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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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CTF fitting examples. Top: 2D representation of the experimental and theoretical PSDs for the Full model (left), and Simplified models 1, 2 and 3. Bottom: Radial average of the fitting for the Full model and the Simplified model 3.
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Figure 4: CTF fitting examples. Top: 2D representation of the experimental and theoretical PSDs for the Full model (left), and Simplified models 1, 2 and 3. Bottom: Radial average of the fitting for the Full model and the Simplified model 3.

Mentions: On the other extreme, we have identified variables that are not so sensitive, meaning that they allow to be estimated with large errors without affecting much to our overall comprehension of the CTF effects. These are mostly related to the background (Ks, Cm, Kg, GM, CM, Gm, cm, θG, gM, gm, cM, θs, θg) but we also found some of them related to the CTF model: the spherical aberration (Cs), the drift (ΔR and ΔF), and the sampling rate (Tm). Interestingly, the drifted images are usually removed from the experimental datasets, and the spherical aberration and the sampling rate are provided by the user, meaning that fortunately for these parameters, small errors in their estimation translate into small errors in the CTF. We also explored the possibility of simplifying our model to a less accurate model by removing those less sensitive variables. It turned out that the drift parameters can be safely removed, but the background negative Gaussian parameters (the next set of least sensitive parameters) cannot be removed without committing large fitting errors especially in 2D (as can be seen in Fig. 4, the Simplified models 2 and 3 show an extra Thon ring that is not present in the experimental PSD). The reason for this is that the values of gM and gm are 2,256 and 1,432 respectively. Having a low sensitivity means that you can commit small errors around the nominal values without committing large errors in the function being studied, but it does not mean that the corresponding term can be completely removed. This is confirmed by the 95% confidence intervals computed through the experimental parameter distribution estimated by bootstrapping. Since the hypothesis that any of the regression parameters is zero has been rejected for all parameters (except the azimuthal angle), we conclude that all parameters in our model really explain a part of the PSD behavior. It is also interesting to see how a background term as the subtractive Gaussian influences the envelope parameters so that when this Gaussian is removed, the envelope is such that an extra ring is made visible.


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)

CTF fitting examples. Top: 2D representation of the experimental and theoretical PSDs for the Full model (left), and Simplified models 1, 2 and 3. Bottom: Radial average of the fitting for the Full model and the Simplified model 3.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 4: CTF fitting examples. Top: 2D representation of the experimental and theoretical PSDs for the Full model (left), and Simplified models 1, 2 and 3. Bottom: Radial average of the fitting for the Full model and the Simplified model 3.
Mentions: On the other extreme, we have identified variables that are not so sensitive, meaning that they allow to be estimated with large errors without affecting much to our overall comprehension of the CTF effects. These are mostly related to the background (Ks, Cm, Kg, GM, CM, Gm, cm, θG, gM, gm, cM, θs, θg) but we also found some of them related to the CTF model: the spherical aberration (Cs), the drift (ΔR and ΔF), and the sampling rate (Tm). Interestingly, the drifted images are usually removed from the experimental datasets, and the spherical aberration and the sampling rate are provided by the user, meaning that fortunately for these parameters, small errors in their estimation translate into small errors in the CTF. We also explored the possibility of simplifying our model to a less accurate model by removing those less sensitive variables. It turned out that the drift parameters can be safely removed, but the background negative Gaussian parameters (the next set of least sensitive parameters) cannot be removed without committing large fitting errors especially in 2D (as can be seen in Fig. 4, the Simplified models 2 and 3 show an extra Thon ring that is not present in the experimental PSD). The reason for this is that the values of gM and gm are 2,256 and 1,432 respectively. Having a low sensitivity means that you can commit small errors around the nominal values without committing large errors in the function being studied, but it does not mean that the corresponding term can be completely removed. This is confirmed by the 95% confidence intervals computed through the experimental parameter distribution estimated by bootstrapping. Since the hypothesis that any of the regression parameters is zero has been rejected for all parameters (except the azimuthal angle), we conclude that all parameters in our model really explain a part of the PSD behavior. It is also interesting to see how a background term as the subtractive Gaussian influences the envelope parameters so that when this Gaussian is removed, the envelope is such that an extra ring is made visible.

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