Quantitative energy-filtered electron microscopy of biological molecules in ice

The theoretical and experimental bases for quantitative electron microscopy of frozen-hydrated specimens are described, with special considerations of energy filtration to improve the images. The elastic and inelastic scattering from molecules in vacuum and in ice are calculated, and simple methods to approximate scattering are introduced. Multiple scattering calculations are used to describe the scattering from vitreous ice and to predict the characteristics of images of frozen-hydrated molecules as a function of ice thickness and accelerating voltage. Energy filtration is predicted to improve image contrast and signal-to-noise ratio. Experimental values for the inelastic scattering of ice, the energy spectrum of thick ice, and the contrast of biological specimens are determined. The principles of compensation for the contrast transfer function are presented. Tobacco mosaic virus is used to quantify the accuracy of interpreting image intensities to derive the absolute mass, mass per unit length, and internal mass densities of biological molecules. It is shown that compensation for the contrast transfer function is necessary and sufficient to convert the images into accurate representations of molecular density. At a resolution of 2 nm, the radial density reconstructions of tobacco mosaic virus are in quantitative agreement with the atomic model derived from X-ray results.