Resolution measures in molecular electron microscopy - PubMed (original) (raw)

Resolution measures in molecular electron microscopy

Pawel A Penczek. Methods Enzymol. 2010.

Abstract

Resolution measures in molecular electron microscopy provide means to evaluate quality of macromolecular structures computed from sets of their two-dimensional (2D) line projections. When the amount of detail in the computed density map is low there are no external standards by which the resolution of the result can be judged. Instead, resolution measures in molecular electron microscopy evaluate consistency of the results in reciprocal space and present it as a one-dimensional (1D) function of the modulus of spatial frequency. Here we provide description of standard resolution measures commonly used in electron microscopy. We point out that the organizing principle is the relationship between these measures and the spectral signal-to-noise ratio (SSNR) of the computed density map. Within this framework it becomes straightforward to describe the connection between the outcome of resolution evaluations and the quality of electron microscopy maps, in particular, the optimum filtration, in the Wiener sense, of the computed map. We also provide a discussion of practical difficulties of evaluation of resolution in electron microscopy, particularly in terms of its sensitivity to data processing operations used during structure determination process in single particle analysis and in electron tomography (ET).

Copyright © 2010 Elsevier Inc. All rights reserved.

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Figures

Fig. 1

Fig. 1

Optical resolution is defined as the smallest distance between two points on a specimen that can be distinguished as two separate entities. Assuming the blur introduced by the microscope to be Gaussian with a known standard deviation, the resolution is defined as a distance between points that equals at least one standard deviation. For distances smaller or equal one standard deviation, the observed pattern, i.e., sum of two Gaussian functions (green and blue) has an appearance of a pseudo-Gaussian with one maximum (magenta).

Fig. 2

Fig. 2

Simulated FSC curve (red) with confidence intervals plotted at ±3_σ_ (blue) (Eq.18) and 3_σ_ criterion curve (magenta) (van Heel, 1987).

Fig. 3

Fig. 3

Experimental FSC curve encountered in practice of SPR (solid) plotted as a function of magnitude of spatial frequency with 0.5 corresponding to Nyquist frequency. We also show an idealized FSC curve (Eq.24) and a hyperbolic tangent filter (Eq.28) fitted to the experimental FSC.

Fig. 4

Fig. 4

Typical FSC resolution curves encountered in practice of SPR. s - magnitude of spatial frequency with 0.5 corresponding to Nyquist frequency. (a) proper FSC curve remains one at low frequencies, which is followed by a semi-Gaussian fall-off (see Eq.24) and a drop to zero at around 2/3 of Nyquist frequency, in high frequencies oscillates around zero. (b) Artifactual “rectangular” FSC: remains one at low frequencies remains one, followed by a sharp drop, in high frequencies oscillates around zero. Typically it is caused by a combination of alignment of noise and a sharp filtration during the alignment procedure. (c) The FSC never drops to zero in the entire frequency range. Normally, this means that the noise component in the data was aligned, the result are artifactual and the resolution is undetermined. In rare cases it can also mean that the data was severely undersampled (very large pixel size). (d) After the FSC curve drops to zero, it increases again in high frequencies. This artifact can be caused by the low-pass filtration of the data prior to alignment, errors in the image processing code, mainly in interpolation, by the erroneous correction for the CTF, including errors in estimation of SSNR, and finally, incorrect parameters in 3D reconstruction programs (for example iterative 3D reconstruction was terminated too early). It can also mean that all images were rotated by the same angle. (e) FSC oscillates around 0.5. It means that data was dominated by one subset with the same defocus value or there is only one defocus group. The resolution curve is not incorrect per se, but it is unclear what the resolution is. The resulting structure will have strong artifacts in real space.

References

    1. Baker ML, Ju T, Chiu W. Identification of secondary structure elements in intermediate-resolution density maps. Structure. 2007;15:7–19. - PMC - PubMed
    1. Baldwin PR, Penczek PA. Estimating alignment errors in sets of 2-D images. Journal of Structural Biology. 2005;150:211–225. - PubMed
    1. Bartlett RF. Linear modelling of Pearson’s product moment correlation coefficient: an application of Fisher’s z-transformation. Journal of the Royal Statistical Society D. 1993;42:45–53.
    1. Basokur AT. Digital filter design using the hyperbolic tangent functions. Journal of the Balkan Geophysical Society. 1998;1:14–18.
    1. Bershad NJ, Rockmore AJ. On estimating Signal-to-Noise Ratio using the sample correlation coefficient. IEEE Transactions on Information Theory. 1974;IT20:112–113.

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