The role of higher CO-multipole moments in understanding the dynamics of photodissociated carbonmonoxide in myoglobin

The influence of electrostatic multipole moments up to hexadecapole on the dynamics of photodissociated carbon monoxide (CO) in myoglobin is investigated. The CO electrostatic potential is expressed as an expansion into atomic multipole moments of increasing order up to octopole which are obtained from a distributed multipole analysis. Three models with increasingly accurate molecular multipoles (accurate quadrupole, octopole, and hexadecapole moments, respectively) are developed and used in molecular dynamics simulations. All models with a fluctuating quadrupole moment correctly describe the location of the B-state whereas the sign of the octopole moment differentiates between the Fe···CO and Fe···OC orientation. For the infrared spectrum of photodissociated CO, considerable differences between the three electrostatic models are found. The most detailed electrostatic model correctly reproduces the splitting, shift, and width of the CO spectrum in the B-state. From an analysis of the trajectories, the spectroscopic B₁ and B₂ states are assigned to the Fe···CO and Fe···OC substates, respectively.     

Libraries of atomic multipole moments for precise modeling of electrostatic properties of amino acids

Summary Contemporary theoretical models used in describing electrostatic properties of amino acids in polypeptides rely usually on atomic point charges. Recently noted defects of such models in reproducing protein folding originate from the inadequate representation of the electrostatic term, in particular inability of atomic charges to account for local anisotropy of molecular charge distribution. Such defects could be corrected by multicenter multipole moments derived directly from any high quality quantum chemical wavefunctions. This is illustrated by comparison of monopole and multipole electrostatic interactions between some amino acids within glutathione S-transferase.High quality Point Charge Models (PCM) can be derived analytically from multipole moment databases. Preliminary results suggest that torsional potentials are controlled by electrostatic interactions of atomic multipoles.Examples illustrating various uses of multicenter multipole moment databases of protein building blocks in modeling various properties of amino acids and polypeptides have been described, including calculation of molecular electrostatic potentials, electric fields, interactions between amino acid residues, estimates of pK_a shifts and changes in catalytic activity induced by amino acid substitutions in mutated enzymes.     

Higher order multipole moments for molecular dynamics simulations

In conventional force fields, the electrostatic potential is represented by atom-centred point charges. This choice is in principle arbitrary, but technically convenient. Point charges can be understood as the first term of multipole expansions, which converge with an increasing number of terms towards the accurate representation of the molecular potential given by the electron density distribution. The use of multipole expansions can therefore improve the force field accuracy. Technically, the implementation of atomic multipoles is more involved than the use of point charges. Important points to consider are the orientation of the multipole moments during the trajectory, conformational dependence of the atomic moments and stability of the simulations which are discussed here.

Complementary DNA base interactions: application of recently refined electrostatic interaction theory

Electrostatic interactions between the DNA bases in the Watson-Crick hydrogen bonding configuration are examined in both the molecular and the atomic multipole representation using three different methods of calculation: (a) CNDO wave functions and definitions of moments, (b) IEHT wave functions and division of two-center densities and (c) IHET wave functions with equally divided overlap densities. It is shown that the inclusion in the interaction series of terms at least as high as the quadrupole-quadrupole is required to quantitatively characterize the interactions. Convergence is more rapid with the atomic multipole representation and is unaffected by the type of assignment of formal charges. A quantitative approach to the problem of the role of electrostatic interactions in hydrogen bonding in DNA is thus provided, with obvious impact on the investigation of molecular recognition processes.     

Revealing substitution effects on the strength and nature of halogen-hydride interactions: a theoretical study

A quantum chemistry study was carried out to investigate the strength and nature of halogen bond interactions in HXeH···XCCY complexes, where X = Cl, Br and Y = H, F, Cl, Br, CN, NC, C₂H, CH₃, OH, SH, NH₂. Examination of the electrostatic potentials V(r) of the XCCY molecules reveals that the addition of substituents has a significant effect upon the most positive electrostatic potential on the surface of the interacting halogen atom. We found that the magnitude of atomic charges and multipole moments depends upon the halogen atom X and is rather sensitive to the electron-withdrawing/donating power of the remainder of the molecule. An excellent correlation was found between the most positive electrostatic potentials on the halogen atom and the interaction energies. For either HXeH···ClCCY or HXeH···BrCCY complexes, an approximate linear correlation between the interaction energies and halogens multipole moments are established, indicating that the electrostatic and polarization interactions are responsible for the stability of the complexes. According to energy decomposition analysis, it is revealed that the electrostatic interactions are the major source of the attraction in the HXeH···XCCY complexes. Furthermore, the changes in the electrostatic term are mainly responsible for the dependence of interaction energy on the halogen atom.

Point Charges Optimally Placed to Represent the Multipole Expansion of Charge Distributions

We propose an approach for approximating electrostatic charge distributions with a small number of point charges to optimally represent the original charge distribution. By construction, the proposed optimal point charge approximation (OPCA) retains many of the useful properties of point multipole expansion, including the same far-field asymptotic behavior of the approximate potential. A general framework for numerically computing OPCA, for any given number of approximating charges, is described. We then derive a 2-charge practical point charge approximation, PPCA, which approximates the 2-charge OPCA via closed form analytical expressions, and test the PPCA on a set of charge distributions relevant to biomolecular modeling. We measure the accuracy of the new approximations as the RMS error in the electrostatic potential relative to that produced by the original charge distribution, at a distance the extent of the charge distribution–the mid-field. The error for the 2-charge PPCA is found to be on average 23% smaller than that of optimally placed point dipole approximation, and comparable to that of the point quadrupole approximation. The standard deviation in RMS error for the 2-charge PPCA is 53% lower than that of the optimal point dipole approximation, and comparable to that of the point quadrupole approximation. We also calculate the 3-charge OPCA for representing the gas phase quantum mechanical charge distribution of a water molecule. The electrostatic potential calculated by the 3-charge OPCA for water, in the mid-field (2.8 Å from the oxygen atom), is on average 33.3% more accurate than the potential due to the point multipole expansion up to the octupole order. Compared to a 3 point charge approximation in which the charges are placed on the atom centers, the 3-charge OPCA is seven times more accurate, by RMS error. The maximum error at the oxygen-Na distance (2.23 Å ) is half that of the point multipole expansion up to the octupole order.     

Cα torsion angles as a flexible criterion to extract secrets from a molecular dynamics simulation

A multipolar, polarizable electrostatic method for future use in a novel force field is described. Quantum Chemical Topology (QCT) is used to partition the electron density of a chemical system into atoms, then the machine learning method Kriging is used to build models that relate the multipole moments of the atoms to the positions of their surrounding nuclei. The pilot system serine is used to study both the influence of the level of theory and the set of data generator methods used. The latter consists of: (i) sampling of protein structures deposited in the Protein Data Bank (PDB), or (ii) normal mode distortion along either (a) Cartesian coordinates, or (b) redundant internal coordinates. Wavefunctions for the sampled geometries were obtained at the HF/6-31G(d,p), B3LYP/apc-1, and MP2/cc-pVDZ levels of theory, prior to calculation of the atomic multipole moments by volume integration. The average absolute error (over an independent test set of conformations) in the total atom-atom electrostatic interaction energy of serine, using Kriging models built with the three data generator methods is 11.3 kJ mol^-1 (PDB), 8.2 kJ mol^-1 (Cartesian distortion), and 10.1 kJ mol^-1 (redundant internal distortion) at the HF/6-31G(d,p) level. At the B3LYP/apc-1 level, the respective errors are 7.7 kJ mol^-1, 6.7 kJ mol^-1, and 4.9 kJmol^-1, while at the MP2/cc-pVDZ level they are 6.5 kJ mol^-1, 5.3 kJ mol^-1, and 4.0 kJmol^-1. The ranges of geometries generated by the redundant internal coordinate distortion and by extraction from the PDB are much wider than the range generated by Cartesian distortion. The atomic multipole moment and electrostatic interaction energy predictions for the B3LYP/apc-1 and MP2/cc-pVDZ levels are similar, and both are better than the corresponding predictions at the HF/6-31G(d,p) level.     

Charge calculations in molecular mechanics 6: the calculation of partial atomic charges in nucleic acid bases and the electrostatic contribution to DNA base pairing.

A previously described scheme for the direct calculation of the partial atomic charges in molecules (CHARGE2) is applied to the nucleic acid bases. It is shown that inclusion of the omega-technique for the calculation of HMO derived pi charges is of particular importance for these highly polar systems. The molecular dipole moments obtained for the resulting charges are in very good agreement with the observed values for a variety of substituted purine and pyrimidine bases. The partial atomic charges for cytosine, thymine, guanine and adenine (as the 1-methyl and 9-methyl forms) are given and compared with values calculated by a variety of molecular orbital and empirical schemes. All the schemes reproduce the same general trends, with the possible exception of those calculated by the Del Re method, though the charges given by Kollman are in general somewhat larger than the others. The electrostatic contribution to the Watson-Crick base pair interaction energies are calculated using these partial atomic charges. The electrostatic contributions obtained from the M.O. derived atomic charges are less than half the observed values, as are those obtained by the Gasteiger method. The electrostatic contributions calculated from the CHARGE2 atomic charges and those of Kollman are in reasonable agreement with the observed values. The influence of a distant-dependent dielectric constant is examined, but no clear pattern emerges.     

Incorporation of lone pairs into the electrostatic term in the empirical intra- and intermolecular energy calculations

The method hitherto used for estimating the electrostatic term in empirical intramolecular calculations of stable conformations of biologically important molecules and macromolecules and intermolecular calculations of molecular associations or packing energy in molecular crystals had been analyzed. It has been shown that the contribution of atomic hybridization moments is omitted in the calculation of electrostatic interactions from net atomic charges localized on nuclei which have been determined by standard quantum-chemical methods. This contribution plays an important part in determining electrostatic interactions, mainly in molecules containing atoms with lone pairs. Simultaneously, a modified method for calculating the electrostatic term comprising the interaction of the lone pairs, which are represented by atomic hybridization moments, has been proposed. The relationship between the atomic hybridization moment and the bond angle has been expressed for some typical configurations occurring in biologically important molecules. Finally, this new approach is illustrated by results of the conformational analysis of some model compounds for biomolecules and compared with the approach used so far for the estimation of the electrostatic interaction in empirical methods of calculation of the intra- and intermolecular energy.     

Hydration effects on the electrostatic potential around tuftsin

The electrostatic potential and component dielectric constants from molecular dynamics (MD) trajectories of tuftsin, a tetrapeptide with the amino acid sequence Thr–Lys–Pro–Arg in water and in saline solution are presented. The results obtained from the analysis of the MD trajectories for the total electrostatic potential at points on a grid using the Ewald technique are compared with the solution to the Poisson–Boltzmann (PB) equation. The latter was solved using several sets of dielectric constant parameters. The effects of structural averaging on the PB results were also considered. Solute conformational mobility in simulations gives rise to an electrostatic potential map around the solute dominated by the solute monopole (or lowest order multipole). The detailed spatial variation of the electrostatic potential on the molecular surface brought about by the compounded effects of the distribution of water and ions close to the peptide, solvent mobility, and solute conformational mobility are not qualitatively reproducible from a reparametrization of the input solute and solvent dielectric constants to the PB equation for a single structure or for structurally averaged PB calculations. Nevertheless, by fitting the PB to the MD electrostatic potential surfaces with the dielectric constants as fitting parameters, we found that the values that give the best fit are the values calculated from the MD trajectories. Implications of using such field calculations on the design of tuftsin peptide analogues are discussed. © 1999 John Wiley & Sons, Inc. Biopoly 50: 133–143, 1999     

A computational analysis of ordering in ABCHN at the nematic–isotropic transition

A computational analysis of ordering in the nematogenic compound 4-alkenyl bicyclohexylnitrile has been carried out based on quantum mechanics and intermolecular forces. The evaluation of atomic charge and dipole moment at each atomic center has been carried out using the complete neglect differential overlap (CNDO/2) method. Modified Rayleigh–Schrodinger perturbation theory along with a multicentered- multipole expansion method has been employed to evaluate long-range intermolecular interactions, while a ‘6-exp‘ potential function has been assumed for short-range interactions. The total interaction energy values obtained through these computations were used to calculate the probability of each configuration at room temperature (300 K), the nematic–isotropic transition temperature (364.7 K) and above transition temperature (450 K) using the Maxwell–Boltzmann formula. The various possible configurations during the different modes (i.e., stacking, in-plane and terminal) of interactions have been studied in terms of variation of probability due to small departures from the most probable configurations. An attempt has been made to analyze the characteristic features of liquid crystallinity in terms of their relative order with molecular parameters introduced in this paper.     

An optimized potential function for the calculation of nucleic acid interaction energies I. Base stacking

An optimized potential function for base-stacking interaction is constructed. Stacking energies between the complementary pairs of a dimer are calculated as a function of the rotational angle and separation distance. Using several different sets of atomic charges, the electrostatic component in the monopole-monopole approximation (MMA) is compared to the more refined segmented multipole–multipole representation (SMMA); the general features of the stacking minima are found to be correctly reproduced with IEHT or CNDO atomic charges. The electrostatic component is observed to control the location of stacking minima. The MMA, in general, is not a reliable approximation of the SMMA in regions away from minima; however, the MMA is reliable in predicting the location and nature of stacking minima. The attractive part of the Lennard-Jones 6–12 potential is compared to and parameterized against the expression for the second-order interaction terms composed of multipole-bond polarizability for the polarization energy and transition-dipole bond polarizabilities for approximation of the dispersion energy. The repulsive part of the Lennard-Jones potential is compared to a Kitaygorodski-type repulsive function; changing the exponent from its usual value of 12 to 11.7 gives significantly better agreement with the more refined repulsive function. Stacking minima calculated with the optimized potential method are compared with various perturbation-type treatments. The optimized potential method yields results that compare as well with melting data as do any of the more recent and expensive perturbation methods.     

Multipole electrostatic potential derived atomic charges in NDDO-methods with <Emphasis Type="Italic">spd</Emphasis>-basis sets

The recently introduced multipole approach for computing the molecular electrostatic potential (MEP) within the semiempirical neglect of diatomic differential overlap (NDDO) framework [Horn AHC, Lin Jr-H., Clark T (2005) Theor Chem Acc 114:159–168] has been used to obtain atomic charges of nearly ab initio quality by scaling the semiempirical MEP. The parameterization set comprised a total of 797 compounds and included not only the newly parameterized AM1* elements Al, Si, P, S, Cl, Ti, Zr, and Mo but also the standard AM1 elements H, C, N, O and F. For comparison, the ZDO-approximated MEP was also calculated analytically in the spd-basis. For the AM1*-optimized structures, single-point calculations at the B3LYP, HF and MP2 levels with the 6-31G(d) and LanL2DZP basis sets were performed to obtain the MEP. The regression analysis of all 12 combinations of semiempirical and ab initio MEP data yielded correlation coefficients of at least 0.99 in all cases. Scaling the analytical and multipole-derived semiempirical MEP by the regression coefficients yielded mean unsigned errors below 2.6 and 1.9 kcal mol⁻¹, respectively. Subsequently, for 22 drug molecules from the World Drug Index, atomic charges were computed according to the RESP procedure using XX/6-31G(d) (XX=B3LYP, HF, MP2) and scaled AM1* multipole MEP; the correlation coefficients obtained are 0.83, 0.85 and 0.83, respectively. Figure: Schematic representation of the atomic charge generation: The molecular electrostatic potential (MEP) is calculated using the AM1* Hamiltonian; then the semiempirical MEP is scaled to DFT or ab initio level, and atomic charges are generated subsequently by the restraint electrostatic potential (RESP) fit method. Electronic supplementary material Supplementary material is available in the online version of this article at and is accessible to authorized users. Proceedings of “Modeling Interactions in Biomolecules II”, Prague, September 5th–9th, 2005.     

On the graphical display of molecular electrostatic force-fields and gradients of the electron density

Gradients of the electrostatic potential and electron density of methyl fluoride are displayed as coloured regions on isopotential surfaces. Shading is used to achieve 3D perception and also to encode the direction of the gradient. Colouring the density by the magnitude of the gradient is demonstrated to provide an intrinsic mechanism for colouring the molecular density, so that the underlying atomic structure is vividly displayed in hues commonly used in molecular ball and stick models. The algorithm for contouring a 4D object and drawing coloured, shaded isopotential surfaces is described.     

Investigating protein-protein interaction surfaces using a reduced stereochemical and electrostatic model

A method of calculating the electrostatic potential energy between two molecules, using finite difference potential, is presented. A reduced charge set is used so that the interaction energy can be calculated as the two static molecules explore their full six-dimensional configurational space. The energies are contoured over surfaces fixed to each molecule with an interactive computer graphics program. For two crystal structures (trypsin-trypsin inhibitor and anti-lysozyme Fab-lysozyme), it is found that the complex corresponds to highly favourable interacting regions in the contour plots. These matches arise from a small number of protruding basic residues interacting with enhanced negative potential in each case. The redox pair cytochrome c peroxidase-cytochrome c exhibits an extensive favourably interacting surface within which a possible electron transfer complex may be defined by an increased electrostatic complementarity, but a decreased electrostatic energy. A possible substrate transfer configuration for the glycolytic enzyme pair glyceraldehyde phosphate dehydrogenase-phosphoglycerate kinase is presented.     

Recognition and interactions controlling the assemblies of beta barrel domains.

We present a qualitative computer graphics approach to the characterization of forces important to the assembly of beta domains that should have general utility for examining protein interactions and assembly. In our approach, the nature of the molecular surface buried by the domain contacts, the specificity of the residue-to-residue interactions, and the identity of electrostatic, hydrophobic, and hydrophilic interactions are elucidated. These techniques are applied to the beta barrel domains of Cu, Zn superoxide dismutase (SOD), immunoglobulin Fab, and tomato bushy stunt virus coat protein (TBSV), a plant viral capsid protein. By looking at a set of proteins having different numbers of interacting beta domains, we have been able to see some of the variety and also some of the patterns common to these assembled domains. Strong beta domain interactions (identified by their biochemical integrity) are apparently due to chemical, electrostatic, and shape complementarity of the molecular surfaces buried from interaction with solvent molecules. Although the amount of hydrophobic buried surface area appears to correlate with the strength of the interaction, electrostatic forces appear to be important in both stabilizing and destabilizing specific contacts. In TBSV, analysis of electrostatic interactions may help explain mechanisms of subunit accommodation to different environments, particle expansion, and pathways of assembly. The possible molecular basis for observed differences in the stability and flexibility of the domain complexes is discussed.     

Theoretical studies of the electrostatic potential of some enzyme inhibitors using computer graphics techniques

A molecular graphics program is described for the depiction of electrostatic potentials on the van der Waals surface of molecules, using colored polygons. An example is given on the application of this method to the study of coumarins and flavones that inhibit the enzyme Glyoxalase I.