Alignment error envelopes for single particle analysis

To determine the structure of a biological particle to high resolution by e lectron microscopy, image averaging is required to combine information from different views and to increase the signal-to-noise ratio. Starting from t he number of noiseless views necessary to resolve features of a given size, four general factors are considered that increase the number of images act ually needed: (1) the physics of electron scattering introduces shot noise, (2) thermal motion and particle inhomogeneity cause the scattered electron s to describe a mixture of structures, (3) the microscope system fails to u sefully record all the information carried by the scattered electrons, and (4) image misalignment leads to information loss through incoherent averagi ng. The compound effect of factors 2-4 is approximated by the product of en velope functions. The problem of incoherent image averaging is developed in detail through derivation of five envelope functions that account for smal l errors in 11 "alignment" parameters describing particle location, orienta tion, defocus, magnification, and beam tilt. The analysis provides target e rror tolerances for single particle analysis to near-atomic (3.5 Angstrom) resolution, and this prospect is shown to depend critically on image qualit y, defocus determination, and microscope alignment. (C) 2001 Academic Press .