Atomic Resolution Cryo-EM Structure of β-Galactosidase.

KEY RESOURCES TABLE METHOD DETAILS

Data acquisition and movie processing

The cryo-EM density map described in this work was obtained from the 1539 movies comprising the publicly available EMPIAR entry 10061. Each movie contains 38 frames recorded every 0.2 s giving an accumulated dose of ~ 45 e − /Å 2 and a total exposure time of 7.6 s. This same dataset was used to determine the previously reported 2.2 Å structure of β-galactosidase ( Bartesaghi et al., 2015 ). Movies were aligned initially using the whole frame alignment technique described earlier ( Bartesaghi et al., 2014 ) and CTF estimation was done with CTFFIND ( Rohou and Grigorieff, 2015 ) using a frequency range for the defocus fit of 30-3.5 Å. Single particle analysis 298,715 particles were picked automatically using a Gaussian disk of 80 Å in radius (using a less stringent peak thresholding criteria than that used to obtain the 2.2 Å structure), extracted using a binning factor of 8 corresponding to 2.55 Å per pixel, and subjected to 3D refinement in FREALIGN ( Grigorieff, 2016 ). A bimodal distribution of FREALIGN scores was observed and only the 150,321 particles assigned to the lobe with the highest scores were kept for further processing. These particles were then re-extracted from the original micrographs using a binning factor of 2 equivalent to 0.64 Å per pixel (box size of 768×768 pixels), and subjected to an additional 8 rounds of local refinement. D2 symmetry was imposed throughout processing. The highest resolution information used during all stages of refinement carried out in FREALIGN was set to 2.8 Å. The resulting map, which uses the full 45 e − /Å 2 exposure served as a starting point to evaluate the improvements from each of the image processing advances we introduce in the present work. The nominal resolution of this map is 2.3 Å (0.143-cutoff FSC criterion; Supplementary Figure 1c-d , blue curves), which is slightly lower than the previously reported 2.2 Å map which had fewer particles (~40,000) and only used a subset of the data (frames 4-13) to minimize loss of high-resolution information from image drift and radiation damage.

3D refinement and reconstruction

All refinement and reconstruction operations were done with a new version of FREALIGN that uses a matched filter to align particle images. This requires noise-whitening of the particle images based on the noise power spectrum, which is estimated in FREALIGN as the average power spectrum of the particle images outside a specified particle radius. The signal power in the images is estimated using the particle spectral signal-to-noise ratio derived from resolution statistics of the current best reconstruction ( Sindelar and Grigorieff, 2012 ). For the matched filter, the signal in the reference projections is amplitude-scaled to match the predicted signal in the image to be aligned, and the projection direction and x,y translation is then adjusted to maximize the correlation coefficient between image and reference. Improvements to FREALIGN further include speed optimization by on-the-fly real-space image cropping and pixel binning through Fourier cropping where appropriate, as well as the use of processor-optimized libraries. The improved version of FREALIGN is part of cisTEM ( www.cistem.org ), a new image processing software for single particle averaging.

Per-particle frame alignment

To overcome the challenges of dealing with the very low SNR present in the small image area of single particle frames ( Aguerrebere et al., 2016 ), we follow the movement of individual particles throughout the exposure using a strategy similar to the “particle-polishing” procedure ( Scheres, 2014 ). Frames for each particle were extracted from the aligned micrographs (after whole-frame alignment), and weighted running averages for each particle were obtained and re-aligned to projections of the refined 3D model. This produced a set of noisy trajectories for the movement of each particle, which were then regularized using spatio-temporal smoothness constraints. The resulting alignments were used to update the running frame averages for each particle and were re-aligned once again to the 3D reference. Repeating this process until convergence (typically 10 iterations), resulted in the final assignment of local particle trajectories as shown in Figures 1a-c . Compared to the 2.3 Å map obtained using whole-frame alignment, resolution after doing per-particle drift correction using this approach improved by 0.09 Å, Supplementary Figure 1c (left). To compute the running averages of frames we used Gaussian weights with a variance equivalent to 20% the number of frames in each movie, meaning that only the closest ~15 frames (7 before and 7 after) have non-zero contributions to each running average. Re-alignment of the running averages to the 3D reference was implemented using FREALIGN by only allowing translational movements while keeping particle orientations fixed at the values obtained during the initial 3D refinement. To regularize the local trajectories, we averaged the movement of nearby particles using weights drawn from a Gaussian distribution based on the distance between particles (variance of 16 nm), followed by fitting of cubic splines to the net particle trajectories obtained by composing the whole-frame movement with the local drift component. Application of this strategy to particles with lower molecular weight than β-galactosidase may require the use of Gaussians with wider variances, both for the computation of running frame averages and regularization of trajectories, in order to compensate for the reduction in image contrast produced by smaller-sized complexes.

Data-driven dose weighting

Correlation scores assigned to individual frames of every particle were averaged across each micrograph resulting in 1D score-exposure curves ( Figure 1d ). Corresponding 2D frequency weights ( Figure 1e ) were derived using the formula W ( f , s ) = e − 1 2 r ( f ) 4 y ( s ) / ∑ f w ( f , s ) , where f denotes the frame number and s the spatial frequency. The dependency on the normalized score-averages, 0 ≤ p r ( f ) ¯ ≤ 1 , was set to r ( f ) = ( 1 − p r ( f ) 4 ¯ ) to prevent a few top scoring frames from dominating the average in the high-frequency regime, and the frequency modulation was set empirically to y ( s ) = e 7,62 s . For micrographs containing fewer than 10 particles the score averages were too noisy to be reliable, and instead the mean score-exposure curve obtained by averaging across all micrographs in the dataset was used for weighting ( Supplementary Figure 1a ). Compared to using the full unweighted 45 e − /Å 2 exposure to obtain the baseline 2.3 Å map, the improvement in map resolution using the proposed dose weighting scheme was 0.12 Å, Supplementary Figure 1c (middle). Per-particle CTF estimation Initial 3D refinement was carried out with the standard approach of using global defocus/astigmatism parameters for each micrograph estimated using CTFFIND. To account for spatial variations of the CTF within each image, defocus/astigmatism estimation was done on a per particle basis using a strategy similar to that implemented in GCTF ( Zhang, 2016 ). At every particle position, weighted averages of power spectra of neighboring particles were obtained and subjected to CTF estimation using CTFFIND (option --amplitude-spectrum-input), resulting in a smooth distribution of CTF parameters, Figure 1a . Weights were derived from a Gaussian distribution based on the inter-particle distances using a variance of 32 nm. Compared to the 2.3 Å reconstruction that used per-micrograph defocus parameters, the use of local CTF measurements resulted in an improvement in resolution of 0.07 Å, Supplementary Figure 1c (right).

Final map and structure refinement

Combination of the local drift correction, dose weighting and local CTF estimation strategies resulted in an improved map that was iteratively refined in FREALIGN. A negative B-factor was applied to the final map followed by application of a soft shape mask obtained by thresholding the unsharpened density map followed by apodization. Coordinates of one beta-galactosidase protomer with 2 sodium ions, 2 magnesium ions and a 2-phenylethyl 1-thio-beta-D-galactopyranoside extracted from the 2.2 Å resolution structure (Chain A of PDB ID 5A1A) was fitted onto the new cryo-EM map. The backbone of the starting model was manually adjusted in COOT followed by five cycles of real space refinement in PHENIX ( Zwart et al., 2008 ). About 400 water molecules were then modeled at peaks of protein-masked density above 2.0 r.m.s.d. and with distance to protein atom between 2.5 and 3.5 Å. About 600 additional water molecules were placed manually. D2 symmetry was applied on the protomer to generate the whole tetramer of beta-galactosidase. Water molecules at interface of protomers were manually edited to avoid interatomic clashes. Gln, Asn and His sidechains were automatically flipped using MOLPROBITY’s Reduce ( Chen et al., 2010 ) and then manually checked. Finally, three cycles of real space refinement were performed for the whole tetramer in PHENIX. Flexibility analysis of protein structures The refined tetramer structure of β -galactosidase was simulated using the AMBER package ( Case et al., 2016 ) to examine conformational flexibility of the system. The map-restrained self-guided Langevin dynamics (MapSGLD) ( Wu et al., 2013 ) was used to apply map restraints of the following form: (1) E m a p = − c m a p ∑ a N m a p ∧ ( x a , y a , z a ) Which correlates atomic mass, m a , with the normalized map density at the atom position, p ∧ ( x a , y a , z a ) . The restraint constant, c map , sets the strength of the map-restraint. The units of m a and c map are g/mol and kcal/g, respectively. Equation (1) produces an energy landscape in the shape of the density distribution, − c m a p p ∧ ( x a , y a , z a ) , for every restrained atom, a. It induces atoms to move to positions of lower energy, or of higher density. The restraint constant is set to c map = 0.1 kcal/g . The map restraint coupled with the AMBER ff14SB force field ( Maier et al., 2015 ), as well as the generalized Born solvation model ( Gotz et al., 2012 ), makes the desired structure the global minimum. An improved conformational sampling method, self-guided Langevin dynamics via generalized Langevin equation (SGLD-GLE) ( Wu et al., 2016 ), was applied to achieve enhanced conformational sampling while maintaining the correct canonical ensemble distribution. The local averaging time and the guiding factor were 0.2 ps and 1, respectively. The MapSGLD simulations were 1 ns in length with a time step of 1 fs. The conformations were saved every 10 ps for post simulation analysis. AMBER trajectory post analysis was done with Cpptraj ( Roe and Cheatham, 2013 ). Fluctuations of residues and atoms were averaged over the four copies of the tetramer. Statistical differences between groups were calculated with the Wilcoxon rank sum test, and p-values were adjusted for multiple comparisons with the Bonferroni correction. Correlation between mean fluctuation values for unconstrained versus EM-constrained PETG atoms was evaluated using Kendall’s tau .

Generation of figures

Figures of map density and coordinates were created in UCSF Chimera ( Pettersen et al., 2004 ) and Maxon Cinema4D, except for the individual residue images from the 2.2 Å cryo-EM map, which were created in UCSF Chimera. For the images created in Maxon Cinema4D, the coordinates were imported using the Cinema4D plugin Embedded Python Molecular Viewer (ePMV) ( Johnson et al., 2011 ). Supplementary Video 1 . Visualization of atomic resolution features in cryo-EM map of β -galactosidase bound to PETG inhibitor. Related to Figures 2 and 3 . Sequence of screenshots obtained using the program COOT showing the quality of the map across different regions of the protein and comparison of residues for each of the 20-amino acids selected from the new map and from the previously published 2.2 Å map.

METHOD DETAILS Data acquisition and movie processing

The cryo-EM density map described in this work was obtained from the 1539 movies comprising the publicly available EMPIAR entry 10061. Each movie contains 38 frames recorded every 0.2 s giving an accumulated dose of ~ 45 e − /Å 2 and a total exposure time of 7.6 s. This same dataset was used to determine the previously reported 2.2 Å structure of β-galactosidase ( Bartesaghi et al., 2015 ). Movies were aligned initially using the whole frame alignment technique described earlier ( Bartesaghi et al., 2014 ) and CTF estimation was done with CTFFIND ( Rohou and Grigorieff, 2015 ) using a frequency range for the defocus fit of 30-3.5 Å. Single particle analysis 298,715 particles were picked automatically using a Gaussian disk of 80 Å in radius (using a less stringent peak thresholding criteria than that used to obtain the 2.2 Å structure), extracted using a binning factor of 8 corresponding to 2.55 Å per pixel, and subjected to 3D refinement in FREALIGN ( Grigorieff, 2016 ). A bimodal distribution of FREALIGN scores was observed and only the 150,321 particles assigned to the lobe with the highest scores were kept for further processing. These particles were then re-extracted from the original micrographs using a binning factor of 2 equivalent to 0.64 Å per pixel (box size of 768×768 pixels), and subjected to an additional 8 rounds of local refinement. D2 symmetry was imposed throughout processing. The highest resolution information used during all stages of refinement carried out in FREALIGN was set to 2.8 Å. The resulting map, which uses the full 45 e − /Å 2 exposure served as a starting point to evaluate the improvements from each of the image processing advances we introduce in the present work. The nominal resolution of this map is 2.3 Å (0.143-cutoff FSC criterion; Supplementary Figure 1c-d , blue curves), which is slightly lower than the previously reported 2.2 Å map which had fewer particles (~40,000) and only used a subset of the data (frames 4-13) to minimize loss of high-resolution information from image drift and radiation damage.

3D refinement and reconstruction

All refinement and reconstruction operations were done with a new version of FREALIGN that uses a matched filter to align particle images. This requires noise-whitening of the particle images based on the noise power spectrum, which is estimated in FREALIGN as the average power spectrum of the particle images outside a specified particle radius. The signal power in the images is estimated using the particle spectral signal-to-noise ratio derived from resolution statistics of the current best reconstruction ( Sindelar and Grigorieff, 2012 ). For the matched filter, the signal in the reference projections is amplitude-scaled to match the predicted signal in the image to be aligned, and the projection direction and x,y translation is then adjusted to maximize the correlation coefficient between image and reference. Improvements to FREALIGN further include speed optimization by on-the-fly real-space image cropping and pixel binning through Fourier cropping where appropriate, as well as the use of processor-optimized libraries. The improved version of FREALIGN is part of cisTEM ( www.cistem.org ), a new image processing software for single particle averaging.

Per-particle frame alignment

To overcome the challenges of dealing with the very low SNR present in the small image area of single particle frames ( Aguerrebere et al., 2016 ), we follow the movement of individual particles throughout the exposure using a strategy similar to the “particle-polishing” procedure ( Scheres, 2014 ). Frames for each particle were extracted from the aligned micrographs (after whole-frame alignment), and weighted running averages for each particle were obtained and re-aligned to projections of the refined 3D model. This produced a set of noisy trajectories for the movement of each particle, which were then regularized using spatio-temporal smoothness constraints. The resulting alignments were used to update the running frame averages for each particle and were re-aligned once again to the 3D reference. Repeating this process until convergence (typically 10 iterations), resulted in the final assignment of local particle trajectories as shown in Figures 1a-c . Compared to the 2.3 Å map obtained using whole-frame alignment, resolution after doing per-particle drift correction using this approach improved by 0.09 Å, Supplementary Figure 1c (left). To compute the running averages of frames we used Gaussian weights with a variance equivalent to 20% the number of frames in each movie, meaning that only the closest ~15 frames (7 before and 7 after) have non-zero contributions to each running average. Re-alignment of the running averages to the 3D reference was implemented using FREALIGN by only allowing translational movements while keeping particle orientations fixed at the values obtained during the initial 3D refinement. To regularize the local trajectories, we averaged the movement of nearby particles using weights drawn from a Gaussian distribution based on the distance between particles (variance of 16 nm), followed by fitting of cubic splines to the net particle trajectories obtained by composing the whole-frame movement with the local drift component. Application of this strategy to particles with lower molecular weight than β-galactosidase may require the use of Gaussians with wider variances, both for the computation of running frame averages and regularization of trajectories, in order to compensate for the reduction in image contrast produced by smaller-sized complexes.

Data-driven dose weighting

Correlation scores assigned to individual frames of every particle were averaged across each micrograph resulting in 1D score-exposure curves ( Figure 1d ). Corresponding 2D frequency weights ( Figure 1e ) were derived using the formula W ( f , s ) = e − 1 2 r ( f ) 4 y ( s ) / ∑ f w ( f , s ) , where f denotes the frame number and s the spatial frequency. The dependency on the normalized score-averages, 0 ≤ p r ( f ) ¯ ≤ 1 , was set to r ( f ) = ( 1 − p r ( f ) 4 ¯ ) to prevent a few top scoring frames from dominating the average in the high-frequency regime, and the frequency modulation was set empirically to y ( s ) = e 7,62 s . For micrographs containing fewer than 10 particles the score averages were too noisy to be reliable, and instead the mean score-exposure curve obtained by averaging across all micrographs in the dataset was used for weighting ( Supplementary Figure 1a ). Compared to using the full unweighted 45 e − /Å 2 exposure to obtain the baseline 2.3 Å map, the improvement in map resolution using the proposed dose weighting scheme was 0.12 Å, Supplementary Figure 1c (middle). Per-particle CTF estimation Initial 3D refinement was carried out with the standard approach of using global defocus/astigmatism parameters for each micrograph estimated using CTFFIND. To account for spatial variations of the CTF within each image, defocus/astigmatism estimation was done on a per particle basis using a strategy similar to that implemented in GCTF ( Zhang, 2016 ). At every particle position, weighted averages of power spectra of neighboring particles were obtained and subjected to CTF estimation using CTFFIND (option --amplitude-spectrum-input), resulting in a smooth distribution of CTF parameters, Figure 1a . Weights were derived from a Gaussian distribution based on the inter-particle distances using a variance of 32 nm. Compared to the 2.3 Å reconstruction that used per-micrograph defocus parameters, the use of local CTF measurements resulted in an improvement in resolution of 0.07 Å, Supplementary Figure 1c (right).

Final map and structure refinement

Combination of the local drift correction, dose weighting and local CTF estimation strategies resulted in an improved map that was iteratively refined in FREALIGN. A negative B-factor was applied to the final map followed by application of a soft shape mask obtained by thresholding the unsharpened density map followed by apodization. Coordinates of one beta-galactosidase protomer with 2 sodium ions, 2 magnesium ions and a 2-phenylethyl 1-thio-beta-D-galactopyranoside extracted from the 2.2 Å resolution structure (Chain A of PDB ID 5A1A) was fitted onto the new cryo-EM map. The backbone of the starting model was manually adjusted in COOT followed by five cycles of real space refinement in PHENIX ( Zwart et al., 2008 ). About 400 water molecules were then modeled at peaks of protein-masked density above 2.0 r.m.s.d. and with distance to protein atom between 2.5 and 3.5 Å. About 600 additional water molecules were placed manually. D2 symmetry was applied on the protomer to generate the whole tetramer of beta-galactosidase. Water molecules at interface of protomers were manually edited to avoid interatomic clashes. Gln, Asn and His sidechains were automatically flipped using MOLPROBITY’s Reduce ( Chen et al., 2010 ) and then manually checked. Finally, three cycles of real space refinement were performed for the whole tetramer in PHENIX. Flexibility analysis of protein structures The refined tetramer structure of β -galactosidase was simulated using the AMBER package ( Case et al., 2016 ) to examine conformational flexibility of the system. The map-restrained self-guided Langevin dynamics (MapSGLD) ( Wu et al., 2013 ) was used to apply map restraints of the following form: (1) E m a p = − c m a p ∑ a N m a p ∧ ( x a , y a , z a ) Which correlates atomic mass, m a , with the normalized map density at the atom position, p ∧ ( x a , y a , z a ) . The restraint constant, c map , sets the strength of the map-restraint. The units of m a and c map are g/mol and kcal/g, respectively. Equation (1) produces an energy landscape in the shape of the density distribution, − c m a p p ∧ ( x a , y a , z a ) , for every restrained atom, a. It induces atoms to move to positions of lower energy, or of higher density. The restraint constant is set to c map = 0.1 kcal/g . The map restraint coupled with the AMBER ff14SB force field ( Maier et al., 2015 ), as well as the generalized Born solvation model ( Gotz et al., 2012 ), makes the desired structure the global minimum. An improved conformational sampling method, self-guided Langevin dynamics via generalized Langevin equation (SGLD-GLE) ( Wu et al., 2016 ), was applied to achieve enhanced conformational sampling while maintaining the correct canonical ensemble distribution. The local averaging time and the guiding factor were 0.2 ps and 1, respectively. The MapSGLD simulations were 1 ns in length with a time step of 1 fs. The conformations were saved every 10 ps for post simulation analysis. AMBER trajectory post analysis was done with Cpptraj ( Roe and Cheatham, 2013 ). Fluctuations of residues and atoms were averaged over the four copies of the tetramer. Statistical differences between groups were calculated with the Wilcoxon rank sum test, and p-values were adjusted for multiple comparisons with the Bonferroni correction. Correlation between mean fluctuation values for unconstrained versus EM-constrained PETG atoms was evaluated using Kendall’s tau .

Generation of figures

Figures of map density and coordinates were created in UCSF Chimera ( Pettersen et al., 2004 ) and Maxon Cinema4D, except for the individual residue images from the 2.2 Å cryo-EM map, which were created in UCSF Chimera. For the images created in Maxon Cinema4D, the coordinates were imported using the Cinema4D plugin Embedded Python Molecular Viewer (ePMV) ( Johnson et al., 2011 ). Supplementary Video 1 . Visualization of atomic resolution features in cryo-EM map of β -galactosidase bound to PETG inhibitor. Related to Figures 2 and 3 . Sequence of screenshots obtained using the program COOT showing the quality of the map across different regions of the protein and comparison of residues for each of the 20-amino acids selected from the new map and from the previously published 2.2 Å map.

Supplementary Material 1 2