Simulation of charge effects on density maps obtained by high-resolution electron crystallography.

Atomic scattering factors for electrons are strongly affected by the charge status of the scattering atoms. The difference in scattering factors for charged and neutral atoms is most pronounced in the resolution range below 5 A. As a result of the negative scattering factors of negatively charged atoms in the low-resolution range, charged glutamate or aspartate residues produce weaker densities in electron crystallographic maps than their neutral forms. Such charge effects were indeed observed in an experimental map of bacteriorhodopsin. Here we present mathematical simulations of this charge effect on electron crystallographic density maps that corroborate the experimental results. For the simulations, we first evaluated the errors introduced by approximating atomic scattering factors for neutral and charged atoms by Gaussians. The simulations then showed that the effect of a polarized pair of oxygen and hydrogen atoms on the density (polarization effect) was much smaller than that expected from the individual charged atoms (charge effect), due to charge compensation. Still, density maps obtained by electron crystallography are expected to show slightly elongated features toward the positively charged atoms.