Christian Jelsch

Advances in protein and small-molecule charge-density refinement methods using MoPro

With an increasing number of biological macromolecule structures solved at ultra-high resolution and with the advances of supramolecular chemistry, it becomes necessary to extend to large systems experimental charge-density study methods that are usually applied to small molecules. The latest developments in the refinement program MoPro (Molecular Properties), dedicated to the charge-density refinement at (sub)atomic resolution of structures ranging from small molecules to biological macromolecules, are presented. MoPro uses the Hansen & Coppens [Acta Cryst. (1978), A34, 909–921] multipolar pseudo-atom model for the electron-density refinement. Alternative methods are also proposed, such as modelling bonding and lone-pair electron density by virtual spherical atoms. For proteins at atomic resolution, a charge-density database developed in the laboratory enables the transfer of multipolar parameters. The program allows complex refinement strategies to be written and has numerous restraints, constraints and analysis tools for use in the structure and electron-density analysis. New kappa and multipolar parameter restraints/constraints are also implemented and discussed. Furthermore, constraints on the electron density, such as local symmetry and atom equivalence, are easily defined. Some examples of applications, from small molecules to large unit cells (including the enzyme aldose reductase), are given in order to guide the MoPro user and to show the large field of applicability of this code.

Refinement of proteins at subatomic resolution with MOPRO

Crystallography at subatomic resolution permits the observation and measurement of the non-spherical character of the atomic electron density. Charge density studies are being performed on molecules of increasing size. The MOPRO least-squares refinement software has thus been developed, by extensive modifications of the program MOLLY, for protein and supramolecular chemistry applications. The computation times are long because of the large number of reflections and the complexity of the multipolar model of the atomic electron density; the structure factor and derivative calculations have thus been parallelized. Stereochemical and dynamical restraints as well as the conjugate gradient algorithm have been implemented. A large number of the normal matrix off-diagonal terms turn out to be very small and the block diagonal approximation is thus particularly efficient in the case of large structures at very high resolution.

On the application of an experimental multipolar pseudo-atom library for accurate refinement of small-molecule and protein crystal structures

With an increasing number of biomacromolecular crystal structures being measured to ultra-high resolution, it has become possible to extend to large systems experimental charge-density methods that are usually applied to small molecules. A library has been built of average multipole populations describing the electron density of chemical groups in all 20 amino acids found in proteins. The library uses the Hansen & Coppens multipolar pseudo-atom model to derive molecular electron density and electrostatic potential distributions. The library values are obtained from several small peptide or amino acid crystal structures refined against ultra-high-resolution X-ray diffraction data. The library transfer is applied automatically in the MoPro software suite to peptide and protein structures measured at atomic resolution. The transferred multipolar parameters are kept fixed while the positional and thermal parameters are refined. This enables a proper deconvolution of thermal motion and valence-electron-density redistributions, even when the diffraction data do not extend to subatomic resolution. The use of the experimental library multipolar atom model (ELMAM) also has a major impact on crystallographic structure modelling in the case of small-molecule crystals at atomic resolution. Compared to a spherical-atom model, the library transfer results in a more accurate crystal structure, notably in terms of thermal displacement parameters and bond distances involving H atoms. Upon transfer, crystallographic statistics of fit are improved, particularly free R factors, and residual electron-density maps are cleaner.

Electrostatic complementarity in an aldose reductase complex from ultra-high-resolution crystallography and first-principles calculations

The electron density and electrostatic potential in an aldose reductase holoenzyme complex have been studied by density functional theory (DFT) and diffraction methods. Aldose reductase is involved in the reduction of glucose in the polyol pathway by using NADPH as a cofactor. The ultra-high resolution of the diffraction data and the low thermal-displacement parameters of the structure allow accurate atomic positions and an experimental charge density analysis. Based on the x-ray structural data, order-N DFT calculations have been performed on subsets of up to 711 atoms in the active site of the molecule. The charge density refinement of the protein was performed with the program mopro by using the transferability principle and our database of charge density parameters built from crystallographic analyses of peptides and amino acids. Electrostatic potentials calculated from the charge density database, the preliminary experimental electron density analysis, DFT computations, and atomic charges taken from the amber software dictionary are compared. The electrostatic complementarity between the cofactor NADP+ and the active site shows up clearly. The anchoring of the inhibitor is due mainly to hydrophobic forces and to only two polar interaction sites within the enzyme cavity. The potentials calculated by x-ray and DFT techniques agree reasonably well. At the present stage of the refinement, the potentials obtained directly from the database are in excellent agreement with the experimental ones. In addition, these results demonstrate the significant contribution of electron lone pairs and of atomic polarization effects to the host and guest mechanism.

The enrichment ratio of atomic contacts in crystals, an indicator derived from the Hirshfeld surface analysis

An enrichment ratio is derived from the decomposition of the crystal contact surface between pairs of interacting chemical species. The propensity of different contact types to form is investigated.

Transferability of Multipole Charge-Density Parameters: Application to Very High Resolution Oligopeptide and Protein Structures

Crystallography at sub-atomic resolution permits the observation and measurement of the non-spherical character of the electron density (parameterized as multipoles) and of the atomic charges. This fine description of the electron density can be extended to structures of lower resolution by applying the notion of transferability of the charge and multipole parameters. A database of such parameters has been built from charge-density analysis of several peptide crystals. The aim of this study is to assess for which X-ray structures the application of transferability is physically meaningful. The charge-density multipole parameters have been transferred and the X-ray structure of a 310 helix octapeptide Ac-Aib2-L-Lys(Bz)-Aib2-L-Lys(Bz)-Aib2-NHMe refined subsequently, for which diffraction data have been collected to a resolution of 0.82 A at a cryogenic temperature of 100 K. The multipoles transfer resulted in a significant improvement of the crystallographic residual factors wR and wR free. The accumulation of electrons in the covalent bonds and oxygen lone pairs is clearly visible in the deformation electron-density maps at its expected value. The refinement of the charges for nine different atom types led to an additional improvement of the R factor and the refined charges are in good agreement with those of the AMBER molecular modelling dictionary. The use of scattering factors calculated from average results of charge-density work gives a negligible shift of the atomic coordinates in the octapeptide but induces a significant change in the temperature factors (DeltaB approximately 0.4 A2). Under the spherical atom approximation, the temperature factors are biased as they partly model the deformation electron density. The transfer of the multipoles thus improves the physical meaning of the thermal-displacement parameters. The contribution to the diffraction of the different components of the electron density has also been analyzed. This analysis indicates that the electron-density peaks are well defined in the dynamic deformation maps when the thermal motion of the atoms is moderate (B typically lower than 4 A2). In this case, a non-truncated Fourier synthesis of the deformation density requires that the diffraction data are available to a resolution better than 0.9 A.

β-lactamase TEM1 of E. coli Crystal structure determination at 2.5 Å resolution

The crystal structure of β‐lactamase TEM1 from E. coli has been solved to 2.5 Å resolution by X‐ray diffraction methods and refined to a crystallographic R‐factor of 22.7%. The structure was determined by multiple isomorphous replacement using four heavy atom derivatives. The solution from molecular replacement, using a polyalanine model constructed from the Cα coordinates of S. Aureus PC1 enzyme, provided a set of phases used for heavy atom derivatives analysis. The E. coli β‐lactamase TEM1 is made up of two domains whose topology is similar to that of the PC1 enzyme. However, global superposition or the two proteins shows significant differences.

Trypsin Revisited: CRYSTALLOGRAPHY AT (SUB) ATOMIC RESOLUTION AND QUANTUM CHEMISTRY REVEALING DETAILS OF CATALYSIS.

A series of crystal structures of trypsin, containing either an autoproteolytic cleaved peptide fragment or a covalently bound inhibitor, were determined at atomic and ultra-high resolution and subjected to ab initio quantum chemical calculations and multipole refinement. Quantum chemical calculations reproduced the observed active site crystal structure with severe deviations from standard stereochemistry and indicated the protonation state of the catalytic residues. Multipole refinement directly revealed the charge distribution in the active site and proved the validity of the ab initio calculations. The combined results confirmed the catalytic function of the active site residues and the two water molecules acting as the nucleophile and the proton donor. The crystal structures represent snapshots from the reaction pathway, close to a tetrahedral intermediate. The de-acylation of trypsin then occurs in true SN2 fashion.

An improved experimental databank of transferable multipolar atom models – ELMAM2. Construction details and applications

ELMAM2 is a generalized and improved library of experimentally derived multipolar atom types. The previously published ELMAM database is restricted mostly to protein atoms. The current database is extended to common functional groups encountered in organic molecules and is based on optimized local axes systems taking into account the local pseudosymmetry of the molecular fragment. In this approach, the symmetry-restricted multipoles have zero populations, while others take generally significant values. The various applications of the database are described. The deformation electron densities, electrostatic potentials and interaction energies calculated for several tripeptides and aromatic molecules are calculated using ELMAM2 electron-density parameters and compared with the former ELMAM database and density functional theory calculations.

A comparison between experimental and theoretical aspherical-atom scattering factors for charge-density refinement of large molecules

The differences between two databases describing the polypeptide main chain in terms of charge-density parameters, directly usable in protein structure refinements, are discussed. These databases contain averaged multipole populations of peptide pseudo-atoms obtained from refinement against theoretical simulated data and against high-resolution experimental data on small peptide or amino acid molecules. The main discrepancy becomes apparent when electrostatic properties are calculated.