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

Abstract

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 3_{10} helix octapeptide Ac-Aib_2-L-Lys(Bz)-Aib_2-L-Lys(Bz)-Aib_2-NHMe refined subsequently, for which diffraction data have been collected to a resolution of 0.82 Å 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 (\Delta B ≃ 0.4 Å2). 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 Å^2). 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 Å.