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Molecular goniometers for single-particle cryo-electron microscopy of DNA-binding proteins


Correct reconstruction of macromolecular structure by cryo-electron microscopy (cryo-EM) relies on accurate determination of the orientation of single-particle images. For small (<100 kDa) DNA-binding proteins, obtaining particle images with sufficiently asymmetric features to correctly guide alignment is challenging. We apply DNA origami to construct molecular goniometers—instruments that precisely orient objects—and use them to dock a DNA-binding protein on a double-helix stage that has user-programmable tilt and rotation angles. We construct goniometers with 14 different stage configurations to orient and visualize the protein just above the cryo-EM grid surface. Each goniometer has a distinct barcode pattern that we use during particle classification to assign angle priors to the bound protein. We use goniometers to obtain a 6.5-Å structure of BurrH, an 82-kDa DNA-binding protein whose helical pseudosymmetry prevents accurate image orientation using traditional cryo-EM. Our approach should be adaptable to other DNA-binding proteins as well as small proteins fused to DNA-binding domains.

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Fig. 1: Design and grid adsorption of molecular goniometers built from DNA origami.
Fig. 2: Scaffold-integrated BurrH binding site and its relation to folded goniometers.
Fig. 3: Determination of protein classes with angle priors from goniometer image data.
Fig. 4: Cryo-EM data analysis workflow for DNA origami goniometer barcode classification.
Fig. 5: Sankey diagram for particle selection, classification, prior assignment and 3D reconstruction.
Fig. 6: 3D refinement of BurrH structure using molecular goniometer-derived angle priors.

Data availability

The cryo-EM map of BurrH has been deposited in the Electron Microscopy Data Bank (EMD-21443). The cryo-EM movie files have been deposited at the Electron Microscopy Public Image Archive (EMPIAR-10373). The p9344-BurrH scaffold sequence has been submitted to GenBank (MT081208) and the plasmid deposited with AddGene (no. 140326).

Code availability

Source code is available at


  1. 1.

    Bai, X.-C., McMullan, G. & Scheres, S. H. W. How cryo-EM is revolutionizing structural biology. Trends Biochem. Sci. 40, 49–57 (2015).

    CAS  Article  Google Scholar 

  2. 2.

    Cheng, Y. Single-particle cryo-EM—how did it get here and where will it go? Science 361, 876–880 (2018).

    CAS  Article  Google Scholar 

  3. 3.

    Wu, S. et al. Fabs enable single particle cryoEM studies of small proteins. Structure 20, 582–592 (2012).

    CAS  Article  Google Scholar 

  4. 4.

    Zhang, C. et al. Analysis of discrete local variability and structural covariance in macromolecular assemblies using Cryo-EM and focused classification. Ultramicroscopy 203, 170–180 (2019).

    CAS  Article  Google Scholar 

  5. 5.

    Liu, Y., Gonen, S., Gonen, T. & Yeates, T. O. Near-atomic cryo-EM imaging of a small protein displayed on a designed scaffolding system. Proc. Natl Acad. Sci. USA 115, 3362–3367 (2018).

    CAS  Article  Google Scholar 

  6. 6.

    Seeman, N. C. Nucleic acid junctions and lattices. J. Theor. Biol. 99, 237–247 (1982).

    CAS  Article  Google Scholar 

  7. 7.

    Rothemund, P. W. K. Folding DNA to create nanoscale shapes and patterns. Nature 440, 297–302 (2006).

    CAS  Article  Google Scholar 

  8. 8.

    Martin, T. G. et al. Design of a molecular support for cryo-EM structure determination. Proc. Natl Acad. Sci. USA 113, E7456–E7463 (2016).

    CAS  Article  Google Scholar 

  9. 9.

    Juillerat, A. et al. BurrH: a new modular DNA binding protein for genome engineering. Sci. Rep. 4, 3831 (2014).

    Article  Google Scholar 

  10. 10.

    Stella, S. et al. BuD, a helix-loop-helix DNA-binding domain for genome modification. Acta Crystallogr. D. Biol. Crystallogr. 70, 2042–2052 (2014).

    CAS  Article  Google Scholar 

  11. 11.

    Wang, F. et al. Amino and PEG-amino graphene oxide grids enrich and protect samples for high-resolution single particle cryo-electron microscopy.J. Struct. Biol. 209, 107437 (2019).

    Article  Google Scholar 

  12. 12.

    Scheres, S. H. W. RELION: implementation of a Bayesian approach to cryo-EM structure determination. J. Struct. Biol. 180, 519–530 (2012).

    CAS  Article  Google Scholar 

  13. 13.

    Punjani, A., Rubinstein, J. L., Fleet, D. J. & Brubaker, M. A. cryoSPARC: algorithms for rapid unsupervised cryo-EM structure determination. Nat. Methods 14, 290–296 (2017).

    CAS  Article  Google Scholar 

  14. 14.

    Grant, R., Rohou, A. & Grigorieff, N. cisTEM, user-friendly software for single-particle image processing.eLife 7, e35383 (2018).

    Article  Google Scholar 

  15. 15.

    Baldwin, P. R. & Lyumkis, D. Non-uniformity of projection distributions attenuates resolution in Cryo-EM.Prog. Biophys. Mol. Biol. 150, 160–163 (2019).

    Article  Google Scholar 

  16. 16.

    Rosenthal, P. B. & Henderson, R. Optimal determination of particle orientation, absolute hand, and contrast loss in single-particle electron cryomicroscopy. J. Mol. Biol. 333, 721–745 (2003).

    CAS  Article  Google Scholar 

  17. 17.

    Meents, A., Gutmann, S., Wagner, A. & Schulze-Briese, C. Origin and temperature dependence of radiation damage in biological samples at cryogenic temperatures. Proc. Natl Acad. Sci. USA 107, 1094–1099 (2010).

    CAS  Article  Google Scholar 

  18. 18.

    Zhou, K. et al. Toward precise manipulation of DNA–protein hybrid nanoarchitectures. Small 15, 1804044 (2019).

    Article  Google Scholar 

  19. 19.

    Glaeser, R. M. How good can cryo-EM become? Nat. Methods 13, 28–32 (2016).

    CAS  Article  Google Scholar 

  20. 20.

    Lyumkis, D. Challenges and opportunities in cryo-EM single-particle analysis. J. Biol. Chem. 294, 5181–5197 (2019).

    CAS  Article  Google Scholar 

  21. 21.

    Nafisi, P. M., Aksel, T. & Douglas, S. M. Construction of a novel phagemid to produce custom DNA origami scaffolds. Synth. Biol. 3, (2018).

  22. 22.

    Douglas, S. M. et al. Rapid prototyping of 3D DNA-origami shapes with caDNAno. Nucleic Acids Res. 37, 5001–5006 (2009).

    CAS  Article  Google Scholar 

  23. 23.

    Wagenbauer, K. F. et al. How we make DNA origami. Chem. Bio. Chem. 18, 1873–1885 (2017).

    CAS  Article  Google Scholar 

  24. 24.

    Zheng, S. Q. et al. MotionCor2: anisotropic correction of beam-induced motion for improved cryo-electron microscopy. Nat. Methods 14, 331–332 (2017).

    CAS  Article  Google Scholar 

  25. 25.

    Zhang, K. Gctf: Real-time CTF determination and correction. J. Struct. Biol. 193, 1–12 (2016).

    CAS  Article  Google Scholar 

  26. 26.

    Tang, G. et al. EMAN2: an extensible image processing suite for electron microscopy. J. Struct. Biol. 157, 38–46 (2007).

    CAS  Article  Google Scholar 

  27. 27.

    Pettersen, E. F., Goddard, T. D. & Huang, C. C. UCSF Chimera—a visualization system for exploratory research and analysis. J. Comput. Chem. 25, 1605–1612 (2004).

    CAS  Article  Google Scholar 

  28. 28.

    Dang, S. et al. Cryo-EM structures of the TMEM16A calcium-activated chloride channel. Nature 552, 426–429 (2017).

    CAS  Article  Google Scholar 

  29. 29.

    Tan, Y. Z. et al. Addressing preferred specimen orientation in single-particle cryo-EM through tilting. Nat. Methods 14, 793–796 (2017).

    CAS  Article  Google Scholar 

  30. 30.

    Heymann, J. B., Chagoyen, M. & Belnap, D. M. Common conventions for interchange and archiving of three-dimensional electron microscopy information in structural biology. J. Struct. Biol. 151, 196–207 (2005).

    Article  Google Scholar 

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We thank F. Wang for furnishing amino-graphene-oxide grids and protocols for early tests. We thank D. Bulkley and A. Myasnikov for help with cryo-EM data collection. We thank J. Brown and C. Gingold for help with visualization. T.A. was supported by the Ruth L. Kirschstein NRSA Postdoctoral Fellowship grant no. F32GM119322. S.M.D. was supported by the UCSF Program for Breakthrough Biomedical Research, Pew-Stewart Scholars Program, NSF CAREER award no. 1453847 and NIH grant no. R35GM125027. Y.C. is an investigator of the Howard Hughes Medical Institute and was supported by NIH grant nos. R01GM098672, R01HL134183, S10OD021741 and S10OD020054.

Author information




T.A. and S.M.D. conceptualized the project. T.A. performed research, collected data, wrote software and analyzed data. Z.Y. performed research and collected data. All authors discussed data. T.A. and S.M.D. wrote the manuscript with input from all authors. Y.C. and S.M.D. provided resources and supervised the project.

Corresponding author

Correspondence to Shawn M. Douglas.

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The authors declare no competing interests.

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Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Comparison of grid adsorption orientation and signal delocalization for two chassis designs.

a, Representative negative-stain micrographs of chassis with 0.67 aspect ratio. b, Representative cryo-EM micrograph of chassis with 0.59 aspect ratio. Desired orientations assessed by manual counting. c, Top: Representative 2D class average of 0°-rotation goniometer from a. The chassis aperture exhibits a shadow that overlaps the DNA stage and BurrH protein. Bottom: Representative 2D class averages of BurrH, exhibiting artifacts that we hypothesized are due to delocalized origami signal in the 0.5–2.0 µm defocus range used for image acquisition. d, Top: 2D class of 0°-rotation goniometer from b designed to reduce shadow overlap. Bottom: Representative BurrH 2D class averages. Artifacts observed in c are significantly reduced. Scale bars: a, b: 100 nm, c, d: 25 nm (top), 10 nm (bottom).

Extended Data Fig. 2 How we defined “tilt” and “rotation” angles for the molecular goniometers.

Independent 2D views of a 3D object can be derived using only two orthogonal rotational transformations. In cryo-EM, the two orthogonal rotations can be referred to as tilt and rotation angles, respectively12,30. The reference coordinate system for the rotation operations can be chosen arbitrarily, and here we define the goniometer tilt angle as the angle between the stage DNA and the normal vector perpendicular to the goniometer face (the normal vector is parallel to the electron beam (Fig. 1a, orange line labeled e) when the goniometer adsorbs in the desired face-up orientation. We define the goniometer rotation angle as the rotation angle with respect to the axis parallel to the DNA stage helical axis.

Extended Data Fig. 3 Cadnano design strand diagram schematics.

a, Bit and rotation angles for each column. b, +90 tilt, 414-nt rotation bit designs. TILT bit is inactive (red outline in bottom right corner of each schematic). c, –90 tilt, 414-nt rotation bit designs. TILT bit is active. d, +90 tilt, 222-nt rotation bit designs. TILT bit is inactive.

Extended Data Fig. 4 2D cryo-EM class averages goniometers with BurrH.

a, +90 tilt, 414-nt bit b, –90 tilt, 414-nt bit (flipped), c, +90 tilt, 222-nt bit. Scale bars: 100 nm.

Extended Data Fig. 5 Cryo-EM data analysis workflow for BurrH 3D reconstruction and refinement.

a, Centering goniometer classes at tilt DNA. b, Picking protein particles from the center of goniometers. c, 2D classification of BurrH particles and removing “bad” classes. d, Recentering “good” classes. e, Building an initial model 3D model with tilt and rot angle constraints. f, Aligning BurrH particles to initial model with tilt and rot angle constraints and regularization parameter, T, set to 6 for better alignment. g, Classifying particles into five 3D classes with tilt angle constraint on and regularization parameter, T, set to 2 to minimize overfitting during classification. Best 3D class (magenta) is at 7.3 Å resolution. h, Refining the best 3D class with only the tilt angle constraint. Estimated resolution of the refined map is 6.5 Å.

Extended Data Fig. 6 2D classification of goniometer stage DNA with BurrH.

Representative 2D classes of stage DNA with BurrH after one round of 2D classification. Classes with high background signal, with empty tilt DNA and DNA origami signal are removed before further 2D classification of BurrH bound to stage DNA. b, “Good” 2D classes retained for 3D reconstruction and refinement of BurrH. Scale bar is 20 nm.

Extended Data Fig. 7 Measured tilt, rotation, and psi angle distributions for all goniometer designs.

Polar plots and histograms follow the convention from Fig. 6. The inner tick mark represents the goal angle, and the arc shows the bounds of the Gaussian angle prior. Average rotation angles are plotted as magenta lines for tilt and rotation plots.

Extended Data Fig. 8 Directional FSC Plots for BurrH.

a, Individual directional FSCs (gray lines), global FSC value (blue line) and ±1 standard deviation from global FSC (magenta dashed lines). b, Directional FSC map and its 2D projections. The minimum resolution (blue) and maximum resolution (magenta) are indicated for each 2D projection.

Extended Data Fig. 9 Comparison of particle count and defocus effects on final BurrH resolution.

a, ResLog plots showing FSC vs. resolution for 3D refinement of BurrH using 1,000 to 68,482 particles. b, Resolution estimates from FSC0.143 vs. particles count. The resolution plateaus at 40k particles, suggesting our resolution is not limited by particle count. c, BurrH resolution vs. maximum micrograph defocus used in 3D reconstruction. d, Resolution estimates from FSC0.143 vs. maximum defocus. The resolution reaches a plateau at 1.5 µm and the addition of higher defocus particles doesn’t comprise the resolution. Inset shows the distribution of BurrH particle defocus in µm.

Extended Data Fig. 10 Filtering particles by estimated rotation angle.

FSC and ResLog plots for BurrH 3D reconstructions in which particles are filtered when their estimated angles from the unfiltered 3D refinement differ from the goniometer goal angle. a, We compared three conditions: No filter (that is, identical to Fig. 6), and two conditions in which particles with assigned rotation angles that differ by >45°, and >90° from the goal angle. b, FSC curves comparing the 3D reconstruction for the three filtering conditions. c, Plot of particle count versus resolution estimate. Filtering reduces the particle count available for the 3D reconstruction, which in turn reduces the final resolution (see Extended Data Fig. 8b). Compared to the unfiltered reconstructions, removing particles in the indicated angle ranges does not improve the final BurrH resolution.

Supplementary information

Reporting Summary

Supplementary Table 1

Staple sequences for goniometers with +90° tilt and 414-nt barcode bit

Supplementary Table 2

Staple sequences for goniometers with −90° tilt and 414-nt barcode bit

Supplementary Table 3

Staple sequences for goniometers with +90° tilt and 222-nt barcode bit

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Aksel, T., Yu, Z., Cheng, Y. et al. Molecular goniometers for single-particle cryo-electron microscopy of DNA-binding proteins. Nat Biotechnol 39, 378–386 (2021).

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