Abstract
We are currently facing an avalanche of cryo-EM (cryogenic Electron Microscopy) publications presenting beautiful structures at resolution levels of ~3Å: a true “resolution revolution” [Kühlbrandt, Science 343(2014)1443-1444]. Impressive as these results may be, a fundamental statistical error has persisted in the literature that affects the numerical resolution values for practically all published structures. The error goes back to a misinterpretation of basic statistics and pervades virtually all popular cryo-EM quality metrics. The resolution in cryo-EM is typically assessed by the Fourier Shell Correlation “FSC” [Harauz & van Heel: Optik 73(1986)146-156] using a fixed threshold value of 0.143 (“FSC0.143”) [Rosenthal, Henderson, J. Mol. Biol. 333(2003)721–745]. Using a simple model experiment we illustrate why this fixed threshold is flawed and we pinpoint the source of the resolution confusion. When two vectors are uncorrelated the expectation value of their inner-product is zero. That, however, does not imply that each individual inner-product of the vectors is zero (the vectors are not orthogonal). This error was introduced to electron microscopy in [Frank & Al-Ali, Nature 256(1975)376-379] and has since proliferated into virtually all quality and resolution-related metrics in EM. One criterion not affected by this error is the information-based ½-bit FSC threshold [van Heel & Schatz: J. Struct. Biol. 151(2005)250-262].
