Conformational dependence of electrostatic potential-derived charges: Studies of the fitting procedure

Atomic monopole “point charges” are routinely determined through a least squares fit to molecular electrostatic potentials [potential-derived (PD) charges]. Previously, it has been shown that these charges vary with variation in molecular conformation. Also, it has been observed that these swings in charges are highly correlated between neighboring atoms. Here, we examine the least squares variance–covariance data matrices for a set of data in the literature and find further indications of high colinearity within the data. These colinearities effectively reduce the dimensionality of the data to a value well below the number of atoms in the molecules. This suggests that the data is not of sufficient dimensionality to support calculation of the charges for all of the atoms in a statistically significant way. We experiment with fixing the charges of atoms whose PD charges reflect large errors in the fit. The resulting estimates of fit of the remaining charges are little degraded from the estimates of fit when the charges of all of the atoms are fit. In addition, the charges that are fit take what would be considered more reasonable and “chemically intuitive” values, often of smaller magnitude. Although most of the free charges continue to vary with molecular conformation, their range is no larger than when all charges were fit and, in some cases, the ranges of the charges for the fit atoms is actually reduced over those that are found when all of the atoms take part in the fitting procedure. The errors of fit are lower and the unconstrained charges appear more reasonable when more chemically “reasonable” charges are used for the fixed values. This suggests that in many cases charges are transferable between molecules. Further, it shows a way to justifiably reduce the large fluctuations in PD charges that occur with variations in conformation. © 1993 John Wiley & Sons, Inc.     

Analysis of a large data base of electrostatic potential derived atomic charges

A large data base of 6-31G*, MNDO, AM1, and PM3 electrostatic potential (ESP) derived point charges of amino acids and monosaccharides is analyzed. We find that MNDO correlates well with 6-31G* ESP derived point charges, while AM1 and PM3 do so quite poorly. Furthermore, scaling MNDO ESP derived point charges enhances the ability of MNDO to reproduce 6-31G* results. We used our data base to attempt to derive a 6-31G* transferable charge model at an atom-by-atom level. We find that it is simple to derive a transferable model for monosaccharides, but for the amino acids statistical difficulties make this a less attractive approach. The transferable charge model for the monosaccharides is slightly better than MNDO, but scaled MNDO charges perform significantly better than the transferable model. We also carried out a QMD simulation on the alanine dipeptide to assess the fluctuations that would be expected in atomic point charges during the course of an MD simulation. Relatively large charge fluctuations are observed and their impact on molecular simulation is addressed. © 1992 by John Wiley & Sons, Inc.     

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.     

Semiempirical AM1 electrostatic potentials and AM1 electrostatic potential derived charges: A comparison with ab initio values

Electrostatic potentials calculated from AM1 wave functions have been compared with ab initio STO-3G values and qualitative agreement has been found. Atomic charges derived from AM1 electrostatic potentials for both experimental and AM1 optimized geometries are of comparable quality with STO-3G potential derived charges. These results suggest that the AM1 electrostatic potential may be useful both in its own right and also for deriving atomic charges for use in molecular dynamics studies.     

Atomic charges derived from electrostatic potentials: A detailed study

A new algorithm for fitting atomic charges to molecular electrostatic potentials is presented. This method is non-iterative and rapid compared to previous work. Results from a variety of gaussian basis sets, including STO-3G, 3-21G and 6-31G*, are presented. Charges for a representative collection of molecules, comprising both first and second row atoms and anions are tabulated. The effects of using experimental and optimized geometries are explored. Charges derived from these fits are found to adequately reproduce SCF dipole moments. A small split valence representation, 3-21G, appears to yield consistently good results in a reasonable amount of time.     

Conformational sensitivity of polyether macrocycles to electrostatic potential: Partial atomic charges,molecular mechanics,and conformational prediction

Molecular recognition (whether by enzymes, the immune system, or chelating ligands) depends critically on molecular conformation. Molecular mechanics predicts energetically favorable molecular conformations by locating low energy conformations using an empirical fit of molecular potential energy as a function of internal coordinates. Molecular mechanics analysis of 18-crown-6 demonstrates that the nonbonded term (primarily the electrostatic part) is the largest contributor to the conformational energy. Nevertheless, common methods of treating the electrostatic interaction for 18-crown-6 yield inconsistent values for conformational energies partly because partial charges assigned to each atom can change with conformation due to through-space inductive effects which are not considered in most molecular mechanics programs. Similar findings from several other groups are reviewed to support our conclusions. We argue for care and caution in predicting conformational preferences of molecules with two or more highly polar atoms. We also discuss the desirability of using an empirical method of partial charge determination such as the charge equilibration algorithm of Rappé and Goddard (or a suitable generalization which includes polarization) as a method of including these effects in molecular mechanics and molecular dynamics calculations.     

Generation of OPLS-like charges from molecular electrostatic potential using restraints

A new method for generating atom-centered charges for use in condensed phase computer simulations is presented, which is based on a restrained electrostatic potential (RESP) procedure. Charges are calculated from a least-squares fit to the quantum mechanical electrostatic potential with a restraint applied to reduce their magnitude. The restraint developed here offers advantages over that used in RESP. The magnitude of the restraint is optimized to yield charges as close to the equivalent OPLS values as possible while still reproducing the molecule's electrostatic potential. A cross-validation analysis is used to show that the restraint is insensitive to the selection of OPLS molecules from which it is derived. Thus, with this method, OPLS-like charges may be produced from the electrostatic potential for atom types not in the OPLS force field. In addition, the restraint is shown to reduce the conformational dependence of the charges. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 483–498, 1999     

Conformational dependence of the electrostatic potential-derived charges of dopamine: Ramifications in molecular mechanics force field calculations in the gas phase and in aqueous solution

The electrostatic potential-derived charges for the catecholamine neurotransmitter dopamine were calculated at the STO-3G and 6-31G* basis sets for six different molecular conformations. The degree of variance of the charges with changing conformations was examined. The 6-31G* basis set produced charges that were more sensitive to changes in conformation than those derived from the STO-3G electrostatic potentials. The implication of the charge variations in molecular mechanics calculations was also investigated. The molecular mechanics results in the gas phase exhibited a variance depending upon the charge set used. The force field calculations varied much less when aqueous solvation was included in the calculations through a continuum model. © 1993 John Wiley & Sons, Inc.     

Accurate molecular electrostatic potentials based on modified PRDDO/M wave functions. I. Electrostatic potential derived atomic charges

A new approach for the calculation of electrostatic potential derived atomic charges is presented. Based on molecular orbital calculations in the PRDDO/M approximation, the new parametrized electrostatic potential (PESP) method is parametrized against ab initio MP2/6-31G** calculations. For a data set of 820 atoms in 145 molecules containing H, C, N. O, F, P, S, Cl, and Br (including hypervalent species), the PESP method achieves a mean absolute error of 0.037 e⁻ with a correlation coefficient of 0.990. Unlike other approximate approaches, no scaling factor is required to improve the agreement between PESP charges and the underlying ab initio results. PESP calculations are an order of magnitude faster than the simplest ab initio calculation (STO-3G) on large molecules while achieving a level of accuracy that rivals much more elaborate ab initio methods. © 1997 by John Wiley & Sons, Inc. J Comput Chem 18: 955–969, 1997     

New method for the derivation of net atomic charges from the electrostatic potential

Net atomic charges are derived from a least-squares fitting to electrostatic potentials at atomic sites. The method treats atoms in the molecule as having spherically averaged Hartree–Fock densities, the atomic densities overlapping with one another. The method has the advantage of best reproducing the electrostatic potentials at the atomic nuclei and avoiding the arbitrariness in choosing the points used in the fitting. We have written a FORTRAN program, CHELPN92 (Z. Su, Chemistry Department, SUNY at Buffalo, Buffalo, NY, 1992), based on the method and applied it to deuterated benzene, l-alanine, d,l-histidine, 2-methyl-4-nitroaniline, and deuterated pyridinium-1-dicyanomethylide using the molecular geometry and electrostatic potentials from analysis of accurate X-ray diffraction data. The derived charges are used to calculate the molecular dipole moments. While the charges from this method are in general significantly different from those from the kappa refinement [P. Coppens, T.N. Guru Row, P. Leung, E.D. Stevens, P.J. Becker, and Y.W. Yang, Acta Cryst. A, 35 , 63 (1979)], the dipole moments obtained with the new method agree well with those from the kappa refinement. © John Wiley & Sons, Inc.     

On the use of electrostatic potential derived charges in molecular mechanics force fields. The relative solvation free energy of cis- and trans-N-methyl-acetamide

We have carried out free energy perturbation calculations on the relative solvation free energy of cis- and trans-N-methyl-acetamide (NMA). Experimentally, the solvation free energy difference has been found to be near zero. Using 6-31G* ab initio electrostatic potential derived charges for both the cis and trans conformations, we calculate a solvation free energy difference of 0.1 ± 0.1 kcal/mol. Using the 6-31G* charges derived for the trans conformation for both the cis and trans models leads to a solvation free energy difference of 0.9 ± 0.1 kcal/mol, compared to the value of 2.2 kcal/mol determined for the OPLS model for trans-NMA.     

Atomic charges derived from a fast and accurate method for electrostatic potentials based on modified AM1 calculations

Atomic charges derived from a recently described approach to the very rapid computation of AM1 electrostatic potentials (ESP) accurately parallel, but are ca. 20% smaller than, the corresponding HF/6-31G* values. The dipole moments computed from the AM1 charges are virtually identical to those derived directly from the wave function and in rather better agreement with the experimental values than those computed using the HF/6-31G* charges. Unlike other approaches to the semiempirical calculation of ESP-derived charges, the present method also yields near HF/6-31G* quality potentials close to the molecular periphery. For medium-sized organic molecules (40-100 basis functions), the method is approximately two orders of magnitude faster than those involving prior deorthogonalization of AM1 wave function and explicit computation of the full ESP integral matrix. © 1994 by John Wiley & Sons, Inc.     

Conformational sampling of hydrocarbon and lipid chains in an orienting potential

A Distribution Biased Monte Carlo (DBMC) sampling procedure is developed for the efficient generation of chain conformations in the oriented environment of lipid membranes and other liquid crystalline systems. Conformations of the sn-1 chain of dipalmitoyl phosphatidylcholine (DPPC) were generated by independently sampling torsion angles from continuous distributions in an orienting potential based on a Marcelja mean field; depending on the chain position, the convergence in the deuterium order parameters (S_CD ) was 100 to 3000 times more efficient with DBMC than with Brownian dynamics. Optimization using joint distribution and torsional potentials of mean force yielded a further threefold increase in sampling efficiency. Overall chain tilt was included using Euler angle rotations and a separate field strength for the anchor. A segmental DBMC procedure was used to generate a set of complete DPPC conformations with well-converged conformationally averaged S_CD consistent with experimental values. These conformations show considerable flexibility, not only in the hydrocarbon tails, but additionally in both the glycerol and head-group portions of the lipid. An appendix compares DBMC with a number of other Monte Carlo and stochastic dynamics algorithms using the example of a bistable oscillator, and illustrates the tuning of parameters for optimal convergence. © 1994 by John Wiley & Sons, Inc.

1 This article is a US Government work and, as such, is in the public domain in the United States of America.

     

A combined electronegativity equalization and electrostatic potential fit method for the determination of atomic point charges

We report an approach for the determination of atomic monopoles of macromolecular systems using connectivity and geometry parameters alone. The method is appropriate also for the calculation of charge distributions based on the quantum mechanically determined wave function and does not suffer from the mathematical instability of other electrostatic potential fit methods.     

Effect of lipid headgroup composition on the interaction between melittin and lipid bilayers

The effect of the lipid polar headgroup on melittin-phospholipid interaction was investigated by cryo-TEM, fluorescence spectroscopy, ellipsometry, circular dichroism, electrophoresis and photon correlation spectroscopy. In particular, focus was placed on the effect of the lipid polar headgroup on peptide adsorption to, and penetration into, the lipid bilayer, as well as on resulting colloidal stability effects for large unilamellar liposomes. The effect of phospholipid headgroup properties on melittin-bilayer interaction was addressed by comparing liposomes containing phosphatidylcholine, -acid, and -inositol at varying ionic strength. Increasing the bilayer negative charge leads to an increased liposome tolerance toward melittin which is due to an electrostatic arrest of melittin at the membrane interface. Balancing the electrostatic attraction between the melittin positive charges and the phospholipid negative charges through a hydration repulsion, caused by inositol, reduced this surface arrest and increased liposome susceptibility to the disruptive actions of melittin. Furthermore, melittin was demonstrated to induce liposome structural destabilization on a colloidal scale which coincided with leakage induction for both anionic and zwitterionic systems. The latter findings thus clearly show that coalescence, aggregation, and fragmentation contribute to melittin-induced liposome leakage, and that detailed molecular analyses of melittin pore formation are incomplete without considering also these colloidal aspects.     

Charge density distributions derived from smoothed electrostatic potential functions: design of protein reduced point charge models

To generate reduced point charge models of proteins, we developed an original approach to hierarchically locate extrema in charge density distribution functions built from the Poisson equation applied to smoothed molecular electrostatic potential (MEP) functions. A charge fitting program was used to assign charge values to the so-obtained reduced representations. In continuation to a previous work, the Amber99 force field was selected. To easily generate reduced point charge models for protein structures, a library of amino acid templates was designed. Applications to four small peptides, a set of 53 protein structures, and four KcsA ion channel models, are presented. Electrostatic potential and solvation free energy values generated by the reduced models are compared with the corresponding values obtained using the original set of atomic charges. Results are in closer agreement with the original all-atom electrostatic properties than those obtained with a previous reduced model that was directly built from the smoothed MEP functions [Leherte and Vercauteren in J Chem Theory Comput 5:3279–3298, 2009].