M-free: scoring the reference bias in sub-tomogram averaging and template matching.

Cryo-electron tomography provides a snapshot of the cellular proteome. With template matching, the spatial positions of various macromolecular complexes within their native cellular context can be detected. However, the growing awareness of the reference bias introduced by the cross-correlation based approaches, and more importantly the lack of a reliable confidence measurement in the selection of these macromolecular complexes, has restricted the use of these applications. Here we propose a heuristic, in which the reference bias is measured in real space in an analogous way to the R-free value in X-ray crystallography. We measure the reference bias within the mask used to outline the area of the template, and do not modify the template itself. The heuristic works by splitting the mask into a working and a testing area in a volume ratio of 9:1. While the working area is used during the calculation of the cross-correlation function, the information from both areas is explored to calculate the M-free score. We show using artificial data, that the M-free score gives a reliable measure for the reference bias. The heuristic can be applied in template matching and in sub-tomogram averaging. We further test the applicability of the heuristic in tomograms of purified macromolecules, and tomograms of whole Mycoplasma cells.