Redesigning protein pKa values

The ability to re-engineer enzymatic pH-activity profiles is of importance for industrial applications of enzymes. We theoretically explore the feasibility of re-engineering enzymatic pH-activity profiles by changing active site pK(a) values using point mutations. We calculate the maximum achievable DeltapK(a) values for 141 target titratable groups in seven enzymes by introducing conservative net-charge altering point mutations. We examine the importance of the number of mutations introduced, their distance from the target titratable group, and the characteristics of the target group itself. The results show that multiple mutations at 10A can change pK(a) values up to two units, but that the introduction of a requirement to keep other pK(a) values constant reduces the magnitude of the achievable DeltapK(a). The algorithm presented shows a good correlation with existing experimental data and is available for download and via a web server at http://enzyme.ucd.ie/pKD.     

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 pK_a predictions. Structure‐based pK_a 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 pK_a 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 pK_a prediction in complicated biomolecular systems. We use BMA to combine eleven diverse prediction methods that each estimate pK_a values of amino acids in staphylococcal nuclease. These methods are based on work conducted for the pK_a Cooperative and the pK_a 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 pK_a prediction and lays the foundation for future work on aggregate models that balance computational cost with prediction accuracy. Proteins 2014; 82:354–363. © 2013 Wiley Periodicals, Inc.     

Calculating pKa values in the cAMP-dependent protein kinase: the effect of conformational change and ligand binding

The conformational change observed upon ligand binding and phosphorylation for the cAMP-dependent protein kinase (protein kinase A-PKA) is of high importance for the regulation of its activity. We calculate pKa values and net charges for 18 3D structures of PKA in various conformations and liganded states to examine the role of electrostatics in ligand binding and activation. We find that the conformational change of PKA takes place without any significant net proton uptake/release at all pH values, thus indicating that PKA has evolved to reduce any pH-dependent barriers to the conformational motion. We furthermore find that the binding of ligands induces large changes in the net charge of PKA at most pH values, but significantly, we find that the net charge difference at physiological pH is close to zero, thus indicating that the active-site pKa values have been preorganized for substrate binding. We are unable to unequivocally resolve the identity of the groups responsible for determining the pH-activity profile of PKA but speculate that the titration of Lys 168 or the titration of ATP itself could be responsible for the loss of activity at high pH values. Finally, we examine the effect of point mutations on the pKa values of the PKA catalytic residues and find these to be relatively insensitive to both noncharge-altering and charge-altering mutations.     

Predicting protein pKa by environment similarity

A statistical method to predict protein pK_a has been developed by using the 3D structure of a protein and a database of 434 experimental protein pK_a values. Each pK_a in the database is associated with a fingerprint that describes the chemical environment around an ionizable residue. A computational tool, MoKaBio, has been developed to identify automatically ionizable residues in a protein, generate fingerprints that describe the chemical environment around such residues, and predict pK_a from the experimental pK_a values in the database by using a similarity metric. The method, which retrieved the pK_a of 429 of the 434 ionizable sites in the database correctly, was crossvalidated by leave‐one‐out and yielded root mean square error (RMSE) = 0.95, a result that is superior to that obtained by using the Null Model (RMSE 1.07) and other well‐established protein pK_a prediction tools. This novel approach is suitable to rationalize protein pK_a by comparing the region around the ionizable site with similar regions whose ionizable site pK_a is known. The pK_a of residues that have a unique environment not represented in the training set cannot be predicted accurately, however, the method offers the advantage of being trainable to increase its predictive power. Proteins 2009. © 2009 Wiley‐Liss, Inc.     

A statistical approach to the prediction of pK(a) values in proteins

We propose a simple model for the calculation of pK(a) values of ionizable residues in proteins. It is based on the premise that the pK(a) shift of ionizable residues is linearly correlated to the interaction between a particular residue and the local environment created by the surrounding residues. Despite its simplicity, the model displays good prediction performance. Under the sixfold cross test prediction over a data set of 405 experimental pK(a) values in 73 protein chains with known structures, the root-mean-square deviation (RMSD) between the experimental and calculated pK(a) was found to be 0.77. The accuracy of this model increases with increasing size of the data set: the RMSD is 0.609 for glutamate (the largest data set with 141 sites) and approximately 1 pH unit for lysine, with a data set containing 45 sites.     

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

We developed a Poisson‐Boltzmann based approach to calculate the values of protein ionizable residues (Glu, Asp, His, Lys and Arg), nucleotides of RNA and single stranded DNA. Two novel features were utilized: the dielectric properties of the macromolecules and water phase were modeled via the smooth Gaussian‐based dielectric function in DelPhi and the corresponding electrostatic energies were calculated without defining the molecular surface. We tested the algorithm by calculating values for more than 300 residues from 32 proteins from the PPD dataset and achieved an overall RMSD of 0.77. Particularly, the RMSD of 0.55 was achieved for surface residues, while the RMSD of 1.1 for buried residues. The approach was also found capable of capturing the large shifts of various single point mutations in staphylococcal nuclease (SNase) from ‐cooperative dataset, resulting in an overall RMSD of 1.6 for this set of pKa's. Investigations showed that predictions for most of buried mutant residues of SNase could be improved by using higher dielectric constant values. Furthermore, an option to generate different hydrogen positions also improves predictions for buried carboxyl residues. Finally, the calculations on two RNAs demonstrated the capability of this approach for other types of biomolecules. Proteins 2015; 83:2186–2197. © 2015 Wiley Periodicals, Inc.     

Simplified methods for pKa and acid pH-dependent stability estimation in proteins: removing dielectric and counterion boundaries

Much computational research aimed at understanding ionizable group interactions in proteins has focused on numerical solutions of the Poisson-Boltzmann (PB) equation, incorporating protein exclusion zones for solvent and counterions in a continuum model. Poor agreement with measured pKas and pH-dependent stabilities for a (protein, solvent) relative dielectric boundary of (4,80) has lead to the adoption of an intermediate (20,80) boundary. It is now shown that a simple Debye-Huckel (DH) calculation, removing both the low dielectric and counterion exclusion regions associated with protein, is equally effective in general pKa calculations. However, a broad-based discrepancy to measured pH-dependent stabilities is maintained in the absence of ionizable group interactions in the unfolded state. A simple model is introduced for these interactions, with a significantly improved match to experiment that suggests a potential utility in predicting and analyzing the acid pH-dependence of protein stability. The methods are applied to the relative pH-dependent stabilities of the pore-forming domains of colicins A and N. The results relate generally to the well-known preponderance of surface ionizable groups with solvent-mediated interactions. Although numerical PB solutions do not currently have a significant advantage for overall pKa estimations, development based on consideration of microscopic solvation energetics in tandem with the continuum model could combine the large deltapKas of a subset of ionizable groups with the overall robustness of the DH model.     

A buried lysine that titrates with a normal pKa: role of conformational flexibility at the protein-water interface as a determinant of pKa values

Previously we reported that Lys, Asp, and Glu residues at positions 66 and 92 in staphylococcal nuclease (SNase) titrate with pK(a) values shifted by up to 5 pK(a) units in the direction that promotes the neutral state. In contrast, the internal Lys-38 in SNase titrates with a normal pK(a). The crystal structure of the L38K variant shows that the side chain of Lys-38 is buried. The ionizable moiety is approximately 7 A from solvent and ion paired with Glu-122. This suggests that the pK(a) value of Lys-38 is normal because the energetic penalty for dehydration is offset by a favorable Coulomb interaction. However, the pK(a) of Lys-38 was also normal when Glu-122 was replaced with Gln or with Ala. Continuum electrostatics calculations were unable to reproduce the pK(a) of Lys-38 unless the protein was treated with an artificially high dielectric constant, consistent with structural reorganization being responsible for the normal pK(a) value of Lys-38. This reorganization must be local because circular dichroism and NMR spectroscopy indicate that the L38K protein is native-like under all conditions studied. In molecular dynamics simulations, the ion pair between Lys-38 and Glu-122 is unstable. The simulations show that a minor rearrangement of a loop is sufficient to allow penetration of water to the amino moiety of Lys-38. This illustrates both the important roles of local flexibility and water penetration as determinants of pK(a) values of ionizable groups buried near the protein-water interface, and the challenges faced by structure-based pK(a) calculations in reproducing these effects.     

On the evaluation and optimization of protein X-ray structures for pKa calculations

The calculation of the physical properties of a protein from its X-ray structure is of importance in virtually every aspect of modern biology. Although computational algorithms have been developed for calculating everything from the dynamics of a protein to its binding specificity, only limited information is available on the ability of these methods to give accurate results when used with a particular X-ray structure. We examine the ability of a pKa calculation algorithm to predict the proton-donating residue in the catalytic mechanism of hen egg white lysozyme. We examine the correlation between the ability of the pKa calculation method to obtain the correct result and the overall characteristics of 41 X-ray structures such as crystallization conditions, resolution, and the output of structure validation software. We furthermore examine the ability of energy minimizations (EM), molecular dynamics (MD) simulations, and structure-perturbation methods to optimize the X-ray structures such that these give correct results with the pKa calculation algorithm. We propose a set of criteria for identifying the proton donor in a catalytic mechanism, and demonstrate that the application of these criteria give highly accurate prediction results when using unmodified X-ray structures. More specifically, we are able to successfully identify the proton donor in 85% of the X-ray structures when excluding structures with crystal contacts near the active site. Neither the use of the overall characteristics of the X-ray structures nor the optimization of the structure by EM, MD, or other methods improves the results of the pKa calculation algorithm. We discuss these results and their implications for the design of structure-based energy calculation algorithms in general.     

pKa calculations for class A beta-lactamases: influence of substrate binding

Beta-Lactamases are responsible for bacterial resistance to beta-lactams and are thus of major clinical importance. However, the identity of the general base involved in their mechanism of action is still unclear. Two candidate residues, Glu166 and Lys73, have been proposed to fulfill this role. Previous studies support the proposal that Glu166 acts during the deacylation, but there is no consensus on the possible role of this residue in the acylation step. Recent experimental data and theoretical considerations indicate that Lys73 is protonated in the free beta-lactamases, showing that this residue is unlikely to act as a proton abstractor. On the other hand, it has been proposed that the pKa of Lys73 would be dramatically reduced upon substrate binding and would thus be able to act as a base. To check this hypothesis, we performed continuum electrostatic calculations for five wild-type and three beta-lactamase mutants to estimate the pKa of Lys73 in the presence of substrates, both in the Henri-Michaelis complex and in the tetrahedral intermediate. In all cases, the pKa of Lys73 was computed to be above 10, showing that it is unlikely to act as a proton abstractor, even when a beta-lactam substrate is bound in the enzyme active site. The pKa of Lys234 is also raised in the tetrahedral intermediate, thus confirming a probable role of this residue in the stabilization of the tetrahedral intermediate. The influence of the beta-lactam carboxylate on the pKa values of the active-site lysines is also discussed.     

Intrinsically disordered inhibitor of glutamine synthetase is a functional protein with random‐coil‐like pKa values

The sequential action of glutamine synthetase (GS) and glutamate synthase (GOGAT) in cyanobacteria allows the incorporation of ammonium into carbon skeletons. In the cyanobacterium Synechocystis sp. PCC 6803, the activity of GS is modulated by the interaction with proteins, which include a 65‐residue‐long intrinsically disordered protein (IDP), the inactivating factor IF7. This interaction is regulated by the presence of charged residues in both IF7 and GS. To understand how charged amino acids can affect the binding of an IDP with its target and to provide clues on electrostatic interactions in disordered states of proteins, we measured the pK_a values of all IF7 acidic groups (Glu32, Glu36, Glu38, Asp40, Asp58, and Ser65, the backbone C‐terminus) at 100 mM NaCl concentration, by using NMR spectroscopy. We also obtained solution structures of IF7 through molecular dynamics simulation, validated them on the basis of previous experiments, and used them to obtain theoretical estimates of the pK_a values. Titration values for the two Asp and three Glu residues of IF7 were similar to those reported for random‐coil models, suggesting the lack of electrostatic interactions around these residues. Furthermore, our results suggest the presence of helical structure at the N‐terminus of the protein and of conformational changes at acidic pH values. The overall experimental and in silico findings suggest that local interactions and conformational equilibria do not play a role in determining the electrostatic features of the acidic residues of IF7.     

Development, validation, and application of adapted PEOE charges to estimate pKa values of functional groups in protein-ligand complexes

For routine pK(a) calculations of protein-ligand complexes in drug design, the PEOE method to compute partial charges was modified. The new method is applicable to a large scope of proteins and ligands. The adapted charges were parameterized using experimental free energies of solvation of amino acids and small organic ligands. For a data set of 80 small organic molecules, a correlation coefficient of r(2) = 0.78 between calculated and experimental solvation free energies was obtained. Continuum electrostatics pK(a) calculations based on the Poisson-Boltzmann equation were carried out on a validation set of nine proteins for which 132 experimental pK(a) values are known. In total, an overall RMSD of 0.88 log units between calculated and experimentally determined data is achieved. In particular, the predictions of significantly shifted pK(a) values are satisfactory, and reasonable estimates of protonation states in the active sites of lysozyme and xylanase could be obtained. Application of the charge-assignment and pK(a)-calculation procedure to protein-ligand complexes provides clear structural interpretations of experimentally observed changes of protonation states of functional groups upon complex formation. This information is essential for the interpretation of thermodynamic data of protein-ligand complex formation and provides the basis for the reliable factorization of the free energy of binding in enthalpic and entropic contributions. The modified charge-assignment procedure forms the basis for future automated pK(a) calculations of protein-ligand complexes.     

pK values of the ionizable groups of proteins

We have used potentiometric titrations to measure the pK values of the ionizable groups of proteins in alanine pentapeptides with appropriately blocked termini. These pentapeptides provide an improved model for the pK values of the ionizable groups in proteins. Our pK values determined in 0.1 M KCl at 25 degrees C are: 3.67+/-0.03 (alpha-carboxyl), 3.67+/-0.04 (Asp), 4.25+/-0.05 (Glu), 6.54+/-0.04 (His), 8.00+/-0.03 (alpha-amino), 8.55+/-0.03 (Cys), 9.84+/-0.11 (Tyr), and 10.40+/-0.08 (Lys). The pK values of some groups differ from the Nozaki and Tanford (N & T) pK values often used in the literature: Asp (3.67 this work vs. 4.0 N & T); His (6.54 this work vs. 6.3 N & T); alpha-amino (8.00 this work vs. 7.5 N & T); Cys (8.55 this work vs. 9.5 N & T); and Tyr (9.84 this work vs. 9.6 N & T). Our pK values will be useful to those who study pK perturbations in folded and unfolded proteins, and to those who use theory to gain a better understanding of the factors that determine the pK values of the ionizable groups of proteins.     

A continuum model to study the internal fluctuations in globular proteins

The salient features of the differential equation model to study protein dynamics are presented with results for 19 proteins.     

A summary of the measured pK values of the ionizable groups in folded proteins

We tabulated 541 measured pK values reported in the literature for the Asp, Glu, His, Cys, Tyr, and Lys side chains, and the C and N termini of 78 folded proteins. The majority of these values are for the Asp, Glu, and His side chains. The average pK values are Asp 3.5 ± 1.2 (139); Glu 4.2 ± 0.9 (153); His 6.6 ± 1.0 (131); Cys 6.8 ± 2.7 (25); Tyr 10.3 ± 1.2 (20); Lys 10.5 ± 1.1 (35); C‐terminus 3.3 ± 0.8 (22) and N‐terminus 7.7 ± 0.5 (16). We compare these results with the measured pK values of these groups in alanine pentapeptides, and comment on our overall findings.     

An empirical model for electrostatic interactions in proteins incorporating multiple geometry-dependent dielectric constants

Here we introduce an electrostatic model that treats the complexity of electrostatic interactions in a heterogeneous protein environment by using multiple parameters that take into account variations in protein geometry, local structure, and the type of interacting residues. The optimal values for these parameters were obtained by fitting the model to a large dataset of 260 experimentally determined pK(a) values distributed over 41 proteins. We obtain fits between the calculated and observed values that are significantly better than the null model. The model performs well on the groups that exhibit large pK(a) shifts from solution values in response to the protein environment and compares favorably with other, successful continuum models. The empirically determined values of the parameters correlate well with experimentally observed contributions of hydrogen bonds and ion pairs as well as theoretically predicted magnitudes of charge-charge and charge-polar interactions. The magnitudes of the dielectric constants assigned to different regions of the protein rank according to the strength of the relaxation effects expected for the core, boundary, and surface. The electrostatic interactions in this model are pairwise decomposable and can be calculated rapidly. This model is therefore well suited for the large computations required for simulating protein properties and especially for prediction of mutations for protein design.     

A detailed representation of electrostatic energy in prediction of sequence and pH dependence of protein stability

A molecular mechanics model, previously validated in applications to structure prediction, is shown to reproduce experiment in predictions of protein ionization state, and in predictions of sequence and pH dependence of protein stability. Over a large dataset, 1876 values of ΔΔG of folding, the RMSD is 1.34 kcal/mol. Using an alternative measure of accuracy, either the sign of the calculated ΔΔG agrees with experiment or the absolute value of the deviation is less than 1.0 kcal/mol, 1660 of 1876 data points (88.5%) pass the condition. Relative to models used previously in computer‐aided protein design, the concept, we propose, most responsible for the performance of our model, and for the extensibility to non‐neutral values of pH, is the treatment of electrostatic energy. The electronic structure of the protein is modeled using distributed atomic multipoles. The structured liquid state of the solvent is modeled using a dielectric continuum. A modification to the energetics of the reaction field, induced by the protein in the dielectric continuum, attempts to account for preformed multipoles of solvent water molecules and ions. An adjustable weight (with optimal value.141) applied to the total vacuum energy accounts implicitly for electronic polarization. A threshold distance, beyond which pairwise atomic interactions are neglected, is not used. In searches through subspaces of sequences and conformations, efficiency remains acceptable for useful applications. Proteins 2014; 82:2497–2511. © 2014 Wiley Periodicals, Inc.     

A fast and accurate computational approach to protein ionization

We report a very fast and accurate physics-based method to calculate pH-dependent electrostatic effects in protein molecules and to predict the pK values of individual sites of titration. In addition, a CHARMm-based algorithm is included to construct and refine the spatial coordinates of all hydrogen atoms at a given pH. The present method combines electrostatic energy calculations based on the Generalized Born approximation with an iterative mobile clustering approach to calculate the equilibria of proton binding to multiple titration sites in protein molecules. The use of the GBIM (Generalized Born with Implicit Membrane) CHARMm module makes it possible to model not only water-soluble proteins but membrane proteins as well. The method includes a novel algorithm for preliminary refinement of hydrogen coordinates. Another difference from existing approaches is that, instead of monopeptides, a set of relaxed pentapeptide structures are used as model compounds. Tests on a set of 24 proteins demonstrate the high accuracy of the method. On average, the RMSD between predicted and experimental pK values is close to 0.5 pK units on this data set, and the accuracy is achieved at very low computational cost. The pH-dependent assignment of hydrogen atoms also shows very good agreement with protonation states and hydrogen-bond network observed in neutron-diffraction structures. The method is implemented as a computational protocol in Accelrys Discovery Studio and provides a fast and easy way to study the effect of pH on many important mechanisms such as enzyme catalysis, ligand binding, protein-protein interactions, and protein stability.