Effect of charge distribution on electrostatic chromophore—protein interactions in Bacteriorhodopsin

Charge distributions of a protonated and unprotonated Schiff base model compound are determined using different quantum chemical methods. After fitting the model molecule onto the protonated retinal Schiff base in Bacteriorhodopsin, electrostatic interaction energies between the model molecule and protein are calculated. Interaction energies as well as the calculated pK_1/2 values of the model molecule are shown to depend considerably on the chosen charge distribution. Electrostatic potential derived partial charges determined at different ab initio levels reveal interaction energies between the model molecule and nearby residues such as ARG-82, ASP-85, and ASP-212, which are relatively method independent. Consequently, such charge distributions also result in pK_1/2 values for the model molecule that are very similar. Larger deviations in the electrostatic interaction energies, however, are found in the case of charge distributions derived according to the Mulliken population analysis. Nevertheless, some sets of Mulliken derived partial charges predicted pK_1/2 values for the model molecule that are close to those determined with electrostatic potential derived partial charges. This agreement, however, is only achieved because the individual errors of the contributing terms are approximately compensated. The use of the extended atom model is shown to be problematic. Although potential derived charges can correctly describe electrostatic interaction energies, they fail to predict pK_1/2 values. On the basis of the present investigation a new set of partial charges for the protonated and unprotonated retinal Schiff base is proposed to be used in molecular dynamics simulations and electrostatics calculations. © 1997 by John Wiley & Sons, Inc.     

Building molecular charge distributions from fragments: Application to HIV-1 protease inhibitors

Interaction energies are a function of the molecular charge distribution. In previous work, we found that the set of atomic partial charges giving the best agreement with experimental vacuum dipole moments were from density functional theory calculations using an extended basis set. Extension of such computations to larger molecules requires an atomic partial charge calculation beyond present computational resources. A solution to this problem is the calculation of atomic partial charges for segments of the molecule and reassociation of such fragments to yield partial charges for the entire molecule. Various partitions and reassociation methods for five molecules relevant to HIV-1 protease inhibitors are examined. A useful method of reassociation is introduced in which atomic partial charges for a large molecule are computed by fitting to the combined electrostatic potential calculated from the fragment partial charges. As expected, the best sites for partitions are shown to be carbon—carbon rather than carbon—nitrogen bonds. © 1997 by John Wiley & Sons, Inc.     

Fluctuating charge normal modes: An algorithm for implementing molecular dynamics simulations with polarizable potentials

A new method for performing molecular dynamics simulations with fluctuating charge polarizable potentials is introduced. In fluctuating charge models, polarizability is treated by allowing the partial charges to be variables, with values that are coupled to charges on the same molecule as well as those on other molecules. The charges can be efficiently propagated in a molecular dynamics simulation using extended Lagrangian dynamics. By making a coordinate change from the charge variables to a set of normal mode charge coordinates for each molecule, a new method is constructed in which the normal mode charge variables uncouple from those on the same molecule. The method is applied to the TIP4P-FQ model of water and compared to other methods for implementing the dynamics. The methods are compared using different molecular dynamics time steps.     

Restrained point-charge models for disaccharides

Various methods for deriving atomic partial charges from the quantum chemical electrostatic potential and moments have been tested for the sucrose molecule. We show that if no further information is used, the charges on some carbon atoms become large and charge patterns involving these atoms are badly determined and poorly transferable. Adding lone-pairs on the ether oxygen atoms or dividing the molecule into smaller fragments did not cure the instabilities. We develop a method, CHELP-BOW0, that restrains charges toward zero with different weights for different atoms. These harmonic restraints preserve the linear form of the least-squares equations, which are solved in a single step using singular-value decomposition. CHELP-BOW0 improves the chemical transferability of the charges compared to unrestrained methods, and slightly improves their conformational transferability. It introduces a modest degradation of the fit compared to unrestrained CHELP-BOW (mean average deviation of the potential 0.00016 vs. 0.00010 a.u.). A second new method, CHELP-BOWC, avoids the need for restraints by including several conformations in the fit, weighting each according to its estimated energy in solution. CHELP-BOWC charges are more transferable than CHELP-BOW or CHELP-BOW0 charges to conformations not included in the training set. Restraints to zero charge do not further improve transferability of the CHELP-BOWC charges. We, therefore, recommend CHELP-BOW charges for rigid molecules and CHELP-BOWC charges for flexible molecules.     

Prediction of hydration free energies for aliphatic and aromatic chloro derivatives using molecular dynamics simulations with the OPLS-AA force field

All-atom molecular dynamics computer simulations were used to blindly predict the hydration free energies of a range of chloro-organic compounds as part of the SAMPL3 challenge. All compounds were parameterized within the framework of the OPLS-AA force field, using an established protocol to compute the absolute hydration free energy via a windowed free energy perturbation approach and thermodynamic integration. Three different approaches to deriving partial charge parameters were pursued: (1) using existing OPLS-AA atom types and charges with minor adjustments of partial charges on equivalent connecting atoms; (2) calculation of quantum mechanical charges via geometry optimization, followed by electrostatic potential (ESP) fitting, using Jaguar at the LMP2/cc-pVTZ(-F) level; and (3) via geometry optimization and CHelpG charges (Gaussian03 at the HF/6-31G* level), followed by two-stage RESP fitting. Protocol 3 generated the most accurate predictions with a root mean square (RMS) error of 1.2 kcal mol(-1) for the entire data set. It was found that the deficiency of the standard OPLS-AA parameters, protocol 1 (RMS error 2.4 kcal mol(-1) overall), was mostly due to compounds with more than three chlorine substituents on an aromatic ring. For this latter subset, the RMS errors were 1.4 kcal mol(-1) (protocol 3) and 4.3 kcal mol(-1) (protocol 1), respectively. We propose new OPLS-AA atom types for aromatic carbon and chlorine atoms in rings with ≥4 Cl-substituents that perform better than the best QM-based approach, resulting in an RMS error of 1.2 kcal mol(-1) for these difficult compounds.     

Comparison of two simulation methods to compute solvation free energies and partition coefficients

The thermodynamic integration (TI) and expanded ensemble (EE) methods are used here to calculate the hydration free energy in water, the solvation free energy in 1‐octanol, and the octanol‐water partition coefficient for a six compounds of varying functionality using the optimized potentials for liquid simulations (OPLS) all‐atom (AA) force field parameters and atomic charges. Both methods use the molecular dynamics algorithm as a primary component of the simulation protocol, and both have found wide applications in fields such as the calculation of activity coefficients, phase behavior, and partition coefficients. Both methods result in solvation free energies and 1‐octanol/water partition coefficients with average absolute deviations (AAD) from experimental data to within 4 kJ/mol and 0.5 log units, respectively. Here, we find that in simulations the OPLS‐AA force field parameters (with fixed charges) can reproduce solvation free energies of solutes in 1‐octanol with AAD of about half that for the solute hydration free energies using a extended simple point charge (SPC/E) model of water. The computational efficiency of the two simulation methods are compared based on the time (in nanoseconds) required to obtain similar standard deviations in the solvation free energies and 1‐octanol/water partition coefficients. By this analysis, the EE method is found to be a factor of nine more efficient than the TI algorithm. For both methods, solvation free energy calculations in 1‐octanol consume roughly an order of magnitude more CPU hours than the hydration free energy calculations. © 2012 Wiley Periodicals, Inc.     

Dependency of ligand free energy landscapes on charge parameters and solvent models

We performed replica-exchange molecular dynamics (REMD) simulations of six ligands to examine the dependency of their free energy landscapes on charge parameters and solvent models. Six different charge parameter sets for each ligand were first generated by RESP and AM1-BCC methods using three different conformations independently. RESP charges showed some conformational dependency. On the other hand, AM1-BCC charges did not show conformational dependency and well reproduced the overall trend of RESP charges. The free energy landscapes obtained from the REMD simulations of ligands in vacuum, Generalized-Born (GB), and TIP3P solutions were then analyzed. We found that even small charge differences can produce qualitatively different landscapes in vacuum condition, but the differences tend to be much smaller under GB and TIP3P conditions. The simulations in the GB model well reproduced the landscapes in the TIP3P model using only a fraction of the computational cost. The protein-bound ligand conformations were rarely the global minimum states, but similar conformations were found to exist in aqueous solution without proteins in regions close to the global minimum, local minimum or intermediate states.     

Transferable potentials for phase equilibria. 9. Explicit hydrogen description of benzene and five-membered and six-membered heterocyclic aromatic compounds

The explicit hydrogen version of the transferable potentials for phase equilibria (TraPPE-EH) force field is extended to benzene, pyridine, pyrimidine, pyrazine, pyridazine, thiophene, furan, pyrrole, thiazole, oxazole, isoxazole, imidazole, and pyrazole. While the Lennard-Jones parameters for carbon, hydrogen (two types), nitrogen (two types), oxygen, and sulfur are transferable for all 13 compounds, the partial charges are specific for each compound. The benzene dimer energies for sandwich, T-shape, and parallel-displaced configurations obtained for the TraPPE-EH force field compare favorably with high-level electronic structure calculations. Gibbs ensemble Monte Carlo simulations were carried out to compute the single-component vapor-liquid equilibria for benzene, pyridine, three diazenes, and eight five-membered heterocycles. The agreement with experimental data is excellent with the liquid densities and vapor pressures reproduced within 1 and 5%, respectively. The critical temperatures and normal boiling points are predicted with mean deviations of 0.8 and 1.6%, respectively.     

The influence of electrostatic forces on the structure and dynamics of molecular ionic liquids

The vast majority of molecular dynamics simulations are based on nonpolarizable force fields with fixed partial charges for all atoms. The traditional way to obtain these charges are quantum-mechanical calculations performed prior to simulation. Unfortunately, the set of the partial charges heavily relies on the method and the basis set used. Therefore, investigations of the influence of charge variation on simulation data are necessary in order to validate various charge sets. This paper elucidates the consequences of different charge sets on the structure and dynamics of the ionic liquid: 1-ethyl-3-methyl-imidazolium dicyanoamide. The structural features seem to be more or less independent of the partial charge set pointing to a dominance of shape force as modeled by Lennard-Jones parameters. This can be seen in the radial distribution and orientational correlation functions. The role of electrostatic forces comes in when studying dynamical properties. Here, significant deviations between different charge sets can be observed. Overall, dynamics seems to be governed by viscosity. In fact, all dynamical parameters presented in this work can be converted from one charge set to another by viscosity scaling.     

Conformational dependence of electrostatic potential derived charges of a lipid headgroup: Glycerylphosphorylcholine

Atomic monopoles are routinely determined through a least squares fit to molecular electrostatic potentials. We report studies of the variation in atomic monopoles with variation in conformation for the zwitterionic polar head group of lecithins, a common class of lipid. The monopole of one atom, a relatively buried carbon, varied by 1.3 electron units between different conformers. “Exterior” atoms, as seen previously, showed smaller changes in charge and smaller estimated standard deviations. The total charge of local groups of atoms varied less than the charge of individual atoms, indicating that shifts in charge occurred mostly between neighboring atoms. This effect might be reflected in the high correlations seen between charges of many neighboring atoms. These correlations, while present for many logical groupings of atoms (such as within methylene and methyl groups), are curiously absent between some bonded atoms. Monopoles were fit to multiple conformations simultaneously to provide a charge set that could optimally reproduce the electrostatic potential of all the conformers as a means of generating monopoles for molecular dynamics simulations or other studies where conformation varies. In some cases, the charges on chemically equivalent atoms (e.g., the hydrogen atoms in a methyl group) were different by more than their estimated error of fit. These studies lead to the suggestion that a minimum error in reported charges is on the order of 10%. All conformations show that the positive charge of the trimethylalkyl ammonium group is carried by the methyl hydrogens; the total charge on the nine hydrogens is over 2 electron units, counterbalanced by negative monopoles on the carbons. The presence of this diffuse cloud of substantial charge would appear to be a disindicator of the use of a “united” atoms approach for these methyl groups. The effects of the charge variation on intermolecular interactions is also examined.     

An efficient method for calculating atomic charges of peptides and proteins from electronic populations

An efficient method is presented to calculate atomic charges of peptides and proteins derived from Mulliken electronic populations for terminally blocked amino acids (Ac-X-NHMe, X = any neutral or charged residue) calculated at the B3LYP/6-31G(d,p)//HF/6-31G(d,p) level of theory. This electronic population-derived atomic charges (EPAC) method is based on the geometry-dependent atomic charge (GDAC) method proposed by Cho et al. (J. Phys. Chem. B 2001, 105, 3624), in which atomic charges are calculated by using the partial equalization of atomic electronegativities with electronegativity parameters and damping factors given by interatomic distances between covalently bonded atoms in a molecule. The overall mean absolute difference (mad) and root-mean-square deviation (rmsd) between dipole moments micro(EPAC) and micro(B3LYP), obtained from EPAC charges and from B3LYP/6-31G(d,p) level calculations, respectively, for Ac-X-NHMe are estimated to be 0.38 and 0.59 D, respectively, for 26 representative conformations in the training set, and 0.54 and 0.79 D, respectively, for 172 representative conformations not used for parametrization. For Ac-(Ala)(n)-NHMe (n = 2-6), the EPAC method reasonably predicts the increase of the dipole moment with increase of the chain length, although the deviations from the micro(B3LYP) values are somewhat larger. For Ac-Ala-NHMe and Ac-(Ala)(3)-NHMe, the EPAC charge for a specific type of atom does not depend on its position in the sequence or on the length of the sequence. In addition, charge neutrality holds for any Ala residue of these two peptides. Thus, these results suggest that the EPAC charges derived from B3LYP/6-31G(d,p) Mulliken populations can be used reliably for conformational analysis of peptides and proteins.     

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. © 2013 Wiley Periodicals, Inc.     

Continuum treatment of electronic polarization effect

A continuum treatment of electronic polarization has been explored for in molecular mechanics simulations in implicit solvents. The dielectric constant for molecule interior is the only parameter in the continuum polarizable model. A value of 4 is found to yield optimal agreement with high-level ab initio quantum mechanical calculations for the tested molecular systems. Interestingly, its performance is not sensitive to the definition of molecular volume, in which the continuum electronic polarization is defined. In this model, quantum mechanical electrostatic field in different dielectric environments from vacuum, low-dielectric organic solvent, and water can be used simultaneously in atomic charge fitting to achieve consistent treatment of electrostatic interactions. The tests show that a single set of atomic charges can be used consistently in different dielectric environments and different molecular conformations, and the atomic charges transfer well from training monomers to tested dimers. The preliminary study gives us the hope of developing a continuum polarizable force field for more consistent simulations of proteins and nucleic acids in implicit solvents.     

Studies on the Conformations and Hydrogen Bonding of ACE Inhibitory Tripeptide VEF by All-atom Molecular Dynamics Simulations and Molecular Docking

Molecular dynamic simulations and molecular docking are performed to study the conformations and hydrogen bonding interactions of ACE inhibitory tripeptide VEF. Intramolecular distance, radius of gyration, solvent-accessible surface, and root-mean-square deviations are used to characterize the properties of VEF in aqueous solution. The VEF molecule is highly flexible in water and conformations can shift between the extended and folded states. The VEF molecule exists in extended state mostly in aqueous solution and the conformations bonded with ACE are also the extended ones. The findings indicate that MD simulations have a good agreement with the molecular docking analysis.     

Coupling constants again: Experimental restraints in structure refinement

Summary Utilization of coupling constants as restraints in computational structure refinement is reviewed. In addition, we address the effect of conformational averaging and examine different approaches to apply the restraints when the experimental observable is obviously a result of averaging. Here, two different computational methods are compared. The simulation of a single structure with time-dependent restraints produces results very similar to those obtained with the calculation of numerous copies of the molecule (an ensemble of structures) and ensemble averaging. The advantages and disadvantages of the two methods are illustrated with simulations of cyclosporin A, for which 117 NOEs and 62 homo- and heteronuclear coupling constants have been measured.     

Atomic multipoles: Electrostatic potential fit,local reference axis systems,and conformational dependence

Currently, all standard force fields for biomolecular simulations use point charges to model intermolecular electrostatic interactions. This is a fast and simple approach but has deficiencies when the electrostatic potential (ESP) is compared to that from ab initio methods. Here, we show how atomic multipoles can be rigorously implemented into common biomolecular force fields. For this, a comprehensive set of local reference axis systems is introduced, which represents a universal solution for treating atom‐centered multipoles for all small organic molecules and proteins. Furthermore, we introduce a new method for fitting atomic multipole moments to the quantum mechanically derived ESP. This methods yields a 50–90% error reduction compared to both point charges fit to the ESP and multipoles directly calculated from the ab initio electron density. It is shown that it is necessary to directly fit the multipole moments of conformational ensembles to the ESP. Ignoring the conformational dependence or averaging over parameters from different conformations dramatically deteriorates the results obtained with atomic multipole moments, rendering multipoles worse than partial charges. © 2012 Wiley Periodicals, Inc.     

Comparison of charge models for fixed-charge force fields: small-molecule hydration free energies in explicit solvent

In molecular simulations with fixed-charge force fields, the choice of partial atomic charges influences numerous computed physical properties, including binding free energies. Many molecular mechanics force fields specify how nonbonded parameters should be determined, but various choices are often available for how these charges are to be determined for arbitrary small molecules. Here, we compute hydration free energies for a set of 44 small, neutral molecules in two different explicit water models (TIP3P and TIP4P-Ew) to examine the influence of charge model on agreement with experiment. Using the AMBER GAFF force field for nonbonded parameters, we test several different methods for obtaining partial atomic charges, including two fast methods exploiting semiempirical quantum calculations and methods deriving charges from the electrostatic potentials computed with several different levels of ab initio quantum calculations with and without a continuum reaction field treatment of solvent. We find that the best charge sets give a root-mean-square error from experiment of roughly 1 kcal/mol. Surprisingly, agreement with experimental hydration free energies does not increase substantially with increasing level of quantum theory, even when the quantum calculations are performed with a reaction field treatment to better model the aqueous phase. We also find that the semiempirical AM1-BCC method for computing charges works almost as well as any of the more computationally expensive ab initio methods and that the root-mean-square error reported here is similar to that for implicit solvent models reported in the literature. Further, we find that the discrepancy with experimental hydration free energies grows substantially with the polarity of the compound, as does its variation across theory levels.     

Fast,efficient generation of high‐quality atomic charges. AM1‐BCC model: I. Method

The AM1‐BCC method quickly and efficiently generates high‐quality atomic charges for use in condensed‐phase simulations. The underlying features of the electron distribution including formal charge and delocalization are first captured by AM1 atomic charges for the individual molecule. Bond charge corrections (BCCs), which have been parameterized against the HF/6‐31G* electrostatic potential (ESP) of a training set of compounds containing relevant functional groups, are then added using a formalism identical to the consensus BCI (bond charge increment) approach. As a proof of the concept, we fit BCCs simultaneously to 45 compounds including O‐, N‐, and S‐containing functionalities, aromatics, and heteroaromatics, using only 41 BCC parameters. AM1‐BCC yields charge sets of comparable quality to HF/6‐31G* ESP‐derived charges in a fraction of the time while reducing instabilities in the atomic charges compared to direct ESP‐fit methods. We then apply the BCC parameters to a small “test set” consisting of aspirin, d ‐glucose, and eryodictyol; the AM1‐BCC model again provides atomic charges of quality comparable with HF/6‐31G* RESP charges, as judged by an increase of only 0.01 to 0.02 atomic units in the root‐mean‐square (RMS) error in ESP. Based on these encouraging results, we intend to parameterize the AM1‐BCC model to provide a consistent charge model for any organic or biological molecule. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 132–146, 2000