Acta Cryst. (1999). A55, 305–313 Chemical bonding effects in the determination of protein structures by electron crystallography Steven Chang, a Teresa Head-Gordon, a Robert M. Glaeser a,b and Kenneth H. Downing a * a Life Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA, and b Department of Molecular and Cell Biology, University of California, Berkeley, CA 94720, USA. E-mail: khdowning@lbl.gov (Received 28 January 1998; accepted 16 July 1998 ) Abstract Scattering of electrons is affected by the distribution of valence electrons that participate in chemical bonding and thus change the electrostatic shielding of the nucleus. This effect is particularly significant for low- angle scattering. Thus, while chemical bonding effects are difficult to measure with small-unit cell materials, they can be substantial in the study of proteins by electron crystallography. This work investigates the magnitude of chemical bonding effects for a represen- tative collection of protein fragments and a model ligand for nucleotide-binding proteins within the resolution range generally used in determining protein structures by electron crystallography. Electrostatic potentials were calculated by ab initio methods for both the test molecules and for superpositions of their free atoms. Differences in scattering amplitudes can be well over 10% in the resolution range below 5A ˚ and are especially large in the case of ionized side chains and ligands. We conclude that the use of molecule-based scattering factors can provide a much more accurate representation of the low-resolution data obtained in electron crystallographic studies. The comparison of neutral and ionic structure factors at resolutions below 5A ˚ can also provide a sensitive determination of charge states, important for biological function, that is not accessible from X-ray crystallographic measurements. 1. Introduction Electron crystallography is developing as a complement to X-ray crystallography in the determination of protein structures. The very strong scattering of electrons by matter makes it possible to work with extremely small amounts of material and indeed to use crystals no more than a single layer thick. Electron crystallography is thus particularly good for the study of monolayer crystals, such as those formed by integral membrane proteins, which have so frequently resisted attempts to form crystals suitable for X-ray work. Because electrons are scattered by the (shielded) Coulomb potential, electron crystallography produces a map of the potential within the sample. X-ray crystal- lography, on the other hand, produces a map of the electron charge density. The electron density () and the Coulomb potential (’) maps are related to each other by the Poisson equation, r 2 ’ 4="; 1 where " is the dielectric constant. The Coulomb poten- tial and the electron charge density functions for isolated atoms are similar to one another in that they both are cusp-shaped functions, centered on the nucleus, with a width that approximates the size of the atom. Thus both the potential and the electron charge density give accurate descriptions of the atomic positions. To date, atomic models of three proteins have been determined from electron crystallographic data. Although the resolution of the data was not high by the standards of current work in X-ray protein crystal- lography, the reliability of phases determined by analysis of high-resolution micrographs makes it possible to obtain a density map that can be interpreted with little ambiguity. A model of bacteriorhodopsin (bR) was constructed starting with a density map that had 3.5 A ˚ resolution in the plane of the crystal and around 6 A ˚ perpendicular (Henderson et al., 1990). This model was subsequently refined to more isotropic resolution, with the inclusion of diffraction data that extended to higher tilt angles (Grigorieff et al., 1996), and more recently an independent density map has been obtained at a reso- lution of 3.0 A ˚ (Kimura et al., 1997). A model for the green plant light harvesting complex (LHC) was based on a density map with nominal resolution of 3.4 A ˚ (Ku¨ hlbrandt et al., 1994). The structure of the tubulin  dimer has recently been determined with a resolution of 3.7 A ˚ (Nogales et al., 1998). In all of these structures, the -helix and -strand segments were well resolved. Loop regions were not always as well defined in the density maps, but the resolution in each case was good enough to ensure that the correct topology was determined. In each of these cases though, electron diffraction inten- sities are available that extend to higher resolution than phases from the images, and extension of the map resolution would be beneficial in defining amino acid side-chain positions and interactions more clearly. This can be performed by refinement of the atomic model, following procedures that are routine in X-ray crystal- lography. 305 # 1999 International Union of Crystallography Acta Crystallographica Section A Printed in Great Britain – all rights reserved ISSN 0108-7673 # 1999