  Motivation: Cellular Electron CryoTomography (CECT) is an emerging 3D imaging
technique that visualizes subcellular organization of single cells at
submolecular resolution and in near-native state. CECT captures large numbers
of macromolecular complexes of highly diverse structures and abundances.
However, the structural complexity and imaging limits complicate the systematic
de novo structural recovery and recognition of these macromolecular complexes.
Efficient and accurate reference-free subtomogram averaging and classification
represent the most critical tasks for such analysis. Existing subtomogram
alignment based methods are prone to the missing wedge effects and low
signal-to-noise ratio (SNR). Moreover, existing maximum-likelihood based
methods rely on integration operations, which are in principle computationally
infeasible for accurate calculation.
  Results: Built on existing works, we propose an integrated method, Fast
Alignment Maximum Likelihood method (FAML), which uses fast subtomogram
alignment to sample sub-optimal rigid transformations. The transformations are
then used to approximate integrals for maximum-likelihood update of subtomogram
averages through expectation-maximization algorithm. Our tests on simulated and
experimental subtomograms showed that, compared to our previously developed
fast alignment method (FA), FAML is significantly more robust to noise and
missing wedge effects with moderate increases of computation cost.Besides, FAML
performs well with significantly fewer input subtomograms when the FA method
fails. Therefore, FAML can serve as a key component for improved construction
of initial structural models from macromolecules captured by CECT.
