Maximum likelihood refinement of electron microscopy data with normalization errors

Commonly employed data models for maximum likelihood refinement of electron microscopy images behave poorly in the presence of normalization errors. Small variations in background mean or signal brightness are relatively common in cryo-electron microscopy data, and varying signal-to-noise ratios or artifacts in the images interfere with standard normalization procedures. In this paper, a statistical data model that accounts for normalization errors is presented, and a corresponding algorithm for maximum likelihood classification of structurally heterogeneous projection data is derived. The extended data model has general relevance, since similar algorithms may be derived for other maximum likelihood approaches in the field. The potentials of this approach are illustrated for two structurally heterogeneous data sets: 70S E.coli ribosomes and human RNA polymerase II complexes. In both cases, maximum likelihood classification based on the conventional data model failed, whereas the new approach was capable of revealing previously unobserved conformations.