Nonuniform charge scaling (NUCS): a practical approximation of solvent electrostatic screening in proteins

In molecular mechanics calculations, electrostatic interactions between chemical groups are usually represented by a Coulomb potential between the partial atomic charges of the groups. In aqueous solution these interactions are modified by the polarizable solvent. Although the electrostatic effects of the polarized solvent on the protein are well described by the Poisson--Boltzmann equation, its numerical solution is computationally expensive for large molecules such as proteins. The procedure of nonuniform charge scaling (NUCS) is a pragmatic approach to implicit solvation that approximates the solvent screening effect by individually scaling the partial charges on the explicit atoms of the macromolecule so as to reproduce electrostatic interaction energies obtained from an initial Poisson--Boltzmann analysis. Once the screening factors have been determined for a protein the scaled charges can be easily used in any molecular mechanics program that implements a Coulomb term. The approach is particularly suitable for minimization-based simulations, such as normal mode analysis, certain conformational reaction path or ligand binding techniques for which bulk solvent cannot be included explicitly, and for combined quantum mechanical/molecular mechanical calculations when the interface to more elaborate continuum solvent models is lacking. The method is illustrated using reaction path calculations of the Tyr 35 ring flip in the bovine pancreatic trypsin inhibitor.     

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.     

On the use of AM1 and MNDO wave functions to compute accurate electrostatic charges

A new strategy to evaluate accurate electrostatic charges from semiempirical wave functions is reported. The rigorous quantum mechanical molecular electrostatic potentials computed from both MNDO and AM1 wave functions are fitted to the point-charge molecular electrostatic potential to obtain the electrostatic charges. The reliability of this strategy is tested by comparing the semiempirical electrostatic charges for 21 molecules with the semiempirical Mulliken charges and with the ab initio STO-3G and 6-31G* electrostatic charges. The ability of the dipoles derived from the semiempirical electrostatic and Mulliken charges as well as from the SCF charge distributions to reproduce the ab initio 6-31G* electrostatic dipoles and the gas phase experimental values is determined. The statistical analysis clearly point out the goodness of the semiempirical electrostatic charges, specially when the MNDO method is used. The excellent relationships found between the MNDO and 6-31G* electrostatic charges permit to define a scaling factor which allows to accurately reproduce the 6-31G* electrostatic charge distribution as well as the experimental dipoles from the semiempirical electrostatic charges.     

QM:QM electronic embedding using Mulliken atomic charges: energies and analytic gradients in an ONIOM framework

An accurate first-principles treatment of chemical reactions for large systems remains a significant challenge facing electronic structure theory. Hybrid models, such as quantum mechanics:molecular mechanics (QM:MM) and quantum mechanics:quantum mechanics (QM:QM) schemes, provide a promising avenue for such studies. For many chemistries, including important reactions in materials science, molecular mechanics or semiempirical methods may not be appropriate, or parameters may not be available (e.g., surface chemistry of compound semiconductors such as indium phosphide or catalytic chemistry of transition metal oxides). In such cases, QM:QM schemes are of particular interest. In this work, a QM:QM electronic embedding model within the ONIOM (our own N-layer integrated molecular orbital molecular mechanics) extrapolation framework is presented. To define the embedding potential, we choose the real-system low-level Mulliken atomic charges. This results in a set of well-defined and unique embedding charges. However, the parametric dependence of the charges on molecular geometry complicates the energy gradient that is necessary for the efficient exploration of potential energy surfaces. We derive an efficient form for the forces where a single set of self-consistent field response equations is solved. Initial tests of the method and key algorithmic issues are discussed.     

On the representation of electrostatic fields around ab initio charge distributions

Summary We compare two methods (Mulliken charges and a distributed multipole analysis, DMA) of representing an ab initio charge distribution for calculating the electrostatic field and potential outside the molecule, using pyrimidine and the RNA base uracil as examples. This is done using a 3-D graphical display of the electrostatic fields, which, when used with real-time rotation, zooming and clipping, has many advantages for qualitatively assessing the electrostatic interactions of a molecule. The errors involved in using Mulliken point charges may be of similar magnitude to the total electrostatic field in regions which are important in recognition processes. The DMA representation automatically includes the anisotropic electrostatic effects of non-spherical features in the charge distribution of each atom, and yet the displayed electrostatic fields around the atoms which have lone-pair density do not show marked anisotropy.     

High Resolution Synchrotron Diffraction Study on Charge Density Distribution of Ampicillin Trihydrate

Charge density distribution in ampicillin trihydrate was investigated experimentally. Results were compared with the quantum calculations using density functional theory. The charge derived properties including Mulliken atomic charges, dipole moment, and molecular electrostatic potential were calculated. The multipole analysis was done for the refinement of experimental population parameters. The structure factors obtained from multipole treatment were used for the construction of Fourier maps. Topological properties of the charge distribution were discussed and the characteristics of (3,-1) critical points were analyzed.     

Reliable treatment of electrostatics in combined QM/MM simulation of macromolecules

A robust approach for dealing with electrostatic interactions for spherical boundary conditions has been implemented in the QM/MM framework. The development was based on the generalized solvent boundary potential (GSBP) method proposed by Im et al. [J. Chem. Phys. 114, 2924 (2001)], and the specific implementation was applied to the self-consistent-charge density-functional tight-binding approach as the quantum mechanics (QM) level, although extension to other QM methods is straightforward. Compared to the popular stochastic boundary-condition scheme, the new protocol offers a balanced treatment between quantum mechanics/molecular mechanics (QM/MM) and MM/MM interactions; it also includes the effect of the bulk solvent and macromolecule atoms outside of the microscopic region at the Poisson-Boltzmann level. The new method was illustrated with application to the enzyme human carbonic anhydrase II and compared to stochastic boundary-condition simulations using different electrostatic treatments. The GSBP-based QM/MM simulations were most consistent with available experimental data, while conventional stochastic boundary simulations yielded various artifacts depending on different electrostatic models. The results highlight the importance of carefully treating electrostatics in QM/MM simulations of biomolecules and suggest that the commonly used truncation schemes should be avoided in QM/MM simulations, especially in simulations that involve extensive conformational samplings. The development of the GSBP-based QM/MM protocol has opened up the exciting possibility of studying chemical events in very complex biomolecular systems in a multiscale framework.     

Communication: Quantum polarized fluctuating charge model: a practical method to include ligand polarizability in biomolecular simulations

We present a simple and practical method to include ligand electronic polarization in molecular dynamics (MD) simulation of biomolecular systems. The method involves periodically spawning quantum mechanical (QM) electrostatic potential (ESP) calculations on an extra set of computer processors using molecular coordinate snapshots from a running parallel MD simulation. The QM ESPs are evaluated for the small-molecule ligand in the presence of the electric field induced by the protein, solvent, and ion charges within the MD snapshot. Partial charges on ligand atom centers are fit through the multi-conformer restrained electrostatic potential (RESP) fit method on several successive ESPs. The RESP method was selected since it produces charges consistent with the AMBER/GAFF force-field used in the simulations. The updated charges are introduced back into the running simulation when the next snapshot is saved. The result is a simulation whose ligand partial charges continuously respond in real-time to the short-term mean electrostatic field of the evolving environment without incurring additional wall-clock time. We show that (1) by incorporating the cost of polarization back into the potential energy of the MD simulation, the algorithm conserves energy when run in the microcanonical ensemble and (2) the mean solvation free energies for 15 neutral amino acid side chains calculated with the quantum polarized fluctuating charge method and thermodynamic integration agree better with experiment relative to the Amber fixed charge force-field.     

Fragment-based quantum mechanical methods for periodic systems with Ewald summation and mean image charge convention for long-range electrostatic interactions

We describe an Ewald-summation method to incorporate long-range electrostatic interactions into fragment-based electronic structure methods for periodic systems. The present method is an extension of the particle-mesh Ewald technique for combined quantum mechanical and molecular mechanical (QM/MM) calculations, and it has been implemented into the explicit polarization (X-Pol) potential to illustrate the computational details. As in the QM/MM-Ewald method, the X-Pol-Ewald approach is a linear-scaling electrostatic method, in which the short-range electrostatic interactions are determined explicitly in real space and the long-range Ewald pair potential is incorporated into the Fock matrix as a correction. To avoid the time-consuming Fock matrix update during the self-consistent field procedure, a mean image charge (MIC) approximation is introduced, in which the running average with a user-chosen correlation time is used to represent the long-range electrostatic correction as an average effect. Test simulations on liquid water show that the present X-Pol-Ewald method takes about 25% more CPU time than the usual X-Pol method using spherical cutoff, whereas the use of the MIC approximation reduces the extra costs for long-range electrostatic interactions by 15%. The present X-Pol-Ewald method provides a general procedure for incorporating long-range electrostatic effects into fragment-based electronic structure methods for treating biomolecular and condensed-phase systems under periodic boundary conditions.     

Atomic charges from IR intensity parameters: theory,implementation and application

Abstract  

A computational method to extract atomic charges (IR charges) from DFT/ab initio-computed atomic polar tensors is presented and compared with commonly available population schemes. The procedure adopted and its implementation in a (freely available) code are also reported and commented. Thanks to the procedure developed, infrared charges can be now readily gathered also by non-experts, provided that Cartesian dipole derivatives from a quantum chemical calculation of the IR spectrum are available. The method has been applied for the calculation of IR charges of about 50 molecules: It performs well in describing peculiar intramolecular interactions, providing a picture of the molecular charge distribution coherent with the chemical intuition. A nice agreement is also found with charges obtained from Hirshfeld algorithm and from the fitting of the electrostatic potential (CHELPG and MK schemes). On this basis, we propose IR charges as a reliable, physically sound and easily accessible alternative to other charge parameters currently adopted.     

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.     

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.     

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.     

Development of a model for the rational design of molecular imprinted polymer: Computational approach for combined molecular dynamics/quantum mechanics calculations

A new rational approach for the preparation of molecularly imprinted polymer (MIP) based on the combination of molecular dynamics (MD) simulations and quantum mechanics (QM) calculations is described in this work. Before performing molecular modeling, a virtual library of functional monomers was created containing forty frequently used monomers. The MD simulations were first conducted to screen the top three monomers from virtual library in each porogen-acetonitrile, chloroform and carbon tetrachloride. QM simulations were then performed with an aim to select the optimum monomer and progen solvent in which the QM simulations were carried out; the monomers giving the highest binding energies were chosen as the candidate to prepare MIP in its corresponding solvent. The acetochlor, a widely used herbicide, was chosen as the target analyte. According to the theoretical calculation results, the MIP with acetochlor as template was prepared by emulsion polymerization method using N,N-methylene bisacrylamide (MBAAM) as functional monomer and divinylbenzene (DVB) as cross-linker in chloroform. The synthesized MIP was then tested by equilibrium-adsorption method, and the MIP demonstrated high removal efficiency to the acetochlor. Mulliken charge distribution and ¹H NMR spectroscopy of the synthesized MIP provided insight on the nature of recognition during the imprinting process probing the governing interactions for selective binding site formation at a molecular level. We think the computer simulation method first proposed in this paper is a novel and reliable method for the design and synthesis of MIP.     

Force-field parametrization of retro-inverso modified residues: Development of torsional and electrostatic parameters

Summary Torsional and the electrostatic parameters for molecular mechanics studies of retro-inverso modified peptides have been developed using quantum mechanical calculations. The resulting parameters have been compared with those calculated for conventional peptides. Rotational profiles, which were obtained spanning the corresponding dihedral angle, were corrected by removing the energy contributions associated to changes in interactions different from torsion under study. For this purpose, the torsional energy associated to each point of the profiles was estimated as the corresponding quantum mechanical energy minus the bonding and nonbonding energy contributions produced by the perturbations that the variation of the spanned dihedral angle causes in the bond distances, bond angles and the other dihedral angles. These energies were calculated using force-field expressions. The corrected profiles were fitted to a three-term Fourier expansion to derive the torsional parameters. Atomic charges for retro-inverso modified residues were derived from the rigorously calculated quantum mechanical electrostatic potential. Furthermore, the reliability of electrostatic models based on geometry-dependent charges and fixed charges has been examined.     

Toward a new approach for determination of solute's charge distribution to analyze interatomic electrostatic interactions in quantum mechanical/molecular mechanical simulations

We present an alternative approach to determine "density-dependent property"-derived charges for molecules in the condensed phase. In the case of a solution, it is essential to take into consideration the electron polarization of molecules in the active site of this system. The solute and solvent molecules in this site have to be described by a quantum mechanical technique and the others are allowed to be treated by a molecular mechanical method (QM/MM scheme). For calculations based on this scheme, using the forces and interaction energy as density-dependent property our charges from interaction energy and forces (CHIEF) approach can provide the atom-centered charges on the solute atoms. These charges reproduce well the electrostatic potentials around the solvent molecules and present properly the picture of the electron density of the QM subsystem in the solution system. Thus, the CHIEF charges can be considered as the atomic charges under the conditions of the QM/MM simulation, and then enable one to analyze electrostatic interactions between atoms in the QM and MM regions. This approach would give a view of the QM nuclei and electrons different from the conventional methods.     

A Molecular Mechanics Model for Flavins

Flavin containing molecules form a group of important cofactors that assist a wide range of enzymatic reactions. Flavins use the redox-active isoalloxazine system, which is capable of one- and two-electron transfer reactions and can exist in several protonation states. In this work, molecular mechanics force field parameters compatible with the CHARMM36 all-atom additive force field were derived for biologically important flavins, including riboflavin, flavin mononucleotide, and flavin adenine dinucleotide. The model was developed for important protonation and redox states of the isoalloxazine group. The partial charges were derived using the CHARMM force field parametrization strategy, where quantum mechanics water–solute interactions are used to target optimization. In addition to monohydrate energies and geometries, electrostatic potential around the compound was used to provide additional restraints during the charge optimization. Taking into account the importance of flavin-containing molecules special attention was given to the quality of bonded terms. All bonded terms, including stiff terms and torsion angle parameters, were parametrized using exhaustive potential energy surface scans. In particular, the model reproduces well the butterfly motion of isoalloxazine in the oxidized and reduced forms as predicted by quantum mechanics in gas phase. The model quality is illustrated by simulations of four flavoproteins. Overall, the presented molecular mechanics model will be of utility to model flavin cofactors in different redox states. © 2019 Wiley Periodicals, Inc.     

Coupled semiempirical quantum mechanics and molecular mechanics (QM/MM) calculations on the aqueous solvation free energies of ionized molecules

The aqueous solvation free energies of ionized molecules were computed using a coupled quantum mechanical and molecular mechanical (QM/MM) model based on the AM1, MNDO, and PM3 semiempirical molecular orbital methods for the solute molecule and the TIP3P molecular mechanics model for liquid water. The present work is an extension of our model for neutral solutes where we assumed that the total free energy is the sum of components derived from the electrostatic/polarization terms in the Hamiltonian plus an empirical “nonpolar” term. The electrostatic/polarization contributions to the solvation free energies were computed using molecular dynamics (MD) simulation and thermodynamic integration techniques, while the nonpolar contributions were taken from the literature. The contribution to the electrostatic/polarization component of the free energy due to nonbonded interactions outside the cutoff radii used in the MD simulations was approximated by a Born solvation term. The experimental free energies were reproduced satisfactorily using variational parameters from the vdW terms as in the original model, in addition to a parameter from the one-electron integral terms. The new one-electron parameter was required to account for the short-range effects of overlapping atomic charge densities. The radial distribution functions obtained from the MD simulations showed the expected H-bonded structures between the ionized solute molecule and solvent molecules. We also obtained satisfactory results by neglecting both the empirical nonpolar term and the electronic polarization of the solute, i.e., by implementing a nonpolarization model. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1028–1038, 1999