides accuracy with MAEs below 0.5 for all amino acid types. It surpasses the accuracy of PROPKA and performs significantly better than the null model. Our model is also sensitive to the local conformational changes and molecular interactions.

Protein pK a Prediction with Machine Learning

Protein pK _a prediction is essential for the investigation of the pH-associated relationship between protein structure and function. In this work, we introduce a deep learning-based protein pK _a predictor DeepKa, which is trained and validated with the pK _a values derived from continuous constant-pH molecular dynamics (CpHMD) simulations of 279 soluble proteins. Here, the CpHMD implemented in the Amber molecular dynamics package has been employed (Huang Y.J. Chem. Inf. Model.2018, 58, 1372-1383). Notably, to avoid discontinuities at the boundary, grid charges are proposed to represent protein electrostatics. We show that the prediction accuracy by DeepKa is close to that by CpHMD benchmarking simulations, validating DeepKa as an efficient protein pK _a predictor. In addition, the training and validation sets created in this study can be applied to the development of machine learning-based protein pK _a predictors in the future. Finally, the grid charge representation is general and applicable to other topics, such as the protein-ligand binding affinity prediction.

Fully Atomistic Multiscale Approach for pKa Prediction

The ionization state of titratable amino acids strongly affects proteins structure and functioning in a large number of biological processes. It is therefore essential to be able to characterize the pK_a of ionizable groups inside proteins and to understand its microscopic determinants in order to gain insights into many functional properties of proteins. A big effort has been devoted to the development of theoretical approaches for the prediction of deprotonation free energies, yet the accurate theoretical/computational calculation of pK_a values is recognized as a current challenge. A methodology based on a hybrid quantum/classical approach is here proposed for the computation of deprotonation free energies. The method is applied to calculate the pK_a of formic acid, methylammonium, and methanethiol, providing results in good agreement with the corresponding experimental estimates. The pK_a is also calculated for aspartic acid and lysine as single residues in solution and for three aspartic/glutamic acids inside a well-characterized protein: hen egg white lysozyme. While for small molecules the method is able to deal with multiple protonation states of all titratable groups, this becomes computationally very expensive for proteins. The calculated pK_a values for the single amino acids (except for the zwitterionic aspartic acid) and inside the protein display a systematic shift with respect to the experimental values that suggests that the fine balance between hydrophobic and polar interactions might be not accurately reproduced by the usual classical force-fields, thus affecting the computation of deprotonation free energies. The calculated pK_a shifts inside the protein are in good agreement with the corresponding experimental ones (within 1 pK_a unit), well reproducing the pK_a changes due to the protein environment even in the case of large pK_a shifts.

A Hierarchical Approach to Predict Conformation-Dependent Histidine Protonation States in Stable and Flexible Proteins

Solution acidity measured by pH is an important environmental factor that affects protein structure. It influences the protonation state of protein residues, which in turn may be coupled to protein conformational changes, unfolding, and ligand binding. It remains difficult to compute and measure the p K_a of individual residues, as well as to relate them to pH-dependent protein transitions. This paper presents a hierarchical approach to compute the p K_a of individual protonatable residues, specifically histidines, coupled with underlying structural changes of a protein. A fast and efficient free energy perturbation (FEP) algorithm has also been developed utilizing a fast implementation of standard molecular dynamics (MD) algorithms. Specifically, a CUDA version of the AMBER MD engine is used in this paper. Eight histidine p K_a's are computed in a diverse set of pH stable proteins to demonstrate the proposed approach's utility and assess the predictive quality of the AMBER FF99SB force field. A reference molecule is carefully selected and tested for convergence. A hierarchical approach is used to model p K_a's of the six histidine residues of the diphtheria toxin translocation domain (DTT), which exhibits a diverse ensemble of individual conformations and pH-dependent unfolding. The hierarchical approach consists of first sampling equilibrium conformational ensembles of a protein with protonated and neutral histidine residues via long equilibrium MD simulations (Flores-Canales, J. C.; et al. bioRxiv, 2019, 572040). A clustering method is then used to identify sampled protein conformations, and p K_a's of histidines in each protein conformation are computed. Finally, an ensemble averaging formalism is developed to compute weighted average histidine p K_a's. These can be compared with an apparent experimentally measured p K_a of the DTT protein and thus allows us to propose a mechanism of pH-dependent unfolding of the DTT protein.

On the energy components governing molecular recognition in the framework of continuum approaches

Molecular recognition is a process that brings together several biological macromolecules to form a complex and one of the most important characteristics of the process is the binding free energy. Various approaches exist to model the binding free energy, provided the knowledge of the 3D structures of bound and unbound molecules. Among them, continuum approaches are quite appealing due to their computational efficiency while at the same time providing predictions with reasonable accuracy. Here we review recent developments in the field emphasizing on the importance of adopting adequate description of physical processes taking place upon the binding. In particular, we focus on the efforts aiming at capturing some of the atomistic details of the binding phenomena into the continuum framework. When possible, the energy components are reviewed independently of each other. However, it is pointed out that rigorous approaches should consider all energy contributions on the same footage. The two major schemes for utilizing the individual energy components to predict binding affinity are outlined as well.

Bayesian model aggregation for ensemble-based estimates of protein pKa values

This article investigates an ensemble-based technique called Bayesian Model Averaging (BMA) to improve the performance of protein amino acid pKa predictions. Structure-based pKa calculations play an important role in the mechanistic interpretation of protein structure and are also used to determine a wide range of protein properties. A diverse set of methods currently exist for pKa prediction, ranging from empirical statistical models to ab initio quantum mechanical approaches. However, each of these methods are based on a set of conceptual assumptions that can effect a model's accuracy and generalizability for pKa prediction in complicated biomolecular systems. We use BMA to combine eleven diverse prediction methods that each estimate pKa values of amino acids in staphylococcal nuclease. These methods are based on work conducted for the pKa Cooperative and the pKa measurements are based on experimental work conducted by the García-Moreno lab. Our cross-validation study demonstrates that the aggregated estimate obtained from BMA outperforms all individual prediction methods with improvements ranging from 45 to 73% over other method classes. This study also compares BMA's predictive performance to other ensemble-based techniques and demonstrates that BMA can outperform these approaches with improvements ranging from 27 to 60%. This work illustrates a new possible mechanism for improving the accuracy of pKa prediction and lays the foundation for future work on aggregate models that balance computational cost with prediction accuracy.

Protonation and pK changes in protein-ligand binding

Formation of protein-ligand complexes causes various changes in both the receptor and the ligand. This review focuses on changes in pK and protonation states of ionizable groups that accompany protein-ligand binding. Physical origins of these effects are outlined, followed by a brief overview of the computational methods to predict them and the associated corrections to receptor-ligand binding affinities. Statistical prevalence, magnitude and spatial distribution of the pK and protonation state changes in protein-ligand binding are discussed in detail, based on both experimental and theoretical studies. While there is no doubt that these changes occur, they do not occur all the time; the estimated prevalence varies, both between individual complexes and by method. The changes occur not only in the immediate vicinity of the interface but also sometimes far away. When receptor-ligand binding is associated with protonation state change at particular pH, the binding becomes pH dependent: we review the interplay between sub-cellular characteristic pH and optimum pH of receptor-ligand binding. It is pointed out that there is a tendency for protonation state changes upon binding to be minimal at physiologically relevant pH for each complex (no net proton uptake/release), suggesting that native receptor-ligand interactions have evolved to reduce the energy cost associated with ionization changes. As a result, previously reported statistical prevalence of these changes - typically computed at the same pH for all complexes - may be higher than what may be expected at optimum pH specific to each complex. We also discuss whether proper account of protonation state changes appears to improve practical docking and scoring outcomes relevant to structure-based drug design. An overview of some of the existing challenges in the field is provided in conclusion.

Rapid calculation of protein pKa values using Rosetta

We developed a Rosetta-based Monte Carlo method to calculate the pK(a) values of protein residues that commonly exhibit variable protonation states (Asp, Glu, Lys, His, and Tyr). We tested the technique by calculating pK(a) values for 264 residues from 34 proteins. The standard Rosetta score function, which is independent of any environmental conditions, failed to capture pK(a) shifts. After incorporating a Coulomb electrostatic potential and optimizing the solvation reference energies for pK(a) calculations, we employed a method that allowed side-chain flexibility and achieved a root mean-square deviation (RMSD) of 0.83 from experimental values (0.68 after discounting 11 predictions with an error over 2 pH units). Additional degrees of side-chain conformational freedom for the proximal residues facilitated the capture of charge-charge interactions in a few cases, resulting in an overall RMSD of 0.85 pH units. The addition of backbone flexibility increased the overall RMSD to 0.93 pH units but improved relative pK(a) predictions for proximal catalytic residues. The method also captures large pK(a) shifts of lysine and some glutamate point mutations in staphylococcal nuclease. Thus, a simple and fast method based on the Rosetta score function and limited conformational sampling produces pK(a) values that will be useful when rapid estimation is essential, such as in docking, design, and folding.

Progress in the prediction of pKa values in proteins

The pK(a) -cooperative aims to provide a forum for experimental and theoretical researchers interested in protein pK(a) values and protein electrostatics in general. The first round of the pK(a) -cooperative, which challenged computational labs to carry out blind predictions against pK(a) s experimentally determined in the laboratory of Bertrand Garcia-Moreno, was completed and results discussed at the Telluride meeting (July 6-10, 2009). This article serves as an introduction to the reports submitted by the blind prediction participants that will be published in a special issue of PROTEINS: Structure, Function and Bioinformatics. Here, we briefly outline existing approaches for pK(a) calculations, emphasizing methods that were used by the participants in calculating the blind pK(a) values in the first round of the cooperative. We then point out some of the difficulties encountered by the participating groups in making their blind predictions, and finally try to provide some insights for future developments aimed at improving the accuracy of pK(a) calculations.

Intracellular pH is a tightly controlled signal in yeast

BACKGROUND

Nearly all processes in living cells are pH dependent, which is why intracellular pH (pH(i)) is a tightly regulated physiological parameter in all cellular systems. However, in microbes such as yeast, pH(i) responds to extracellular conditions such as the availability of nutrients. This raises the question of how pH(i) dynamics affect cellular function.

SCOPE OF REVIEW

We discuss the control of pH(i,) and the regulation of processes by pH(i), focusing on the model organism Saccharomyces cerevisiae. We aim to dissect the effects of pH(i) on various aspects of cell physiology, which are often intertwined. Our goal is to provide a broad overview of how pH(i) is controlled in yeast, and how pH(i) in turn controls physiology, in the context of both general cellular functioning as well as of cellular decision making upon changes in the cell's environment.

MAJOR CONCLUSIONS

Besides a better understanding of the regulation of pH(i), evidence for a signaling role of pH(i) is accumulating. We conclude that pH(i) responds to nutritional cues and relays this information to alter cellular make-up and physiology. The physicochemical properties of pH allow the signal to be fast, and affect multiple regulatory levels simultaneously.

GENERAL SIGNIFICANCE

The mechanisms for regulation of processes by pH(i) are tightly linked to the molecules that are part of all living cells, and the biophysical properties of the signal are universal amongst all living organisms, and similar types of regulation are suggested in mammals. Therefore, dynamic control of cellular decision making by pH(i) is therefore likely a general trait. This article is part of a Special Issue entitled: Systems Biology of Microorganisms.

In silico pKa prediction and ADME profiling

Improving the ADME profile of drug candidates is a critical step in lead optimization, and because pKa affects most ADME properties such as lipophilicity, solubility, and metabolism, it is extremely advantageous to predict pKa in order to guide the design of new compounds. However, accurately (<0.5 log units) predicting pKa by empirical methods can be challenging especially for novel series, because of lack of knowledge on determinants of pKa (steric effects, ring effects, H-bonding, etc.), and because of limited experimental data on the effects of specific chemical groups on the ionization of an atom. To address these issues, we recently developed the computational package MoKa, which integrates graphical and command line tools designed for computational and medicinal chemists to predict the pKa values of organic compounds. Here, we present the major issues considered when we developed MoKa, such as the accurate selection of training data, the fundamentals of the methodology (which has also been extended to predict protein pKa), the treatment of multiprotic compounds, and the selection of the dominant tautomer for the calculation. Last, we illustrate some specific applications of MoKa to predict solubility, lipophilicity, and metabolism.