AMBER Charge Research Articles

Effect of Electronic Polarization to Human α-Thrombin

The polarized protein-specific charges (PPC) of human α-thrombin (thrombin) and its inhibitor (L86) are made possible by employing the recently developed molecular fractionation with conjugate caps approach incorporated the Poisson—Boltzmann model. Molecular dynamics (MD) simulations of thrombin have been carried out to investigate the dynamics and stability of the thrombin-inhibitor using PPC and AMBER charges respectively. Detailed analysis and comparison of MD results show that the PPC can correctly describe the polarized state of the thrombin and L86. Especially, the root-mean-square deviation of backbone atoms and the hydrogen bonds using PPC are more stable than the AMBER charge. The present results indicate that protein polarization plays critical roles in maintaining the compact structure of thrombin.

Development of an Effective Polarizable Bond Method for Biomolecular Simulation

An effective polarizable bond (EPB) model has been developed for computer simulation of proteins. In this partial polarizable approach, all polar groups of amino acids are treated as polarizable, and the relevant polarizable parameters were determined by fitting to quantum calculated electrostatic properties of these polar groups. Extensive numerical tests on a diverse set of proteins (including 1IEP, 1MWE, 1NLJ, 4COX, 1PGB, 1K4C, 1MHN, 1UBQ, 1IGD) showed that this EPB model is robust in MD simulation and can correctly describe the structure and dynamics of proteins (both soluble and membrane proteins). Comparison of the computed hydrogen bond properties and dynamics of proteins with experimental data and with results obtained from the nonpolarizable force field clearly demonstrated that EPB can produce results in much better agreement with experiment. The averaged deviation of the simulated backbone N-H order parameter of the B3 immunoglobobulin-binding domain of streptococcal protein G from experimental observation is 0.0811 and 0.0332 for Amber99SB and EPB, respectively. This new model inherited the effective character of the classic force field and the fluctuating feature of previous polarizable models. Different from other polarizable models, the polarization cost energy is implicitly included in the present method. As a result, the present method avoids the problem of over polarization and is numerically stable and efficient for dynamics simulation. Finally, compared to the traditional fixed AMBER charge model, the present method only adds about 5% additional computational time and is therefore highly efficient for practical applications.

The F130L mutation in streptavidin reduces its binding affinity to biotin through electronic polarization effect

Recently, Baugh et al. discovered that a distal point mutation (F130L) in streptavidin causes no distinct variation to the structure of the binding pocket but a 1000-fold reduction in biotin binding affinity. In this work, we carry out molecular dynamics simulations and apply an end-state free energy method to calculate the binding free energies of biotin to wild type streptavidin and its F130L mutant. The absolute binding affinities based on AMBER charge are repulsive, and the mutation induced binding loss is underestimated. When using the polarized protein-specific charge, the absolute binding affinities are significantly enhanced. In particular, both the absolute and relative binding affinities are in line with the experimental measurements. Further investigation indicates that polarization effect is indispensable in both the generation of structural ensembles and the calculation of interaction energies. This work verifies Baugh's conjecture that electrostatic polarization effect plays an essential role in modulating the binding affinity of biotin to the streptavidin through F130L mutation.

Protein‐specific force field derived from the fragment molecular orbital method can improve protein–ligand binding interactions

Accurate computational estimate of the protein-ligand binding affinity is of central importance in rational drug design. To improve accuracy of the molecular mechanics (MM) force field (FF) for protein-ligand simulations, we use a protein-specific FF derived by the fragment molecular orbital (FMO) method and by the restrained electrostatic potential (RESP) method. Applying this FMO-RESP method to two proteins, dodecin, and lysozyme, we found that protein-specific partial charges tend to differ more significantly from the standard AMBER charges for isolated charged atoms. We did not see the dependence of partial charges on the secondary structure. Computing the binding affinities of dodecin with five ligands by MM PBSA protocol with the FMO-RESP charge set as well as with the standard AMBER charges, we found that the former gives better correlation with experimental affinities than the latter. While, for lysozyme with five ligands, both charge sets gave similar and relatively accurate estimates of binding affinities.

Derivation of fixed partial charges for amino acids accommodating a specific water model and implicit polarization.

We have developed the IPolQ method for fitting nonpolarizable point charges to implicitly represent the energy of polarization for systems in pure water. The method involves iterative cycles of molecular dynamics simulations to estimate the water charge density around the solute of interest, followed by quantum mechanical calculations at the MP2/cc-pV(T+d)Z level to determine updated solute charges. Lennard-Jones parameters are updated starting from the Amber FF99SB nonbonded parameter set to accommodate the new charge model, guided by the comparisons to experimental hydration free energies (HFEs) of neutral amino acid side chain analogs and assumptions about the computed HFEs for charged side chains. These Lennard-Jones parameter adjustments for side-chain analogs are assumed to be transferable to amino acids generally, and new charges for all standard amino acids are then derived in the presence of water modeled by TIP4P-Ew. Overall, the new charges depict substantially more polarized amino acids, particularly in the backbone moieties, than previous Amber charge sets. Efforts to complete a new force field with appropriate torsion parameters for this charge model are underway. The IPolQ method is general and applicable to arbitrary solutes.

A numerically stable restrained electrostatic potential charge fitting method

Inspired by the idea of charge decomposition in calculation of the dipole preserving and polarization consistent charges (Zhang et al., J. Comput. Chem. 2011, 32, 2127), we have proposed a numerically stable restrained electrostatic potential (ESP)-based charge fitting method for protein. The atomic charge is composed of two parts. The dominant part is fixed to a predefined value (e.g., AMBER charge), and the residual part is to be determined by restrained fitting to residual ESP on grid points around the molecule. Nonuniform weighting factors as a function of the dominant charge are assigned to the atoms. Because the residual part is several folds to several orders smaller than the dominant part, the impact of ill-conditioning is alleviated. This charge fitting method can be used in quantum mechanical/molecular mechanical (QM/MM) simulations and similar studies, where QM calculated electronic properties are frequently mapped to partial atomic charges.

Electrostatic polarization is critical for the strong binding in streptavidin‐biotin system

The origin of strong affinity of biotin and its analogs binding to (strept)avidin is still the subject of an ongoing controversy. In this work, thermodynamic integration is carried out to study of the difference of binding free energies between biotin and iminobiotin to streptavidin. Three atomic charge schemes are implemented and compared. One is the traditional AMBER charge, and the other two, termed the polarized protein-specific charge, are based on a linear scaling quantum mechanical method and a continuous solvation model and have polarization effect partially or fully included. The result indicates that when nonpolarized AMBER force field is applied, the result is much underestimated. When electronic polarization is gradually included, the difference of binding affinity increases along with it. Using the linear-response approximation to eliminate the error in self-charging process, the corrected binding affinity agrees well with the experimental observation. This study is direct evidence indicating that polarization effect is critical for the strong binding in streptavidin-biotin system.

Transferability of conformational dependent charges from protein simulations

AbstractWe have studied the transferability of atomic charges for proteins, fitted to the quantum mechanical electrostatic potential and extensively averaged over a set of structures sampled by molecular dynamics (MD) and over all residues of the same kind in the protein sequence (xAvESP). Previously, such charges were obtained for one single protein (avidin). In this study, we use five additional proteins. The aim of this study is fourfold. First, we provide xAvESP charges for all amino acids, including amino‐ and carboxy‐terminal variants of all, as well as alternative protonation states of His, Asp, Glu, Lys, Arg, Cys, and Tyr. Second, we show that the xAvESP charges averaged over the five new proteins are similar to charges obtained in the same way for avidin, with a correlation coefficient of 0.997. This shows that the charges are transferable and system‐independent. Electrostatic protein–ligand interaction energies calculated with charges obtained from different proteins differ by only 1–3 kJ/mol on average. The xAvESP charges correlate rather well with Amber charges (except for the N atom of amino‐terminal residues that are erroneous in Amber), although they are obtained in a more general way. Third, the conformational dependence of the charges is significant and gives rise to quite large differences in energies. However, these differences are to a large extent screened by solvation effects. For example, the solvent‐screened electrostatic interaction energy between the protein galectin‐3 and five different ligands varies with the charge sets by less than 3 kJ/mol on average. Finally, we show that the xAvESP charges give a comparable root‐mean‐squared deviation as the Amber charges for the MD simulations of 18 protein–ligand complexes, they give comparable or slightly worse backbone NH order parameters for two galectin‐3 complexes, but they give a better correlation between calculated and experimental affinities for the binding of seven biotin analogues to avidin and for nine inhibitors of factor Xa. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem 112:1768–1785, 2012

Folding of a Helix at Room Temperature Is Critically Aided by Electrostatic Polarization of Intraprotein Hydrogen Bonds

We report direct folding of a 17-residue helix protein (pdb:2I9M) by standard molecular dynamics simulation (single trajectory) at room temperature with implicit solvent. Starting from a fully extended structure, 2I9M successfully folds into the native conformation within 16 ns using adaptive hydrogen bond-specific charges to take into account the electrostatic polarization effect. Cluster analysis shows that conformations in the native state cluster have the highest population (78.4%) among all sampled conformations. Folding snapshots and the secondary structure analysis demonstrate that the folding of 2I9M begins at terminals and progresses toward the center. A plot of the free energy landscape indicates that there is no significant free energy barrier during folding, which explains the observed fast folding speed. For comparison, exactly the same molecular dynamics simulation but carried out under existing AMBER charges failed to fold 2I9M into native-like structures. The current study demonstrates that electrostatic polarization of intraprotein hydrogen bonding, which stabilizes the helix, is critical to the successful folding of 2I9m.

Intra-protein hydrogen bonding is dynamically stabilized by electronic polarization

Molecular dynamics (MD) simulation has been carried out to study dynamical stability of intra-protein hydrogen bonds based on two set of atomic charges, the standard AMBER charge and the polarized protein-specific charge (PPC). The latter is derived from quantum mechanical calculation for protein in solution using a recently developed molecular fractionation with conjugate caps-Poisson-Boltzmann (MFCC-PB) approach and therefore includes electronic polarization effect of the protein at native structure. MD simulations are performed for a number of benchmark proteins containing helix and/or beta sheet secondary structures. The computational result shows that occupancy percentage of hydrogen bonds averaged over simulation time, as well as the number of hydrogen bonds as a function of simulation time, is consistently higher under PPC than AMBER charge. In particular, some intra-protein hydrogen bonds are found broken during MD simulation using AMBER charge but they are stable using PPC. The breaking of some intra-protein hydrogen bonds in AMBER simulation is responsible for deformation or denaturing of some local structures of proteins during MD simulation. The current study provides strong evidence that hydrogen bonding is dynamically more stable using PPC than AMBER charge, highlighting the stabilizing effect of electronic polarization on protein structure.

Conformational dependence of charges in protein simulations

We have studied the conformational dependence of molecular mechanics atomic charges for proteins by calculating the charges fitted to the quantum mechanical (QM) electrostatic potential (ESP) for all atoms in complexes between avidin and seven biotin analogues for 20 snapshots from molecular dynamics simulations. We have studied how various other charge sets reproduce those charges. The QM charges, even if averaged over all snapshots or all residues, in general have a larger magnitude than standard Amber charges, indicating that the restraint toward zero in the restrained ESP method is too strong. This has a significant influence on the electrostatic conformational energies and the interaction energy between the biotin ligand and the protein, giving a difference between the QM and Amber charges of 43 and 8 kJ/mol for the negatively charged and neutral biotin analogues, respectively (3-4%). However, this energy difference is strongly reduced if the solvation energy (calculated by the Poisson-Boltzmann or Generalized Born methods) is added, viz., to 7 kJ/mol for charged and 3 kJ/mol for uncharged ligand. In fact, charges need to be recalculated with a QM method only for residues within 7 or 4 A of the ligand, if the error should be less than 4 kJ/mol. Unfortunately, the QM charges do not give significantly better MM/PBSA estimates of ligand-binding affinities than standard Amber charges.

Developing Polarized Protein-Specific Charges for Protein Dynamics: MD Free Energy Calculation of pK a Shifts for Asp 26/Asp 20 in Thioredoxin

Ab initio quantum mechanical calculation of protein in solution is carried out to generate polarized protein-specific charge(s) (PPC) for molecular dynamics (MD) stimulation of protein. The quantum calculation of protein is made possible by developing a fragment-based quantum chemistry approach in combination with the implicit continuum solvent model. The computed electron density of protein is utilized to derive PPCs that represent the polarized electrostatic state of protein near the native structure. These PPCs are atom-centered like those in the standard force fields and are thus computationally attractive for molecular dynamics simulation of protein. Extensive MD simulations have been carried out to investigate the effect of electronic polarization on the structure and dynamics of thioredoxin. Our study shows that the dynamics of thioredoxin is stabilized by electronic polarization through explicit comparison between MD results using PPC and AMBER charges. In particular, MD free-energy calculation using PPCs accurately reproduced the experimental value of pK a shift for ionizable residue Asp 26 buried inside thioredoxin, whereas previous calculations using standard force fields overestimated pK a shift by twice as much. Accurate prediction of pK a shifts by rigorous MD free energy simulation for ionizable residues buried inside protein has been a significant challenge in computational biology for decades. This study presented strong evidence that electronic polarization of protein plays an important role in protein dynamics.

Optimized Radii for Poisson-Boltzmann Calculations with the AMBER Force Field.

Implicit solvent models are a standard tool for assessing the electrostatics of biomolecular systems. The accuracy of quantitative predictions, such as pKa values, transfer free energies, binding energies, and solvation forces, is strongly dependent on one's choice of continuum parameters: the solute charges, dielectric coefficient, and radii, which define the dielectric boundary. To ensure quantitative accuracy, these parameters can be benchmarked against explicit solvent simulations. Here we present two sets of optimized radii to define either abrupt or cubic-spline smoothed dielectric boundaries in Poisson-Boltzmann calculations of protein systems with AMBER (parm99) charges. Spline smoothing stabilizes the electrostatic potential at the molecular surface, allowing for continuum force calculations. Most implementations, however, require significantly different radii than the abrupt boundary surfaces. The optimal continuum radii are initially approximated from the solvent radial charge distribution surrounding each atom type. A genetic algorithm is then used to fine-tune the starting values to reproduce charging free energies measured from explicit solvent simulations. The optimized radii are tested on four protein-like polypeptides. The results show increased accuracy of molecular solvation energies and atomic forces relative to commonly used continuum parameter sets. These radii are suitable for Poisson-Boltzmann calculations with the AMBER force field and offer energetic congruence to any model that combines molecular mechanics and Poisson-Boltzmann solvation energies.

Comparison of electrostatic potential around proteins calculated from Amber and AM1 charges: application to mutants of prion protein

On the basis of arguments of complementary fit of shape and charge polarity or hydrophobicity, molecular electrostatic potentials (MEPs) around proteins are commonly used to deduce likely sites for interaction with ligands or other proteins, including for variations such as mutations. But protein MEPs calculated classically from fixed force field descriptions, including those with implicit solvent models such as in Delphi, do not allow for repolarization of protein residues within the protein system; hence, their representations are likely to be variably inaccurate. Linear-scaling methods now allow calculation of MEPs quantum mechanically for systems as large as proteins, and can account for polarization explicitly. Here we compare MEPs derived from AM1 charge distributions calculated by Mopac2000 with those from the classical Amber force field. Our models are mutants of prion protein (PrP), a protein with an unusually high number of charged residues. The results demonstrate that static point charges, as used in most current force fields, cannot reproduce the MEP of macromolecules. Also, it is not sufficient to account for the influence of nearby atoms connected by chemical bonds; the influence of nearby atoms in space is at least as important. Thus, further progress in the accuracy and wider applicability of force fields requires proper accounting for polarization. Mopac2000 calculations can provide the necessary data for checking new force fields and/or parameter fitting.

Conformation of the trypanocidal pharmaceutical suramin in its free and bound forms: transferred nuclear overhauser studies.

Suramin is a lead compound for treatment of cancer, HIV, and trypanosomiasis. The conformations of suramin in its free form and bound to phosphoglycerate kinases from T. brucei and S. cerevisae, have been studied in aqueous solutions using nuclear Overhauser effect (NOE) and transferred NOE NMR spectroscopies. The NOE data of the free drug can be accommodated by a model in which many of the single bonds of suramin are unrestricted at room temperature, consistent with molecular mechanics calculations. The angle between the naphthalene ring and the adjoining amide is essentially locked by a strong amide-sulfonate hydrogen bond into one preferred conformation. Another degree of freedom near the termini of the molecule has a rather pronounced preference, and a third exhibits a nearly perpendicular arrangement between the amide and adjacent aromatic ring. The other two degrees of freedom have weaker preferences. Molecular mechanics calculations using AMBER force field and charges on amides and sulfonates obtained from semiempirical or ab initio calculations reproduced the extent of nonplanarity but not the detailed preferences. 13C spin-lattice relaxation, proton NOE, and light-scattering measurements for free suramin indicate that the correlation time of the molecule is approximately 3 ns at 5 mM concentration, suggesting that suramin is multimeric. Lowering the temperature to 5 degrees C causes a dramatic broadening of all of the resonances in the NMR spectra of 5 mM suramin. This broadening probably is associated with further aggregation into micelles. Suramin is monomeric at 0.5 mM and room temperature, and the NOE cross-relaxation rate constants are close to the cancellation condition for a 500 MHz proton frequency; this concentration is typical of blood serum concentrations when the drug is utilized in humans. Changes in the conformational preferences for terminal degrees of freedom are observed in the bound states of suramin based upon the transferred NOE data. The data for the bound state cannot be accommodated by a symmetric conformer. Analysis of the transferred NOESY buildup curves indicates complex kinetics of binding, probably involving an electrostatically bound encounter complex. Despite the weak binding constant, the buildup curves cannot be treated as population-weighted averages of the free and bound cross-relaxation rates, and therefore complete relaxation-exchange matrix analysis has been performed to simulate the data sets.

Stereochemistry. 82. Conformation of fused five-membered heterocyclic rings derived from the intramolecular oxime olefin cycloaddition reaction

Thermal intramolecular oxime olefin cycloaddition of α-allylamino aldoximes and ketoximes 4 led stereospecifically to formation of oxadiazabicyclo[3.3.0]octanes 6. The presence of heteroatoms in these bicyclic fused 5-membered rings permits for the first time an evaluation of the conformation of this system by means of NMR. We found that some substituents in 6 restrict the conformational mobility of these five-membered rings to the extent that only one conformer was detected at 20 o C. In other cases an equilibrium between two major conformers was revealed by NMR. Equilibrium measurements indicated a free energy of conversion of 13.2-13.4 kcal/mol, apparently a manifestation of the N-inversion in the isoxazolidine ring. NMR studies also showed that the NH-proton in isoxazolidines 6 prefers an axial orientation. Empirical force field data were adjusted for MM calculations in these bicyclic heterocycles. The MM2 force field with AMBER charge gave the best fit between calculated and experimental coupling constants

Charge calculations in molecular mechanics. Part 8 Partial atomic charges from classical calculations

The CHARGE2 programme, which involves the classical calculation of both the inductive and resonance contributions to the partial atomic charges in molecules is described, and the charges and electrostatic potentials obtained presented for some illustrative examples. In substituted methanes (CH3X, CF3X, CCl3X) the effects of varying the electronegativity of the substituents and the alpha- and beta-substituent contributions are clearly illustrated for a variety of substituent groups X. The problems involved in the inclusion of silicon into this scheme are detailed, together with the methods of overcoming them. The partial atomic charges (sigma and pi contributions) and electrostatic potentials for some silicon oxygen compounds are presented and discussed. The partial atomic charges from CHARGE2 for all the natural amino acids as their N-acetyl, N'-methylamides are given and compared with those obtained from the AMBER and ECEPP/2 force fields. Considerable differences in these figures are observed, with the AMBER charges consistently much larger than those from the other two methods. The CHARGE2 partial atomic charges and electrostatic potentials for the four common nucleic acids, adenine, cytosine, guanine and thymine, are given and compared with those derived from other calculations. Again there is general similarity but also there are considerable differences, with those from the AMBER force field somewhat larger than the other methods.