Reproducing basic pKa values for turkey ovomucoid third domain using a polarizable force field

AMOEBA Force Field Trajectories Improve Predictions of Accurate pKa Values of the GFP Fluorophore: The Importance of Polarizability and Water Interactions

Precisely quantifying the magnitude, direction, and biological functions of electric fields in proteins has long been an outstanding challenge in the field. The most widely implemented experimental method to measure such electric fields at a particular residue in a protein has been through changes in pKa of titratable residues. While many computational strategies exist to predict these values, it has been difficult to do this accurately or connect predicted results to key structural or mechanistic features of the molecule. Here, we used experimentally determined pKa values of the fluorophore in superfolder green fluorescent protein (GFP) with amino acid mutations made at position Thr 203 to evaluate the pKa prediction ability of molecular dynamics (MD) simulations using a polarizable force field, AMOEBA. Structure ensembles from AMOEBA were used to calculate pKa values of the GFP fluorophore. The calculated pKa values were then compared to trajectories using a conventional fixed charge force field (Amber03 ff). We found that the position of water molecules included in the pKa calculation had opposite effects on the pKa values between the trajectories from AMOEBA and Amber03 force fields. In AMOEBA trajectories, the inclusion of water molecules within 35 Å of the fluorophore decreased the difference between the predicted and experimental values, resulting in calculated pKa values that were within an average of 0.8 pKa unit from the experimental results. On the other hand, in Amber03 trajectories, including water molecules that were more than 5 Å from the fluorophore increased the differences between the calculated and experimental pKa values. The inaccuracy of pKa predictions determined from Amber03 trajectories was caused by a significant stabilization of the deprotonated chromophore's free energy compared to the result in AMOEBA. We rationalize the cutoffs for explicit water molecules when calculating pKa to better predict the electrostatic environment surrounding the fluorophore buried in GFP. We discuss how the results from this work will assist the prospective prediction of pKa values or other electrostatic effects in a wide variety of folded proteins.

Automation of some macromolecular properties using a machine learning approach

In this study, we employed a newly developed method to predict macromolecular properties using a swarm artificial neural network (ANN) method as a machine learning approach. In this method, the molecular structures are represented by the feature description vectors used as training input data for a neural network. This study aims to develop an efficient approach for training an ANN using either experimental or quantum mechanics data. We aim to introduce an error model controlling the reliability of the prediction confidence interval using a bootstrapping swarm approach. We created different datasets of selected experimental or quantum mechanics results. Using this optimized ANN, we hope to predict properties and their statistical errors for new molecules. There are four datasets used in this study. That includes the dataset of 642 small organic molecules with known experimental hydration free energies, the dataset of 1475 experimental pKa values of ionizable groups in 192 proteins, the dataset of 2693 mutants in 14 proteins with given experimental values of changes in the Gibbs free energy, and a dataset of 7101 quantum mechanics heat of formation calculations. All the data are prepared and optimized using the AMBER force field in the CHARMM macromolecular computer simulation program. The bootstrapping swarm ANN code for performing the optimization and prediction is written in Python computer programming language. The descriptor vectors of the small molecules are based on the Coulomb matrix and sum over bond properties. For the macromolecular systems, they consider the chemical-physical fingerprints of the region in the vicinity of each amino acid.

Using polarizable POSSIM force field and fuzzy-border continuum solvent model to calculate pK(a) shifts of protein residues

Our Fuzzy-Border (FB) continuum solvent model has been extended and modified to produce hydration parameters for small molecules using POlarizable Simulations Second-order Interaction Model (POSSIM) framework with an average error of 0.136 kcal/mol. It was then used to compute pKa shifts for carboxylic and basic residues of the turkey ovomucoid third domain (OMTKY3) protein. The average unsigned errors in the acid and base pKa values were 0.37 and 0.4 pH units, respectively, versus 0.58 and 0.7 pH units as calculated with a previous version of polarizable protein force field and Poisson Boltzmann continuum solvent. This POSSIM/FB result is produced with explicit refitting of the hydration parameters to the pKa values of the carboxylic and basic residues of the OMTKY3 protein; thus, the values of the acidity constants can be viewed as additional fitting target data. In addition to calculating pKa shifts for the OMTKY3 residues, we have studied aspartic acid residues of Rnase Sa. This was done without any further refitting of the parameters and agreement with the experimental pKa values is within an average unsigned error of 0.65 pH units. This result included the Asp79 residue that is buried and thus has a high experimental pKa value of 7.37 units. Thus, the presented model is capable or reproducing pKa results for residues in an environment that is significantly different from the solvated protein surface used in the fitting. Therefore, the POSSIM force field and the FB continuum solvent parameters have been demonstrated to be sufficiently robust and transferable. © 2016 Wiley Periodicals, Inc.

Developing multisite empirical force field models for Pt(II) and cisplatin

We have developed empirical force field parameters for Pt(II) and cisplatin. Two force field frameworks were used-modified OPLS-AA and our second-order polarizable POSSIM. A seven-site model was used for the Pt(II) ion. The goal was to create transferable parameter sets compatible with the force field models for proteins and general organic compounds. A number of properties of the Pt(II) ion and its coordination compounds have been considered, including geometries and energies of the complexes, hydration free energy, and radial distribution functions in water. Comparison has been made with experimental and quantum mechanical results. We have demonstrated that both versions are generally capable of reproducing key properties of the system, but the second-order polarizable POSSIM formalism permits more accurate quantitative results to be obtained. For example, the energy of formation of cisplatin as calculated with the modified OPLS-AA exhibited an error of 9.9%, while the POSSIM error for the same quantity was 6.2%. The produced parameter sets are transferable and suitable to be used in protein-metal binding simulations in which position or even coordination of the ion does not have to be constrained using preexisting knowledge. © 2016 Wiley Periodicals, Inc.

POSSIM: Parameterizing Complete Second-Order Polarizable Force Field for Proteins

Previously, we reported development of a fast polarizable force field and software named POSSIM (POlarizable Simulations with Second order Interaction Model). The second-order approximation permits the speed up of the polarizable component of the calculations by ca. an order of magnitude. We have now expanded the POSSIM framework to include a complete polarizable force field for proteins. Most of the parameter fitting was done to high-level quantum mechanical data. Conformational geometries and energies for dipeptides have been reproduced within average errors of ca. 0.5 kcal/mol for energies of the conformers (for the electrostatically neutral residues) and 9.7° for key dihedral angles. We have also validated this force field by running Monte Carlo simulations of collagen-like proteins in water. The resulting geometries were within 0.94 Å root-mean-square deviation (RMSD) from the experimental data. We have performed additional validation by studying conformational properties of three oligopeptides relevant in the context of N-glycoprotein secondary structure. These systems have been previously studied with combined experimental and computational methods, and both POSSIM and benchmark OPLS-AA simulations that we carried out produced geometries within ca. 0.9 Å RMSD of the literature structures. Thus, the performance of POSSIM in reproducing the structures is comparable with that of the widely used OPLS-AA force field. Furthermore, our fitting of the force field parameters for peptides and proteins has been streamlined compared with the previous generation of the complete polarizable force field and relied more on transferability of parameters for nonbonded interactions (including the electrostatic component). The resulting deviations from the quantum mechanical data are similar to those achieved with the previous generation; thus, the technique is robust, and the parameters are transferable. At the same time, the number of parameters used in this work was noticeably smaller than that of the previous generation of our complete polarizable force field for proteins; thus, the transferability of this set can be expected to be greater, and the danger of force field fitting artifacts is lower. Therefore, we believe that this force field can be successfully applied in a wide variety of applications to proteins and protein–ligand complexes.

Force Field for Peptides and Proteins based on the Classical Drude Oscillator

Presented is a polarizable force field based on a classical Drude oscillator framework, currently implemented in the programs CHARMM and NAMD, for modeling and molecular dynamics (MD) simulation studies of peptides and proteins. Building upon parameters for model compounds representative of the functional groups in proteins, the development of the force field focused on the optimization of the parameters for the polypeptide backbone and the connectivity between the backbone and side chains. Optimization of the backbone electrostatic parameters targeted quantum mechanical conformational energies, interactions with water, molecular dipole moments and polarizabilities and experimental condensed phase data for short polypeptides such as (Ala)₅. Additional optimization of the backbone φ, ψ conformational preferences included adjustments of the tabulated two-dimensional spline function through the CMAP term. Validation of the model included simulations of a collection of peptides and proteins. This 1^st generation polarizable model is shown to maintain the folded state of the studied systems on the 100 ns timescale in explicit solvent MD simulations. The Drude model typically yields larger RMS differences as compared to the additive CHARMM36 force field (C36) and shows additional flexibility as compared to the additive model. Comparison with NMR chemical shift data shows a small degradation of the polarizable model with respect to the additive, though the level of agreement may be considered satisfactory, while for residues shown to have significantly underestimated S² order parameters in the additive model, improvements are calculated with the polarizable model. Analysis of dipole moments associated with the peptide backbone and tryptophan side chains show the Drude model to have significantly larger values than those present in C36, with the dipole moments of the peptide backbone enhanced to a greater extent in sheets versus helices and the dipoles of individual moieties observed to undergo significant variations during the MD simulations. Although there are still some limitations, the presented model, termed Drude-2013, is anticipated to yield a molecular picture of peptide and protein structure and function that will be of increased physical validity and internal consistency in a computationally accessible fashion.

Uncovering the determinants of a highly perturbed tyrosine pKa in the active site of ketosteroid isomerase

Within the idiosyncratic enzyme active-site environment, side chain and ligand pKa values can be profoundly perturbed relative to their values in aqueous solution. Whereas structural inspection of systems has often attributed perturbed pKa values to dominant contributions from placement near charged groups or within hydrophobic pockets, Tyr57 of a Pseudomonas putida ketosteroid isomerase (KSI) mutant, suggested to have a pKa perturbed by nearly 4 units to 6.3, is situated within a solvent-exposed active site devoid of cationic side chains, metal ions, or cofactors. Extensive comparisons among 45 variants with mutations in and around the KSI active site, along with protein semisynthesis, (13)C NMR spectroscopy, absorbance spectroscopy, and X-ray crystallography, was used to unravel the basis for this perturbed Tyr pKa. The results suggest that the origin of large energetic perturbations are more complex than suggested by visual inspection. For example, the introduction of positively charged residues near Tyr57 raises its pKa rather than lowers it; this effect, and part of the increase in the Tyr pKa from the introduction of nearby anionic groups, arises from accompanying active-site structural rearrangements. Other mutations with large effects also cause structural perturbations or appear to displace a structured water molecule that is part of a stabilizing hydrogen-bond network. Our results lead to a model in which three hydrogen bonds are donated to the stabilized ionized Tyr, with these hydrogen-bond donors, two Tyr side chains, and a water molecule positioned by other side chains and by a water-mediated hydrogen-bond network. These results support the notion that large energetic effects are often the consequence of multiple stabilizing interactions rather than a single dominant interaction. Most generally, this work provides a case study for how extensive and comprehensive comparisons via site-directed mutagenesis in a tight feedback loop with structural analysis can greatly facilitate our understanding of enzyme active-site energetics. The extensive data set provided may also be a valuable resource for those wishing to extensively test computational approaches for determining enzymatic pKa values and energetic effects.

Polarizable simulations with second order interaction model (POSSIM) force field: developing parameters for protein side-chain analogues

A previously introduced polarizable simulations with second-order interaction model (POSSIM) force field has been extended to include parameters for small molecules serving as models for peptide and protein side-chains. Parameters have been fitted to permit reproducing many-body energies, gas-phase dimerization energies, and geometries and liquid-phase heats of vaporization and densities. Quantum mechanical and experimental data have been used as the target for the fitting. The POSSIM framework combines accuracy of a polarizable force field and computational efficiency of the second-order approximation of the full-scale induced point dipole polarization formalism. The resulting parameters can be used for simulations of the parameterized molecules themselves or their analogues. In addition to this, these force field parameters are currently being used in further development of the POSSIM fast polarizable force field for proteins.

Understanding the pK(a) of redox cysteines: the key role of hydrogen bonding

Many cellular functions involve cysteine chemistry via thiol-disulfide exchange pathways. The nucleophilic cysteines of the enzymes involved are activated as thiolate. A thiolate is much more reactive than a neutral thiol. Therefore, determining and understanding the pK(a)s of functional cysteines are important aspects of biochemistry and molecular biology with direct implications for redox signaling. Here, we describe the experimental and theoretical methods to determine cysteine pK(a) values, and we examine the factors that control these pK(a)s. Drawing largely on experience gained with the thioredoxin superfamily, we examine the roles of solvation, charge-charge, helix macrodipole, and hydrogen bonding interactions as pK(a)-modulating factors. The contributions of these factors in influencing cysteine pK(a)s and the associated chemistry, including the relevance for the reaction kinetics and thermodynamics, are discussed. This analysis highlights the critical role of direct hydrogen bonding to the cysteine sulfur as a key factor modulating the equilibrium between thiol S-H and thiolate S(-). This role is easily understood intuitively and provides a framework for biochemical functional insights.

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.

Reduction potentials and acidity constants of Mn superoxide dismutase calculated by QM/MM free-energy methods

We used two theoretical methods to estimate reduction potentials and acidity constants in Mn superoxide dismutase (MnSOD), namely combined quantum mechanical and molecular mechanics (QM/MM) thermodynamic cycle perturbation (QTCP) and the QM/MM-PBSA approach. In the latter, QM/MM energies are combined with continuum solvation energies calculated by solving the Poisson-Boltzmann equation (PB) or by the generalised Born approach (GB) and non-polar solvation energies calculated from the solvent-exposed surface area. We show that using the QTCP method, we can obtain accurate and precise estimates of the proton-coupled reduction potential for MnSOD, 0.30±0.01 V, which compares favourably with experimental estimates of 0.26-0.40 V. However, the calculated potentials depend strongly on the DFT functional used: The B3LYP functional gives 0.6 V more positive potentials than the PBE functional. The QM/MM-PBSA approach leads to somewhat too high reduction potentials for the coupled reaction and the results depend on the solvation model used. For reactions involving a change in the net charge of the metal site, the corresponding results differ by up to 1.3 V or 24 pK(a) units, rendering the QM/MM-PBSA method useless to determine absolute potentials. However, it may still be useful to estimate relative shifts, although the QTCP method is expected to be more accurate.

Absolute pKa Values and Solvation Structure of Amino Acids from Density Functional Based Molecular Dynamics Simulation

Absolute pKa values of the amino acid side chains of arginine, aspartate, cysteine, histidine, and tyrosine; the C- and N-terminal group of tyrosine; and the tryptophan radical cation are calculated using a revised density functional based molecular dynamics simulation technique introduced previously [ Cheng , J. ; Sulpizi , M. ; Sprik , M. J. Chem. Phys. 2009 , 131 , 154504 ]. In the revised scheme, acid deprotonation is considered as a dissociation rather than a proton transfer reaction, and a correction term for treating the proton as a hydronium ion is suggested. The acidity constants of the amino acids are obtained from the vertical energy gaps for removal or insertion of the acidic proton and the computed solvation free energy of the proton. The unsigned mean error relative to experimental results is 2.1 pKa units with a maximum error of 4.0 pKa units. The estimated mean statistical uncertainty due to the finite length of the trajectories is ±1.1 pKa units. The solvation structures of the protonated and deprotonated amino acids are analyzed in terms of radial distribution functions, which can serve as reference data for future force field developments.

Polarizable Simulations with Second order Interaction Model (POSSIM) force field: Developing parameters for alanine peptides and protein backbone

A previously introduced POSSIM (POlarizable Simulations with Second order Interaction Model) force field has been extended to include parameters for alanine peptides and protein backbones. New features were introduced into the fitting protocol, as compared to the previous generation of the polarizable force field for proteins. A reduced amount of quantum mechanical data was employed in fitting the electrostatic parameters. Transferability of the electrostatics between our recently developed NMA model and the protein backbone was confirmed. Binding energy and geometry for complexes of alanine dipeptide with a water molecule were estimated and found in a good agreement with high-level quantum mechanical results (for example, the intermolecular distances agreeing within ca. 0.06Å). Following the previously devised procedure, we calculated average errors in alanine di- and tetra-peptide conformational energies and backbone angles and found the agreement to be adequate (for example, the alanine tetrapeptide extended-globular conformational energy gap was calculated to be 3.09 kcal/mol quantim mechanically and 3.14 kcal/mol with the POSSIM force field). However, we have now also included simulation of a simple alpha-helix in both gas-phase and water as the ultimate test of the backbone conformational behavior. The resulting alanine and protein backbone force field is currently being employed in further development of the POSSIM fast polarizable force field for proteins.

Accurate proton affinity and gas-phase basicity values for molecules important in biocatalysis

Benchmark quantum calculations of proton affinities and gas-phase basicities of molecules relevant to biochemical processes, particularly acid/base catalysis, are presented and compared for a variety of multilevel and density functional quantum models. Included are nucleic acid bases in both keto and enol tautomeric forms, ribose in B-form and A-form sugar pucker conformations, amino acid side chains and backbone molecules, and various phosphates and phosphoranes, including thio substitutions. This work presents a high-level thermodynamic characterization of biologically relevant protonation states and provides a benchmark database for development of next-generation semiempirical and approximate density functional quantum models and parametrization of methods to predict pK(a) values and relative solvation energies.

Polarizable Simulations with Second order Interaction Model - force field and software for fast polarizable calculations: Parameters for small model systems and free energy calculations

We are presenting POSSIM (POlarizable Simulations with Second order Interaction Model) - a software package and a set of parameters designed for molecular simulations. The key feature of POSSIM is that the electrostatic polarization is taken into account using a previously introduced fast formalism. This permits cutting computational cost of using the explicit polarization by about an order of magnitude. In this article, parameters for water, methane, ethane, propane, butane, methanol and NMA are introduced. These molecules are viewed as model systems for protein simulations. We have achieved our goal of ca. 0.5 kcal/mol accuracy for gas-phase dimerization energies and no more than 2% deviations in liquid state heats of vaporization and densities. Moreover, free energies of hydration of the polarizable methane, ethane and methanol have been calculated using the statistical perturbation theory. These calculations are a model for calculating protein pKa shifts and ligand binding affinities. The free energies of hydration were found to be 2.12 kcal/mol, 1.80 kcal/mol and -4.95 kcal/mol for methane, ethane and methanol, respectively. The experimentally determined literature values are 1.91 kcal/mol, 1.83 kcal/mol and -5.11 kcal/mol. The POSSIM average error in these absolute free energies of hydration is only about 0.13 kcal/mol. Using the statistical perturbation theory with polarizable force fields is not widespread, and we believe that this work opens road to further development of the POSSIM force field and its applications for obtaining accurate energies in protein-related computer modeling.