Central European Institute of Technology BRNO | CZECH REPUBLIC Single-particle reconstruction With an emphasis on Random Conical Tilt in SPIDER March 9th, 2015 european union european regional development fund investing in your future OP Research and Development for Innovation What information do we need for 3D reconstruction? 1. different orientations 2. known orientations J^CEITEC What happens when we don't have enough views? What happens when we're missing views? sparse sampling missing sparse missing good views sampling views Baumeister et al. (1999), Trends in Cell Biol., 9: 81-5. Your sample isn't guaranteed to adopt different orientations, in which case you many need to explicitly tilt the microscope stage. (more later...) What information do we need for 3D reconstruction? 1. different orientations |2. known orientations J^CEITEC Required orientation parameters Two translational: ■ Ax ■ Ay Three orientational (Euler angles): ■ phi (about z axis) ■ theta (about y) ■ psi (about new z) From http://www.wadsworth.org/spider_doc/spider/docs/euler.html How do we used those orientation parameters? Now that you know the Euler angles for each image, you can compute a back-projection. J^CEITEC Getting different views: Tomography vs. single-particle Tomography From Ken Downing We have: ■ known orientations ■ different views BUT... <^E= I "TEE CI What happens when we image the sample? Baker et al. (1999) Microbiol. Mol. Biol. Rev. 63: 862 We are destroying the sample as we image it. c^ite Consequences of repeated exposure o 1' o From Ken Downing Accumulated beam damage If number of views is limited, then distortions Solution: Qf)we have manyl identical Inolecules, and if we can determine the orientations, we can use one exposure per molecule and use these images in the reconstruction. "Single-particle reconstruction" What information do we need for 3D reconstruction? 1. different orientations 2. known orientations What information do we need for 3D reconstruction? 1. different orientations 2. known orientations [3. many particles J^CEITEC What happens as we include more particles? n=1 n=4 n=16 n=256 n=1024 n=4096 Signal-to-noise ratio increases with Vn But wait Qf)we have manyl identical tnolecules, and if we can determine the orientations, we can use one exposure per molecule and use these images in the reconstruction. J§§ B B B B H B http://spider.wadsworth.org/spider_doc/spider/docs/techs/classification/tuton A more realistic (but still fake) example I.V.*»: *os * v * * ♦ • e °o o o 0 o o ° o o o o o o o © From Nicolas Boisset Synthetic images of worm hemoglobin Shaikh etal., (2008) Nature Protocols 3: 1941-74. What information do we need for 3D reconstruction? 1. different orientations 2. known orientations 3. many particles J^CEITEC What information do we need for 3D reconstruction? 1. different orientations 2. known orientations 3. many particles [4. identical particles J^CEITEC Now we need to find the orientations for each particle. How to determine orientation? Two scenarios* 1. You have a reference. 2. You don't have a reference. Reference-based alignment You will record the direction of projection (the Euler angles), such that if you encounter an experimental image that resembles a reference projection, you will assign that reference projection's Euler angles to the experimental image. Step 1: Generation of projections of the reference. ^ in - x From Penczek etal. (1994), Ultramicroscopy 53: 251-70. Assumption: reference is similar enough to the sample that it can be used to determine orientation. The extra features helped determine handedness in noisy reconstructions V I V phi=000 theta=0 00 psi=000 phi=000 theta=000 psi=000 : I phi=000 theta=000 psi=000 phi=000 theta=0 00 psi=000 phi=000 theta=000 psi=000 ^^^l ^^^l ^^^l ^^^l phi=000 thet a=0 00 psi=000 phi=000 theta=000 psi=000 phi=000 thet a=0 00 psi=000 phi=000 thet a=0 00 psi=000 phi=000 theta=000 psi=000 theta=0 00 phi=192 thet a=045 psi=000 phi=000 theta=045 psi=000 phi=048 theta=045 psi=000 % phi=016 phi=115 theta=075 theta=075 psi=000 psi=000 phi= = 072 theta=045 psi= = 000 i phi=131 theta=090 psi=000 Reference-based alignment Stack of projections Experimental Stack of rotational CCF's projection ^J^ ^= —k- max $ v /—ascr-\ — I _w 3 Eulerian z 5 x r*s*r\ = _i j \ - CCF an9les i i —*— coeff's From Penczek et al. (1994), Ultramicroscopy 53: 251-70. Steps: 1. Compare the experimental image to all of the reference projections. 2. Find the reference projection with which the experimental image matches best. 3. Assign the Euler angles of that reference projection to the experimental image. 0^EITE be novo reconstruction If we don't have a reference reconstruction, how do we proceed? 1. Common lines 2. Random conical tilt Brief summary of Fourier transforms ■ A Fourier transform is an alternative representation of image or volumetric data. ■ A Fourier transformation is a fully reversible mathematical transformation. Projection theorem (or Central Section Theorem) A central section through the 3D Fourier transform is the Fourier transform of the projection in that direction. J^CEITEC Common lines (or Angular ReConstitution) Summary: ■ A central section through the 3D Fourier transform is the Fourier transform of the projection in that direction ■ Two central sections will intersect along a line through the origin of the 3D Fourier transform ■ With two central sections, there is still one degree of freedom to relate the orientations, but a third projection (i.e., central Section) Will fiX the relative Frank, J. (2006) 3D Electron Microscopy of Macromolecular Assemblies orientations of all three. J^CEITEC Common lines (or Angular ReConstitution) Summary: ■ A central section through the 3D Fourier transform is the Fourier transform of the projection in that direction ■ Two central sections will intersect along a line through the origin of the 3D Fourier transform ■ With two central sections, there is still one degree of freedom to relate the orientations, but a third projection (i.e., central section) will fix the relative orientations of all three. de novo reconstruction If we don't have a reference reconstruction, how do we proceed? 1. Common lines [2. Random conical tilt | Random-conical tilt: Determination of Euler angles /- .jft"^^! Jät triff H in * • * ^# jT^v 45° Tilt • • Ä A at ■ I ♦ " ^Wi^--,-^.=--,.?*:,#'''!:s ^^^^^H • • 0° Tilt This scenario describes a worst case, when there is exactly one orientation in the 0° image. Since the in-plane angle varies, in the tilted image, we have different views available. From Nicolas Boisset Random-conical tilt: Geometry Two images are taken: one at 0° and one tilted at an angle of 45°. ♦ 0 D t> 0 □ tf_* ^pjf* ^8*" □ □ • • □ Radermacher, M., Wagenknecht, T., Verschoor, A. & Frank, J. Three-dimensional reconstruction from a single-exposure, random conical tilt series applied to the 50S ribosomal subunit of Escherichia coli. J Microsc 146, 113-36 (1987). From Nicolas Boisset See movie rct-part1 .avi CIE= ITEC See movie rct-part2.avi One problem though: We can't tilt the stage all the way to 90 degrees. Projection theorem Random-conical tilt: The "missing cone" Representation of the distribution of views, if we display a plane perpendicular to each projection direction The missing information, in the shape of a cone, elongates features in the direction of the cone's axis. spider spi \_^0 □'_/ SPIDER -- COPYRIGHT ,_xXXXx_ HEALTH RESEARCH INC., ALBANY, NY. _xXXXx_ / /xxx\ \ VERSION: UNIX 21.13 ISSUED: 12/16/2013 / \ DATE: 17-SEP-2014 AT 12:44:11 If SPIDER is useful, please cite: Frank J, Radermacher M, Penczek P, Zhu J, Li Y, Ladjadj M, Leith A. SPIDER and WEB: Processing and visualization of images in 3D electron microscopy and related fields. J. Struct. Biol. 1996; 116: 190-199. Results file: results.spi.6 Running : /home/tapu/local/spide r/bin/spide r_linux_mp_intel64 .OPERATION: WI WI .INPUT FILE: testimg testimg testimg (R ) 230 230 CREATED 17-SEP-2014 AT 12:44:04 0 HEADER BYTES: 1840 .OUTPUT FILE: testwin testwin .X S Y DIMENSIONS: 128,128 128 128 testwin (R ) 128 128 CREATED 17-SEP-2014 AT 12:44:59 N HEADER BYTES: 1024 .TOP LEFT COORDINATES: 52,52 52 52 .OPERATION: f Tilt-pair selection p| *k Jkk 19 63 .?0 O O 0 o o o O 0 o o o o File Edit Analysis i § 'V É t -V From Nicolas Boisset Synthetic images of worm hemoglobin Shaikh etal., (2008) Nature Protocols 3: 1941-74. Classification of 0° images O^At Web - A SPIDER image viewer and analyzer COPYRIGHT (c) 1992-2011 Health Research Inc., Menands, NY Worm hemoglobin (phantom data) Worm hemoglobin (side view) IT Central European Institute of Technology Masaryk University Kamenice 753/5 625 00 Brno, Czech Republic www.ceitec.muni.cz | info@ceitec.muni.cz /mi« > I RJI I ^ european jnic w r IIWII ■ european regional development fund OP Research and ~Kti UTLw ji' 1 investing in your future Development for Innovation ^s5f