Gctf: Real-time CTF determination and correction

Abstract

Accurate estimation of the contrast transfer function (CTF) is critical for a near-atomic resolution cryo electron microscopy (cryoEM) reconstruction. Here, a GPU-accelerated computer program, Gctf, for accurate and robust, real-time CTF determination is presented. The main target of Gctf is to maximize the cross-correlation of a simulated CTF with the logarithmic amplitude spectra (LAS) of observed micrographs after background subtraction. Novel approaches in Gctf improve both speed and accuracy. In addition to GPU acceleration (e.g. 10-50×), a fast '1-dimensional search plus 2-dimensional refinement (1S2R)' procedure further speeds up Gctf. Based on the global CTF determination, the local defocus for each particle and for single frames of movies is accurately refined, which improves CTF parameters of all particles for subsequent image processing. Novel diagnosis method using equiphase averaging (EPA) and self-consistency verification procedures have also been implemented in the program for practical use, especially for aims of near-atomic reconstruction. Gctf is an independent program and the outputs can be easily imported into other cryoEM software such as Relion (Scheres, 2012) and Frealign (Grigorieff, 2007). The results from several representative datasets are shown and discussed in this paper.

Keywords: CTF determination; Contrast transfer function; Cryo-electron microscopy; GPU program.

Fig. 1

Relationship between CTF phase error and defocus inaccuracy. (a) The errors of CTF phases by different levels of defocus inaccuracy at 300 kV high tension. The dashed gray line represents the threshold for 90° phase shift criterion. (b) Based on the 90° criterion from (a), the maximum defocus inaccuracy allowed at various resolutions for three typical high tension values (300 kV, 200 kV and 100 kV) are plotted.

Fig. 2

Flow chart of Gctf.

Fig. 3

Flow chart of Gctf using a real micrograph. A micrograph with significant astigmatism is presented to demonstrate the procedure clearly.

Fig. 4

Equiphase average. (a) The logarithmic amplitude spectra (LAS) after background reduction. The green point is the target pixel to be averaged. The red line represents all pixels with equiphases for the green point in this image. (b) A typical equiphase averaged LAS image. Resolution lower than 50 Å or higher than 7 Å has been excluded.

Fig. 5

Speed comparison of several popular programs with Gctf. All parameters of each program were set as the default (CTFFIND3/4 called by Relion). Due to the large speed differences among programs, they were tested using different number of micrographs for multiple times: CTFFIND3 on one micrograph, CTFFIND4, FASTDEF, ACE2 on 10 micrographs, while Gctf on 1000 micrographs. Gctf was running on a single GTX 980 GPU and the other programs on Intel Xeon E5-2643 v2 CPU.

Fig. 6

Statistics of the defocus differences between Gctf and CTFFIND3 for the nine benchmark datasets. Number 10 is a dynactin dataset used in Fig. 5 of (Zhang, 2015). Blue columns represent the averaged differences; red columns represent the middle differences, meaning 50% micrographs have the differences lower or higher than this value in each dataset.

Fig. 7

Equiphase average for better diagnosis. (a) Different spectra images of a typical cryoEM micrograph of HAV (Dataset-8) with ∼1800 Å astigmatism; left top: background-subtracted LAS; right top: circular average; left bottom: equiphase average; right bottom: simulated. (b) Enlarged region from 9 Å to 4 Å for detailed comparison of different diagnostic methods. Thong rings on the left sides in all the three images represent the simulated amplitude spectra; the right sides represent the observed spectra visualized in different methods. Obviously, Thong rings from the original spectra (i) are almost invisible at higher than 9 Å even after background reduction. After circular average (ii), the rings become clearer but significantly off the correct peak because of the large astigmatism. Some rings are almost in reverse contrast, indicating the circular average is meaningless at such resolution. The equiphase average (iii) makes all the rings clearly visible up to 4 Å.

Fig. 8

Robustness test of CTF determination using varying resolution cutoff or estimated astigmatism as input. (a) Typical CryoEM micrograph of HAV was selected and systemically examined to test the robustness of Gctf. The blue points represent results by high resolution cutoff and the red points by low resolution cutoff. (b) The input values of astigmatism ranging from 10 Å to 10,000 Å were used as initial estimation for CTF determination. All input values in this range generated almost identical results. Therefore, there is no need for optimizing the input astigmatism in this case. Blue and red lines represent defocus U and V respectively. Green line represents the azimuthal angle.

Fig. 9

CTF determination of single frames of a movie. (a)Averaged movie (top) and single frame (bottom) of dynactin (Dataset-5). Movie was taken on FEI Titan Krios, Falcon II detector at the dose of 1.6 e/(Ų·frame). (b)CTF determination using the averaged movie (top) or a single frame (bottom). For both images, the left is simulated CTF and the right is observed LAS. The determined defocus $(z_u\text{,}{z}_v\text{,}{\theta }_{\mathit{ast}})$ of the averaged movie is (41,642.58 Å, 41,140.62 Å, 61.67°) and the first frame is (41,711.86 Å, 41,196.36 Å, 52.80°). The difference is (69.28 Å, 55.74 Å, 8.87°). (c) The changes of averaged defocus $(z_u+z_v)/2$ with the accumulation of doses on the micrograph. Slightly different from (b), the CTF determination for each frame was performed by averaging 9 adjacent frames (e.g. 11–19 for frame 15) to enhance the SNR.

Fig. 10

An example showing the importance of local CTF refinement. (a) The raw micrograph of dynactin (Dataset-6). (b) The local defocus for this particle determined by Gctf is 3.92 μm. The red arrow indicates the fitting is almost perfect up to 5 Å. The black curve represents the circularly averaged LAS of particle 1; the blue curve represents the comparison with Gctf determination. (c) Similar to (b) but for particle 2. The defocus of this particle is 3.87 μm. The fitting of CTF is also perfect up to 5 Å. (d) Comparison between the circularly averaged LAS of particle 1 and simulated amplitude spectra using defocus of particle 2. In contrast to (b) or (c), the simulated CTF curve does not fit the observed curve at high resolution, indicating the importance the local refinement for near atomic resolution reconstruction.

Fig. 11

FSC comparison between global and local CTF. (a) Comparison of Dynactin FSC curves with (green) and without (red) doing local defocus refinement. 86,916 particles were used for final reconstruction from Dataset-7. (b) Comparison of FSC curves of HAV with (green) and without (red) doing local defocus refinement. 2025 particles were used for final reconstruction in Dataset-8.