M-free: Mask-independent scoring of the reference bias

The M-free score is a heuristic to measure the reference bias in applications such as template matching and sub-tomogram averaging. In the original formulation the mask typically used in these applications had to be separated into a working and a testing area. Here we present a variant of the calculation of the M-free score, which under certain conditions does not require adapting the mask used during the processing. This is made possible by a modified algorithm that allows for arbitrary variances in the testing and in the working area. Consequently, the reference bias can be estimated with knowledge of only the starting reference, the final average and the mask used for processing. We show that the new formulation of the M-free score gives a reliable measure of the reference bias for any sub-tomogram average that has ancillary data, such as when the averaged structure contains density in the periphery, when a complex is attached to a membrane (membrane-associated complexes) or when one subunit is attached to others (e.g. in viruses). Further, we show that in contrast to correlation-based measurements, the M-free score is sensitive to wrong-alignments and contaminations present in the data set. The scope of this new calculation of the M-free score is to reduce the constraints of the previous approach and in certain cases to avoid an adaptation of the mask. The M-free score gives a separate reliability measure for sub-tomogram averaging and template matching.