Improved pKa calculations through flexibility based sampling of a water-dominated interaction scheme

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.

Computational Investigation of Mechanisms for pH Modulation of Human Chloride Channels

Many transmembrane proteins are modulated by intracellular or extracellular pH. Investigation of pH dependence generally proceeds by mutagenesis of a wide set of amino acids, guided by properties such as amino-acid conservation and structure. Prediction of pKas can streamline this process, allowing rapid and effective identification of amino acids of interest with respect to pH dependence. Commencing with the calcium-activated chloride channel bestrophin 1, the carboxylate ligand structure around calcium sites relaxes in the absence of calcium, consistent with a measured lack of pH dependence. By contrast, less relaxation in the absence of calcium in TMEM16A, and maintenance of elevated carboxylate sidechain pKas, is suggested to give rise to pH-dependent chloride channel activity. This hypothesis, modulation of calcium/proton coupling and pH-dependent activity through the extent of structural relaxation, is shown to apply to the well-characterised cytosolic proteins calmodulin (pH-independent) and calbindin D9k (pH-dependent). Further application of destabilised, ionisable charge sites, or electrostatic frustration, is made to other human chloride channels (that are not calcium-activated), ClC-2, GABAA, and GlyR. Experimentally determined sites of pH modulation are readily identified. Structure-based tools for pKa prediction are freely available, allowing users to focus on mutagenesis studies, construct hypothetical proton pathways, and derive hypotheses such as the model for control of pH-dependent calcium activation through structural flexibility. Predicting altered pH dependence for mutations in ion channel disorders can support experimentation and, ultimately, clinical intervention.

How Is Substrate Halogenation Triggered by the Vanadium Haloperoxidase from Curvularia inaequalis?

Vanadium haloperoxidases (VHPOs) are unique enzymes in biology that catalyze a challenging halogen transfer reaction and convert a strong aromatic C-H bond into C-X (X = Cl, Br, I) with the use of a vanadium cofactor and H₂O₂. The VHPO catalytic cycle starts with the conversion of hydrogen peroxide and halide (X = Cl, Br, I) into hypohalide on the vanadate cofactor, and the hypohalide subsequently reacts with a substrate. However, it is unclear whether the hypohalide is released from the enzyme or otherwise trapped within the enzyme structure for the halogenation of organic substrates. A substrate-binding pocket has never been identified for the VHPO enzyme, which questions the role of the protein in the overall reaction mechanism. Probing its role in the halogenation of small molecules will enable further engineering of the enzyme and expand its substrate scope and selectivity further for use in biotechnological applications as an environmentally benign alternative to current organic chemistry synthesis. Using a combined experimental and computational approach, we elucidate the role of the vanadium haloperoxidase protein in substrate halogenation. Activity studies show that binding of the substrate to the enzyme is essential for the reaction of the hypohalide with substrate. Stopped-flow measurements demonstrate that the rate-determining step is not dependent on substrate binding but partially on hypohalide formation. Using a combination of molecular mechanics (MM) and molecular dynamics (MD) simulations, the substrate binding area in the protein is identified and even though the selected substrates (methylphenylindole and 2-phenylindole) have limited hydrogen-bonding abilities, they are found to bind relatively strongly and remain stable in a binding tunnel. A subsequent analysis of the MD snapshots characterizes two small tunnels leading from the vanadate active site to the surface that could fit small molecules such as hypohalide, halide, and hydrogen peroxide. Density functional theory studies using electric field effects show that a polarized environment in a specific direction can substantially lower barriers for halogen transfer. A further analysis of the protein structure indeed shows a large dipole orientation in the substrate-binding pocket that could enable halogen transfer through an applied local electric field. These findings highlight the importance of the enzyme in catalyzing substrate halogenation by providing an optimal environment to lower the energy barrier for this challenging aromatic halide insertion reaction.

A pH-dependent cluster of charges in a conserved cryptic pocket on flaviviral envelopes

Flaviviruses are enveloped viruses which include human pathogens that are predominantly transmitted by mosquitoes and ticks. Some, such as dengue virus, exhibit the phenomenon of antibody-dependent enhancement (ADE) of disease, making vaccine-based routes of fighting infections problematic. The pH-dependent conformational change of the envelope (E) protein required for fusion between the viral and endosomal membranes is an attractive point of inhibition by antivirals as it has the potential to diminish the effects of ADE. We examined six flaviviruses by employing large-scale molecular dynamics (MD) simulations of raft systems that represent a substantial portion of the flaviviral envelope. We utilised a benzene-mapping approach that led to a discovery of shared hotspots and conserved cryptic sites. A cryptic pocket previously shown to bind a detergent molecule exhibited strain-specific characteristics. An alternative conserved cryptic site at the E protein domain interfaces showed a consistent dynamic behaviour across flaviviruses and contained a conserved cluster of ionisable residues. Constant-pH simulations revealed cluster and domain-interface disruption under low pH conditions. Based on this, we propose a cluster-dependent mechanism that addresses inconsistencies in the histidine-switch hypothesis and highlights the role of cluster protonation in orchestrating the domain dissociation pivotal for the formation of the fusogenic trimer.

The Physical Basis for pH Sensitivity in Biomolecular Structure and Function, With Application to the Spike Protein of SARS-CoV-2

Since pH sensitivity has a fundamental role in biology, much effort has been committed to establishing physical models to rationalize and predict pH dependence from molecular structures. Two of the key challenges are to accurately calculate ionizable group solvation and hydration and then to apply this modeling to all conformations relevant to the process in question. Explicit solvent methods coupled to molecular dynamics simulation are increasingly complementing lower resolution implicit solvent techniques, but equally, the scale of biological data acquisition leaves a role for high-throughput modeling. Additionally, determination of ranges of structures for a system allows sampling of key stages in solvation. In a review of the area, it is emphasized that pH sensors in biology beyond the most obvious candidate (histidine side chain, with an unshifted pK a near neutral pH) should be considered; that modeling can benefit from other concepts in bioinformatics, in particular modulation of interactions and function in families of homologs; and that it can also be beneficial to incorporate as many experimental structures as possible, to mitigate against small variations in conformation and to analyze larger, functional, conformational changes. These aspects are then demonstrated with new work on the spike protein of SARS-CoV-2, looking at the pH dependence of variants, including prediction of a change in the balance of locked, closed, and open forms at neutral pH for the Omicron variant spike protein.

Predicted pH-dependent stability of SARS-CoV-2 spike protein trimer from interfacial acidic groups

Transition between receptor binding domain (RBD) up and down forms of the SARS-CoV-2 spike protein trimer is coupled to receptor binding and is one route by which variants can alter viral properties. It is becoming apparent that key roles in the transition are played by pH and a more compact closed form, termed locked. Calculations of pH-dependence are made for a large set of spike trimers, including locked form trimer structures that have recently become available. Several acidic sidechains become sufficiently buried in the locked form to give a predicted pH-dependence in the mild acidic range, with stabilisation of the locked form as pH reduces from 7.5 to 5, consistent with emerging characterisation by cryo-electron microscopy. The calculated pH effects in pre-fusion spike trimers are modulated mainly by aspartic acid residues, rather than the more familiar histidine role at mild acidic pH. These acidic sidechains are generally surface located and weakly interacting when not in a locked conformation. According to this model, their replacement (perhaps with asparagine) would remove the pH-dependent destabilisation of locked spike trimer conformations, and increase their recovery at neutral pH. This would provide an alternative or supplement to the insertion of disulphide linkages for stabilising spike protein trimers, with potential relevance for vaccine design.

A model for pH coupling of the SARS-CoV-2 spike protein open/closed equilibrium

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), causative agent of the coronavirus disease 2019 (COVID-19) pandemic, is thought to release its RNA genome at either the cell surface or within endosomes, the balance being dependent on spike protein stability, and the complement of receptors, co-receptors and proteases. To investigate possible mediators of pH-dependence, pKa calculations have been made on a set of structures for spike protein ectodomain and fragments from SARS-CoV-2 and other coronaviruses. Dominating a heat map of the aggregated predictions, three histidine residues in S2 are consistently predicted as destabilizing in pre-fusion (all three) and post-fusion (two of the three) structures. Other predicted features include the more moderate energetics of surface salt–bridge interactions and sidechain–mainchain interactions. Two aspartic acid residues in partially buried salt-bridges (D290–R273 and R355–D398) have pKas that are calculated to be elevated and destabilizing in more open forms of the spike trimer. These aspartic acids are most stabilized in a tightly closed conformation that has been observed when linoleic acid is bound, and which also affects the interactions of D614. The D614G mutation is known to modulate the balance of closed to open trimer. It is suggested that D398 in particular contributes to a pH-dependence of the open/closed equilibrium, potentially coupled to the effects of linoleic acid binding and D614G mutation, and possibly also A570D mutation. These observations are discussed in the context of SARS-CoV-2 infection, mutagenesis studies, and other human coronaviruses.

Protein-sol pKa: prediction of electrostatic frustration, with application to coronaviruses

Motivation

Evolution couples differences in ambient pH to biological function through protonatable groups, in particular, those that switch from buried to exposed and alter protonation state in doing so. We present a tool focusing on structure-based discovery and display of these groups.

Results

Since prediction of buried group pKas is computationally intensive, solvent accessibility of ionizable groups is displayed, from which the user can iteratively select pKa calculation centers. Results are color-coded, with emphasis on buried groups. Utility is demonstrated with benchmarking against known pH sensing sites in influenza virus hemagglutinin and in variants of murine hepatitis virus, a coronavirus. A pair of histidine residues, which are conserved in coronavirus spike proteins, are predicted to be electrostatically frustrated at acidic pH in both pre- and post-fusion conformations. We suggest that an intermediate expanded conformation at endosomal pH could relax the frustration, allowing histidine protonation and facilitating conformational conversion of coronavirus spike protein.

Availability and implementation

This tool is available at http://www.protein-sol.manchester.ac.uk/pka/.

Modelling of pH-dependence to develop a strategy for stabilising mAbs at acidic steps in production

Engineered proteins are increasingly being required to function or pass through environmental stresses for which the underlying protein has not evolved. A major example in health are antibody therapeutics, where a low pH step is used for purification and viral inactivation. In order to develop a computational model for analysis of pH-stability, predictions are compared with experimental data for the relative pH-sensitivities of antibody domains. The model is then applied to proteases that have evolved to be functional in an acid environment, showing a clear signature for low pH-dependence of stability in the neutral to acidic pH region, largely through reduction of salt-bridges. Interestingly, an extensively acidic protein surface can maintain contribution to structural stabilisation at acidic pH through replacement of basic sidechains with polar, hydrogen-bonding groups. These observations form a design principle for engineering acid-stable proteins.

PKA17-A Coarse-Grain Grid-Based Methodology and Web-Based Software for Predicting Protein pK a Shifts

We have developed and tested PKA17, a coarse-grain grid-based model for predicting protein pK _a shifts. Our pK _a predictor is currently deployed via a website interface. We have carried out parameter fitting using 442 Asp, Glu, His, Lys, and Arg residues for which experimental results are available in the literature. PROPKA software has been used for benchmarking. The average unsigned error and root-mean-square deviation (RMSD) have been found to be 0.628 and 0.831 pH units, respectively, for PKA17. The corresponding results with PROPKA are 0.761 and 1.063 units. We have assessed the robustness of the developed PKA17 methodology with a number of tests and have also explored the possibility of using a combination of PROPKA and PKA17 calculations in order to improve the accuracy of predicted pK _a values for protein residues. We have also once again confirmed that protein acidity constants are influenced almost entirely by residues in the immediate spatial proximity of the ionizable amino acids. The resulting PKA17 software has been deployed online with a web-based interface at http://users.wpi.edu/~jpcvitkovic/pka_calc.html. © 2019 Wiley Periodicals, Inc.

Web-based display of protein surface and pH-dependent properties for assessing the developability of biotherapeutics

Protein instability leads to reversible self-association and irreversible aggregation which is a major concern for developing new biopharmaceutical leads. Protein solution behaviour is dictated by the physicochemical properties of the protein and the solution. Optimising protein solutions through experimental screens and targeted protein engineering can be a difficult and time consuming process. Here, we describe development of the protein-sol web server, which was previously restricted to protein solubility prediction from amino acid sequence. Tools are presented for calculating and mapping patches of hydrophobicity and charge on the protein surface. In addition, predictions of folded state stability and net charge are displayed as a heatmap for a range of pH and ionic strength conditions. Tools are evaluated in the context of antibodies, their fragments and interactions. Surprisingly, antibody-antigen interfaces are, on average, at least as polar as Fab surfaces. This benchmarking process provides the user with thresholds with which to assess non-polar surface patches, and possible solubility implications, in proteins of interest. Stability heatmaps compare favourably with experimental data for CH2 and CH3 domains. Display and quantification of surface polarity and pH/ionic strength dependence will be useful generally for investigation of protein biophysics.

Robustness and Efficiency of Poisson-Boltzmann Modeling on Graphics Processing Units

Poisson-Boltzmann equation (PBE) based continuum electrostatics models have been widely used in modeling electrostatic interactions in biochemical processes, particularly in estimating protein-ligand binding affinities. Fast convergence of PBE solvers is crucial in binding affinity computations as numerous snapshots need to be processed. Efforts have been reported to develop PBE solvers on graphics processing units (GPUs) for efficient modeling of biomolecules, though only relatively simple successive over-relaxation and conjugate gradient methods were implemented. However, neither convergence nor scaling properties of the two methods are optimal for large biomolecules. On the other hand, geometric multigrid (MG) has been shown to be an optimal solver on CPUs, though no MG have been reported for biomolecular applications on GPUs. This is not a surprise as it is a more complex method and depends on simpler but limited iterative methods such as Gauss-Seidel in its core relaxation procedure. The robustness and efficiency of MG on GPUs are also unclear. Here we present an implementation and a thorough analysis of MG on GPUs. Our analysis shows that robustness is a more pronounced issue than efficiency for both MG and other tested solvers when the single precision is used for complex biomolecules. We further show how to balance robustness and efficiency utilizing MG's overall efficiency and conjugate gradient's robustness, pointing to a hybrid GPU solver with a good balance of efficiency and accuracy. The new PBE solver will significantly improve the computational throughput for a range of biomolecular applications on the GPU platforms.

DelPhiPKa: Including salt in the calculations and enabling polar residues to titrate

DelPhiPKa is a widely used and unique approach to compute pK_a 's of ionizable groups that does not require molecular surface to be defined. Instead, it uses smooth Gaussian-based dielectric function to treat computational space via Poisson-Boltzmann equation (PBE). Here, we report an expansion of DelPhiPKa functionality to enable inclusion of salt in the modeling protocol. The method considers the salt mobile ions in solvent phase without defining solute-solvent boundary. Instead, the ions are penalized to enter solute interior via a desolvation penalty term in the Boltzmann factor in the framework of PBE. Hence, the concentration of ions near the protein is balanced by the desolvation penalty and electrostatic interactions. The study reveals that correlation between experimental and calculated pK_a 's is improved significantly by taking into consideration the presence of salt. Furthermore, it is demonstrated that DelphiPKa reproduces the salt sensitivity of experimentally measured pK_a 's. Another new development of DelPhiPKa allows for computing the pK_a 's of polar residues such as cysteine, serine, threonine and tyrosine. With this regard, DelPhiPKa is benchmarked against experimentally measured cysteine and tyrosine pK_a 's and for cysteine it is shown to outperform other existing methods (DelPhiPKa RMSD of 1.73 vs RMSD between 2.40 and 4.72 obtained by other existing pK_a prediction methods).

Exploring a multi-scale method for molecular simulation in continuum solvent model: Explicit simulation of continuum solvent as an incompressible fluid

We explored a multi-scale algorithm for the Poisson-Boltzmann continuum solvent model for more robust simulations of biomolecules. In this method, the continuum solvent/solute interface is explicitly simulated with a numerical fluid dynamics procedure, which is tightly coupled to the solute molecular dynamics simulation. There are multiple benefits to adopt such a strategy as presented below. At this stage of the development, only nonelectrostatic interactions, i.e., van der Waals and hydrophobic interactions, are included in the algorithm to assess the quality of the solvent-solute interface generated by the new method. Nevertheless, numerical challenges exist in accurately interpolating the highly nonlinear van der Waals term when solving the finite-difference fluid dynamics equations. We were able to bypass the challenge rigorously by merging the van der Waals potential and pressure together when solving the fluid dynamics equations and by considering its contribution in the free-boundary condition analytically. The multi-scale simulation method was first validated by reproducing the solute-solvent interface of a single atom with analytical solution. Next, we performed the relaxation simulation of a restrained symmetrical monomer and observed a symmetrical solvent interface at equilibrium with detailed surface features resembling those found on the solvent excluded surface. Four typical small molecular complexes were then tested, both volume and force balancing analyses showing that these simple complexes can reach equilibrium within the simulation time window. Finally, we studied the quality of the multi-scale solute-solvent interfaces for the four tested dimer complexes and found that they agree well with the boundaries as sampled in the explicit water simulations.

Recent Developments and Applications of the MMPBSA Method

The Molecular Mechanics Poisson-Boltzmann Surface Area (MMPBSA) approach has been widely applied as an efficient and reliable free energy simulation method to model molecular recognition, such as for protein-ligand binding interactions. In this review, we focus on recent developments and applications of the MMPBSA method. The methodology review covers solvation terms, the entropy term, extensions to membrane proteins and high-speed screening, and new automation toolkits. Recent applications in various important biomedical and chemical fields are also reviewed. We conclude with a few future directions aimed at making MMPBSA a more robust and efficient method.

Features of reactive cysteines discovered through computation: from kinase inhibition to enrichment around protein degrons

Large-scale characterisation of cysteine modification is enabling study of the physicochemical determinants of reactivity. We find that location of cysteine at the amino terminus of an α-helix, associated with activity in thioredoxins, is under-represented in human protein structures, perhaps indicative of selection against background reactivity. An amino-terminal helix location underpins the covalent linkage for one class of kinase inhibitors. Cysteine targets for S-palmitoylation, S-glutathionylation, and S-nitrosylation show little correlation with pKa values predicted from structures, although flanking sequences of S-palmitoylated sites are enriched in positively-charged amino acids, which could facilitate palmitoyl group transfer to substrate cysteine. A surprisingly large fraction of modified sites, across the three modifications, would be buried in native protein structure. Furthermore, modified cysteines are (on average) closer to lysine ubiquitinations than are unmodified cysteines, indicating that cysteine redox biology could be associated with protein degradation and degron recognition.

Sequence composition predicts immunoglobulin superfamily members that could share the intrinsically disordered properties of antibody CH1 domains

Antibodies are central to the growing sector of protein therapeutics, and increasingly they are being manipulated as fragments and combinations. An improved understanding of the properties of antibody domains in isolation would aid in their engineering. We have conducted an analysis of sequence and domain interactions for IgG antibodies and Fab fragments in the structural database. Of sequence-related properties studied, relative lysine to arginine content was found to be higher in CH1 and CL than in variable domains. As earlier work shows that lysine is favoured over arginine in more soluble proteins, this suggests that individual domains may not be optimised for greater solubility, giving scope for fragment engineering. Across other sequence-based features, CH1 is anomalous. A sequence-based scheme predicts CH1 to be folded, although it is known that CH1 folding is linked to IgG assembly and secretion. Calculations indicate that charge interactions in CH1 domains contribute less to folded state stability than in other Fab domains. Expanding to the immunoglobulin superfamily reveals that a subset of non-antibody domains shares sequence composition properties with CH1, leading us to suggest that some of these may also couple folding, assembly and secretion.

Prediction of Reduction Potentials of Copper Proteins with Continuum Electrostatics and Density Functional Theory

Blue copper proteins, such as azurin, show dramatic changes in Cu²⁺/Cu⁺ reduction potential upon mutation over the full physiological range. Hence, they have important functions in electron transfer and oxidation chemistry and have applications in industrial biotechnology. The details of what determines these reduction potential changes upon mutation are still unclear. Moreover, it has been difficult to model and predict the reduction potential of azurin mutants and currently no unique procedure or workflow pattern exists. Furthermore, high‐level computational methods can be accurate but are too time consuming for practical use. In this work, a novel approach for calculating reduction potentials of azurin mutants is shown, based on a combination of continuum electrostatics, density functional theory and empirical hydrophobicity factors. Our method accurately reproduces experimental reduction potential changes of 30 mutants with respect to wildtype within experimental error and highlights the factors contributing to the reduction potential change. Finally, reduction potentials are predicted for a series of 124 new mutants that have not yet been investigated experimentally. Several mutants are identified that are located well over 10 Å from the copper center that change the reduction potential by more than 85 mV. The work shows that secondary coordination sphere mutations mostly lead to long‐range electrostatic changes and hence can be modeled accurately with continuum electrostatics.

A Continuum Poisson-Boltzmann Model for Membrane Channel Proteins

Membrane proteins constitute a large portion of the human proteome and perform a variety of important functions as membrane receptors, transport proteins, enzymes, signaling proteins, and more. Computational studies of membrane proteins are usually much more complicated than those of globular proteins. Here, we propose a new continuum model for Poisson-Boltzmann calculations of membrane channel proteins. Major improvements over the existing continuum slab model are as follows: (1) The location and thickness of the slab model are fine-tuned based on explicit-solvent MD simulations. (2) The highly different accessibilities in the membrane and water regions are addressed with a two-step, two-probe grid-labeling procedure. (3) The water pores/channels are automatically identified. The new continuum membrane model is optimized (by adjusting the membrane probe, as well as the slab thickness and center) to best reproduce the distributions of buried water molecules in the membrane region as sampled in explicit water simulations. Our optimization also shows that the widely adopted water probe of 1.4 Å for globular proteins is a very reasonable default value for membrane protein simulations. It gives the best compromise in reproducing the explicit water distributions in membrane channel proteins, at least in the water accessible pore/channel regions. Finally, we validate the new membrane model by carrying out binding affinity calculations for a potassium channel, and we observe good agreement with the experimental results.

Acceleration of Linear Finite-Difference Poisson-Boltzmann Methods on Graphics Processing Units

Electrostatic interactions play crucial roles in biophysical processes such as protein folding and molecular recognition. Poisson-Boltzmann equation (PBE)-based models have emerged as widely used in modeling these important processes. Though great efforts have been put into developing efficient PBE numerical models, challenges still remain due to the high dimensionality of typical biomolecular systems. In this study, we implemented and analyzed commonly used linear PBE solvers for the ever-improving graphics processing units (GPU) for biomolecular simulations, including both standard and preconditioned conjugate gradient (CG) solvers with several alternative preconditioners. Our implementation utilizes the standard Nvidia CUDA libraries cuSPARSE, cuBLAS, and CUSP. Extensive tests show that good numerical accuracy can be achieved given that the single precision is often used for numerical applications on GPU platforms. The optimal GPU performance was observed with the Jacobi-preconditioned CG solver, with a significant speedup over standard CG solver on CPU in our diversified test cases. Our analysis further shows that different matrix storage formats also considerably affect the efficiency of different linear PBE solvers on GPU, with the diagonal format best suited for our standard finite-difference linear systems. Further efficiency may be possible with matrix-free operations and integrated grid stencil setup specifically tailored for the banded matrices in PBE-specific linear systems.

Numerical interpretation of molecular surface field in dielectric modeling of solvation

Continuum solvent models, particularly those based on the Poisson-Boltzmann equation (PBE), are widely used in the studies of biomolecular structures and functions. Existing PBE developments have been mainly focused on how to obtain more accurate and/or more efficient numerical potentials and energies. However to adopt the PBE models for molecular dynamics simulations, a difficulty is how to interpret dielectric boundary forces accurately and efficiently for robust dynamics simulations. This study documents the implementation and analysis of a range of standard fitting schemes, including both one-sided and two-sided methods with both first-order and second-order Taylor expansions, to calculate molecular surface electric fields to facilitate the numerical calculation of dielectric boundary forces. These efforts prompted us to develop an efficient approximated one-dimensional method, which is to fit the surface field one dimension at a time, for biomolecular applications without much compromise in accuracy. We also developed a surface-to-atom force partition scheme given a level set representation of analytical molecular surfaces to facilitate their applications to molecular simulations. Testing of these fitting methods in the dielectric boundary force calculations shows that the second-order methods, including the one-dimensional method, consistently perform among the best in the molecular test cases. Finally, the timing analysis shows the approximated one-dimensional method is far more efficient than standard second-order methods in the PBE force calculations. © 2017 Wiley Periodicals, Inc.

Modeling Membrane Protein-Ligand Binding Interactions: The Human Purinergic Platelet Receptor

Membrane proteins, due to their roles as cell receptors and signaling mediators, make prime candidates for drug targets. The computational analysis of protein-ligand binding affinities has been widely employed as a tool in rational drug design efforts. Although efficient implicit solvent-based methods for modeling globular protein-ligand binding have been around for many years, the extension of such methods to membrane protein-ligand binding is still in its infancy. In this study, we extended the widely used Amber/MMPBSA method to model membrane protein-ligand systems, and we used it to analyze protein-ligand binding for the human purinergic platelet receptor (P2Y12R), a prominent drug target in the inhibition of platelet aggregation for the prevention of myocardial infarction and stroke. The binding affinities, computed by the Amber/MMPBSA method using standard parameters, correlate well with experiment. A detailed investigation of these parameters was conducted to assess their impact on the accuracy of the method. These analyses show the importance of properly treating the nonpolar solvation interactions and the electrostatic polarization in the binding of nucleotide agonists and non-nucleotide antagonists to P2Y12R. On the basis of the crystal structures and the experimental conditions in the binding assay, we further hypothesized that the nucleotide agonists lose their bound magnesium ion upon binding to P2Y12R, and our computational study supports this hypothesis. Ultimately, this work illustrates the value of computational analysis in the interpretation of experimental binding reactions.

Calculating protein-ligand binding affinities with MMPBSA: Method and error analysis

Molecular Mechanics Poisson-Boltzmann Surface Area (MMPBSA) methods have become widely adopted in estimating protein-ligand binding affinities due to their efficiency and high correlation with experiment. Here different computational alternatives were investigated to assess their impact to the agreement of MMPBSA calculations with experiment. Seven receptor families with both high-quality crystal structures and binding affinities were selected. First the performance of nonpolar solvation models was studied and it was found that the modern approach that separately models hydrophobic and dispersion interactions dramatically reduces RMSD's of computed relative binding affinities. The numerical setup of the Poisson-Boltzmann methods was analyzed next. The data shows that the impact of grid spacing to the quality of MMPBSA calculations is small: the numerical error at the grid spacing of 0.5 Å is already small enough to be negligible. The impact of different atomic radius sets and different molecular surface definitions was further analyzed and weak influences were found on the agreement with experiment. The influence of solute dielectric constant was also analyzed: a higher dielectric constant generally improves the overall agreement with experiment, especially for highly charged binding pockets. The data also showed that the converged simulations caused slight reduction in the agreement with experiment. Finally the direction of estimating absolute binding free energies was briefly explored. Upon correction of the binding-induced rearrangement free energy and the binding entropy lost, the errors in absolute binding affinities were also reduced dramatically when the modern nonpolar solvent model was used, although further developments were apparently necessary to further improve the MMPBSA methods. © 2016 Wiley Periodicals, Inc.

Polyunsaturated fatty acids inhibit Kv1.4 by interacting with positively charged extracellular pore residues

Polyunsaturated fatty acids (PUFAs) modulate voltage-gated K(+) channel inactivation by an unknown site and mechanism. The effects of ω-6 and ω-3 PUFAs were investigated on the heterologously expressed Kv1.4 channel. PUFAs inhibited wild-type Kv1.4 during repetitive pulsing as a result of slowing of recovery from inactivation. In a mutant Kv1.4 channel lacking N-type inactivation, PUFAs reversibly enhanced C-type inactivation (Kd, 15-43 μM). C-type inactivation was affected by extracellular H(+) and K(+) as well as PUFAs and there was an interaction among the three: the effect of PUFAs was reversed during acidosis and abolished on raising K(+) Replacement of two positively charged residues in the extracellular pore (H508 and K532) abolished the effects of the PUFAs (and extracellular H(+) and K(+)) on C-type inactivation but had no effect on the lipoelectric modulation of voltage sensor activation, suggesting two separable interaction sites/mechanisms of action of PUFAs. Charge calculations suggest that the acidic head group of the PUFAs raises the pKa of H508 and this reduces the K(+) occupancy of the selectivity filter, stabilizing the C-type inactivated state.

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 pKa 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 pKa 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 pKa shifts of various single point mutations in staphylococcal nuclease (SNase) from pKa-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 pKa predictions for buried carboxyl residues. Finally, the pKa calculations on two RNAs demonstrated the capability of this approach for other types of biomolecules.

Energetic Calculations to Decipher pH-Dependent Oligomerization and Domain Swapping of Proteins

Domain swapping mechanism is a specialised mode of oligomerization of proteins in which part of a protein is exchanged in a non-covalent manner between constituent subunits. This mechanism is highly affected by several physiological conditions. Here, we present a detailed analysis ofthe effect of pH on different regions of the domain swapped oligomer by considering examples which are known to be sensitive to pH in transiting from monomeric to domain-swapped dimeric form. The energetic calculations were performed using a specialized method which considers changes in pH and subsequent changes in the interactions between subunits. This analysis provides definitive hints about the pH-dependence switch from monomer to domain-swapped oligomer and the steps that may be involved in the swapping mechanism.

Computational Tools for Interpreting Ion Channel pH-Dependence

Activity in many biological systems is mediated by pH, involving proton titratable groups with pKas in the relevant pH range. Experimental analysis of pH-dependence in proteins focusses on particular sidechains, often with mutagenesis of histidine, due to its pKa near to neutral pH. The key question for algorithms that predict pKas is whether they are sufficiently accurate to effectively narrow the search for molecular determinants of pH-dependence. Through analysis of inwardly rectifying potassium (Kir) channels and acid-sensing ion channels (ASICs), mutational effects on pH-dependence are probed, distinguishing between groups described as pH-coupled or pH-sensor. Whereas mutation can lead to a shift in transition pH between open and closed forms for either type of group, only for pH-sensor groups does mutation modulate the amplitude of the transition. It is shown that a hybrid Finite Difference Poisson-Boltzmann (FDPB) – Debye-Hückel continuum electrostatic model can filter mutation candidates, providing enrichment for key pH-coupled and pH-sensor residues in both ASICs and Kir channels, in comparison with application of FDPB alone.

Structure and mechanism of the bifunctional CinA enzyme from Thermus thermophilus

CinA is a widely distributed protein in Gram-positive and Gram-negative bacteria. It is associated with natural competence and is proposed to have a function as an enzyme participating in the pyridine nucleotide cycle, which recycles products formed by non-redox uses of NAD. Here we report the determination of the crystal structure of CinA from Thermus thermophilus, in complex with several ligands. CinA was shown to have both nicotinamide mononucleotide deamidase and ADP-ribose pyrophosphatase activities. The crystal structure shows an unusual asymmetric dimer, with three domains for each chain; the C-terminal domain harbors the nicotinamide mononucleotide deamidase activity, and the structure of a complex with the product nicotinate mononucleotide suggests a mechanism for deamidation. The N-terminal domain belongs to the COG1058 family and is associated with the ADP-ribose pyrophosphatase activity. The asymmetry in the CinA dimer arises from two alternative orientations of the COG1058 domains, only one of which forms a contact with the KH-type domain from the other chain, effectively closing the active site into, we propose, a catalytically competent state. Structures of complexes with Mg²⁺/ADP-ribose, Mg²⁺/ATP, and Mg²⁺/AMP suggest a mechanism for the ADP-ribose pyrophosphatase reaction that involves a rotation of the COG1058 domain dimer as part of the reaction cycle, so that each active site oscillates between open and closed forms, thus promoting catalysis.

Biological applications of classical electrostatics methods

Continuum electrostatics modeling of solvation based on the Poisson–Boltzmann (PB) equation has gained wide acceptance in biomolecular applications such as energetic analysis and structural visualization. Successful application of the PB solvent models requires careful calibration of the solvation parameters. Extensive testing and validation is also important to ensure accuracy in their applications. Limitation in the continuum modeling of solvation is also a known issue in certain biomolecular applications. Growing interest in membrane systems has further spurred developmental efforts to allow inclusion of membrane in the PB solvent models. Despite their past successes due to careful parameterization, algorithm development and parallel implementation, there is still much to be done to improve their transferability from the small molecular systems upon which they were developed and validated to complex macromolecular systems as advances in technology continue to push forward, providing ever greater computational resources to researchers to study more interesting biological systems of higher complexity.

Visualization of poly(ADP-ribose) bound to PARG reveals inherent balance between exo- and endo-glycohydrolase activities

Poly-ADP-ribosylation is a post-translational modification that regulates processes involved in genome stability. Breakdown of the poly(ADP-ribose) (PAR) polymer is catalysed by poly(ADP-ribose) glycohydrolase (PARG), whose endo-glycohydrolase activity generates PAR fragments. Here we present the crystal structure of PARG incorporating the PAR substrate. The two terminal ADP-ribose units of the polymeric substrate are bound in exo-mode. Biochemical and modelling studies reveal that PARG acts predominantly as an exo-glycohydrolase. This preference is linked to Phe902 (human numbering), which is responsible for low-affinity binding of the substrate in endo-mode. Our data reveal the mechanism of poly-ADP-ribosylation reversal, with ADP-ribose as the dominant product, and suggest that the release of apoptotic PAR fragments occurs at unusual PAR/PARG ratios.

Decrease in fruit moisture content heralds and might launch the onset of ripening processes

It is known that fruit ripening is a genetically programmed event but it is not entirely clear what metabolic cue(s) stimulate the onset of ripening, ethylene action notwithstanding. Here, we examined the conjecture that fruit ripening might be evoked by an autonomously induced decrease in tissue water status. We found decline in water content occurring at the onset of ripening in climacteric and nonclimacteric fruit, suggesting that this phenomenon might be universal. This decline in water content persisted throughout the ripening process in some fruit, whereas in others it reversed during the progression of the ripening process. Applied ethylene also induced a decrease in water content in potato (Solanum tuberosum) tubers. In ethylene-mutant tomato (Solanum lycopersicum) fruit (antisense to1-aminocyclopropane carboxylate synthase), cold-induced decline in water content stimulated onset of ripening processes apparently independently of ethylene action, suggesting cause-and-effect relationship between decreasing water content and onset of ripening. The decline in tissue water content, occurring naturally or induced by ethylene, was strongly correlated with a decrease in hydration (swelling) efficacy of cell wall preparations suggesting that hydration dynamics of cell walls might account for changes in tissue moisture content. Extent of cell wall swelling was, in turn, related to the degree of oxidative cross-linking of wall-bound phenolic acids, suggesting that oxidant-induced wall restructuring might mediate cell wall and, thus, fruit tissue hydration status. We propose that oxidant-induced cell wall remodeling and consequent wall dehydration might evoke stress signaling for the onset of ripening processes.

PRACTICAL APPLICATION

This study suggests that decline in fruit water content is an early event in fruit ripening. This information may be used to gauge fruit maturity for appropriate harvest date and for processing. Control of fruit hydration state might be used to regulate the onset of fruit ripening.

The transcriptional regulator CprK detects chlorination by combining direct and indirect readout mechanisms

The transcriptional regulator CprK controls the expression of the reductive dehalogenase CprA in organohalide-respiring bacteria. Desulfitobacterium hafniense CprA catalyses the reductive dechlorination of the terminal electron acceptor o-chlorophenol acetic acid, generating the phenol acetic acid product. It has been shown that CprK has ability to distinguish between the chlorinated CprA substrate and the de-halogenated end product, with an estimated an estimated 10⁴-fold difference in affinity. Using a green fluorescent protein GFP_UV-based transcriptional reporter system, we establish that CprK can sense o-chlorophenol acetic acid at the nanomolar level, whereas phenol acetic acid leads to transcriptional activation only when approaching micromolar levels. A structure–activity relationship study, using a range of o-chlorophenol acetic-acid-related compounds and key CprK mutants, combined with pK_a calculations on the effector binding site, suggests that the sensitive detection of chlorination is achieved through a combination of direct and indirect readout mechanisms. Both the physical presence of the bulky chloride substituent as well as the accompanying electronic effects lowering the inherent phenol pK_a are required for high affinity. Indeed, transcriptional activation by CprK appears strictly dependent on establishing a phenolate–K133 salt bridge interaction, rather than on the presence of a halogen atom per se. As K133 is strictly conserved within the CprK family, our data suggest that physiological function and future applications in biosensing are probably restricted to phenolic compounds.

pH-replica exchange molecular dynamics in proteins using a discrete protonation method

Protonation equilibria in biological molecules modulates structure, dynamics, and function. A pH-replica exchange molecular dynamics (pH-REMD) method is described here to improve the coupling between conformational and protonation sampling. Under a Hamiltonian replica exchange setup, conformations are swapped between two neighboring replicas, which themselves are at different pHs. The method has been validated on a series of biological systems. We applied pH-REMD to a series of model compounds, to an terminally charged ADFDA pentapeptide, and to a heptapeptide derived from the ovomucoid third domain (OMTKY3). In all of those systems, the predicted pK(a) by pH-REMD is very close to the experimental value and almost identical to the ones obtained by constant pH molecular dynamics (CpH MD). The method presented here, pH-REMD, has the advantage of faster convergence properties due to enhanced sampling of both conformation and protonation spaces.

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.

Developing hybrid approaches to predict pKa values of ionizable groups

Accurate predictions of pKa values of titratable groups require taking into account all relevant processes associated with the ionization/deionization. Frequently, however, the ionization does not involve significant structural changes and the dominating effects are purely electrostatic in origin allowing accurate predictions to be made based on the electrostatic energy difference between ionized and neutral forms alone using a static structure and the subtle structural changes be accounted by using dielectric constant larger than two. On another hand, if the change of the charge state is accompanied by a large structural reorganization of the target protein, then the relevant conformational changes have to be explicitly taken into account in the pKa calculations. Here we report a hybrid approach that first predicts the titratable groups whose ionization is expected to cause large conformational changes, termed "problematic" residues, and then applies a special protocol on them, while the rest of the pK(a)s are predicted with rigid backbone approach as implemented in multi-conformation continuum electrostatics (MCCE) method. The backbone representative conformations for "problematic" groups are generated with either molecular dynamics simulations with charged and uncharged amino acid or with ab-initio local segment modeling. The corresponding ensembles are then used to calculate the titration curves of the "problematic" residues and then the results are averaged to obtain the corresponding pKa.

pKa predictions with a coupled finite difference Poisson-Boltzmann and Debye-Hückel method

Modeling charge interactions is important for understanding many aspects of biological structure and function, and continuum methods such as Finite Difference Poisson-Boltzmann (FDPB) are commonly employed. Calculations of pH-dependence have identified separate populations; surface groups that can be modeled with a simple Debye-Hückel (DH) model, and buried groups, with stronger resultant interactions that are dependent on detailed conformation. This observation led to the development of a combined FDPB and DH method for pK(a) prediction (termed FD/DH). This study reports application of this method to ionizable groups, including engineered buried charges, in staphylococcal nuclease. The data had been made available to interested research groups before publication of mutant structures and/or pK(a) values. Overall, FD/DH calculations perform as intended with low ΔpK(a) values for surface groups (RMSD between predicted and experimental pK(a) values of 0.74), and much larger ΔpK(a) values for the engineered internal groups, with RMSD = 1.64, where mutant structures were known and RMSD = 1.80, where they were modeled. The weaker resultant interactions of the surface groups are determined mostly by charge-charge interactions. For the buried groups, R(2) for correlation between predicted and measured ΔpK(a) values is 0.74, despite the high RMSDs. Charge-charge interactions are much less important, with the R(2) value for buried group ΔpK(a) values increasing to 0.80 when the term describing charge desolvation alone is used. Engineered charge burial delivers a relatively uniform, nonspecific effect, in terms of pK(a) . How the protein environment adapts in atomic detail to deliver this resultant effect is still an open question.

Multiscale molecular dynamics using the matched interface and boundary method

The Poisson-Boltzmann (PB) equation is an established multiscale model for electrostatic analysis of biomolecules and other dielectric systems. PB based molecular dynamics (MD) approach has a potential to tackle large biological systems. Obstacles that hinder the current development of PB based MD methods are concerns in accuracy, stability, efficiency and reliability. The presence of complex solvent-solute interface, geometric singularities and charge singularities leads to challenges in the numerical solution of the PB equation and electrostatic force evaluation in PB based MD methods. Recently, the matched interface and boundary (MIB) method has been utilized to develop the first second order accurate PB solver that is numerically stable in dealing with discontinuous dielectric coefficients, complex geometric singularities and singular source charges. The present work develops the PB based MD approach using the MIB method. New formulation of electrostatic forces is derived to allow the use of sharp molecular surfaces. Accurate reaction field forces are obtained by directly differentiating the electrostatic potential. Dielectric boundary forces are evaluated at the solvent-solute interface using an accurate Cartesian-grid surface integration method. The electrostatic forces located at reentrant surfaces are appropriately assigned to related atoms. Extensive numerical tests are carried out to validate the accuracy and stability of the present electrostatic force calculation. The new PB based MD method is implemented in conjunction with the AMBER package. MIB based MD simulations of biomolecules are demonstrated via a few example systems.

The K5 lyase KflA combines a viral tail spike structure with a bacterial polysaccharide lyase mechanism

K5 lyase A (KflA) is a tail spike protein (TSP) encoded by a K5A coliphage, which cleaves K5 capsular polysaccharide, a glycosaminoglycan with the repeat unit [-4)-betaGlcA-(1,4)- alphaGlcNAc(1-], displayed on the surface of Escherichia coli K5 strains. The crystal structure of KflA reveals a trimeric arrangement, with each monomer containing a right-handed, single-stranded parallel beta-helix domain. Stable trimer formation by the intertwining of strands in the C-terminal domain, followed by proteolytic maturation, is likely to be catalyzed by an autochaperone as described for K1F endosialidase. The structure of KflA represents the first bacteriophage tail spike protein combining polysaccharide lyase activity with a single-stranded parallel beta-helix fold. We propose a catalytic site and mechanism representing convergence with the syn-beta-elimination site of heparinase II from Pedobacter heparinus.

Continuum electrostatic calculations of the pKa of ionizable residues in an ion channel: dynamic vs. static input structure

We have computed the pK(a)'s of the ionizable residues of a protein ion channel, the Staphylococcus aureus toxin alpha-hemolysin, by using two types of input structures, namely the crystal structure of the heptameric alpha-hemolysin and a set of over four hundred snapshots from a 4.38 ns Molecular Dynamics simulation of the protein inserted in a phospholipid planar bilayer. The comparison of the dynamic picture provided by the Molecular Simulation with the static one based on the X-ray crystal structure of the protein embedded in a lipid membrane allows analyzing the influence of the fluctuations in the protein structure on its ionization properties. We find that the use of the dynamic structure provides interesting information about the sensitivity of the computed pK(a) of a given residue to small changes in the local structure. The calculated pK(a) are consistent with previous indirect estimations obtained from single-channel conductance and selectivity measurements.

Predicting pKa

One of the most important physicochemical properties of small molecules and macromolecules are the dissociation constants for any weakly acidic or basic groups, generally expressed as the pK(a) of each group. This is a major factor in the pharmacokinetics of drugs and in the interactions of proteins with other molecules. For both the protein and small molecule cases, we survey the sources of experimental pK(a) values and then focus on current methods for predicting them. Of particular concern is an analysis of the scope, statistical validity, and predictive power of methods as well as their accuracy.

MCCE2: improving protein pKa calculations with extensive side chain rotamer sampling

Multiconformation continuum electrostatics (MCCE) explores different conformational degrees of freedom in Monte Carlo calculations of protein residue and ligand pK(a)s. Explicit changes in side chain conformations throughout a titration create a position dependent, heterogeneous dielectric response giving a more accurate picture of coupled ionization and position changes. The MCCE2 methods for choosing a group of input heavy atom and proton positions are described. The pK(a)s calculated with different isosteric conformers, heavy atom rotamers and proton positions, with different degrees of optimization are tested against a curated group of 305 experimental pK(a)s in 33 proteins. QUICK calculations, with rotation around Asn and Gln termini, sampling His tautomers and torsion minimum hydroxyls yield an RMSD of 1.34 with 84% of the errors being <1.5 pH units. FULL calculations adding heavy atom rotamers and side chain optimization yield an RMSD of 0.90 with 90% of the errors <1.5 pH unit. Good results are also found for pK(a)s in the membrane protein bacteriorhodopsin. The inclusion of extra side chain positions distorts the dielectric boundary and also biases the calculated pK(a)s by creating more neutral than ionized conformers. Methods for correcting these errors are introduced. Calculations are compared with multiple X-ray and NMR derived structures in 36 soluble proteins. Calculations with X-ray structures give significantly better pK(a)s. Results with the default protein dielectric constant of 4 are as good as those using a value of 8. The MCCE2 program can be downloaded from http://www.sci.ccny.cuny.edu/~mcce.

Evidence for the adaptation of protein pH-dependence to subcellular pH

BACKGROUND

The availability of genome sequences, and inferred protein coding genes, has led to several proteome-wide studies of isoelectric points. Generally, isoelectric points are distributed following variations on a biomodal theme that originates from the predominant acid and base amino acid sidechain pKas. The relative populations of the peaks in such distributions may correlate with environment, either for a whole organism or for subcellular compartments. There is also a tendency for isoelectric points averaged over a subcellular location to not coincide with the local pH, which could be related to solubility. We now calculate the correlation of other pH-dependent properties, calculated from 3D structure, with subcellular pH.

RESULTS

For proteins with known structure and subcellular annotation, the predicted pH at which a protein is most stable, averaged over a location, gives a significantly better correlation with subcellular pH than does isoelectric point. This observation relates to the cumulative properties of proteins, since maximal stability for individual proteins follows the bimodal isoelectric point distribution. Histidine residue location underlies the correlation, a conclusion that is tested against a background of proteins randomised with respect to this feature, and for which the observed correlation drops substantially.

CONCLUSION

There exists a constraint on protein pH-dependence, in relation to the local pH, that is manifested in the pKa distribution of histidine sub-proteomes. This is discussed in terms of protein stability, pH homeostasis, and fluctuations in proton concentration.

Improved pK(a) prediction: combining empirical and semimicroscopic methods

Using three different methods we tried to compute 171 experimentally known pK(a) values of ionizable residues from 15 different proteins and compared the accuracies of computed pK(a) values in terms of the root mean square deviation (RMSD) from experiment. One method is based on a continuum electrostatic model of the protein including conformational flexibility (KBPLUS). The others are empirical approaches with PROPKA deploying physically motivated energy terms with adjustable parameters and PKAcal using an empirical function with no physical basis. PROPKA reproduced the pK(a) values with highest overall accuracy. Differentiating the data set into weakly and strongly shifted experimental pK(a) values, however, we found that PROPKA's accuracy is better if the pK(a) values are weakly shifted but on equal footing with that of KBPLUS for more strongly shifted values. On the other hand, PKAcal reproduces strongly shifted pK(a) values badly but weakly shifted values with the same accuracy as PROPKA. We tested different consensus approaches combining data from all three methods to find a general procedure for most accurate pK(a) predictions. In most of the cases we found that the consensus approach reproduced experimental data with better accuracy than any of the individual methods alone.

Volume-based solvation models out-perform area-based models in combined studies of wild-type and mutated protein-protein interfaces

BACKGROUND

Empirical binding models have previously been investigated for the energetics of protein complexation (DeltaG models) and for the influence of mutations on complexation (i.e. differences between wild-type and mutant complexes, DeltaDeltaG models). We construct binding models to directly compare these processes, which have generally been studied separately.

RESULTS

Although reasonable fit models were found for both DeltaG and DeltaDeltaG cases, they differ substantially. In a dataset curated for the absence of mainchain rearrangement upon binding, non-polar area burial is a major determinant of DeltaG models. However this DeltaG model does not fit well to the data for binding differences upon mutation. Burial of non-polar area is weighted down in fitting of DeltaDeltaG models. These calculations were made with no repacking of sidechains upon complexation, and only minimal packing upon mutation. We investigated the consequences of more extensive packing changes with a modified mean-field packing scheme. Rather than emphasising solvent exposure with relatively extended sidechains, rotamers are selected that exhibit maximal packing with protein. This provides solvent accessible areas for proteins that are much closer to those of experimental structures than the more extended sidechain regime. The new packing scheme increases changes in non-polar burial for mutants compared to wild-type proteins, but does not substantially improve agreement between DeltaG and DeltaDeltaG binding models.

CONCLUSION

We conclude that solvent accessible area, based on modelled mutant structures, is a poor correlate for DeltaDeltaG upon mutation. A simple volume-based, rather than solvent accessibility-based, model is constructed for DeltaG and DeltaDeltaG systems. This shows a more consistent behaviour. We discuss the efficacy of volume, as opposed to area, approaches to describe the energetic consequences of mutations at interfaces. This knowledge can be used to develop simple computational screens for binding in comparative modelled interfaces.

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.

Optimizing pKa computation in proteins with pH adapted conformations

pK(A) in proteins are determined by electrostatic energy computations using a small number of optimized protein conformations derived from crystal structures. In these protein conformations hydrogen positions and geometries of salt bridges on the protein surface were determined self-consistently with the protonation pattern at three pHs (low, ambient, and high). Considering salt bridges at protein surfaces is most relevant, since they open at low and high pH. In the absence of these conformational changes, computed pK(A)(comp) of acidic (basic) groups in salt bridges underestimate (overestimate) experimental pK(A)(exp), dramatically. The pK(A)(comp) for 15 different proteins with 185 known pK(A)(exp) yield an RMSD of 1.12, comparable with two other methods. One of these methods is fully empirical with many adjustable parameters. The other is also based on electrostatic energy computations using many non-optimized side chain conformers but employs larger dielectric constants at short distances of charge pairs that diminish their electrostatic interactions. These empirical corrections that account implicitly for additional conformational flexibility were needed to describe the energetics of salt bridges appropriately. This is not needed in the present approach. The RMSD of the present approach improves if one considers only strongly shifted pK(A)(exp) in contrast to the other methods under these conditions. Our method allows interpreting pK(A)(comp) in terms of pH dependent hydrogen bonding pattern and salt bridge geometries. A web service is provided to perform pK(A) computations.