Cryoelectron Microscopy

The accuracy of defocus determination is very important for high-resolution cryoEM reconstructions. Assuming the difference between the true defocus of a micrograph and the estimated defocus is $\mathrm{\Delta }z$ , the phase error $\mathrm{\Delta }\gamma (s)$ is calculated by Eq. (4): $\mathrm{\Delta }\gamma (s)=\pi \lambda \mathrm{\Delta }{\mathit{zs}}^2$
Derived from Eq. (4), the defocus-inaccuracy dependent phase error is proportional to frequency squared for a certain micrograph Eq. (5). $\frac{\mathrm{\Delta }\gamma (s_1)}{\mathrm{\Delta }\gamma (s_2)}=\frac{s_1^2}{s_2^2}$
Obviously from Eqs. (4), (5), an error in CTF determination, which can be ignored for a lower resolution reconstruction, might cause a critical error at high resolution. If the CTF is not properly determined, there are increasing phase errors against the frequency. The contrast of CTF is inverted for a 180 degree phase error. When this error is smaller than 90 degree, the probability to have the correct contrast of CTF is more than 50%. Gctf uses such a 90 degree criterion in order to guarantee at least half of information from the EM images after CTF correction. Based on this criterion, CTF phase error versus frequency for different defocus errors between 10 nm and 200 nm were plotted (Fig. 1a). The maximum allowed CTF defocus errors were plotted against frequency for three typical voltages used in cryoEM reconstruction s (Fig. 1b).
In practice, defocus inaccuracy is only one of the factors that cause CTF phase error. Magnification distortion, chromatic or comatic aberration (Glaeser et al., 2011 (link)), astigmatism inaccuracy, mechanical and beam induced movement of the samples, curvature or deformation of the carbon substrate (Shatsky et al., 2014 (link)), sample thickness (DeRosier, 2000 (link)) can all contribute to the phase error during an experiment. Data processing can also lead to large phase errors, especially at high frequency. Although Gctf uses this 90 degree criterion, it should be noted that the highest quality micrographs might need a stricter criterion in practice.

We modelled a 13-protofilament MT based on the cryoEM structure of a yeast tubulin dimer polymerized with GTP in vitro (PDB-ID 5W3F) [65 (link)]. As published, we used lattice parameters for the MT tube with a helical rise of 83.3 Å and a rotation of 0.43° between dimers within a protofilament, and a helical rise of 9.65 Å and a rotation of −27.6° between protofilaments. The majority of kinetochore MTs in tomograms recorded from budding yeast were observed in in ‘ram's horn’ geometry [66 (link)], and we modelled the flaring of protofilaments at the MT plus end by matching the average curvature of the tomograms with the curvature observed in various structures of bent tubulin protofilaments (PDB-IDs 3J6H, 3RYH, 4HNA, 4FFB, 6MZG).
To model a MT-bound yeast Ndc80c, we first docked the AF2 prediction of Ndc80 : Nuf2 up to a few residues beyond the hinge (Ndc80^115–444, Nuf2^1–277) onto the MT. For this, we used the structure of the human Ndc80 : Nuf2 head domain bound to the MT lattice (PDB-ID 3iZ0) [7 (link)] for superposition of tubulin and the Ndc80 head domain (H. sapiens residues 110–202). Next, we placed a composite model of two AF2 predictions, comprising sequence from Ndc80 : Nuf2 just before the hinge all the way to the Spc24 : Spc25 head domains (Ndc80^413–691, Nuf2^252–451, Spc25^1–89, Spc25^1–83; and Ndc80^619–691, Nuf2^404–451, Spc24^1–213, Spc25^1–221) with a hinge angle such that the coiled-coils of Ndc80 : Nuf2 (after the hinge) and Spc24 : Spc25 were approximately parallel to the microtubule axis. Finally, we re-modelled the hinge residues in plausible conformation using RosettaRemodel [67 (link)].
For the DASH/Dam1c, we manually placed one heterodecamer of the S. cerevisiae full-length AF2 prediction, including only the well-structured regions of the core complex with high confidence scores (Ask1^2–69, Dad1^14–73, Dad2^{2–85, 116–133}, Dad3^6–94, Dad4^2–72, Dam1^54–162, Duo1^61–180, Hsk3^2–69, Spc19^2–106, Spc34^{2–118,157–264}), into the cryoEM map of a DASH/Dam1c ring assembled around a MT [68 (link)] (note that the deposited map, EMD-5254, has the wrong hand and needs to be inverted), followed by rigid-body fitting with phenix.real_space_refine [69 (link)]. The full-length complex was then placed on the fitted core complex and 17-fold rotationally expanded around the MT axis. The whole DASH/Dam1c ring was then rotated around and translated along the MT axis such that interaction C [1 (link),19 (link)] between the protrusion domain of one DASH/Dam1c heterodecamer and the MT-bound Ndc80c could be established. This juxtaposed Thr199 of Spc34, the residue that is phosphorylated by Ipl1 and regulates interaction C [19 (link)], and residue 583 of Ndc80, the position of a five amino acid mutation (insertion) that abrogates interaction C [1 (link)]. It also allows for establishment of the interaction between Spc19 residues 128–165 and Nuf2 residues 399–429 [70 (link)]. The C termini of Spc19 and Sp34 form a coiled-coil at the tip of the DASH/Dam1c protrusion domain, which was not observed in the cryoEM reconstruction of the C. thermophilum DASH/Dam1c complex (because of its flexible attachment) but was inferred from sequence analysis [16 (link)]; AF2 also predicts it now. We used HADDOCK 2.4 [71 (link)] to dock the C-terminal Spc19 : Spc34 coiled-coil onto Ndc80 : Nuf2 and re-modelled the residues that connect it to the protrusion domain with RosettaRemodel [67 (link)]. The model of the DASH/Dam1c ring shown in figure 5 contains the following residues for each subunit: Ask1^1–70, Dad1^15–77, Dad2^{1–73, 119–133}, Dad3^{6–35, 49–94}, Dad4^3–70, Dam1^53–156, Duo1^58–179, Hsk3^3–66, Spc19^1–165, Spc34^1–295. We added the C-terminal Dam1 segment (residues 254–270, 290–305) from the crystal structure determined here by superposition of the Ndc80 head domains.

Multiple sequence alignment of Atp19 and Mco10 was performed using ClustalOmega^{54 (link)}. Hydropathy plots were generated by ProtScale on the ExPASy Server using Kate and Doolittle for predicted proteins of S. cerevisiae. Homology modelling of the ATP synthase complex was based on the atomic model built in the cryo-electron microscopy density map of S. cerevisiae ATP synthase, PDB: 6B8H^{6 (link)}, and Alphafold2 predicted structures of subunits in S. cerevisiae^{55 (link),56 (link)}. Structures of the homologs of Mco10 and Atp19 in Candida albicans and Pichia angusta were analyzed using the available structures in Alphafold2 database and also verified using ColabFold which offers an accelerated protein structure predictions by combining MMseqs2 with AlphaFold2 or RoseTTAFold⁵⁷ . Structural visualization was carried out using PyMOL software.