Fully Mechanically Controlled Automated Electron Microscopic Tomography - PubMed (original) (raw)

Hongchang Li 1 3, Lei Zhang 1, Matthew Rames 1, Meng Zhang 1, Yadong Yu 1, Bo Peng 1, César Díaz Celis 4, April Xu 5, Qin Zou 6, Xu Yang 3, Xuefeng Chen 2, Gang Ren 1

Affiliations

Fully Mechanically Controlled Automated Electron Microscopic Tomography

Jinxin Liu et al. Sci Rep. 2016.

Abstract

Knowledge of three-dimensional (3D) structures of each individual particles of asymmetric and flexible proteins is essential in understanding those proteins' functions; but their structures are difficult to determine. Electron tomography (ET) provides a tool for imaging a single and unique biological object from a series of tilted angles, but it is challenging to image a single protein for three-dimensional (3D) reconstruction due to the imperfect mechanical control capability of the specimen goniometer under both a medium to high magnification (approximately 50,000-160,000×) and an optimized beam coherence condition. Here, we report a fully mechanical control method for automating ET data acquisition without using beam tilt/shift processes. This method could reduce the accumulation of beam tilt/shift that used to compensate the error from the mechanical control, but downgraded the beam coherence. Our method was developed by minimizing the error of the target object center during the tilting process through a closed-loop proportional-integral (PI) control algorithm. The validations by both negative staining (NS) and cryo-electron microscopy (cryo-EM) suggest that this method has a comparable capability to other ET methods in tracking target proteins while maintaining optimized beam coherence conditions for imaging.

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Conflict of interest statement

Q.Z. and A.X. are current employees for Pfizer Inc.

Figures

Figure 1

Figure 1. Schematics of the relationship between the optic axis and tilt axis within the TEM.

(A) A cartoon view of tomography, through a tilted sample stage. (B) 3D schematic view of the relationship between the optical axis and tilt axis within the TEM goniometer, specimen and imaging target diagram, where d z and d y determine the displacement from the tilt axis to the target position. (C) Side view of B, where θ = φ is the zero-tilt angle of the target position relative to the tilt axis.

Figure 2

Figure 2. Three major sources of mechanical errors and backlash correction.

(A) Motion control error from repeated X and Y motions with steps of 400 and 10 nm. (B) Backlash error from X and Y motion, caused by uneven gear meshing within the stage driver. (C) Trajectory error: unrepeatable tilt trajectory of X and Y resulting from non-ideal mechanical alignment. (D) Motion control error after backlash correction. Residual backlash error plot of X and Y motion after backlash elimination.

Figure 3

Figure 3. Overview of the Proportional-Integral (PI) control system.

Overview of the PI control system. Initially, the PI controller uses the previous errors to calculate the push formula image[_n_] for the next goniometer motion to correct the previous positional error. Goniometer motion incurs additional environmental error formula image[_n_], which yields the shift formula image[_n_] through imaging and cross-correlation. The accumulated shift formula image[_n_] is calculated by incorporating the historical motion formula image[n − _1_] and the current shift formula image[_n_]. This formula image[_n_] is used as historical data for the next tilt loop. The difference of formula image[_n_] from the target formula image[_n_] is the residual error formula image[n]. Within the proportional integral (PI) controller, the accumulated residual error formula image[_n_] is calculated by incorporating the historical error formula image[n − _1_] and current residual error formula image[n].

Figure 4

Figure 4. The procedure for measuring the XY shift of tilted images.

(A) the (n − 1)th tilted image is first stretched along the perpendicular direction to the tilting axis to compensate the effect of the tilt angle difference from the n th image, and then padded into an area twice as large before Fourier transfer. (B) The n th tilted image was directly padded into an area twice as large for Fourier transfer. (C) Based on inputted cut-off frequencies for band-pass filtering, a mask in reciprocal space was generated and applied to calculate the modified cross-correlation. (D) The revised Fourier transfer of the modified cross-correlation showed a peak to represent the defined XY shift.

Figure 5

Figure 5. The procedure for defining the defocus of a tilted image.

(A) The whole micrograph is divided into 8 × 8 mosaic tiles. (B) Each sub-image was used to measure the defocus after Fourier transfer. (C) Though a modified power spectrum (PS) of the sub-image, (D) the curve was compared with the theoretical contrast transfer function (CTF) curve via the calculation of the cross-correlation within a defined frequency range. (E) By screening the defocus within a searching range, the defocus which maximized the cross-correlation (CC) between the modified experimental curve and theoretical curve was used as the measured defocus for this sub-image. (F) By repeating the above procedure on each of the other sub-images, we obtained the defocus distribution against their whole micrograph. (G) The distribution can be fitted with a linear gradient distribution plane. (H) By subtracting this plane from the original 2D distribution, we could obtain a distribution of the residuals for defining the “bad” defocus measurements within the sub-images. The bad measured defocus was defined as any residual above twice the standard deviation (such as the two defocuses marked in red crosses). After the bad defocus tiles are removed, the defocus distribution was then re-fitted a linear distribution plane, and the defocus at the center was used as the defocus of the tilted micrograph.

Figure 6

Figure 6. Graphical user interface of the tomography software.

(A) Imaging area of the current, (B,C) previous and next previous collected images. (D) Plot of the positional and defocus errors during tomography collection. (E) Fast-Fourier transformation (FFT) of the current image and fitted contrast transfer function (CTF) curve. (F) Control panel for tomographic parameters, options, and process status. (G) Control panel for position tracking, defocus tracking and fitting.

Figure 7

Figure 7. Automatic tomography data collection of negative-stained nucleosome-DNA complex and antibody conjugate.

(A) A negatively stained nucleosome-DNA sample collected from −60° to +60° with a 1.5° step under 160,000× magnification and an expected defocus of 400 nm. (B) This series took 1.5 h to collect, with X/Y mean absolute positional errors and a defocus error of 17.8, 17.6, and 21.6 nm, respectively, with standard deviations of 24.6, 21.1 and 26.9 nm, respectively. (C) A negatively stained antibody conjugate sample collected from −60° to +60° with a 1.5° step under 80,000× magnification and an expected defocus of 800 nm. (D) This series took 1.5 h to collect, with X/Y mean absolute positional errors and a defocus error of 13.1, 17.1, and 22.9 nm, respectively, with standard deviations of 18.3, 20.7 and 29.1 nm, respectively.

Figure 8

Figure 8. Automatic tomography data collection of low-density lipoprotein.

(A) A Cryo-EM LDL sample collected from −60° to +58° with a 2° step under 50,000× magnification and an expected defocus of 2,000 nm. (B) This series took 1 h and 15 min to collect, with X/Y mean absolute positional errors and a defocus error of 43.0 nm 78.4, and 221.8 nm, respectively, with standard deviations of 61.1, 108.6 and 340.2 nm, respectively.

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