Lecture 9 Interpretation and optimization of cryo-EM maps 22nd November 2022 Jiri Novacek Content - symmetries - map validation - map interpretation - model building - map improvement Symmetries - regular assemblies of protein oligomers are common in nature - oligomeric protein structures obey certain rules - no mirror symmetry - understanding symmetry rules may prevent incorrect interpretation of the data - presence of symmetry generally facilitates determination of the density map C3 symmetry C4 tetramer C4 symmetry C22 symmetry D4 octamer (Xu et al., Curr Opin Struct Biol 2019) Symmetries Projection Theorem, Euler angles -Acentral section through the 3D Fourier transform is the Fourier transform to the projection in that direction Symmetries Projection Theorem, Euler angles -Acentral section through the 3D Fourier transform is the Fourier transform to the projection in that direction - Images for all possible projection directions are required to obtain structure with homogeneous resolution in all directions Symmetries Projection Theorem, Euler angles -Acentral section through the 3D Fourier transform is the Fourier transform to the projection in that direction - Images for all possible projection directions are required to obtain structure with homogeneous resolution in all directions - Euler angles cp and 9 cover ranges of (0° - 360°) and (-90° - +90°) Z Symmetries Rotational (cyclic) symmetries - one symmetry axis (usually molecules oriented with the symmetry axis alongside z) - Asymmetric unit - the smallest portion of the angular space to which symmetry operation can be applied in order to completely fill the angular space - CI - the most trivial case, no symmetry, cp (0° 360°), 9 (-90° - +90°) Symmetries Rotational (cyclic) symmetries - one symmetry axis (usually molecules oriented with the symmetry axis alongside z) - Asymmetric unit - the smallest portion of the angular space to which symmetry operation can be applied in order to completely fill the angular space - C2 - cp (0° - 180°), 9 (-90° - +90°) - C3 - cp (0° - 120°), 9 (-90° - +90°) - C4 - cp (0° - 90°), 9 (-90° - +90°) - C6 - cp (0° - 60°), 9 (-90° - +90°) (Levy et al., PLoS computational Biology 2006) Symmetries Dihedral symmetries - one n-fold rotational axis and two-fold axis perpendicular to it -Asymmetric unit - D2 - cp (0° -180°), 9 (0° - +90°) - D5 - cp (0° - 72°), 0 (0° - +90°) - D7 - cp (0° - -51°), 9 (0° - +90°) (Levy et al., PLoS computational Biology 2006) Symmetries Platonic symmetries - faces, edges, and corners are related by symmetry operations - tetrahedral - 4 3-fold axes and 3 2-fold axes - octahedral - 3 4-fold axes of symmetry, 4 3-fold axes of symmetry, and 6 2-fold axes - icosahedral - 6 5-fold, 10 3-fold and 15 2-fold axes Symmetries Platonic symmetries - faces, edges, and corners are related by symmetry operations - tetrahedral - 4 3-fold axes and 3 2-fold axes - octahedral - 3 4-fold axes of symmetry, 4 3-fold axes of symmetry, and 6 2-fold axes - icosahedral - 6 5-fold, 10 3-fold and 15 2-fold axes EMAN2 Symmetries Helical symmetry -Asingle view contains all the necessary info for 3D reconstruction - 2D surface lattice rolled into 3D - 3D reconstruction approaches: - Fourier-Bessel analysis - Iterative Real-Space Refinement (IHRSR) Symmetries Helical symmetry - A single view contains all the necessary info for 3D reconstruction - 2D surface lattice rolled into 3D - 3D reconstruction approaches: - Fourier-Bessel analysis - Iterative Real-Space Refinement (IHRSR) ■ • • ■ ■ • • ■ • • •»* * I • • ■ - ■ - small inaccuracies in indexing lead to incorrect structure - requires strict helical symmetry - requires flat straight helices - laborious Symmetries Helical symmetry - A single view contains all the necessary info for 3D reconstruction - 2D surface lattice rolled into 3D - 3D reconstruction approaches: - Fourier-Bessel analysis - Iterative Real-Space Refinement (IHRSR) El II 11 11 11 2D Templates Systematically generated reference projections nö: next iteration - requires fairly good estimate of the cylinder diameter, rise, and twist - can cope with heterogeneous data - manages to reconstruct weakly diffracting filaments (where layer lines are not visible) (Behnnann et al., J Struct Biol 2012) Projection Matching Orientation parameters: shifts and Euler angles 3D Reconstruction (optional point symmetry) Structure without helical symmetry Symmetry Search Helical symmetry parameters iA;£> 4.5Aand better: de novo CA tracing and model building Baker et al. Structure 2007 Pathwalker Model Baker et al. Structure 2012 - programs: SSEhunter, SSEtracer, Ematch, Pathwalker, Coot, Buccaneer, EM-fold, Rosseta, Phenix, ARP/wARP, MAINMAST Map interpretation known component structure —[segmentation]- 10-20A Fit known structures Fold assignment from sequence No template found Yes Template-free' modelling Homology modelling 1 ?Resolution? 4-10A ) C i Sec. str. assign. I Sec. Str. Sequence assignment Rigid body fit J fit different from map Multiple conformations EMN/NMA Real-space methods MD-based methods <4A Model building Map interpretation Fold recognition from sequence GFCHIKAYTRLIMVG. Template-free Template-based Ab initio (de novo) prediction Fragment Assembly Evolutionary Couplings Threading Comparative (Homology) Modelling programs: MODELLER, SWISS-MODEL, Phyre2, RaptorX, l-TASSER, Rosetta, EVfold Map interpretation Villa & Lasker, Curr Opin Struct Biol, 2014, Cassidy et al, Curr Opin Microbiology 2018 Map interpretation Density fitting - manual fitting - positioning of the atomic structure into the cryo-EM density using visualization programs - usually efficient (human brain efficient in pattern recognition) - direct feedback - good for initial placement of the component in to the map - high level of subjectivity may lead to errors - depends on contour level at which the map is visualized - conformational rearangements cannot be modelled Map interpretation Density fitting - automated fitting - requires common representation of both the structure and the density map - measure of the quality of the fit - optimization protocol for fit improvement Density map Component atomic structure Component representation and placement Optimisation based on goodness-of-fit Map interpretation Problems of density fitting - limited resolution - many local optima with similar numerical values at low resolution - local resolution, noise, scaling, filtering, masking - blurring of the atomic structure - better resolution - improve scoring for goodness-of-fit - coarse-graining (change represenation) - fit/model validation Map interpretation Problems of density fitting - conformational variability - many Iconformations which are observed in density maps deviate from the conformations of the atomic models which are fitted dynamics crystal packing effects errors in structure prediction - allow for the conformational changes during model fitting process = flexible fitting Map interpretation Model refinement - without any restraints a model may fit well with a high score in near-atomic to low resolution density - such a model will, however, not have standard protein geometry: backbone torsions (Ramachandran diagram), peptide planarity, chirality (trans/cis), bond lengths and angles, side chain torsions / rotamers - refinement methods try to maintain standard geometry while fitting the model into the density map. The geometry restraints reduce the levels of freedom. - map density contributes as an additional penalty in the scoring function Programs: MDFF, Refmac, Rosetta, Coot, Phenix, Isolde, iMODFIT Map interpretation Model validation Model fit Model geometry peptide planarity backbone torsions (Ramachandran) bond lengths bond angles side chain rotamers v1' ••; *c Molprobity: http://molprobity.biochem.duke.edu/ What check: http://swift.cmbi.ru.nl/gv/whatcheck/ PROCHECK: http://www.ebi.ac.uk/thornton-srv/software/PROCHECK/ Map improvement - in order to facilitate map interpretation, the data processing should correct for the imperfections of the imaging system to the highest possible level - these imperfections comprise: - aberrations of microscope optical system (higher-order) - sample drift and distortions caused by interaction of the electrons with a matter - the effect is primarily pronounced at high frequencies (resolution) - parameter optimization and additional data processing primarily concerns improving the quality of high resolution maps (<4.5A resolution) - the effect on medium and low resolution (>8A) is limited and additional data processing usually does not result in any map improvement Map improvement Electron lens aberrations - objective lens of the transmission electron microscope is really bad 2.2: Description of aberration constants to 6th order W(k) =m{A0Ak B(k) =exp ' In A0 Lateral image shift Ai Two-fold astigmatism Ci Defocus A2 Three-fold astigmatism B2 Axial coma A3 Four-fold astigmatism Axial star aberration c3 = cs Spherical aberration A4 Five-fold astigmatism D4 Three-lobe aberration B4 Fourth-order axial coma A5 Six-fold astigmatism s5 Fifth-order star aberration Cg Fifth-order spherical aberrat R5 Fifth-order rosette aberratioi + iA1A2k*2+ic1A2k*k + ;U2A3k*3 + iB2A3k*2k 3 3 + ^A3A4k*4 + is3A4k*3k + ^C3A4k*2k2 + ;U4A5k*5 + ^D4A5k*4k + ir34A5k*3k2 5 5 5 + yA5A6k*6 + ^S5A6k*4k2 + ^C5A6k*3k3 + 6 6 6 1 R5A6k*5k Map improvement Zernike polynomials - complete set of orthogonal functions - Zernike transform analogous to Fourier transform - can be used to visualize lens aberrations - the aberrations can be corrected for by introducing additional lens to the microscope or by software during the image processing -z." -z; Z a --Z a ♦ t v. II Z/4 Frits Zernike, 1953 Nobel Prize in Physics inventor of phase contrast microscopy -2f>K _Zrf3 ^JT1 Map improvement Lens aberrations 0.2 0.3 Spatial frequency 0.5 - 200nm error in defocus estimation (1.2um instead of l.Oum) 0.2 0.3 Spatial frequency 0.5 iDefocus z\ J3 ^-^3 - CA z{2 vlzj z\ > -Z^ V -zrA -zi;* -Jr1 zl Z\ 11 3 \ 7;' Map improvement Lens aberrations Original Compromise aio aio Horizontal Focus Vertical Focus aio aio Map improvement Lens aberrations - certain level of underfocus is necessary during cryo-EM data collection - corrected during CTF correction - astigmatism can be eliminated to high extent by proper microscope alignment - only aberrations which are relevant for the quality of medium and low resolution maps - correct estimation of CTF parameters (defocus,astigmatism) - quality control - goodness of fit Astigmatism ( iDefocus z\ J,A--^3 a Z'a ^"«.----Z a Z/4 n J4 -2f>K -ZZ" ^JT1 Z, I i 3 \ 7r' Map improvement Map improvement Lens aberrations - dependence on fourth power of the frequency - lens is stronger off axis, plane of least confusion - considered constant for microscope, furjtier optimization in software possible Spherical aberration Lens Cs = 0 Plane of least confusion Disk diameter = Csfi3 Map improvement Sample distorsions during imaging - local motion different in distinct parts of the image Compare particle in each frame to sum of frames D 5M 10W 1HH 2000 2500 3000 S5O0 x-position (pixels) n Compare particle in each frame Compare patch from each frame to map to sum of frames ^rr . ■■■■■■ 7™—[j. ■'" ■— ■ ■' .■ ' '' w ''. Alignpartsjmbfgs (Rubinstein & Brubaker, Relion Polishing (Scheres, 2014, MotionCor2 (Zheng...Agard, 2015, JSB 192, 188-95) eLife 3:e03665) 2017, Nat Meth 14, 331-2) [improved version in cryoSPARC ver 2] [improved version with Alignparts-like smoothing in Bayesian polishing] -1» -8 -6 -4 -2 0 ; Map improvement Sample distorsions during imaging - the information in each frame is damped by different B-factor due to distinct effects during data collection - compensation for local motion (per particle) + per frame amplitude weighting with corresponding B-factor => particle polishing -400 1-■-1-■-1-1-1-1-1-1-1 0 5 10 15 20 25 Electron fluence (e~/A2) Map improvement Sample distorsions during imaging - distortion of sample surface due to illumination with electron beam - particles located in different depth of the specimen layer - defocus variance for particles within single micrograph - per particle defocus (astigmatism) estimation = ctf refinement 3B4t Apoferritirt (0.5 mg/mL) 39 CI Apoferntin with 0.5 mM TCEP 40 Protein with Carbon Over Hol&s 41 Protein and DNA Strands with Carbon Over Holes 42" T20S Proteasome Noble etaleLife2018 Map improvement a Ewald sphere correction - the assumption that the image is 2D projection of the 3D object does not hold for thick specimens - wave-function at the image plane samples surface of the sphere in 3D FT of the object - Friedel symmetry is lost - depends on electron wavelength - stronger effect (more important to consider) for lOOkeV than for 300keV o o co rap ,«s (SMS> incident beam -single particle specimen diffracted beams «— t'is ^diffraction plane - «—underfocus B '- - 4r- u nde rtdcu s A <^in-facus image A in image AafterCTFP AafterCTFCr Ewald sphere 2Az' Russo & Henderson (2018), Ultramicroscopy