3D Helix Reconstruction from Cryo-Electron Micrographs

After an initial estimation of the helix pitch in the TORC1 filaments, we performed a large range search for the number of units per turn to establish the full helix symmetry parameters, as follows. Several 678 Å wide and at least 2300 Å long sections in the images of TORC1 filaments were extracted using e2helixboxer.py in EMAN2 package³⁸, after aligning the filament axis with the y-axis of the micrograph. Those segments were then padded and floated into a 4628 * 4628 Å box (2048*2048 pixel) and the computed Fourier transform (FT) examined. Bshow in Bsoft package was used to measure the positions of and the amplitude maxima in the visible layer lines. Although an unambiguous assignment of Bessel order was not possible for most layer lines using an approximate diameter of 560 Å for the filaments, a Bessel function of order 1 at ~1/215 Å and order 2 at ~1/107 Å was indicated, corresponding to a pitch of ~215 Å for a TORC1 helix with no symmetry parallel to the helix axis. Further refinement of helix symmetry parameters was carried out using an iterative helical real space reconstruction approach (IHRSR)³⁹ and the final 3D structure was determined using SPRING⁴⁰. For this purpose, 4352 segments of 1024*1024 Å size were excised using a regular step size of 50 Å and the images were corrected for the effect of CTF determined by using CTFFIND3⁴¹.

Using a pitch of 215 Å as a starting value and a solid cylinder of 560 Å in diameter as a starting model, a set of 30 cycles IHRSR refinement was carried out wherein the number of subunits was varied from 5.1 to 7.9 in steps of 0.1. For each initial symmetry choice, the symmetry parameters were refined with the hsearch program using a step size of 0.01 Å and 0.01° for helical rise and azimuthal rotation respectively for iterations 2 to 15. For cycles 16 to 30, the steps were increased to 0.02 Å and 0.02° in order to increase the radius of convergence. The refinement of the symmetry parameters was monitored, and the convergence points analyzed given that ambiguities between certain sets of helical parameters are possible⁴⁰ (Extended Data Figure 8a). For each of the different possible solutions of refined symmetry, we carried out a 3D structure refinement using the segrefined3d module in SPRING, and visually inspected the reconstructions using Chimera ⁴². The comparison of the density corresponding to one subunit and the known isolated mTORC1 structure⁴³, established the correct set of helical parameters (Figure 3).

Fitting of the atomic model of mTORC1⁴³ in the reconstruction was done in Chimera, either as a rigid body, or by fitting the individual domains. For the latter, the sequential fitting command after including 5 symmetry-related neighboring TORC1 complexes was used to take into account the inter-subunit interfaces. After fitting, the domains corresponding to the central subunit were combined in a new model used for making figures in Chimera (Figure 3). To get a better insight into the docking precision, the variation of the correlation upon rotation of the rigid body model around its principal axes of inertia was plotted using the software VEDA (http://www.ibs.fr/research/research-groups/methods-and-electron-microscopy-group/schoehn-team/methodology/modeling-interpretation-of-em-maps/article/veda), the graphical version of URO⁴⁴.