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Error analysis in the determination of the electron microscopical contrast transfer function parameters from experimental power Spectra.

Sorzano CO, Otero A, Olmos EM, Carazo JM - BMC Struct. Biol. (2009)

Bottom Line: Finally, we explore the effect of the variability in the detection of the CTF for CTF phase and amplitude correction.We show that the estimation errors for the CTF detection methodology proposed in 1 does not show a significant deterioration of the CTF correction capabilities of subsequent algorithms.All together, the methodology described in this paper constitutes a powerful tool for the quantitative analysis of CTF models that can be applied to other models different from the one analyzed here.

View Article: PubMed Central - HTML - PubMed

Affiliation: Escuela Politécnica Superior, Universidad San Pablo-CEU, Campus Urb, Montepríncipe s/n, E-28668 Boadilla del Monte, Madrid, Spain. coss@cnb.csic.es

ABSTRACT

Background: The transmission electron microscope is used to acquire structural information of macromolecular complexes. However, as any other imaging device, it introduces optical aberrations that must be corrected if high-resolution structural information is to be obtained. The set of all aberrations are usually modeled in Fourier space by the so-called Contrast Transfer Function (CTF). Before correcting for the CTF, we must first estimate it from the electron micrographs. This is usually done by estimating a number of parameters specifying a theoretical model of the CTF. This estimation is performed by minimizing some error measure between the theoretical Power Spectrum Density (PSD) and the experimentally observed PSD. The high noise present in the micrographs, the possible local minima of the error function for estimating the CTF parameters, and the cross-talking between CTF parameters may cause errors in the estimated CTF parameters.

Results: In this paper, we explore the effect of these estimation errors on the theoretical CTF. For the CTF model proposed in 1 we show which are the most sensitive CTF parameters as well as the most sensitive background parameters. Moreover, we provide a methodology to reveal the internal structure of the CTF model (which parameters influence in which parameters) and to estimate the accuracy of each model parameter. Finally, we explore the effect of the variability in the detection of the CTF for CTF phase and amplitude correction.

Conclusion: We show that the estimation errors for the CTF detection methodology proposed in 1 does not show a significant deterioration of the CTF correction capabilities of subsequent algorithms. All together, the methodology described in this paper constitutes a powerful tool for the quantitative analysis of CTF models that can be applied to other models different from the one analyzed here.

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Fourier Shell Correlation after phase correction. Solid line: FSC of the GroEL phantom and the volume reconstructed with the phase corrected images using the truly applied CTF. Dashed line: FSC of GroEL phantom and the volume reconstructed with the phase corrected images using the bootstrapped ensemble.
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Figure 2: Fourier Shell Correlation after phase correction. Solid line: FSC of the GroEL phantom and the volume reconstructed with the phase corrected images using the truly applied CTF. Dashed line: FSC of GroEL phantom and the volume reconstructed with the phase corrected images using the bootstrapped ensemble.

Mentions: Finally, we used the bootstrapped ensemble to evaluate the effect of the variability of the CTF detection in the CTF correction capabilities of subsequent algorithms, particularly, those of CTF phase correction and CTF amplitude correction through IDR. For exploring this effect we used 97.4% CTFs considered to be non-failures of the CTF detection algorithm (see description of the bootstrap ensemble experiment). One of them was selected to be the true underlying CTF, while the rest were used as estimates of this true CTF. As many projections as good CTF in the ensemble were simulated of the GroEl atomic structure [20] (PDB entry code: 1GRL) with a random angular distribution, a sampling rate of 2 Å/pixel. Noise was added with a final Signal-to-Noise Ratio (SNR) of 1/3 (see Fig. 1). We corrected the CTF phase using the truly applied CTF and its pretended bootstrap estimates (one different estimate for each projection). We compared the Fourier Shell Correlation (FSC, [21]) of the volume reconstructed out of each one of these different corrections with respect to the atomic model (see Fig. 2). We also corrected the CTF amplitude using IDR with a relaxation factor of 1.8. After 10 iterations we did not observe any further impShould we haverovement of the FSC. The FSC of the volumes reconstructed using the truly applied CTF and the pretended bootstrap estimates are shown in Fig. 3. Note that in this experiment we used a single defocus value in the set of images used for reconstruction. This was done with the aim of isolating the effect of the miscorrected phase flips. The use of more defoci in the dataset would have translated in results more difficult to interpret since the zeros of one defocus group would have been masked by other defocus groups having a larger CTF value at that frequency. It is expected that if the effect of miscorrecting the phase of a single defocus groups is negligible, the combined effect of miscorrecting each defocus group independently is also negligible on the final reconstruction.


Error analysis in the determination of the electron microscopical contrast transfer function parameters from experimental power Spectra.

Sorzano CO, Otero A, Olmos EM, Carazo JM - BMC Struct. Biol. (2009)

Fourier Shell Correlation after phase correction. Solid line: FSC of the GroEL phantom and the volume reconstructed with the phase corrected images using the truly applied CTF. Dashed line: FSC of GroEL phantom and the volume reconstructed with the phase corrected images using the bootstrapped ensemble.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2683171&req=5

Figure 2: Fourier Shell Correlation after phase correction. Solid line: FSC of the GroEL phantom and the volume reconstructed with the phase corrected images using the truly applied CTF. Dashed line: FSC of GroEL phantom and the volume reconstructed with the phase corrected images using the bootstrapped ensemble.
Mentions: Finally, we used the bootstrapped ensemble to evaluate the effect of the variability of the CTF detection in the CTF correction capabilities of subsequent algorithms, particularly, those of CTF phase correction and CTF amplitude correction through IDR. For exploring this effect we used 97.4% CTFs considered to be non-failures of the CTF detection algorithm (see description of the bootstrap ensemble experiment). One of them was selected to be the true underlying CTF, while the rest were used as estimates of this true CTF. As many projections as good CTF in the ensemble were simulated of the GroEl atomic structure [20] (PDB entry code: 1GRL) with a random angular distribution, a sampling rate of 2 Å/pixel. Noise was added with a final Signal-to-Noise Ratio (SNR) of 1/3 (see Fig. 1). We corrected the CTF phase using the truly applied CTF and its pretended bootstrap estimates (one different estimate for each projection). We compared the Fourier Shell Correlation (FSC, [21]) of the volume reconstructed out of each one of these different corrections with respect to the atomic model (see Fig. 2). We also corrected the CTF amplitude using IDR with a relaxation factor of 1.8. After 10 iterations we did not observe any further impShould we haverovement of the FSC. The FSC of the volumes reconstructed using the truly applied CTF and the pretended bootstrap estimates are shown in Fig. 3. Note that in this experiment we used a single defocus value in the set of images used for reconstruction. This was done with the aim of isolating the effect of the miscorrected phase flips. The use of more defoci in the dataset would have translated in results more difficult to interpret since the zeros of one defocus group would have been masked by other defocus groups having a larger CTF value at that frequency. It is expected that if the effect of miscorrecting the phase of a single defocus groups is negligible, the combined effect of miscorrecting each defocus group independently is also negligible on the final reconstruction.

Bottom Line: Finally, we explore the effect of the variability in the detection of the CTF for CTF phase and amplitude correction.We show that the estimation errors for the CTF detection methodology proposed in 1 does not show a significant deterioration of the CTF correction capabilities of subsequent algorithms.All together, the methodology described in this paper constitutes a powerful tool for the quantitative analysis of CTF models that can be applied to other models different from the one analyzed here.

View Article: PubMed Central - HTML - PubMed

Affiliation: Escuela Politécnica Superior, Universidad San Pablo-CEU, Campus Urb, Montepríncipe s/n, E-28668 Boadilla del Monte, Madrid, Spain. coss@cnb.csic.es

ABSTRACT

Background: The transmission electron microscope is used to acquire structural information of macromolecular complexes. However, as any other imaging device, it introduces optical aberrations that must be corrected if high-resolution structural information is to be obtained. The set of all aberrations are usually modeled in Fourier space by the so-called Contrast Transfer Function (CTF). Before correcting for the CTF, we must first estimate it from the electron micrographs. This is usually done by estimating a number of parameters specifying a theoretical model of the CTF. This estimation is performed by minimizing some error measure between the theoretical Power Spectrum Density (PSD) and the experimentally observed PSD. The high noise present in the micrographs, the possible local minima of the error function for estimating the CTF parameters, and the cross-talking between CTF parameters may cause errors in the estimated CTF parameters.

Results: In this paper, we explore the effect of these estimation errors on the theoretical CTF. For the CTF model proposed in 1 we show which are the most sensitive CTF parameters as well as the most sensitive background parameters. Moreover, we provide a methodology to reveal the internal structure of the CTF model (which parameters influence in which parameters) and to estimate the accuracy of each model parameter. Finally, we explore the effect of the variability in the detection of the CTF for CTF phase and amplitude correction.

Conclusion: We show that the estimation errors for the CTF detection methodology proposed in 1 does not show a significant deterioration of the CTF correction capabilities of subsequent algorithms. All together, the methodology described in this paper constitutes a powerful tool for the quantitative analysis of CTF models that can be applied to other models different from the one analyzed here.

Show MeSH
Related in: MedlinePlus