Anatoliy Volkov

Aspherical-atom scattering factors from molecular wave functions. 1. Transferability and conformation dependence of atomic electron densities of peptides within the multipole formalism

In this study, the feasibility of building a database of theoretical atomic deformation density parameters applicable to the construction of the densities of biomacromolecules and to the interpretation of their X-ray diffraction data is discussed. The procedure described involves generation of valence-only structure factors of tripeptides calculated from theoretical densities at the B3LYP level and the refinement of multipole parameters against these simulated data. Our results so far indicate that the backbone pseudoatoms extracted in such a way are highly transferable and fairly invariant with respect to rotations around single bonds in the peptide framework. The ultimate goal is to use the aspherical-atom database for improved macromolecular refinements that are based on high-resolution data and for prediction of electrostatic properties of larger molecules.

On the evaluation of molecular dipole moments from multipole refinement of X-ray diffraction data

Abstract Lack of physical constraints in the purely mathematical multipole refinement model can lead to basis set overlap errors in the evaluation of static molecular properties from X-ray diffraction data. For the molecular dipole moment, the error is large for several of the crystals tested in this study: dl -histidine, dl -proline, p-nitroaniline and p-amino-p′-nitrobiphenyl. Two restricted models are tested. In the first, atomic charges are constrained at κ-refinement values, while in the second κ′-values based on multipole refinements of theoretical ab-initio structure factors are used to reduce the flexibility of the model. Both models provide a more localized description of the pseudo atoms compared with an unrestricted refinement, but the κ′-restricted model gives a more consistent representation of the molecular dipole moments and superior agreement with the theoretical deformation density for dl -histidine.

A Theoretical Databank of Transferable Aspherical Atoms and Its Application to Electrostatic Interaction Energy Calculations of Macromolecules

A comprehensive version of the theoretical databank of transferable aspherical pseudoatoms is described, and its first application to protein-ligand interaction energies is discussed. The databank contains all atom types present in natural amino acid residues and other biologically relevant molecules. Each atom type results from averaging over a family of chemically unique pseudoatoms, taking into account both first and second neighbors. The spawning procedure is used to ensure that close transferability is obeyed. The databank is applied to the syntenin PDZ2 domain complexed with four-residue peptides and to the PDZ2 dimer. Analysis of the electrostatic interactions energies calculated by the exact-potential/multipole-moment-databank method stresses the importance of the P0 and P-2 residues of the peptide in establishing the interaction, whereas the P-1 residue is shown to play a much smaller role. Unexpectedly, the charged P-3 residue contributes significantly to the interaction. The class I and II peptides are bound with the same strength by the syntenin PDZ2 domain, though the electrostatic interaction energy of the P-2 residue is smaller for class I peptides. There is no difference between the interaction energies of the peptides with PDZ2 domains from single-domain protein fragments and those from PDZ1-PDZ2 tandems.

Critical examination of the radial functions in the Hansen-Coppens multipole model through topological analysis of primary and refined theoretical densities

A double-zeta (DZ) multipolar model has been applied to theoretical structure factors of four organic molecular crystals as a test of the ability of the multipole model to faithfully retrieve a theoretical charge density. The DZ model leads to significant improvement in the agreement with the theoretical charge density along the covalent bonds and its topological parameters, and eliminates some of the bias introduced by the limited flexibility of the radial functions when a theoretical density is projected into the conventional multipole formalism. The DZ model may be too detailed for analysis of experimental data sets of the accuracy and resolution typically achieved at present, but provides guidance for the type of algorithms to be adapted in future studies.

Calculation of electrostatic interaction energies in molecular dimers from atomic multipole moments obtained by different methods of electron density partitioning

Accurate and fast evaluation of electrostatic interactions in molecular systems is still one of the most challenging tasks in the rapidly advancing field of macromolecular chemistry, including molecular recognition, protein modeling and drug design. One of the most convenient and accurate approaches is based on a Buckingham‐type approximation that uses the multipole moment expansion of molecular/atomic charge distributions. In the mid‐1980s it was shown that the pseudoatom model commonly used in experimental X‐ray charge density studies can be easily combined with the Buckingham‐type approach for calculation of electrostatic interactions, plus atom–atom potentials for evaluation of the total interaction energies in molecular systems. While many such studies have been reported, little attention has been paid to the accuracy of evaluation of the purely electrostatic interactions as errors may be absorbed in the semiempirical atom–atom potentials that have to be used to account for exchange repulsion and dispersion forces. This study is aimed at the evaluation of the accuracy of the calculation of electrostatic interaction energies with the Buckingham approach. To eliminate experimental uncertainties, the atomic moments are based on theoretical single‐molecule electron densities calculated at various levels of theory. The electrostatic interaction energies for a total of 11 dimers of α‐glycine, N‐acetylglycine and L‐(+)‐lactic acid structures calculated according to Buckingham with pseudoatom, stockholder and atoms‐in‐molecules moments are compared with those evaluated with the Morokuma–Ziegler energy decomposition scheme. For α‐glycine a comparison with direct “pixel‐by‐pixel” integration method, recently developed Gavezzotti, is also made. It is found that the theoretical pseudoatom moments combined with the Buckingham model do predict the correct relative electrostatic interactions energies, although the absolute interaction energies are underestimated in some cases. The good agreement between electrostatic interaction energies computed with Morokuma–Ziegler partitioning, Gavezzottis method, and the Buckingham approach with atoms‐in‐molecules moments demonstrates that reliable and accurate evaluation of electrostatic interactions in molecular systems of considerable complexity is now feasible.

The interplay between experiment and theory in charge-density analysis

The comparison of theory and experiment remains a cornerstone of scientific inquiry. Various levels of such comparison applicable to charge-density analysis are discussed, including static and dynamic electron densities, topological properties, d-orbital occupancies and electrostatic moments. The advantages and drawbacks of the pseudoatom multipole are discussed, as are the experimentally constrained wavefunctions introduced by Jayatilaka and co-workers, which combine energy minimization with the requirement to provide a reasonable fit to the X-ray structure factors. The transferability of atomic densities can be exploited through construction of a pseudoatom databank, which may be based on analysis of ab initio molecular electron densities, and can be used to evaluate a host of physical properties. Partitioning of theoretical energies with the Morokuma-Ziegler energy decomposition scheme allows direct comparison with electrostatic interaction energies obtained from electron densities represented by the pseudoatom formalism. Compared with the Buckingham expression for the interaction between non-overlapping densities, the agreement with theory is much improved when a newly developed hybrid EP/MM (exact potential/multipole model) method is employed.

Charge Density Analysis of the (C−C)→Ti Agostic Interactions in a Titanacyclobutane Complex

The experimental electron density study of Ti(C(5)H(4)Me)(2)[(CH(2))(2)CMe(2)] provides direct evidence for the presence of (C-C)-->Ti agostic interactions. In accord with the model of Scherer and McGrady, the C(alpha)-C(beta) bond densities no longer show cylindrical symmetry in the vicinity of the Ti atom and differ markedly from those of the other C-C bonds. At the points along the C(alpha)-C(beta) bond where the deviation is maximal the electron density is elongated toward the metal center. The distortion is supported by parallel theoretical calculations. A calculation on an Mo complex in which the agostic interaction is absent supports the Scherer and McGrady criterion for agostic interactions. Despite the formal d(0) electron configuration for this Ti(IV) species, a significant nonzero population is observed for the d orbitals, the d orbital population is largest for the d(xy) orbital, the lobes of which point toward the two C(alpha) atoms. Of the three different basis sets for the Ti atom used in theoretical calculations with the B3LYP functional, only the 6-311++G** set for Ti agrees well with the experimental charge density distribution in the Ti-(C(alpha)-C(beta))(2) plane.

Combining crystallographic information and an aspherical-atom data bank in the evaluation of the electrostatic interaction energy in an enzyme-substrate complex: influenza neuraminidase inhibition.

Although electrostatic interactions contribute only a part of the interaction energies between macromolecules, unlike dispersion forces they are highly directional and therefore dominate the nature of molecular packing in crystals and in biological complexes and contribute significantly to differences in inhibition strength among related enzyme inhibitors. In the reported study, a wide range of complexes of influenza neuraminidases with inhibitor molecules (sialic acid derivatives and others) have been analyzed using charge densities from a transferable aspherical-atom data bank. The strongest interactions of the residues are with the acidic group at the C2 position of the inhibitor ( approximately -300 kJ mol(-1) for -COO(-) in non-aromatic inhibitors, approximately -120-210 kJ mol(-1) for -COO(-) in aromatic inhibitors and approximately -450 kJ mol(-1) for -PO(3)(2-)) and with the amino and guanidine groups at C4 ( approximately -250 kJ mol(-1)). Other groups contribute less than approximately 100 kJ mol(-1). Residues Glu119, Asp151, Glu227, Glu276 and Arg371 show the largest variation in electrostatic energies of interaction with different groups of inhibitors, which points to their important role in the inhibitor recognition. The Arg292-->Lys mutation reduces the electrostatic interactions of the enzyme with the acidic group at C2 for all inhibitors that have been studied (SIA, DAN, 4AM, ZMR, G20, G28, G39 and BCZ), but enhances the interactions with the glycerol group at C6 for inhibitors that contain it. This is in agreement with the lower level of resistance of the mutated virus to glycerol-containing inhibitors compared with the more hydrophobic derivatives.

Dependence of the Intermolecular Electrostatic Interaction Energy on the Level of Theory and the Basis Set

As electrostatic forces play a prominent role in the process of folding and binding of biological macromolecules, an examination of the method dependence of the electrostatic interaction energy is of great importance. An extensive analysis of the basis set and method dependence of electrostatic interaction energies (Ees) in molecular systems using six test dimers of α-glycine is presented. A number of Hartree-Fock, Kohn-Sham, Møller-Plesset, configuration interaction (CI), quadratic CI, and coupled cluster calculations were performed using several double-, triple-, and quadruple-ζ-quality Gaussian- and Slater-type (Kohn-Sham calculations only) basis sets. The main factor affecting Ees was found to be the inclusion of diffuse functions in the basis set expansions. Møller-Plesset (even at second order), quadratic CI, and coupled cluster calculations produce the most consistent results. Hartree-Fock and CI methods usually overestimate the Ees, while the Kohn-Sham approach tends to underestimate the magnitude of the electrostatic interaction. The combination of the transferable-pseudoatom databank and the exact potential and multipole moment method reproduces Kohn-Sham B3LYP/6-31G** results on which it is based, confirming the excellent transferability of the pseudoatom densities within the systems studied. However, because Kohn-Sham calculations with double-ζ-quality basis sets show considerable deviations from advanced correlated methods, further development of the databank using electron densities from such methods is highly desirable.

Interaction energies between glycopeptide antibiotics and substrates in complexes determined by X-ray crystallography: application of a theoretical databank of aspherical atoms and a symmetry-adapted perturbation theory-based set of interatomic potentials.

Intermolecular interaction energies between fragments of glycopeptide antibiotics and small peptide ligands are evaluated using geometries determined by X-ray crystallography and recently developed methods suitable for application to very large molecular complexes. The calculation of the electrostatic contributions is based on charge densities constructed with a databank of transferable aspherical atoms described by nucleus-centered spherical harmonic density functions, and uses the accurate and fast EPMM method. Dispersion, induction and exchange-repulsion contributions are evaluated with atom-atom potentials fitted to intermolecular energies from SAPT (symmetry-adapted perturbation theory) calculations on a large number of molecules. For a number of the complexes, first-principle calculations using density functional theory have been performed for comparison. Results of the new methods agree within reasonable bounds with those from DFT calculations, while being obtained at a fraction (less than 1%) of the computer time. A strong dependence on the geometry of the interaction is found, even when the number of hydrogen bonds between the substrate and antibiotic fragment is the same. While high-resolution X-ray data are required to obtain interaction energies at a quantitative level, the techniques developed have potential for joint X-ray/energy refinement of macromolecular structures.