Measurement of atomic scattering factors by cryoelectron microscopy

Determination of specimen structure from cryoelectron microscopy (cryo-EM) experiments relies on an accurate model of the electrostatic potential of the specimen. For biological macromolecules, the potential is strongly influenced by the presence of chemical bonds between atoms, a fact unaccounted for by models of electron scattering that are currently standard in the field. We propose a Bayesian approach to the estimation of atomic scattering factors which incorporates the effect of the molecular environment while remaining fast, interpretable, and transferable between molecules. Our algorithm infers atomic scattering factors directly from maps of the electrostatic potential determined by cryo-EM single particle analysis, bypassing the need for computationally intensive theoretical calculations. The algorithm is used to infer empirical scattering factors from high-resolution reconstructions of catalase enzymes. To illustrate its broad applicability, the algorithm is also applied to a training set of publicly available cryo-EM data. The empirical scattering factors show improved agreement with a test set of cryo-EM reconstructions, decreasing the variance of unmodeled signal in the data by up to a factor of three in the resolution range 1/15 to 1/3 Å^-1. The predictions are further validated by comparison with magnetic susceptibility values of organic compounds, as well as by application to the refinement of atomic models.