CTF determination and correction in electron cryotomography
Introduction
Electron cryotomography (cryoET) has a unique potential to elucidate the structure of large biological specimens at molecular resolution [1]. However, technical and computational advances are required to realize this potential [2]. This article addresses one of the current computational limitations in cryoET: determination and correction of the contrast transfer function (CTF) of the electron microscope.
CTF determination has been a subject of intense study in the last decade in three dimensional electron microscopy (3DEM) [3], [4], [5], [6], [7], [8], [9], [10], [11]. An approach based on periodogram averaging [5], [6], [8] has become well established. CTF correction is a crucial stage in any high resolution structural analysis by 3DEM. Phase flipping ensures contrast to be consistent at all spatial frequencies [12]. Amplitude correction is usually carried out by a Wiener-like weighted combination of the data, either projection images [12] or 3D maps [13], and a sharpening by an inverse temperature factor [14].
In cryoET, there has not been pressing need of CTF correction so far, because typical nominal defocus values are in the range 8– underfocus [15], [16], [17], [18], [19], [20], which allow a resolution up to 4.0–5.5 nm. However, if molecular resolution is to become attainable, CTF correction will be critical [21]. This article presents an approach that overcomes the extremely low signal-to-noise ratio (SNR) in tomographic data and the defocus gradient in images of tilted specimens.
Section snippets
Background on CTF determination
The CTF models the linear image formation system of the microscope [22], [23]. The CTF gives rise to oscillations in the power spectrum of the image. The location of these oscillations is essential for accurate determination of defocus and astigmatism, but it is difficult in cryomicroscopy due to the extremely low SNR. The strategies devised to facilitate their detection try to smooth the spectrum by azimuthal averaging [3], [4], [10], [11] or by pure spectral estimation methods [5], [6], [7],
An approach to CTF correction in cryoET
To deal with the defocus gradient in images of tilted specimens (Eq. (3)), we exploit a similar concept of strip to that described for CTF determination, except that now the strip is not restricted to be around the tilt axis (Fig. 4). Considering the parameter as described before, a strip can be extracted along any x-line of the image. A single constant defocus value can be considered for the strip, being computed by Eq. (3), where x is the index of the center line of the strip.
The algorithm
Results
The evaluation of CTF determination and correction has been carried out using experimental cryoET datasets of yeast spindle pole body (SPB) [27], vaccinia virus (VV) [18] and hepatitis B virus (HBV) core [28].
Discussion
CTF determination and correction are becoming necessary as structural studies by cryoET approach molecular resolution [1], [2], [21]. We have presented here an approach to CTF determination and correction that deals with the low SNR and the defocus gradient in images of tilted specimens. It is based on the assumption of eucentric tilt series. It also assumes the same defocus along the projection path through the specimen, since the projection approximation [25] is valid for the thickness of
Conclusion
This work has addressed CTF determination and correction, one of the current computational problems in cryoET that limits the resolution attainable. We have proposed an approach to CTF determination that overcomes the low SNR in cryoET by strip-based periodogram averaging extended throughout the tilt series and a spline-based strategy for background subtraction. The method of CTF correction deals with the defocus gradient in images of tilted specimens by decomposing the global restoration
Acknowledgements
The authors wish to thank A. Roseman for fruitful discussions, help with FindEM and revising the manuscript, N. Grigorieff for kindly providing CTFFIND3, S. Wynne for HBV core samples, J.L. Carrascosa for vaccinia data, L. Amos for the PDB of the microtubule model and T. Horsnell for his support and help with the computer farm. This work has been partially supported by the UK Medical Research Council and HFSP, EMBO, Spanish MEC and EU (Grants: MEC-TIC2002-00228, HFSP2003-ST00107,
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