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1. Micrograph tools 5 Particle Se Local average search ocal variance search DER Con maki EL Particle set tools 3D Density tools Jobs Figure 6 Cyclops has a friendly graphic user interface GUL and plug in architecture The new algorithms for carbon masking and uniform sampling of rotation space applied in model based particle searching are marked by green ellipses In the sub window of micrograph the black area is the result of automated carbon masking blue boxes indicate selected particles which are segmented and shown in the sub window of particles gallery below The new algorithms were written in C Python They communicate with Cyclops through XML files The XML file describes the input and the type of output it produces e g a new particle set An XML file example of automated carbon masker lt CyclopsPlugin gt lt module gt Carbon masker lt module gt 36 Automated carbon masking and particle picking lt category gt Micrograph lt category gt lt program gt T Mmicromasker exe lt program gt lt input gt lt label gt Inputfile lt label gt lt type gt micrograph lt type gt lt nr gt multiple lt nr gt lt input gt lt output gt lt type gt mask lt type gt lt nr gt mutliple lt nr gt lt output gt lt CyclopsPlugin gt The information of the XML file is used to construct an input dialog window shown in Fig 7 A simple wrapper of Cyclops
2. and the mosaic Threshold are required Selecting the correct parameters for MosaicType and mosaic Threshold can be critical for the program to find the correct orientation The program samples all different tilt orientations based on the orientation and indices of V1 amp V2 and selects the best fit between the simulated and the observed diffraction pattern In RF2 the rocking curve or spike function of the reflections is not considered In RF3 The difference between RF and RF3 is spike function of a reflection is considered in RF3 an elongation in reciprocal space of a reflection is simulated The most meaningful MosaicType is 3 for RF3 although you could try selecting mosaic type 1 or 2 there is no error message MosaicType 3 indicates a lengthwise elongation of the diffraction spot in a principal direction of the lattice its default threshold value is 0 05 See section 6 7 for an explanation of the various mosaic types For inorganic materials that have crisp diffraction patterns RefineOrient and RF2 will be fine for reasonable indexing For the crystals with a large unit cell e g the protein nano crystals the reflection spots can be elongated along the unit cell edge direction normal to the plane of the crystal In this case RF3 is a wise choice 3 Potential orientations found by RefineOrient RF2 or RF3 are stored in a list of rotat
3. single particle reconstruction Chapter 5 presents a novel algorithm for 3D unit cell determination using randomly oriented electron diffraction patterns Unit cell determination is important because it is the first step towards the structure solution of an unknown crystal form Most of the current unit cell determination methods use tilt series in which the angular relationship between the diffraction patterns is known Our method uses single diffraction patterns 142 from multiple crystals each with unknown orientation The significance of our method is that for beam sensitive protein nano crystals more exposures in the same place burns the crystals Thus single diffraction patterns from multiple crystals are the only data that we can get The new algorithm searches the best matching unit cell parameters through checking all possible combinations of parameters To accomplish the search task two data sets are utilized One data set contains the observed electron diffraction patterns the other data set contains the simulated electron diffraction patterns from all potential unit cell models A target function evaluates the similarity between these two data sets The model with the smallest error is selected Chapter 6 gives a detailed tutorial of the EDiff software which implements the new algorithms described in Chapter 5 This chapter is not only limited to teaching the use of EDiff but also discusses new problems and solutions in unit cell
4. Fourier Shell Correlation Threshold Criteria J Struct Biol 151 250 262 Velazquez Muriel J A Sorzano C O S Fernandez J J Carazo J M 2003 A method for estimating the CTF in electron microscopy based on ARMA models and parameter adjusting Ultramicroscopy 96 17 35 Wan Y Chiu W Zhou Z H 2004 Full contrast transfer function correction in 3D cryo EM reconstruction International Conference on Communications Circuits and Systems ICCCAS 2004 June 2004 Zhou Z H Hardt S Wang B Sherman M B Jakana J Chiu W 1996 CTF determination of images of ice embedded single particles using a graphics interface J Struct Biol 116 216 222 Zhou Z H 2008 Towards atomic resolution structural determination by single particle cryo electron microscopy Curr Opin Struc Biol 18 218 228 Zhu J Penczek P A Schr der R Frank J 1997 Three dimensional reconstruction with contrast transfer function correction from energy filtered cryoelectron micrographs procedure and application to the 70S Escherichia coli ribosome J Struct Biol 118 197 219 Zubelli J P Marabini R Sorzano C O S Herman G T 2003 Three dimensional reconstruction by Chahine s method from electron microscopic projections corrupted by instrumental aberrations Inverse Probl 19 933 949 66 Chapter 4 Reconstruction of the complexes of the ribosomal large subunit 50S with Hsp15 and t RNA reveals the rescue mechanism
5. Jiang L Abrahams JP 2007 Cyclops New modular software suite for cryo EM J Struct Biol 157 19 27 Rawat UBS Zavialov AV Sengupta J Valle M Grassucci RA Linde J Vestergaard B Ehrenberg M Frank J 2003 A ecryo electron microscopic study of ribosome bound termination factor RF2 Nature 421 87 90 Richmond CS Glasner JD Mau R Jin H Blattner FR 1999 Genome wide expression profiling in Escherichia coli K 12 Nucleic Acids Res 27 3821 3835 Schaffitzel C amp Ban N 2007 Generation of ribosome nascent chain complexes for structural and functional studies J Struct Biol 158 463 471 Schliinzen F Zarivach R Harms J Bashan A Tocilj A Albrecht R Yonath A Franceschi F 2001 Structural basis for the interaction of antibiotics with the peptidyl transferase centre in eubacteria Nature 413 814 821 Schmitt E Mechulam Y Fromant M Plateau P Blanquet S 1997 Crystal structure at 1 2 A resolution and active site mapping of Escherichia coli peptidyl tRNA hydrolase EMBO J 16 4760 4769 Schuwirth BS Borovinskaya MA Hau CW Zhang W Vila Sanjurjo A Holton JM Cate JHD 2005 Structures of the bacterial ribosome at 3 5 angstrom resolution Science 310 827 834 Staker BL Korber P Bardwell JCA Saper MA 2000 Structure of Hsp15 reveals a novel RNA binding motif EMBO J 19 749 757 Stark H Orlova EV Rinke Appel J Junke N Mueller F Rodnina M 1997 89 Chapter 4 Arrangement of tRNAs in pre and
6. Towards atomic resolution structural determination by single particle cryo electron microscopy Curr Opin Struc Biol 18 218 228 19 Chapter 1 20 Chapter 2 Automated carbon masking and particle picking in data preparation for single particles Adapted from Plaisier J R Jiang L Abrahams J P 2007 Cyclops New modular software suite for cryo EM J Struct Biol 157 19 27 Abstract Two new algorithms automated carbon masking and quaternion based rotation space sampling for automated particle picking are presented here They are implemented as plug ins in the Cyclops software suite and are intended for data preparation for 3D single particle reconstruction Cyclops is a new computer program designed as a graphical front end that allows easy control and interaction with tasks and programs for 3D reconstruction Automating a particle search needs an algorithm that finds out where in the image the search has to be done Normally only the particles in the holes circular or irregular of the carbon layer are of use Currently no other automatic carbon masking algorithm for EM image processing exists Traditional edge detection and segmentation algorithms do not work due to the extremely high noise in cryo EM images The new masking algorithm is based on the relatively high variance within carbon regions and gives good results A quaternion is a 4D number that can be used to represent and manipulate rotations in 3D space
7. between the two new objects that are generated by rotating an object using either ql or with q2 respectively cos A 2 2 1 qi qo 2 3 Hence the problem of uniformly sampling 3D rotations is reduced to the more straightforward task of uniformly sampling the 4D hypersphere of unit quaternions In other words we need to uniformly distribute the quaternions over the hypersurface When done uniformly the nearest neighbor distance can substitute qi q2 in Eq 3 establishing its association with A the precision of sampling Platonic solids also exist in 4D space where beasts like the hexacosichoron live which has 1200 triangular faces and 120 legs vertices Similar to sub sampling 3D platonic solids which can generate better spherical approximations like the soccer ball 4D platonic solids can also be sub sampled if a higher precision is required Yershova and LaValle 2004 Fig 2 shows a polar representation of 5880 rotations generated by subsampling the hexacosichoron The angular distance between the rotations is about 7 59 For comparison naive Euler sampling of rotational space with a similar angular distance yields 53 088 rotations 28 Automated carbon masking and particle picking z axis x axis Figure 2 Polar representation of 5880 sampled rotation quaternions using subsampling of the 4D hexacosichoron Green points represent the viewing directions whereas the red bars indicate the in plane rota
8. it s not a correct simulation 124 User manual of EDiff 8 ShowSimu show the simulated lattice as small blue circles by tiling the main facet 9 ShowV1V2 show in red labels V1 and V2 in the image 10 ResetV1 reset the main vector V1 spot in the image V1 or V2 will be automatically switched if the length of V1 is larger than V2 11 ResetV2 reset the main vector V2 spot in the image 20 Refine use all the spots on a single line or a multi regression method if option regression 24 is selected to recalculate the V1 and V2 the operation makes V1 and V2 fit the image better and their coordinates can now be non integer pixel multiples 21 All Refine all the images not only current one 24 Use the multi regression method to for Refine and refine All 12 amp 13 Save V1V2 In order to validate the main facets vectors selected here the user has to save the main vectors by clicking the Save V1V2 button or Save As a V1 V2 file 14 Close this window 20 21 amp 24 are optional tools while 22 23 27 29 are only used in the Brightest Spots Matching method 6 6 Unit cell Determination One of the main functions of EDiff is to determine the unit cell of nano crystals from the randomly oriented electron diffraction data Our algorithm is based on matching the observed crystal facets to model facets extracted from a simulated 3D lattice or a detailed descripti
9. memory available which allows a maximum of 50 figure windows to be open simultaneously If you have a lot of images in one directory make sure you have disabled the option of figure output To work efficiently it is advised to work with electron diffraction data sets that all have been recorded in the same session For a quick test do not save any autocorrelation maps or plt files just yet because this option extends the running time by roughly one 113 Chapter 6 minute Removing the background can still go wrong so a user should only enable the option Removed beamstop to see the results of one single image If one is satisfied the user can proceed by enabling the autocorrelation map and show plt output When this output is reasonable as well the user can disable all figure outputs and process all images of the data set in a single run 6 3 3 Output Data of the Pre processing Program AMP This program calculates autocorrelation images and extracts peak positions from diffraction patterns and their corresponding autocorrelation images Four output files of each EM image are generated e lt image name gt atc plt the peaks positions of autocorrelation map e lt image name gt atc jpg the autocorrelation map e lt image name gt ctr pks the peak positions of centered background removed diffraction image e lt image name gt ctr png the centered background removed diffraction image It is good
10. size and the new technique of precession of the electron beam were used to reduce dynamic scatter to acquire the electron diffraction patterns e g Figure 3B In the current practice in electron diffraction a single nano crystal must be selected in image TEM mode and then the microscope must be switched to diffraction mode This is not possible in X ray diffraction limiting this technique to the study of the micro crystals or powders of nanocrystals Another apparent advantage of using nano crystals is it is much easier to grow nano crystals than to obtain micro crystals with micrometer scale size Georgieva et al 2007 In high resolution 3D EM single particle reconstruction crystals are not necessary Particles embedded in vitreous ice can have random orientations and arrangements Very small amounts of sample are required for a 3D reconstruction compared to the amount required for growing a crystal Besides in 3DEM structural homogeneity or integrity is more important than purity as opposed to X ray crystallography and NMR in which sample purity is essential Zhou 2008 Generally speaking both different experimental and computational methods have their advantages and disadvantages Advantages of X ray crystallography method Well established techniques and software Highest atomic resolution structure achieved Disadvantages of X ray crystallography method Difficult to grow crystals Single conformation or bindin
11. the image measured in TEM normally can be described in Fourier space as a function of the spatial frequency vector s by 42 A novel method of CTF correction M s CTF s F s N s 1 M s is the Fourier transform of the measured image CTF s is the contrast transfer function which we assume here to be radially symmetrical CTF s can be further described as consisting of two parts C s and E s that is CTF s C s E s E s is the envelope function essentially the Fourier transform of the image of the extended source in the back focal plane of the imaging system the phase variable part C s is sometimes confusingly also called contrast transfer function The CTF essentially is a dampened oscillating real function that passes through zero many times F s is the structure factor assuming the kinematic approximation Frank 1996 and N s is Fourier transform of the detector readout and quantum noise Strictly speaking F s has a random component too caused by disordered solvent density This term is usually ignored as it is subject to the same corrections as the structure factors corresponding to ordered density Estimation procedures determine the parameters of the functions CTF s and N s to optimally fit the observed power spectral curve of rotation average of M s Different researchers may use different denotations for the frequency variable s for example f k etc Here we use s uniformly The detailed formulation of t
12. 2 Results 4 2 1 Generation of stable 50Senc tRNA complexes Stable homogenous 70Senc tRNA complexes were generated by in vitro transcription and in vitro translation using the plasmid pUC19Strep3FtsQSecM with an N terminal triple Strep tag for affinity purification Schaffitzel amp Ban 2007 To span the ribosomal exit tunnel the FtsQ sequence and the 17 amino acids long SecM translational arrest motif were C terminally fused to the affinity tag The SecM peptide interacts tightly with the ribosomal tunnel Nakatogawa amp Ito 2002 and thereby significantly stabilizes the 70Senc tRNA complexes without the need of using chloramphenicol antibiotic After in vitro translation the translating ribosomes were loaded onto a sucrose gradient with low concentration of magnesium ions causing dissociation of the 70Senc tRNA complexes into 50Senc tRNA and 30S Figure 2A complexes The 50Senc tRNA complexes were further purified and separated from empty 50S using a Strep Tactin sepharose column and finally pelleted by ultracentrifugation The complex with Hsp15 was reconstituted by adding a 20 fold molar excess of Hsp15 Binding assays confirmed that Hsp15 neither binds 70S ribosomes nor empty 50S subunits under the assay conditions Figure 2B However lower affinity binding to the empty 50S subunit was observed when the sucrose cushion was omitted from the sedimentation assay not shown This is in agreement with the previously described non spe
13. 4 size by averaging 2 2 boxes which decreased the resolution to 2 54 A pixel See Figure S1 for an example of some selected particles We used focal pair images for reconstructing the 50Senc tRNA Hsp15 and 50Senc tRNA complexes Each defocus pair of micrographs was aligned by refining shift rotation and scaling parameters prior to selecting the particles Using Cyclops we selected particles in the far from focus micrographs and mapped the coordinates to the corresponding close to focus micrographs Obvious noise and ice images were filtered from the model based auto selected images using Cyclops Before reconstruction we merged the large defocus and close to focus images The particle projections were limited to 128 128 pixels covering 325 325 A Except for the reconstruction of the free 50S subunit the defocus was corrected with the CTFIT program of EMAN Ludtke et al 1999 For free 50S subunit no CTF correction was applied all the images were low pass filtered at the first zero crossing of the CTF and no starting model was used The first 3D model of 50S was reconstructed with the startAny program of EMAN Ludtke et al 1999 from a set of class averages using cross common lines The reconstruction of the complex converged only slowly because of the low signal to noise ratio resulting from the low dose conditions In order to speed up convergence we used our cryo EM structure of the 50S subunit with a resolution of 22 A a
14. A site where it cannot be cleaved by puromycin A S50Senc tRNA Hsp15 SOSenc tRNA a mn a e netRNA X 2 Released gt En nascent chain En 0 l 2 3 4 0 l 2 3 4 77 Chapter 4 B 0 2 5 p 12 mM Mg g 0 15 4 2 100 mM Mg S X 0 1 35 A 12 mM Mg no e z m puromycin S 0 05 4 a A 100 mM Mg no 5 m puromycin 7 A 5 0 A 0 1 2 3 4 hours Figure 7 A Puromycin reaction of 50S nc tRNA Hsp15 at 37 C in 12 mM left and 100 mM Mg right Controls without puromycin do not show any cleavage of the ester bond between tRNA and nascent chain even after 3 h of incubation At the outset of the reaction there is already a substantial amount of released nascent chain present lower band B The negative natural logarithm of the remaining nc tRNA was plotted against the incubation time In a first order reaction this is expected to be a straight line which we indeed observed for 2 3 h after initiating the reaction The data shown in A are plotted The puromycin induced cleavage of nc tRNA was determined by measuring the increase of the intensity of the band corresponding to the released nascent chain as a fraction of the total intensity corresponding to the nascent chain whether bound to tRNA or not The higher reactivity at 12 mM Mg can be explained by the fixation of tRNA at the P site by Hs
15. Dowse H 1981 SPIDER a modular software system for electron image processing Ultramicroscopy 6 343 358 Frank J Penczek P 1995 On the correction of the contrast function in biological electron microscopy Optik 98 125 129 Frank J Radermacher M Penczek P Zhu J Li Y Ladjadj M Leith A 1996 SPIDER and WEB Processing and Visualization of Images in 3D Electron Microscopy and Related Fields J Structural Biol 116 190 199 Frank J 1996 Three Dimensional Electron Microscopy of Macromolecular Assemblies Academic Press San Diego Gonzalez R Woods R Eddins S 2003 Digital Image Processing Using Matlab Prentice Hall Grigorieff N 2007 FREALIGN High resolution refinement of single particle structures J Struct Biol 157 117 125 Hanszen K J 1971 The optical transfer theory of the electron microscope fundamental principles and applications Adv Opt Elec Microsc R Barer amp V 63 Chapter 3 E Cosslett eds 4 1 84 Hartl F U 1996 Molecular chaperones in cellular protein folding Nature 381 571 579 Huang Z Baldwin P R Penczek P A 2003 Automated determination of parameters describing power spectra of micrograph images in electron microscopy J Struct Biol 144 79 94 Jiang W Chiu W 2001 Web based Simulation for Contrast Transfer Function and Envelope Functions Microsc Microanal 7 329 334 Jiang L Schaffitzel C Bingel Erlenmeyer R Ban N
16. Korber P Koning R I de Geus D C Plaisier J R Abrahams J P 2008 Recycling of Aborted Ribosomal 50S Subunit Nascent Chain tRNA Complexes by the Heat Shock Protein Hsp15 J Mol Biol doi 10 1016 j jmb 2008 10 079 Liang Y Ke E Y Zhou Z H 2002 IMIRS a high resolution 3D reconstruction package integrated with a relational image database J Struct Biol 137 292 304 Ludtke S J Baldwin P R Chiu W 1999 EMAN Semiautomated Software for High Resolution Single Particle Reconstructions J Struct Biol 128 82 97 Ludtke S J Jakana J Song J L Chuang D Chiu W 2001 A 11 5 A single particle reconstruction of GroEL using EMAN J Mol Biol 314 253 262 Ludtke S J Chen D H Song J L Chuang D T Chiu W 2004 Seeing GroEL at 6 A resolution by single particle electron cryomicroscopy Structure 12 1129 1136 Ludtke S J Baker M L Chen D H Song J L Chuang D T Chiu W 2008 De novo backbone trace of GroEL from single particle electron cryomicroscopy Structure 16 3 441 8 Mallick S P Carragher B Potter C S and Kriegman D J 2005 ACE automated CTF estimation Ultramicroscopy 104 8 29 Marabini R Masegosa I M San Martin M C Marco S Fernandez J J de la Fraga L G Vaquerizo C Carazo J M 1996 Xmipp An image processing package for electron microscopy J Struct Biol 116 237 240 Medipix a photon counting pixel detector http medipix web cern ch
17. MEDIPIX Penczek P A Zhu J Schr der R Frank J 1997 Three Dimensional Reconstruction with Contrast Transfer Compensation from Defocus Series Scanning Microscopy 11 147 154 Pettersen E F Goddard T D Huang C C Couch GS Greenblatt D M Meng E C Ferrin T E 2004 UCSF Chimera A Visualization System for Exploratory 64 A novel method of CTF correction Research and Analysis J Comput Chem 25 1605 1612 Plaisier J R Koning R I Koerten H K van Roon A M Thomassen E A J Kuil M E Hendrix J Broennimann C Pannu N S Abrahams J P 2003 Area detectors in structural biology Nuclear Instruments and Methods in Physics Research Section A 509 274 282 Plaisier J R Jiang L Abrahams J P 2007 Cyclops New modular software suite for cryo EM J Struct Biol 157 19 27 Ramachandran G N amp Srinivasan R 1970 Fourier Methods in Crystallography pp 60 71 New York Wiley Sander B Golas M M Stark H 2003 Automatic CTF correction for single particles based upon multivariate statistical analysis of individual power spectra J Struct Biol 142 392 401 Schiske P 1973 Image processing using additional statistical information about the object in P Hawkes Ed Image Processing and Computer aided Design in Electron Optics Academic Press London 82 90 Sorzano C O S Marabini R Velazquez Muriel J Bilbao Castro J R Scheres S H W Carazo J M Pasc
18. aan nano kristallen heeft een software pakket Ediff opgeleverd hoofdstukken 5 en 6 Het programma is gericht op het bepalen van de eenheidscel parameters en de indexering van verkregen diffractogrammen De methode maakt gebruik van losse diffractogrammen verkregen van meerdere kristallen elk met een eigen onbekende ori ntatie Het belang van de methode is dat voor stralingsgevoelige nano kristallen van bio materialen losse diffractogrammen van meerdere kristallen de enige diffractiegegevens zijn die verkregen kunnen worden Meer dan n blootstelling op dezelfde plaats in het preparaat leidt tot overmatige kristal beschadiging 145 Curriculum Vitae Linhua Jiang was born on November 12 1977 in Yongzhou China In 1995 he finished his studies in secondary school and started Computer Science education in Shanghai Jiaotong University China He also studied Economics as a minor subject at Jiaotong University In 1999 he obtained a bachelor degree in Computer Science and a second bachelor degree in Economics After years of work experience as network engineer and software engineer he decided to extend his expertise by studying abroad in an advanced master program of Artificial Intelligence at the Katholieke Universiteit Leuven in Belgium 2003 In 2003 and 2004 the internship in the Multimedia Lab in IMEC Interuniversity MicroElectronics Center Belgium fostered his interests in scientific research Shortly after he received a
19. algorithm was tested with electron diffraction data from random orientations of protein lysozyme organic potassium penicillin G and sodium oxacillin and inorganic mayenite nano crystals Autocorrelation of diffraction pattern Decomposed to unique Facets For every Image find the best matching Facets Calculate residual n gt gt 1 Least_Square_Difference Calculate square difference of the best matching Facets Decomposed to unique Facets Simulated 30 teciprocal cell mn lattice lodet Figure 2 Fora given unit cell a 3D reflection lattice can be calculated For each characteristic facet from the experimental diffraction pattern the corresponding facet in the 3D reflection lattice which fits best is identified The squared distance differences between calculated and experimentally found facets are accumulated in a penalty function 95 Chapter 5 5 2 Methods 5 2 1 Data collection Potassium penicillin G and sodium oxacillin were available as white crystalline powders To obtain thin crystals suitable for EM studies the powder was crushed in a mortar A small amount of the sample was placed on a 300 mesh holey carbon electron microscopy grid Crystals suitable for electron diffraction studies in terms of size thickness and crystallinity were selected Diffraction experiments were performed at cryogenic conditions to increase the stability of the sample in the beam Diffraction
20. allow the resolution to be extended beyond the first zero of the oscillating contrast transfer function CTF Multiple reconstruction software packages were adapted in this fashion to allow constructing high resolution 3D models e g IMAGIC van Heel 1979 amp 1996 SPIDER Frank et al 1981 amp 1996 XMIPP Marabini et al 1996 Sorzano et al 2004a EMAN Ludtke et al 1999 IMIRS Liang et al 2002 and others About seven parameters depending on the CTF model used need to be determined in the CTF estimation for an accurate approximation These parameters are subsequently used in the CTF correction procedure The quality of the final 3DEM model relies on accurate CTF estimation and correction This makes CTF estimation and correction one of the most delicate problems in 3D single particle reconstruction For CTF estimation a number of semi automatic tools are available e g Zhou et al 1996 van Heel et al 2000 Huang et al 2003 Fernandez et al 2006 There are also fully automatic CTF estimation tools based on different methods e g ARMA models of Xmipp Velazquez Muriel et al 2003 ACE Automated CTF Estimation Mallick et al 2005 Automatic CTF estimation based on multivariate statistical analysis Sander et al 2003 Here we describe a new method for correcting images optimally when initial estimates of the CTF parameters are available According to the theory Erickson and Klug 1970 Thon 1971 Hanszen 1971
21. cross correlating the autocorrelation pattern of the diffractogram with the diffractogram 96 Unit cell determination from randomly oriented electron diffraction patterns itself and by making use of the point symmetry of the low resolution reflections the point symmetry is caused by the low curvature of the Ewald sphere The crystal facet describing the lattice of the autocorrelation pattern was determined by locating the two peaks close to the centre ensuring that the angle they defined together with the centre was between 7 2 and 7 3 These two peaks can be located interactively or automatically in our algorithm Visual inspection ensured that the facet indeed correlated to the 2D lattice of the autocorrelation pattern and that it did not correspond to low resolution noise peaks 5 2 3 Simulating a 3D reflection lattice and extracting low resolution model facets Six cell parameters axes a b c and angles a B and y define a primitive cell Using these 6 parameters a systematic set of possible unit cells can be simulated in a grid search of axes and angles Good guesses for the dimensions of the parameters and the step size can be made on the basis of the observed spacings and angles in the experimentally determined crystal facets but we also allow the user to select the search range and step size From a set of cell parameters a reciprocal cell matrix C can be constructed The crystal orientation can be defined by a rotation ma
22. determination For instance there is an assumption in our new algorithm that the diffraction data are randomly oriented However in real life some types of crystals have an orientational preference for instance because they are flat limiting the relative orientation of incident beam to a conical region This means that the collected data is not really randomly oriented These data suffer from a missing cone problem similar to that in EM tomography One parameter of the unit cell may then be missed An improved method which uses brightest spots in searching solves this missing cone problem 143 Samenvatting Titel Beeldbewerking en Gegevensverwerking in relatie tot Structurele Biologie Met behulp van moderne technieken van beeldbewerking en het verwerken van experimentele gegevens kunnen beelden verkregen met cryo EM van bio macromoleculen gereconstrueerd worden tot driedimensionale modellen van sub nanometer resolutie De twee belangrijkste methoden die nu in gebruik zijn zijn 3DEM single particle reconstruction en elektronendiffractie Dit proefschrift is gericht op onderzoek naar betere methoden van 3DEM hoofdstukken 2 4 zowel als elektronendiffractie hoofstukken 5 amp 6 In hoofdstuk 2 worden twee nieuwe algoritmen gepresenteerd geautomatiseerde carbon masking en rotational space sampling gebaseerd op het gebruik van quaternionen Gebruik van deze methodieken bevordert het proces van deeltjes
23. diffraction image is a well oriented pattern and the main facet was correctly found by the program Sometimes the program can t find the correct main facet in which case the user has to set it manually by first choosing ResetV1 or ResetV2 and then double clicking the correct peak cross in the image The selected V1 or V2 will be automatically switched if the length of V1 is larger than V2 There are lots of tricks for making your life easier lt double click left mouse button gt will capture a cross near the place you clicked lt double click middle mouse button gt will locate the exact place that you clicked by pressing lt Ctrl gt at the same time it will try to find a intensity peak near the place you clicked There are more complicated options for advanced users if you press the key lt Shift gt lt Alt gt or lt Ctrl gt when you do lt double click left mouse button gt or lt double click middle mouse button gt on the peaks of the image the 1 2 1 3 or 1 4 position is located relative to the cross that you selected or the point that you clicked You even can combine use the lt Shift gt and lt Alt gt key which will locate 1 6 position When the peaks are not correctly generated by the pre processing program AMP these operations are very useful to help you to manually reset the correct V1 and V2 provided you know what you re doing which requires understanding reciprocal space The user can run CheckData to fin
24. filtered CTF correction algorithm which combines the approximated inverse filter and the weighted average method 53 Chapter 3 MI M2 M3 Figure 4 Reconstructed models of GroEL generated with different CTF correction algorithms M1 Column Left The model obtained by conventional full CTF correction resolution 7 94 M2 Middle The model obtained by the direct CTF deconvolution algorithm 7 0A M3 Right The result of the filtered CTF correction algorithm 8 64 A Top views of three different models B Side views corresponding to A The black dash line boxes indicate subunits for visually comparison C Views zoomed in for the indicated subunits in B 54 A novel method of CTF correction In Figure 4 the result of the direct CTF deconvolution algorithm Middle model M2 shows more detail than the conventional CTF correction algorithm Left model M1 The result of the filtered CTF correction algorithm Right model M3 looks like a low pass filtered model of the normal CTF correction When the approximation deconvolution filter is combined with the normal CTF correction it works more like a selective filter suppressing the noise strongly The result of the direct CTF deconvolution algorithm M2 has the best resolution based on an even odd test and Fourier Shell Correlation FSC Van Heel et al 1986 with a threshold of 0 5 Beckmann et al 1997 7 0 A Table I It should be realized th
25. grid and hence we also collected diffractograms at various random tilt angles to also get more samplings of spacings that preferred to point in the direction normal to the EM grid Overweighting crystals with such rare orientations made the cell determination more robust but in general very similar answers were obtained if we did not include this weighting We do not exclude the possibility that the nano crystals of lysozyme correspond to a new polymorph but it may also be that the algorithm for some reason produces large error up to around 4 for large unit cells Table 2 gives an overview of unit cells of some known polymorphs of lysozyme together with the unit cell produced by our new algorithm Table 2 Representative unit cell parameters of orthorhombic hen egg lysozyme determined by single X ray diffraction first 3 entries and electron diffraction of single nano crystals from a powder sample using the new algorithm Method a A X ray diffraction 1 lwtm 30 43 X ray diffraction 2 1jj1 30 56 X ray diffraction 3 1f10 30 58 Electron diffraction 31 5 52 5 89 3x90 103 Chapter 5 5 4 Discussion and conclusions Our new algorithm for unit cell determination is independent of knowledge about the angular relationship between experimentally determined diffraction patterns It does assume that all diffraction patterns share a similar 3D lattice Because it can deal with a limited number of outlier
26. is no in plane rotation included no red bar indicates the in plane rotation compared with Figure 2 The new algorithm can be applied in model based particle searching in which the projections generated from a starting model and a set of Euler angles are used as references For this searching the in plane rotation is not necessary because the in plane rotation is already included in the procedure 2 3 3 Implementation as plug ins in Cyclops As mentioned above new methods for automated carbon masking and uniform sampling of rotational space have been implemented as plug ins in the Cyclops software Fig 6 Other methods currently implemented as Cyclops plug ins cover a wide range of common image processing techniques such as compression low high and band pass filtering and edge detection Methods previously implemented in the Tyson program Plaisier 2004 for automated selection of particles have now been 35 Chapter 2 re written as Cyclops plug ins The sorting of particles a prominent feature of Tyson is an intrinsic part of the Cyclops program Cyclops0 8 Release Candidate 1 File Edit Project Micrograph Gallery Model View Help Dem 40 Project data ax l fox Job tracker Data Details Micrographs O items S Batch 1 1 micrographs 1 Carbon masker 2260 545 particles Particle sets E 3D models threed 2 Module 2 Carbon masker 3 Local average se General tools
27. leidenuniv nl software Cyclops 38 Automated carbon masking and particle picking References Bourke P 1997 http local wasp uwa edu au pbourke geometry platonic4d Chang M Kang S Rho W Kim H Kim D 1995 Improved binarization algorithm for document image by histogram and edge detection Third International Conference on Document Analysis and Recognition ICDAR 95 vol 2 636 643 Plaisier J R Koning R I Koerten H K van Heel M Abrahams J P 2004 TYSON robust searching sorting and selecting of single particles in electron micrographs J Struct Biol 145 76 83 Prewitt J M S 1970 Object enhancement and extraction In Lipkin B S Rosenfield A Eds In Picture Processing and Psychopictorics Academic Press New York pp 5 149 Yershova A LaValle S M 2004 Deterministic sampling methods for spheres and SO 3 In Proceedings of the IEEE International Conference on Robotics and Automation ICRA 39 Chapter 2 40 Chapter 3 A Novel Approximation Method of CTF Amplitude Correction for 3D Single Particle Reconstruction Submitted as Jiang L Liu Z Georgieva D Maxim K Abrahams J P 2009 A novel approximation method of CTF amplitude correction for 3D single particle reconstruction Ultramicroscopy Abstract The typical resolution of three dimensional reconstruction by cryo EM single particle analysis is now being pushed up to and beyond the nanometer scale
28. number of plt data files that are read in memory MinPattFitRatio for all patterns Minimal fraction of properly fitting diffraction patterns If this is high many patterns must be explained well by the proposed unit cell Unit cells that fail to reach this threshold are discarded Normal values are 0 5 50 0 66 0 8 MinSpotsFitRatio For one pattern minimum spots fit ratio to detect correct fitting if larger mean fit typical 0 5 50 0 66 MaxFitError For one spot max distance error in pixels the distance between fitted and real spots should be smaller typical value 7 pixels ScaleTolerance max value of scale tolerance 0 01 is 1 typical 0 01 0 03 0 05 VectLengthTolerance Vector Length Tolerance 0 1 is 10 for fitFacet of FullVector amp MainVector matching method fitFacet is a function to calculate the fitting residue of two facets which is used to judge the similarity of two facets 120 User manual of EDiff VectAngleTolerance Vector Angle Tolerance in degrees for fitFacet of Full Vector amp MainVector Matching Method AngleLowerBoundary Angular Lower Boundary in degrees for UniqFacet in lattice Lattice2MainFacet BEval AngleUpperBoundary Angular Upper Boundary in degrees for UniqFacet in lattice Lattice2MainFacet_BEval AngleLowerBoundary Angular Lower Boundary for MainVectorPair in lattice Lattice2FacetTri_BEval AngleUpperBoundary Angular Upper Boundary f
29. of the stalled 50S Published as Jiang L Schaffitzel C Bingel Erlenmeyer R Ban N Korber P Koning R I de Geus D C Plaisier J R Abrahams J P 2009 Recycling of aborted ribosomal 50S subunit nascent chain t RNA complexes by the heat shock protein Hsp15 J Mol Biol 386 1357 1367 Abstract When heat shock prematurely dissociates a translating bacterial ribosome its 50S subunit is prevented from reinitiating protein synthesis by tRNA covalently linked to the unfinished protein chain that remains threaded through the exit tunnel Hsp15 a highly upregulated bacterial heat shock protein reactivates such dead end complexes Here we show with cryo electron microscopy reconstructions and functional assays that Hsp15 translocates the tRNA moiety from the A site to the P site of stalled 50S subunits By stabilizing the tRNA in the P site Hsp15 indirectly frees up the A site allowing a release factor to land there and cleave off the tRNA Such a release factor must be stop codon independent suggesting a possible role for a poorly characterized class of putative release factors that are upregulated by cellular stress lack a codon recognition domain and are conserved in eukaryotes Chapter 4 4 1 Introduction Heat shock upregulates many proteins that function as chaperones or as proteases It also increases the transcription of the small heat shock protein Hsp15 which is an RNA DNA binding protein It targets aborted
30. of using the GroEL images data We are grateful to Dr RAG de Graaff for revising the manuscript The figures for showing 3D models were made by using UCSF s Chimera Pattersen et al 2004 This work was financially supported by the Cyttron Foundation http www cyttron org 62 A novel method of CTF correction References Beckmann R Bubeck D Grassucci R Penczek P Verschoor A Blobel G Frank J 1997 Alignment of conduits for the nascent polypeptide chain in the Ribosome Sec61 complex Science 278 2123 2126 Braig K Otwinowski Z Hegde R Boisvert D C Joachimiak A Horwich A L Sigler P B 1994 The crystal structure of the bacterial chaperonin GroEL at 2 8A Nature 371 578 586 Braig K Adams P D Brunger A T 1995 Conformational variability in the refined structure of the chaperonin GroEL at 2 8 A resolution Nat Struct Biol 2 1083 1094 Chiu W Baker M L Jiang W Dougherty M Schmid M F 2005 Electron cryomicroscopy of biological machines at subnanometer resolution Structure 13 363 372 Erickson H P Klug A 1970 The Fourier transform of an electron micrograph Effects of defocussing and aberrations and implications for the use of underfocus contrast enhancement Ber Bunsenges Phys Chem 74 1129 1137 Fernandez J J Li S Crowther R A 2006 CTF determination and correction in electron cryotomography Ultramicroscopy 106 587 596 Frank J Shimkin B
31. patterns were collected from randomly oriented crystals with a CM30T LaB6 microscope operating at 300keV in microdiffraction mode A condenser aperture C2 of 30um and spot size 8 were used the diameter of the beam on the crystal was approximatelly 1 um The data were recorded at a camera length of 420mm on DITABIS image plates and digitalized at a resolution of 0 025 millimetres per pixel with the DITABIS Micron Imaging plate read out system 5 2 2 Data pre processing and determining the crystal facets First the digitized diffraction patterns were processed The approximate centre of the diffraction patterns was found the central beam or backstop shadow was removed the resolution dependent background was subtracted the autocorrelation patterns were determined and the beam centre was refined Peak positions were automatically extracted from the autocorrelation patterns using the automated particle picking tool of the Cyclops software suite Plaisier et al 2007 At low resolution the peak positions of the diffractogram coincide with those of the autocorrelation pattern see fig 1 From these peak positions we calculated a low resolution facet for each diffraction pattern and stored these in Jist In the absence of a beam stop the centre of a diffraction pattern was found by a search for the most intense connected spot using an adaptation of a standard peak search When a beam stop occluded the direct beam the centre was located by
32. posttranslocational ribosomes revealed by electron cryomicroscopy Cell 88 19 28 van Belzen N Dinjens WNM Eussen BHJ Bosman FT 1998 Expression of differentiation related genes in colorectal cancer possible implications for prognosis Histology and Histopathology 13 1233 1242 Wilson KS Ito K Noller HF Nakamura Y 2000 Functional sites of interaction between release factor RF1 and the ribosome Nature Struct Biol 7 866 870 Wohlgemuth I Beringer M Rodnina MV 2006 Rapid peptide bond formation on isolated 50S ribosomal subunits EMBO Rep 7 699 703 Wriggers W Milligan RA McCammon JA 1999 Situs A Package for Docking Crystal Structures into Low Resolution Maps from Electron Microscopy J Struct Biol 133 185 195 90 Chapter 5 Unit cell determination from randomly oriented electron diffraction patterns Published as Jiang L Georgieva D Zandbergen H W Abrahams J P 2009 Unit cell determination from randomly oriented electron diffraction patterns Acta Cryst D 65 625 632 Abstract Unit cell determination is the first step towards the structure solution of an unknown crystal form Standard procedures for unit cell determination cannot cope with collections that consist of single diffraction patterns of multiple crystals each with an unknown orientation However for beam sensitive nano crystals such is often the only data that can be obtained An algorithm for unit cell determination that use
33. practice to save these output files in another directory to avoid mixing with the original diffraction data 6 4 EDiff Finding Units Cells EDiff exe is the main program of the electron diffraction EDiff software package It finds and optimizes unit cell parameters and fits and indexes diffraction patterns The input data for EDiff are not the original electron diffraction images but the pre processed output data from AMP see above Please read the part of manual on the pre processing program AMP for more details All the input data should be in one directory typically 4 files for each electron diffraction image lt image name gt atc plt lt image name gt atc jpg lt image name gt ctr pks lt image name gt ctr png All the data in one directory are assumed to be generated from one EM session that is with the same voltage camera length of microscopy and digitization parameter If not the data have to be separated into different directories 114 User manual of EDiff For unit cell determination only lt image name gt atc plt and lt image name gt atc jpg files are required For indexing lt image name gt ctr pks and lt image name gt ctr png files are required please see the part of Indexing an Electron Diffraction Image with Known Unit cell Parameters Click the SetDataDir button to set the directory with the data that need to be processed The selected directory will be shown in a line above the button Some
34. ribosomal subunits rather than misfolded proteins Korber et al 1999 Its 50 fold transcriptional increase is even higher than the upshift in expression of such well characterized heat shock proteins such as GroEL ES DnaK and ClpA indicating the high relevance of Hsp15 for adapting to thermal stress Richmond et al 1999 Translating ribosomes can dissociate prematurely upon heat shock resulting in 50S subunits that carry tRNA covalently attached to the nascent chain nc tRNA of an incomplete protein that is threaded through the 50S exit tunnel see also fig 1 These 50Senc tRNA subunits cannot reinitiate protein synthesis unless the tRNA and nascent chain are removed Accumulation these blocked 50Senc tRNA would therefore constitute a problem for the cell Korber et al 2000 demonstrated that Hsp15 specifically binds with high affinity Kg lt 5 nM to such blocked 50Senc tRNA ribosomal subunits The affinity of Hsp15 for 50Senc tRNA complexes is significantly higher than for empty functional 50S subunits However it remained unclear how Hsp15 discriminates between active and aberrantly terminated 50S subunits and how it contributes to recycling blocked non functional 50Senc tRNA complexes To answer these questions we determined the structure of the complex of the 50Senc tRNA subunit both in the absence and presence of Hsp15 by cryo EM and single particle analysis to resolutions of 14 and 10 A respectively The resolution was suf
35. strong background caused by the undiffracted electron beam A Patterson map can be used for centering If a beam stop exists its shadow should be taken into account Then one needs to locate diffraction spots extract their coordinates and calculate the intensities of the spots in the pattern 16 Introduction Gii Unit cell determination Finding the unit cell parameters from randomly oriented diffraction patterns is essential for structure determination Existing algorithms from X ray crystallography and tilt series are not usable as only single shots of crystals can be recorded hence a new algorithm had to be created to deal with the multiple patterns with unknown orientation from multiple crystals iii Indexing The randomly distributed orientation angles need to be determined using the found unit cell in step two The reflections of every electron diffraction image are thus indexed iv Intensity integration and subsequent steps in structure determination and refinement When the indices and their corresponding locations on the diffraction pattern are known methods from X ray crystallography can be used to reconstruct the 3D spot lattices in reciprocal space Phase recovery and iterative refinement are essential for determining the atomic structure 1 5 Outline of this thesis Chapter 2 to chapter 4 focus on single particle analysis which includes both the methods employed in the single particle reconstruction and the prac
36. the density The high resolution structure of the 50S T thermophilus subunit and its cognate tRNA Korostelev et al 2006 are shown as a purple and red ribbons respectively The position of the blue density indicates a 20 rotation of the tRNA in the 50Senc tRNA Hsp15 complex about its aminoacyl acceptor stem compared to the position of the tRNA in the 70S crystal structure The main axes of the tRNAs are indicated by arrows 73 Chapter 4 The location of Hsp15 was not immediately obvious In view of the small size of Hsp15 this is not surprising the diameter of its globular domain not much more than 15 A Staker et al 2000 In order to locate any additional density in our reconstruction of the 50Senc tRNA Hsp15 complex we fitted the high resolution crystal structure of the coli 50S subunit Schuwirth et al 2005 into our density using multi rigid body fitting for the ribosomal RNA and proteins Proteins L1 L11 L7 and L12 could not be fitted well into our density map Most of these proteins are known to be flexible and therefore were not included in the final model We identified well ordered extra density close to the P site nc tRNA This extra density was located between the bottom left of the central protuberance of 50S and the elbow region of the tRNA No known part of the 50S subunit could explain this extra density and the tRNA could not be docked into it without gross distortions and vacating other density At increased
37. the calculation and circles indicate the peak positions of the simulated diffraction pattern The extra peaks in the second autocorrelation pattern were caused by low intensity extra lattices in the original diffractogram not shown B Fine grid search of the unit cell based on 8 images The Residual value on the horizontal axis is defined as the square root of the average weighted residual in equation 4 100 Unit cell determination from randomly oriented electron diffraction patterns 5 3 2 Unit cell determination of potassium penicillin G and sodium oxacillin from electron diffraction data Table 1 Unit cell parameters of potassium penicillin G determined by single crystal X ray diffraction and electron diffraction of single nano crystals from a powder sample using our algorithm Sample Method a A b A c A a B y Potassium X ray diffraction 6 342 9 303 30 015 3x90 penicillin G literature Potassium Electron diffraction 6 4 9 3 31 3x90 penicillin G Sodium oxacillin X ray diffraction 7 342 10 303 26 7 3x90 literature Sodium oxacillin Electron diffraction 7 3 10 1 27 3x90 Electron diffraction data of potassium penicillin G CjsHj7KN2O 4S and sodium oxacillin Cj9HisN3NaOs5S H2O were analysed using our new algorithm The unit cell parameters that our algorithm suggested are given in table 1 together with X ray diffraction data taken from literature Dex
38. the ribosomal complex we first determined the structure of the 50S subunit containing nc tRNA in the absence of Hsp15 In two separate reconstructions we used as starting reference models 1 the cryo EM reconstruction of the empty 50S subunit see supplement and ii the model of the 50S nascent chain tRNA complex that did contain Hsp15 see below The two reconstructions converged to a similar structure of about 14 A resolution 50 FSC criterion The L7 L12 stalk of the 50S subunit is not fully visible in this reconstruction This region is responsible for binding translation factors in the actively translating ribosome and is known to be flexible and conformationally heterogeneous in isolated large ribosomal subunits Helgstrand et al 2007 More importantly the structure revealed clear additional density located at the A site Figure 3A This density most likely corresponds to poorly ordered tRNA which is covalently attached to the nascent polypeptide extending through the ribosomal exit tunnel 4 2 3 Structure of the 50Senc tRNA Hsp15 Complex The reconstruction of the 50Senc tRNA Hsp15 complex yielded a resolution of 10 A based on the Fourier shell correlation Figure S2 Clear additional density which could accommodate tRNA is visible in the P site Figure 3B Based on supervised classification which was performed to sort out and remove any empty 50S particles we concluded that the P site was virtually fully occupied with tRNA This
39. this option to be meaningful 8 AtcBackground show the autocorrelation image or background removed diffraction image as background The default for Pattern Fitting is to show the autocorrelation image for Indexing Refinement the default is to show the background removed diffraction image 6 Rotation matrix defining the potential orientations found by RefineOrient RF2 or 133 Chapter 6 RF3 The matrices are sorted by quality the top matrices fit best 10 RefineOrient finds a more accurate orientation of a diffraction image using known and or found unit cell parameters by selecting pairs of high resolution reflections and fitting and indexing these pairs 19 RF2 provides a different method for orientation refinement sampling all different tilt orientations based on the orientation of V1 amp V2 and their indices to find the best fitting 18 RF3 provides yet another method for orientation refinement sampling all different tilt orientations based on the orientation of V1 amp V2 to find the best fitting The spike function of the reflection is considered that is the elongation of the reflection is simulated The MosaicType must be 3 side elongation threshold default value 0 05 9 ShowRF show turn off the simulated refined pattern and its indices for indexing an autocorrelation image ShowMosaic may be a better choice 12 ShowMosaic show turn off the simulated pattern with incr
40. window is the diffraction image while the default background for Pattern Fitting is the autocorrelation image After having found unit cell parameters the global Resolution Range set in the EDiff main window can be increased for Indexing Refinement The Search Algorithm should be changed to MainVectorMatching no matter what algorithm was used for getting the unit cell parameters It is necessary to run Check Data in order to select a main facet on which the indexing refinement will be based When the window opens a rough fitting is showing It s the same as in the Pattern Fitting window the program finds the best fitting facet in a simulated 3D unit cell model for the main facet V1 amp V2 then cuts through the 3D model lattice along the plane defined by the selected facet in order to generate a simulated 2D diffraction pattern show as small blue circles If the diffraction image is taken right from the main zone this provides an accurate indexing However in more usual cases the experimental diffraction pattern is tilted away from the main zone In order to find the exact orientation of an individual diffraction image so as to index the reflections correctly we need to select Refine Orient which opens a new window fig 6 The RefineOrient is based on the index of the main facet VI amp V2 Hence the MainVectorMatching or BrightestSpots algorithms are strongly
41. 0Senc tRNA Hsp15 complex 75 Chapter 4 A Figure 6 Comparison of the RNA binding mode of S4 and Hspl5 A Top view and side view below of S4 interacting through its aL binding motif with its cognate 16S RNA fragment B Top and side views of Hsp15 interacting through its aL binding motif with helix84 of 23S rRNA C Superimposition of A and B The RNA binding motifs of Hsp15 blue and S4 orange were superimposed the fragment of 16S RNA that is recognized by S4 is shown in yellow and fits well with 23S RNA indicating Asp15 and S4 bind in a similar fashion to dsRNA The long C terminal a helix opposite the RNA binding motif of Hsp15 and the ultimate 23 C terminal residues which are disordered in the crystal structure carry a substantial number of positive charges This C terminal a helix contacted the D T loops of the nc tRNA and although the disordered the C terminus could not be visualized we observed there to be sufficient space for its positive charges to interact with the nc tRNA and or proximal regions of 23S rRNA 4 2 4 Functional assay of Hsp15 induced tRNA translocation The P site specific antibiotic puromycin is a functional equivalent of a stop codon independent release factor Mimicking the 3 end of aminoacyl tRNA at the A 76 Recycling of aborted ribosomal 50S complex by Hsp15 site it binds at the A site and cleaves off P site tRNA from the nascent chain It is used in functional ass
42. 2 gt Aff in figure 4 is used to add V1 amp V2 to an affiliate spots list Button 23 BrightV1V2 will find the brightest two spots in the diffraction image and reset VI amp V2 to them The user can switch the background from the autocorrelation pattern to centered diffraction pattern for a better visualisation by turning off the radio button 25 AtcBackground Be careful of Button 22 and 29 as their operation will affect all the images not just current one Find the proper ResolutionRange In the window of CheckData adjust the resolution range to cover all the brightest spots and affiliate spots in all images that must be used in the calculation Save V1V2 or Save As a VI amp V2 file and then close the window of CheckData Click the DoSearch button to perform unit cell search The console window running in the background will indicate progress The best fitting unit cell parameters will be displayed in the BestFit UnitCell column and the best five results will be shown in the console window Use Show Fitting to check whether the result is reasonable or not When the user clicks the DoSearch button the program will use both the VI amp V2 and main facets as affiliate spots saved in CheckData step In the searching every diffraction simulation of a potential unit cell has to match the V1 amp V2 spots and all the affiliate spots at the same time Because this method n
43. 20 nm and weight of 1 600 kDa We used a set of 33 900 images containing 128 x 128 pixels recorded with a defocus ranging from 0 6 to 1 8 um See Jiang et al 2008 We collected close to focus micrographs with a low dose exposure lt 10e and therefore collected relatively noisy images Single particles were selected and maintained by using the Cyclops software Plaisier et al 2007 For the 981 projections classes used in the reconstruction the average number of images per projection is around 34 A model that had nearly converged to the final model Jiang et al 2008 was used as a common starting model for all the algorithms tested After four iterations of refinement using the same data set and starting model but using different CTF correction 56 A novel method of CTF correction algorithms we compared the class average images and 3D reconstruction results in Figure 5 amp 6 If we ran more rounds of iterative refinement the method of normal CTF correction blew up because of the high level of noise in the test data Class average of Class average of Class average of Projection normal full CTF Projection direct deconvolution Projection filtered CTF correction CTF correction correction Figure 5 Representative class average images of the complex of ribosomal 50S particle with nascent chain tRNA and Hsp15 The projections and average images are selected from the fourth round of iterative refinement well before the conven
44. 3D structures electron microscopy and image processing techniques comparing different atomic structure determination methods and summarizing the basics of 3DEM single particle reconstruction and electron crystallography In Chapter 2 new methods for automated particle picking and their software implementation are presented Two new algorithms automated carbon masking and quaternion based rotation space sampling were designed and implemented The algorithm of automated carbon masking can boost the particle selection process by automatically masking the carbon regions in micrographs These regions should in general not be used for 3D structure determination as the particles may be distorted by interactions with the carbon and also the carbon will increase the background signal The algorithm of quaternion based rotation space sampling provides a common software library for sampling rotation space evenly Currently it is used in generating a list of evenly distributed projections from a starting 3D model for the model based particle picking method Chapter 3 presents a novel approximation method that corrects the amplitude modulation introduced by the contrast transfer function CTF by convoluting the images with a piecewise continuous function As the resolution of 3DEM single particle analysis is being pushed down into sub nanometer range any new method that can increase the resolution of existing methods towards the atomic level is timely a
45. Correction of the contrast transfer function CTF of electron microscopic images is essential for achieving such a high resolution Various correction methods exist and are employed in popular reconstruction software packages Here we present a novel approximation method that corrects the amplitude modulation introduced by the contrast transfer function by convoluting the images with a piecewise continuous function Our new approach can easily be implemented and incorporated into other packages The implemented method yielded higher resolution reconstructions with data sets from both highly symmetric and asymmetric structures It is an efficient alternative correction method that allows quick convergence of the 3D reconstruction and has a high tolerance for noisy images thus easing a bottleneck in practical reconstruction of macromolecules Chapter 3 3 1 Introduction The last decade saw a substantial increase in the number of 3D structures determined by single particle cryo EM reconstruction and the resolution of these reconstructions 4 10 A is starting to approach a level that allows atomic interpretation of the structures see reviews by Zhou 2008 Chiu et al 2005 Essential was the development of procedures for accurate CTF estimation and correction of the measured image data The instrumental aberration problem that affects electron microscopy images was recognized early Thon 1966 Erickson and Klug 1970 and must be corrected for to
46. Hence we could not corroborate the new unit cell by X ray analysis and in the absence of independent proof we cannot exclude the possibility that our algorithm failed to identify the correct unit cell of nano crystalline lysozyme It may be that the combination of randomly oriented diffraction patterns a relatively large unit cell and a potentially anisotropic rocking curve frustrates our algorithm and we are further investigating potential improvements However using the large unit cell we were able to index well aligned diffraction patterns using the program ELD Zou et al 1993 yet we failed to index these patterns if we used the unit cells of known orthorhombic polymorphs of hen egg 104 Unit cell determination from randomly oriented electron diffraction patterns lysozyme fig 5 Furthermore all the known unit cells of lysozyme gave considerably worse residuals as defined by lemma 4 and therefore were not supported by our experimental data In this light we propose that the nano crystals are a new polymorph of lysozyme and that it was induced by the heterogeneous nucleation on human hair as described in Georgieva et al 2007 a b Figure 5 a Diffraction pattern from a lysozyme nano crystal b lattice indexing performed with ELD using the cell parameters for lysozyme obtained by the algorithm described here The directions of the shortest reciprocal spacings given in blue and red and corresponding to the 100 an
47. Image Processing and Computing in Structural Biology PROEFSCHRIFT ter verkrijging van de graad van Doctor aan de Universiteit Leiden op gezag van Rector Magnificus prof mr P F van der Heijden volgens besluit van het College voor Promoties te verdedigen op donderdag 12 November 2009 klokke 15 00 uur door Linhua Jiang Geboren te Yongzhou China in 1977 Promotiecommissie Promotor Prof dr J P Abrahams Overige leden Prof dr H W Zandbergen TUD Delft Prof dr M van Heel Imperial College London Prof dr M H M Noteborn Prof dr N Ban ETH Zurich Dr F J Verbeek Dr J R Plaisier ELETTRA Trieste Dr M E Kuil Dr R A G de Graaff Cover The ribosomal large subunit 50S and cryo electron microscopy ISBN 978 90 8570 293 1 Copyright by Linhua Jiang 2009 All rights reserved No part of this publication may be reproduced stored in a retrieval system or transmitted in any form or by any means without the prior written permission of the copyright owner Printed by W hrmann Print Service The Netherlands Contents Chapter 1 Introduction 5 Chapter 2 Automated carbon masking and particle picking in data preparation of single particles 21 Chapter 3 A novel approximation method of CTF amplitude correction for 3D single particle reconstruction 41 Chapter 4 Reconstruction of the complexes of the ribosomal large subunit 50S with Hsp15 and t RNA reveals the rescue mechanism of the st
48. Search button the program first generates a main facet for each autocorrelation pattern and accumulates all the facets in Listl then analyses List to remove any congruent facets shrinking Listl to contain only unique facets The matching procedure is described in fig 5 6 6 2 Algorithm 2 Main Vector Matching This algorithm requires more user interaction compared to the Unique Facet Matching algorithm The most important difference is that the main facets V1 amp V2 have to be examined and possibly reset by the user using the CheckData tool The main facets in Listl are checked by hand and a quality remark Bad Normal Good or Important can be given to each individual image Congruent facets extracted from different diffraction pattern are not removed from Listl When the experimental data are very noisy and lots of mis tilted diffractions were collected this solution is more reliable in the hands of an experienced user The user is encouraged to run CheckData and try this method for more accurate results Main steps 126 User manual of EDiff Set the basic microscope and diffraction parameters in the graphic interface figure 2 Choose a data directory with SetDataDir If you know the crystal system or want to test out whether your assumption of the crystal system is reasonable select it otherwise select Triclinic Set the search range of edges and angles Set the SearchAlgorithm to Main
49. TF has many zeros with the changing of phase it is relatively small at low frequencies and tends to zero at the high frequency end due to the shape of the envelope function The restored image will be corrupted by noise which will be enhanced upon division by the CTF in regions where the CTF is small Penczek et al 1997 All these features of CTF render the straightforward division by the CTF sub optimal In full CTF correction after the phase is flipped several methods may be employed in amplitude correction to avoid dividing by zero and to prevent amplifying the noise while deconvoluting the contrast transfer function A Wiener deconvolution The Wiener filter is used widely in imaging processing Gonzalez et al 2003 An application of the Wiener filter Schiske 1973 is used for amplitude correction e g in SPIDER EMAN The Wiener deconvolution filter can be formulated in the frequency domain as follows o1 HO H s H s 1 SNR s G s 4 Here H s is the frequency transfer function 1 H s is the inverse of the original system corresponding to 1 CTF s in the CTF correction SNR s S s N s is the signal to noise ratio SNR S s is the signal intensity C7TF SJF 5 and N s is the noise intensity N s In order to use the Wiener filter one has to estimate or determine the SNR Consequently solution structure factors the rotationally averaged curve of F s need to be estimated independently e g
50. The uniform sampling of rotations in 2D space is straightforward but for rotations in 3D space uniform sampling is more problematic With the help of quaternion theory we implemented an algorithm for uniform sampling in 3D rotation space that is based on subdivision of the regular polytopes in 4 dimensions The algorithm can be used in single particle picking and alignment using a set of projection Chapter 2 classes from a known or inferred low resolution 3D model 2 1 Introduction In recent years the resolution obtained in three dimensional reconstruction of biological complexes using cryo EM has been considerably improved both through better instrumentation and new software tools Simultaneously more effort has been put into automation of the data collection and processing steps As a result of these developments a large amount of software for cryo EM is now available At the same time there is still considerable potential for improvement in terms of resolution automation and ease of use In cryo EM single particle reconstruction the vast majority of particle projections are picked when the low resolution 3D structure of the complex is or could be known This additional information should be used as it allows cross correlation searches which are more objective than hand picking projections and have a better yield than automatic procedures based on local density or variance However such cross correlation searches are expensive in
51. Use Show Fitting to check whether the result is reasonable When the user clicks the DoSearch button the program will use all the possible vectors pairs not only the main facet in each autocorrelation image for its calculations For matching an observed vector pair a facet in Listl to a simulated facet in List2 a 2D lattice is generated from the simulated facet and compared with the observed diffraction pattern to get a fitting value The fitting value is used as the accumulated residual which is different from the residual of two fitted facets in the other solutions By using all the vector pairs and simulating 2D diffraction patterns this algorithm requires heavy computing and is therefore slow 6 6 4 Algorithm 4 Brightest Spots Matching especially suited for large unit cells The Brightest Spots Matching algorithm is a variation of the Main Vector Matching algorithm It s the most accurate algorithm and is especially useful for thin nano crystals with large unit cell However it does require some expertise and you need to know what you re doing Try it out if you have plate like nano crystals that lie in preferred orientations on the grid If this is the case the information of the unit cell dimension in the direction of the beam is not well determined If this is the case 128 User manual of EDiff make sure to tilt the samples away from the main zones before diffracting them by as high an angle a
52. VectorMatching Find the proper ResolutionRange click CheckData and adjust the resolution range to cover all the main vectors in different images In the window of CheckData verify that the V1 and V2 spots auto selected by the program are the closest two spots near the center If there are any other spots closer to the center reset the V1 or V2 to these spots Normally a correct choice for V1 amp V2 result in a high fitting value between the image peaks and a lattice using V1 amp V2 as a basis Please read the section 6 5 on Checking the Data for more details Save VIV or Save As a V1 amp V2 file before closing the window of CheckData Click the DoSearch button to perform unit cell parameters search The console window running in the background will indicate progress The best fitting unit cell parameters will be displayed in the BestFit UnitCell column and the best five results will be shown in the console window Use Show Fitting to check whether the result is reasonable or not When the user clicks the DoSearch button the program will use the main facets saved in the CheckData step in Listl For the Main Vector Matching algorithm this List is filled interactively using the CheckData tool In testing out potential unit cells unit cells are skipped if none of its facets can be matched to the measured patterns marked as Important 6 6 3 Algorith
53. ajima K and Matsuura Y 2005 Acta Cryst D61 207 217 Vainshtein B K 1964 Structure Analysis by Electron Diffraction Oxford Pergamon Zou X D Hovm ller A and Hovm ller S 2004 Ultramicroscopy 98 187 193 Zou X D Sukharev Y and Hovm ller S 1993 Ultramicroscopy 49 147 158 107 Chapter 5 108 Chapter 6 User manual of EDiff A unit cell determination and indexing software EDiff is a scientific software package to determine the unit cell of nano crystals from the randomly oriented electron diffraction data EDiff is used to index the reflections in the electron diffraction images and is the first step in reconstructing the 3D atomic structure of organic and inorganic molecules and proteins EDiff includes the data pre processing program AMP which cleans up diffraction patterns and calculates their autocorrelation patterns which serve as input for EDiff EDiff Copyright 2007 2008 BFSC Leiden Univ the Netherlands A paper about the pre processing program AMP was accepted and will be published in the proceeding of the 2009 IEEE International Conference on Image and Signal Processing CISP 09 Jiang L Georgieva D IJspeert K Abrahams J P 2009 An Intelligent Peak Search Program for Digital Electron Diffraction Images of 3D Nano crystals Chapter 6 6 1 The Electron Diffraction Software EDiff Package for Windows Users The package includes the following executable fil
54. alled 50S 67 Chapter 5 Unit cell determination from randomly oriented electron diffraction patterns 91 Chapter 6 User manual of EDiff A unit cell determination and indexing software 109 Chapter 7 Conclusion and Perspectives 139 Summary 141 Samenvatting 144 Curriculum Vitae 146 A Special Word of Thanks 147 Chapter 1 Introduction 1 1 Structural biology cryo EM and image processing Structural biology is a branch of life science which focuses on the structures of biological macromolecules investigating what the structure looks like and how alterations in the structure affect the biological functions This subject is of great interest to biologists because macromolecules carry out most of the cellular functions which exclusively depend on their specific three dimensional 3D structure This 3D structure or tertiary structure of molecules depends on their basic sequence or primary structure However the 3D structure cannot be calculated directly from the sequence In order to understand the complicated biological processes at the cellular level it is therefore essential to determine the 3D structure of molecules The research of structural biology is intimately relevant to human health A healthy body requires the coordinated action of billions of indispensable proteins Each protein has a unique molecular shape that exactly fits its particular function Determining the 3D structures of key proteins and viruses at the atomic
55. at such a test does not give an absolute resolution but is a reflection of the internal consistency between model and data This can be clouded by bias introduced by specific choices of envelopes samplings symmetries and starting models Van Heel 2005 and we were careful to ensure that these were identical for the various algorithms we tested The resolution of M2 is around 1 A better than that of M1 while M3 is a little bit over filtered and lost some high resolution detail Table I Fourier Shell Correlation FSC 0 5 criterion of different models of GroEL M1 conventional CTF correction M2 direct CTF convolution M3 filtered CTF correction The table indicates that for highly symmetrical particles the direct CTF convolution algorithm converges to a more self consistent model that suffers less from model bias Table I Comparison of resolutions and inter models similarity Model M1 M2 M3 Resolution FSC at 0 5 7 9 7 0 8 6 Similarity with Starting 5 3 6 7 8 3 Model FSC at 0 5 FSC Fourier Shell Correlation One will also notice that the densities in the inner channels of these three modes are apparently different It seems that M2 amp M3 have less resolved structure in the channel but actually there is almost no density in the inner channel within 4 5nm diameter of the X ray structure of unliganded GroEL PDBid 1OEL Braig et al 1995 A recent 55 Chapter 3 published higher reso
56. ays to distinguish P site tRNA from Asite tRNA and establish A site occupancy It was established that puromycin abolishes binding of Hsp15 to 50Senc tRNA complexes in cell extracts Korber et al 2000 Presumably puromycin released the tRNA from the 50S subunit and the resulting empty 50S subunits would no longer have a high affinity for Hsp15 This observation already indicated that the tRNA must reside in the P site in the 50Senc tRNA Hsp15 complex in cell extracts Here we show that no additional factor was involved also in highly purified 50Senc tRNA Hsp15 samples puromycin was able to cleave off the nascent chain Fig 7 N acetylated Phe tRNAPhe is an nc tRNA homolog that can freely diffuse into and out of the P site of 50S subunits where it can react with A site bound puromycin This reaction proceeds optimally at 100 mM Mg in isolated 50S subunits but is slower at lower Mg concentrations Wohlgemuth et al 2006 However for the 50Senc tRNA Hspl5 complex we found the opposite effect raising the Mg concentration reduced the puromycin reactivity The cryo EM structure provided a straightforward explanation for this observation At 100 mM Mg Hsp15 dissociates more easily from 50Senc tRNA complexes Korber et al 2000 If Hsp15 is essential for stabilizing the tRNA moiety in the P site as suggested by the structures then its dissociation from the 50SenctRNAsHsp15 complex should result in a relocation of the tRNA to the
57. by a small angle X ray scattering SAX experiment When there is low noise SNR is very large the term in the square brackets tends to 1 and the Wiener filter equals approximately the inverse of H s However when the noise is strong SNR is very small the term in the square brackets will decrease thus suppressing the intensity of the noise note that in this case also the signal is 45 Chapter 3 suppressed strongly The term within the square brackets is therefore a kind of amplitude optimization fine tuning the amplitude of the restored signal to minimize the mean square error between the original and the estimated signal The Wiener filter cannot recover missing information in the zero regions and an adapted Wiener filter is needed to mediate the information of different defocus images at the same frequency and generate an integrated image In 3D reconstruction a set of images assigned to the same class is used in calculating such an integrated image or class average image Application of a Wiener filter in 3D reconstruction was described by Penczek et al 1997 To describe the filter of the n th data set in a formula the notation is adapted here for convenience SNR CTF s GS gt SNR n l 3 5 CTF s 1 1 Where CTF s CTF s Collecting a defocus series data set CTF s covering the whole range of frequencies from zero to some limit of frequency of sampling the adapt
58. ching and FullVectorMatching methods which allow the user to include extra information on the symmetry of the crystal If this parameter is not selected MaxMissingNo is zero only prime index reflections will be considered in the unit cell searching Prime means no common factor for the h k l index e g index 5 4 3 is prime but 6 4 2 isn t because the h k and 1 have 2 as a common divisor If you don t have information about known missing reflections just leave it unchecked 27 SetDataDir set the input data directory which is the output directory of the pre processing program AMP see 6 3 28 CheckData allows some types of verification It allows checking whether the peak positions of the auto correlation images and peak positions of the background removed diffraction pattern coincide This helps the user to select the proper ResolutionRange for the unit cell parameter search Setting CheckData allows checking the main vectors for the MainVectorMatching and Brightest Spots Matching methods The option saves the main vectors to a V1V2 file 40 ReadV1V2 reads the main vectors V1V2 the main facet from a file 41 ClearV1V2 clears the main vectors and unique facets from memory If the user wants to re select the main vectors or redo the unit cell parameters search it s better to erase the old settings or to restart the EDiff program altogether 32 Information Panel some sta
59. cific nucleic acid binding activity of Hsp15 Korber et al 1999 2000 Hsp15 only bound with high affinity to 50S subunits containing nc tRNA at a 1 10 molar ratio Figure 2B 70 Recycling of aborted ribosomal 50S complex by Hspl5 1 10 1 10 c 1 1 1 10 c 12 Bee 47 gt 34 26 20 H pop 5 9 ty a yuan ihi j p py 50S nc Hsp15 5 o S 7 Figure 2 A Preparation of 5O0Senascent chain tRNA complexes 50S nc 50S nc tRNA Sucrose gradient profile of an in vitro translation reaction in the presence of 0 3 mM Mg OAc 2 The two peaks 50S and 30S are analyzed on a Coomassie stained SDS gel The presence of the nascent chain in the 50S is shown by Western blotting left side using Streptactin alkaline phosphatase conjugate The upper band at 34 kDa corresponds to nc tRNA the lower band to the nascent peptide alone B Binding assay of Hsp15 Binding of purified Hspl5 to 50S nc to 50S and to 70S was analyzed by ribosomal pelleting through a sucrose cushion As a control indicated with c 50S and 70S was loaded alone Hsp15 did not migrate through the sucrose cushion not shown Hsp15 was added in a 1 1 and 1 10 molar ratio Hsp15 was found only in the pellet of 50S nc as indicated with an arrow As a positive control 100 ng Hsp15 was loaded onto the SDS gel 71 Chapter 4 4 2 2 Structure of the 50Senc tRNA Complex In order to identify the position of Hspl5 in
60. confirmed our biochemical characterization of the purity of the sample see above The extra density in the P site matched the atomic model of tRNA suggested by other parts of the structure indicating that the tRNA is well ordered in the 50Senc tRNA Hsp15 complex Its anticodon stem was rotated about 20 about its at contouring levels acceptor stem towards ribosomal protein L1 compared to its location in the crystal structure of the T thermophilus 70S ribosome complexed with mRNA and two tRNAs Korostelev et al 2006 Figure 4 Since the angle between the aminoacy acceptor stem and the anticodon stem can vary in tRNAs Moras et al 1980 we refined the angle between the these stems This resulted in a small increase 15 compared to the crystal structure of tRNA conformation of the tRNA thus somewhat opening up the canonical L shaped 72 Recycling of aborted ribosomal 50S complex by Hsp15 Figure 3 Reconstructions of A the 50S nc tRNA complex the density of tRNA is in cyan 14 A resolution and B the 50S nc tRNA Hsp15 complex the density of tRNA is in cyan and of Hsp15 in blue 10 A resolution Figure 4 Side A and top B views of the 50S subunit and tRNA of crystal structure of the T thermophilus 70S tRNA complex was docked into the density of the SOSenc tRNA Hsp15 complex The density corresponding to 50S is depicted in grey tRNA density in cyan and Hsp15 density in blue C as B without showing
61. contour levels corresponding to highly ordered parts of the structure a tube like feature in this extra density was visible Assuming that this feature corresponded to the a helix of Hspl5 we docked monomeric Hspl5 into the extra density and subsequently refined its position using our program LOCALFIT The resulting atomic model is shown in Figure 5 Hspl5 is known to have an aL RNA binding motif which it shares with ribosomal protein S4 and threonyl tRNA synthetase amongst others Staker et al 2000 Our docking result was confirmed by the observation that the aL RNA binding domains of Hspl5 and of S4 both interacted in the same fashion with their cognate RNA double helical targets helix H84 of 23S rRNA and a fragment of 16S rRNA respectively Figure 6 74 Recycling of aborted ribosomal 50S complex by Hsp15 Figure 5 Hspl 5 attaches the H84 Helix of 23S rRNA and interacts with the D T loops of the tRNA A View from the left with respect to the standard orientation of the 50S subunit see Figure 2 The 50S subunit is depicted in magenta and the tRNA in cyan B as A including the 50Senc tRNA complex density density covering Hspl5 in blue density covering tRNA in cyan density covering 50S in grey C The interaction of the tail of Hsp15 and tRNA right side view the C terminal positively charged a helix of Hsp15 is show in as spheres D as C showing density contoured at a level predicted by the molecular weight of the 5
62. contrast particles selected from the original 39 085 particles Next they were used to reconstruct a 6 A structure Ludtke et al 2004 In contrast the data of the ribosome complex were collected with a relatively smaller defocus near lm resulting in a lower contrast and more noisy images Better contrast of the original images used in reconstruction usually results in better contrast in the average images eThe effective number of particles used in reconstruction for the GroEL is much larger than the number used for the ribosomal subunit due to the high symmetry of GroEL causing the SNR to be higher in the average images of GroEL eThe asymmetric ribosome structure is more irregular thus the projections looks less like stripes and more like blobs In Figure 5 the averaged images of the new algorithms images in the middle amp right columns look better with more detail than the conventional results images in left column The substantial improvement in the quality of the class average images directly results in better 3D models being reconstructed as is shown in Figure 6 In Figure 6 the results of filtered CTF correction Right model and direct CTF deconvolution Middle model show similar fine detail Many high resolution structural features of rRNA s double helices can be observed including for instance 59 Chapter 3 the turns and major and minor grooves Even the general shapes and densities of helices o
63. crystal system we have to use the most time consuming option Triclinic 66 Parameter Suggestion gives the user a suggestion for filling in the UnitCellSearchRange based on an analysis of the main vectors generated in CheckData step This option requires first running CheckData and saving the main vectors V1 V2 17 19 UpperBoundary largest unit cell edge in Angstrom for a unit cell parameter search 20 22 LowerBoundary smallest unit cell edge in Angstrom for a unit cell parameter search 23 25 SearchStepSize step size in Angstrom for unit cell parameter search Usual values are about 0 5 or 1 Angstrom 60 62 UpperBoundary upper boundary in degrees for unit cell parameters search 57 59 LowerBoundary Lower Boundary in degrees for unit cell parameters search 54 56 SearchStepSize Step Size in degrees for unit cell angle search Initially set this to about 1 degree 63 SearchList the user can define a list of angles to be checked instead of performing exhaustive angle searching The angle list should be saved as a text file with each line a tri angle group alpha beta and gamma in degrees and separated by blank space 64 The file of the angle search list 65 Remove the angle search list 26 SearchAlgorithm there are three unit cell parameters search algorithms that can be selected e Unique Facet Matching the friendliest algorithm you don t even need to run CheckDa
64. ction technique are well established algorithms in electron crystallography A crystal lattice can be characterized by the choice of reduced cell There are 44 primitive reduced Niggli cells corresponding to 14 Bravais lattices The determination of the unit cell is done by first determining the reduced direct primitive cell and then transforming it to a conventional cell The recognition and interpretation of the reduced form are often difficult and aggravated by errors in the cell parameters or rounding errors in calculations Thus procedures aimed at reducing these errors need to be performed An approach suggested by Clegg et al 1981 to minimize the errors implies the generation of a list of lattice vectors sorted on length together with angles between pairs of them Besides the conventional algorithms Grosse Kunstleve and co workers Grosse Kunstleve et al 2004 implemented two numerically stable algorithms to generate the reduced cell However all these methods require the collection of at least two diffraction patterns of one single crystal each collected at precisely known angles This is not always possible For instance in the case of 3D organic crystals of proteins and pharmaceuticals the high beam sensitivity of the materials often does not allow collecting a tilts series from a single nano crystal So far this limits the application of electron diffraction for studying beam sensitive molecules Here we present an al
65. d 011 axes respectively are indicated How many diffractograms are needed to estimate the unit cell There is not a straightforward answer to this question but in general it is better to include as much data in the analysis as possible If the crystals have a favoured orientation on the grid as the lysozyme crystals did then it is important to collect tilted data as otherwise the possibility exists that one of the spacings is not observed However there are also other issues that influence the robustness of our algorithm for instance the symmetry of the unit cell higher symmetry gives better results or peculiarities of a specific 105 Chapter 5 combination of unit cell parameters if for instance in an orthorhombic unit cell the 100 and 021 directions have similar lengths indexing may become confused With our new algorithm we have made progress in enabling structure determination by electron diffraction of beam sensitive 3D nano crystals Subsequent steps involve testing our algorithm on lower symmetry space groups monoclinic and triclinic refining the unit cell dimensions indexing the electron diffraction patterns integrating the diffraction intensities merging the data and phasing However these subsequent steps crucially depend on knowledge of the unit cell and in many cases we can use algorithms and programs developed for X ray crystallography Acknowledgements The authors would like to thank Dr Ulrike Ze
66. d the proper ResolutionRange for the unit cell parameter search A very large resolution range is fine from a theoretical perspective but may include too many spots in the calculation and therefore cost too much computing time A resolution range that is too narrow may lose essential information When adjusting the resolution range don t forget to press enter after having filled in the numbers Let the resolution range shown as two black circles in the image window just cover all the main vectors or make it just a little larger A reasonable resolution range extends from half of the estimated smallest unit cell dimension to double the largest unit cell dimension e g if the smallest unit cell dimension is around 30 A and the largest dimension is around 80 A a reasonable resolution range extends from 15 to 160 A The main vectors generated in CheckData will be used in the MainVectorMatching algorithm and in the Brightest Spots Matching method In order to validate the main facets vectors selected here the user has to save the main vectors by clicking the Save 122 User manual of EDiff V1V2 button or Save As a V1V2 file For the UniqFacetMatching method the program will generate the main facets automatically when the unit cell parameter search is started Running CheckData is not required for the UniqFacetMatching and Full VectorMatching algorithms Fitting Values 1 040708_12 atc
67. definitions of electron diffraction images that are used in this document e A reflection is a spot corresponding to a vector from beam or image center to this spot e Two reflection spots together with the beam or image center point form a triangle we call this a facet e The facet defined by the two shortest vectors corresponding to two reflection spots closest to the center is called a main facet In short every reflection pair defines a facet The main facet defines the smallest repeating unit of the 2D lattice defined by the low resolution spacings but not any higher order Laue zone HOLZ that may be visible at high resolution EDiff exe also has a Graphical User Interface GUI a snapshot is shown in figure 2 115 Chapter 6 File Tool Help a wm Microscopy Voltage Ke WaveLength Ang ImageD ata ScaleB arParam 1 4 pixel C Digitization mm pixel Search Params ResolutionRangelAng CrystalSystem i CH Cubic Crystal f Monoclinic exagonal 3 pects Tetragonal Orthorhombic Triclinic Rhombo UnitCellE dgesS earchR ange Angstrom LowerBoundary UpperBoundary 888 ET mf m 61 AutoCorrelation ImageCenter Pixel MissingSpots SearchStepSize 7 27 ea 28 mere Deer A EA SearchAlgorithm Overman z Ore vaer OD osoarcn Dorete poise nn BestFit UritCel 889 888 Refined UnitCelt WE WWW Dow Fit
68. diffraction pattern which fills up gaps or absences in the data enhances the signal to noise ratio and centers the diffraction pattern The autocorrelation map and peak coordinates serve as input files for EDiff the main program that determines the unit cell of a crystal The autocorrelation patterns are essential for finding the unit cell but cannot be used for further steps in the structure determination 6 3 1 Preparing the Input Data for the Pre processing Program AMP AMP expects electron diffraction images of about 1024 by 1024 pixels though they needn t to be exactly this size Furthermore diffracted intensity should be positive white on most display programs if the spots are black on a white background you have to invert the image The beam center of the diffraction pattern should be more or less in the centered Make sure that all the images that you want to process are in the same directory It is good practice to store all the data of one EM session in a single directory ensuring that all diffraction patterns were collected with the same voltage camera length and digitization parameters If these microscopy parameters are changed during a session then separate the data set into different directories for proper processing 111 Chapter 6 6 3 2 Working with the Pre processing Program AMP Image Data Type As nat ef j a Options Center beam threshold Irregular center tolerance 30 Use beam
69. dispensable to calculate a 3D structure from the EM micrographs This thesis mainly focuses on the image processing techniques of 3DEM and electron crystallography and solves biological problems based on the 3D structures I determined 1 2 Nano techniques in structural biology X ray NMR electron diffraction and 3DEM X ray diffraction NMR spectroscopy and 2D 1D electron crystallography involve measurements of vast numbers of identical molecules at the same time Most of the solved atomic structures use micro crystals and X ray diffraction In a crystal all molecules are in the same conformation and binding state Their uniform orientation and ordered arrangement enable the X ray diffraction The wavelength of the electron beam generated in a TEM is much shorter than that of the radiation which is usually used in X ray crystallography E g for 300KeV TEM the wavelength is 0 019A for 200KeV 0 025A X rays used for atomic structure determination have wavelengths between 2 A and 0 5 A Theoretically electrons diffraction therefore has a higher resolution limit than X ray diffraction But electron diffraction suffers from the dynamic diffraction problem caused by the strong interactions between electrons and the matter Only single layer crystals 2D Chapter 1 crystal or helical arrays 1D crystals have been investigated successfully with electron diffraction In this thesis nano crystals 3D protein crystals with nano scale
70. domain but lacks a stop codon recognizing domain Nevertheless due to the presence of the GGQ motif YaeJ is placed in the same cluster of orthologous groups as the release factors RF and RF2 Baranov et al 2006 Thus YaeJ could bind to the A site of the 50Senc tRNA Hsp15 complex and hydrolyze the peptidyl tRNA ester bond without needing a stop codon recognizing domain Residues 10 to 112 of YaeJ have a 29 identity and 55 homology with the small human protein ICT1 a 23 6 kD protein with unknown function that becomes more highly expressed upon neoplastic transformation of colon epithelial cells Van Belzen et al 1998 On the basis of its GGQ domain ICT1 is classified as a putative release factor even though like Yael it lacks an anticodon recognizing domain If Yeal and ICT1 have homologous functions in recycling prematurely dissociated mitochondrial ribosomes Hsp15 might also have a eukaryotic homologue 80 Recycling of aborted ribosomal 50S complex by Hspl5 In summary we propose that Hspl5 rescues heat induced abortive 50S subunits carrying a peptidyl tRNA by fixing the tRNA moiety to the P site Figure 1 This allows a specialized release factor to bind at the A site and cleave the aminoacylester bond between tRNA and nascent chain which is optimally positioned for this hydrophilic attack in the peptidyl transferase centre The cleavage allows tRNA and nascent chain to diffuse away and the 50S particle to become translatio
71. e as described Korber et al 1999 The purified protein was dialyzed against 30 mM Hepes KOH 1 mM EDTA pH 7 0 concentrated with a Centriplus concentrator MWCO 3 kDa Amicon flash frozen and stored at 80 C 4 4 3 Binding assays of Hsp15 15 ug 50S nc 50S and 70S were incubated in a 1 1 and 1 10 molar ratio with purified Hsp15 in buffer 3 20 mM Hepes KOH 100 mM NH4CI 25 mM Mg OAc pH 7 5 82 Recycling of aborted ribosomal 50S complex by Hspl5 on ice for 30 min The mix was centrifuged 5 min at 14000 rpm in a table top centrifuge at 4 C and then loaded onto a 1 5 ml sucrose cushion 30 w v sucrose in buffer 3 The ribosomes and ribosomal subunits were pelleted by ultracentrifugation 5 h 55000 rpm 4 C TLA 55 rotor Beckman The ribosomal pellet was quantified and loaded onto a 16 SDS gel 4 4 4 Puromycin assay 50Senc tRNA Hsp15 complex 60 nM in buffer 2 or buffer 2 with increased Mg concentration to 100 mM to favor Hsp15 dissociation was incubated with 2 mM puromycin for 3 h at 37 C Samples at 45 min intervals were withdrawn mixed with an equal volume of loading buffer and separated on low pH SDS based Tris acetate gel to minimize hydrolysis of the ester bond linking tRNA to the nascent chain Immunodetection of the nascent chain was carried out on PVDF membrane using a Streptag monoclonal antibody conjugated to horseradish peroxidase IBA Detection was performed by electrochemiluminescence and spots o
72. e bacterial genomes encode an operon of two genes one of which is an unusual class I release factor that potentially recognizes atypical mRNA signals other than normal stop codons Biology Direct 1 28 Brehmer D Gassler C Rist W Mayer MP Bukau B 2004 Influence of GrpE on DnaK substrate interactions J Biol Chem 279 27957 27964 M Connolly L Penas AD Alba BM Gross CA 1997 The response to exoplasmatic stress in Escherichia coli is controlled by partially over lapping pathways Genes Dey 11 2012 2021 El Samad H Kurata H Doyle JC Gross CA Khammash M 2005 Surviving heat shock control strategies for robustness and performance Proc Natl Acad Sci USA 102 2736 2741 Helgstrand M Mandava CS Mulder FAA Liljas A Sanyal S Akke M 2007 The ribosomal stalk binds to translation factors IF2 EF Tu EF G and RF3 via a conserved region of the L12 C terminal domain J Mol Biol 365 468 479 Klaholz BP Pape T Zavialov AV Myasnikov AG Orlova EV Vestergaard B Ehrenberg M van Heel M 2003 Structure of the Escherichia coli ribosomal termination complex with release factor 2 Nature 421 90 94 Korber P Zander T Herschlag D Bardwell JCA 1999 A new heat shock protein that binds nucleic acids J Biol Chem 274 249 256 Korber P Stahl JM Nierhaus KH Bardwell JCA 2000 Hsp 15 a ribosome associated heat shock protein EMBO J 19 741 748 Korostelev A Trakhanov S Laurberg M Noller HF 2006 Crystal structure o
73. e first step to solve a structure in crystallography Chapter 6 describes the implementation of these algorithms and includes a user manual of the EDiff software which is used for searching unit cell parameters and indexing well oriented patterns Finally chapter 7 gives a summary and concludes with future perspectives of my research 18 Introduction References Bragg W L 1913 The Diffraction of Short Electromagnetic Waves by a Crystal Proceedings of the Cambridge Philosophical Society 17 43 57 Georgieva D G Kuil M E Oosterkamp T H Zandbergen H W Abrahams J P 2007 Heterogeneous crystallization of protein nano crystals Acta Crystallogr D 63 564 570 Henderson R 2004 Realizing the potential of electron cryo microcopy Q Rev Biophys 37 3 13 Plaisier J R Jiang L Abrahams J P 2007 Cyclops New modular software suite for cryo EM J Struct Biol 157 19 27 van Heel M Gowen B Matadeen R Orlova E V Finn R Pape T Cohen D Stark H Schmidt R Schatz M Patwardhan A 2000 Single particle electron cryo microscopy towards atomic resolution Q Rev Biophys 33 307 69 Williams D B Carter C B 1996 Transmission electron microscopy a textbook for materials science New York Plenum Press ISBN 030645324X Yu X Jin L Zhou Z H 2008 3 88 A structure of cytoplasmic polyhedrosis virus by cryo electron microscopy NATURE 453 415 419 Zhou Z H 2008
74. e important to be correct rather than having lots of uncertain detail in order to avoid model bias when we are trying to push the final model towards atomic resolution The new filter is efficient in getting a stable intermediate resolution model in combination with the existing full CTF correction method implemented and tested as the filtered CTF correction algorithm In this combination the algorithm also operates as an extra filter suppressing the noise more strongly Although the result may have a little bit less resolution the enhancement of the signal to noise ratio improves the stability of the model For instance in the first test of GroEL this combined method didn t generate the highest resolution model but it did produce a stable intermediate resolution model the observation of less spurious density in the inner channel of M3 is in line with the X ray structure of GroEL and the higher resolution EM model as presented in the results section It proves that such stable model is also a correct model How much of the improvement in the model resolution is due to better alignment and how much is due to the new CTF correction method We cannot answer this issue unequivocally The alignment and the CTF correction are so closely linked a better CTF correction allows a better alignment that we cannot separate the two Only the first iteration before alignment therefore could settle this issue The differences ar
75. e so small in this case that we assume the major improvement of our method causes from improved alignment due to the alternative CTF correction 61 Chapter 3 3 5 Conclusion A new approximation method of CTF correction has been implemented that was implemented in the EMAN package and can straightforwardly be incorporated into other 3D reconstruction software packages It provides an alternative CTF correction method in generating class average images The method shows better convergence and a better resolution of the final 3D structure even in the presence of relatively high noise levels The applied filter is continuously differentiable and does not introduce Fourier artifacts It effectively avoids instability in regions where the CTF has zeros The CTF correction is thus less sensitive to the zeros of CTF When the zeros of CTF are not or cannot be estimated accurately e g due to the low contrast slightly drift or astigmatism of the micrographs the new algorithm is expected to have higher tolerance The approximation inverse filter is only partially modified the inverse function When calculating the class average image images with different defocus will compensate each other at the zeros of the CTF in the Fourier space It must converge to the complete CTF correction when the number of differently focused images that make up the average images increases Acknowledgements We thank Wah Chiu and Steven Ludtke for the permission
76. eased mosaicity together with its indices 13 Threshold for the simulation an increased mosaicity For mosaic type 1 the default is 0 03 for mosaic type 2 it is 0 004 for mosaic type 3 the default is 0 05 14 MosaicType encodes different models for simulating the mosaic spread of the diffraction pattern It defines whether an off Ewald sphere reflection should be shown on the simulated diffraction or not 1 Angular mosaic the angular error of a reflection 2 Absolute distance the reciprocal distance between a reflection and the Ewald sphere 3 side elongation simulate the spot elongation along the main direction of the unit cell that lies most closely to the direction of the electron beam and calculate the reciprocal distance to the Ewald sphere useful for very thin plate like crystals that have characteristics of 2D crystals 6 8 Indexing an Electron Diffraction Image with Known Unit cell Parameters Once unit cell parameters have been inferred clicking the Indexing 53 in figure 2 button opens the Indexing Refinement window figure 6 This window is used for indexing centered background corrected diffraction images The main difference between Indexing Refinement figure 6 and Pattern Fitting figure 5 is that in the 134 User manual of EDiff former a diffraction pattern is indexed and in the latter an autocorrelation image is indexed The default background of Indexing Refinement
77. ed filter combines the data sets and performs CTF correction in Fourier space The application of the Wiener filter in 3D reconstruction needs an estimate of the spectral SNR e g an X ray scattering curve solution structure factor is necessary for this purpose However this is unavailable in many cases Moreover the assumption that we have a sufficient number of different defocus images and the CTFs can jointly cover the whole Fourier space without a gap is not always true For instance in the reconstruction with a small angular sampling step for projections e g 3 degrees more than one thousand projections classes can be used especially for a model of C1 Symmetry lots of classes contain a few particles only e g less than 10 as a basis for generating a class average image The Wiener filter method is not optimal in this case due to the large probability of superposition of multiple zeros An accurate estimate of the CTF parameters is essential otherwise the 46 A novel method of CTF correction merging of information pertaining to different particle images at the same frequency will lead to a breakdown of the continuity of the image in Fourier space B Spatial frequency weighted averaging Performing a weighted average of the images where the weights vary with spatial frequency EMAN Ludtke et al 1999 amp 2001 uses weight factors to avoid dividing by zero in amplitude correction The weight factors in averaging the
78. eeds to check the additional affiliate spots it s a bit slower than the normal Main Vector Matching method 6 7 Pattern Fitting of the Autocorrelation pattern Verifying the Unit cell Parameters After unit cell parameters have been found Show Fitting 39 in figure 2 can open a pattern fitting window for verification The Pattern Fitting window will fit each 130 User manual of EDiff auto correlation pattern with the Refined UnitCell model or if this does not exist with the BestFit UnitCell instead The Pattern Fitting window will index the auto correlation image Therefore the control panel see fig 5 has the same interface as the Indexing Refinement window This Pattern Fitting algorithm works as follows 1 find the facet in a simulated 3D lattice that best fits the main facet of an autocorrelation pattern 2 then cut through the 3D model lattice using the plane defined by the best fitting facet to generate a 2D diffraction simulation In figure 5 crosses mark the peaks of the spots of the autocorrelation image and blue circles mark the model lattice If the unit cell is correct the crosses and the blue circles should overlap well When almost of the images gt 90 fit well the unit cell most probably is correct The outliers might be caused by the inclusion of some deviant crystals in the data set by poor crystals with streaked rocking curves by unfortunate orien
79. en Objective lens Back focal plane objective aperture intermediate image 1 SAED aperture intermediate image 2 Viewing screen Image Diffraction pattern Figure 2 Image and diffraction modes of transmission electron microscopy Williams amp Carter 1996 SAED Selected Area Electron Diffraction The objective lens forms a diffraction pattern in the back focal plane and generates an image in the image plane intermediate image 1 Diffraction pattern and image are both present in TEM The intermediate lens decides which of them appears in the plane of the second intermediate image intermediate image 2 and is projected on the viewing screen It is easy to switch between image and diffraction modes by adjusting the intermediate lens Chapter 1 3DEM requires the reconstruction of a macromolecular 3D model from large amount of noisy 2D projection images e g Figure 3A of a specimen Electron crystallography is a method to gain and analyze diffraction patterns images in Fourier space e g Figure 3B of crystals 1D 2D or 3D crystals for the reconstruction of 3D structure in Fourier space similar as the technique used in X ray crystallography To see the true 3D structure underlying the recorded data sophisticated image processing and computing are indispensable for either method A B 5 Figure 3 Examples of a micrograph of single particles A and of a electron diffraction pattern of frozen nano crystal o
80. enough particle projections or the particles are highly symmetric the new algorithms are probably very useful Our method slightly over filters at high resolution see Figure 2 the red curve is higher than the blue curve at high resolution resulting in a dampening of these frequencies upon correction One should be careful with procedures that boost high spatial frequencies as they may lead to over fitting In order to push the resolution of the final model in 3DEM reconstruction to beyond 1 nm the user normally needs to do many iterations until the refinement has converged This refinement step is important and represents the most time consuming step in the 60 A novel method of CTF correction reconstruction procedure Since refinement does not always converge the new algorithms may provide at least part of the answer to this problem One reason for failure of the iterative refinement is distance in conformational space between the starting reference model and the final model The starting model normally has a resolution lower than 2 nm the expected final model has a resolution higher than 1 nm It would be very helpful and important to get stable intermediate resolution between 1 nm to 2 nm models in the reconstruction filling the gap between the starting model and the final high resolution model leading the iterative reconstruction to converge to the correct density map For these stable intermediate resolution models it is mor
81. ern can be observed on a fluorescent screen or be recorded on film image plate e g Figure 3B or a CCD camera The constructive interference of the electrons observed as spots in the diffraction pattern can be expressed by the Bragg s law Bragg 1913 nA 2d sinO Here n is a given integer is the wavelength of electrons d is the spacing between the planes in the atomic lattice 6 is the angle between the incident beam and the scattering planes Figure 5 explain both the constructive and destructive interferences Figure 5 According to the 20 deviation the phase shift causes constructive left figure or destructive right figure interferences The interference is constructive when the phase shift is a multiple of 2x From Wikipedia Theoretically diffraction patterns are Fourier transformations of their projection images on the Ewald sphere If the phases of the diffraction patterns from a crystal are known these patterns are mathematically equivalent to the projection images hence they can be used to reconstruct the atomic structure 15 Chapter 1 Electron diffraction is widely used in material science for analyzing the structure of metals and alloys In structural biology the application is still limited to for instance structure analysis of 2D and 1D crystals Up to now there is no existing way to obtain a 3D structure from the diffraction images of a 3D protein crystal The difficulties mainly lie in i The mat
82. es e EDiff exe e Patternson_dir_gui exe e FirstInstall bat e MCRInstaller msi and other supporting archives 6 2 Configuring and running EDiff on Windows Platforms 1 Open Unpack the package in a new directory 2 Run FirstInstall bat once on the machine where you want to use the software MATLAB Component Runtime MCR Libraries will install automatically 300M space on the C disk is needed Note if installation fails double click the file MCRiInstaller msi to install it 3 Run Patternson_dir_gui exe to start working with electron diffraction EM images The fist time this program is started it will unpack the supporting archives taking several minutes This software will generate four output files for each EM image lt image name gt atc plt lt image name gt atc jpg lt image name gt ctr pks and lt image name gt ctr png Put these outputs in a separate directory for the next step 4 Run EDiff exe to determine the Unit Cell parameters and index individual EM image 6 3 AMP Pre processing diffraction data The pre processing program AMP Autocorrelation Mapping Program with the executable file name Patternson_dir_gui exe has a Graphical User Interface GUI 110 User manual of EDiff This program is used to remove the background and for picking reflection spots from diffraction images A snapshot of the user interface is shown in figure 1 This program creates an autocorrelation pattern of the electron
83. es right pentagon 5 edges right hexagon 6 edges etc In 3 dimensions there are 5 regular polytopes regular 3 polytopes Fig 3 Tetrahedron 4 faces Cube 6 faces Octahedron 8 faces Dodecahedron 12 faces Icosahedron 20 faces In 4 dimensions there are just 6 regular polytopes regular 4 polytopes Fig 4 Simplex 5 tetrahedral cells Hypercube 8 cubic cells Cross polytope 16 tetrahedral cells 24 cell 24 octahedral cells 120 cell 120 dodecahedral cells 600 cell 600 tetrahedral cells In geometry a four dimensional polytope is sometimes called a polychoron plural polychora v amp O Tetrahedron Cube Octahedron Dodecahedron Icosahedron Figure 3 Five plantonic solids From wikipedia 32 Automated carbon masking and particle picking 16 cell 24 cell 120 cell 600 cell 5 cell Figure 4 Wireframe perspective projections of six convex regular 4 polytopes From wikipedia The coordinates quaternions of the vertices of these regular 4 polytopes are are known and can be found in numerous tables E g the coordinates quaternions of the vertices of unit 4 simplex are 0 0 0 1 0 559017 0 559017 0 559017 0 25 0 559017 0 559017 0 559017 0 25 0 559017 0 559017 0 559017 0 25 0 559017 0 559017 0 559017 0 25 Evenly sampling rotation space by subdivision of regular polytopes of 4D quaternion and its application in 3DEM As discussed above the problem of uniformly sampl
84. et al 2008 the highest resolution achieved so far by using cryo EM CPV belongs to the virus family of Reoviridae Reoviridae can affect the gastrointestinal system e g Rotavirus and respiratory tract Reovirus infects humans often it is easy to find Reovirus in clinical specimens TEM is suitable for looking into the molecules in atomic detail The cryo EM technique provides a way to observe the real native state structure as it exists in solution by freezing the samples extremely fast in a layer of vitreous ice Freezing reduces electron damage allowing a higher dose of electron exposure to gain better signal to noise ratio SNR images Cryo EM is thus the obvious choice to study large biomolecular complexes The enormous potential of cryo EM in biological structure determination has already been realized since the early 1990 s for a review see R Henderson 2004 Introduction Transmission electron microscopy has two modes available image mode and diffraction mode Figure 2 The 3D structure of a molecule cannot be obtained directly by TEM but must be reconstructed using computational methods In structural biology two new methods using TEM are still developing three dimensional cryo electron microscopy 3DEM also known as single particle reconstruction and electron diffraction or electron crystallography 3DEM uses the image mode of TEM and electron crystallography uses the diffraction mode Specim
85. ewer artifacts in filtering and allow more robust refinement The proposed inverse filter can be described as ae 1 C s E s C s gt 0 5 5 1M J0 5 C sy E s C s lt 0 5 48 A novel method of CTF correction E s E s Sig s s N s a U Sig s s 8 Here E s is an estimation of Es Sig s s is a sigmoid function Sig x 1 1t e as is shown in Figure 1 The idea is to create a continuous and differentiable function also continuous for derivatives of higher order to glue together the functions of E s at low frequency region and N s at the high frequency region where the noise dominates the density measured The scale factor a scales N s to the same level of E s at joint point So The user selected value S defines the frequency joint point of N s and E s The sensible choice is Sp 1 VB where B is the envelope B factor of the CTF estimate At this point the SNR value diminishes quickly l Sig s s Sig s sa Figure 1 The functions Sig s s and 1 Sig s s The modified G s is a piecewise continuous function which is continuous also in its first derivative At the region near zeros where C s lt 0 5 the C s is modified to a piece of continuous arc 1 0 5 C s which has a minimum value of 49 Chapter 3 approximately 0 2929 at the original zeros The inverse of 0 2929 is a small number 3 4 This simple modification makes
86. f a 70S ribosome tRNA complex reveals functional interactions and rearrangements Cell 136 1065 1077 Ludtke SJ Baldwin PR Chiu W 1999 EMAN Semiautomated software for high resolution single particle reconstructions J Struct Biol 128 82 97 Maier T Ferbitz L Deuerling E Ban N 2005 A cradle for new proteins trigger factor at the ribosome Curr Op Struct Biol 15 204 212 Matadeen R Patwardhan A Gowen B Orlova EV Pape T Cuff M Mueller F Brimacombe R van Heel M 1999 The Escherichia coli large ribosomal subunit 88 Recycling of aborted ribosomal 50S complex by Hspl5 at 7 5 angstrom resolution Structure 7 1575 1583 Moras D Comarmond MB Fischer J Weiss R Thierry JC Ebel JP Gieg R 1980 Crystal structure of yeast tRNAAsp Nature 288 669 674 Nakatogawa H amp Ito K 2002 The ribosomal exit tunnel functions as a discriminating gate Cell 108 629 636 Noller HF Hoang L Fredrick K 2005 The 30S ribosomal P site a function of 16S tRNA FEBS Lett 579 855 858 Petry S Brodersen DE Murphy FV Dunham CM Selmer M Tarry MJ Kelley AC Ramakrishnan V 2005 Crystal structures of the ribosome in complex with release factors RF and RF2 bound to a cognate stop codon Cell 123 1255 1266 Pettersen EF Goddard TD Huang CC Couch GS Greenblatt DM Meng EC Ferrin TE 2004 UCSF Chimera A Visualization System for Exploratory Research and Analysis J Comput Chem 25 13 1605 1612 Plaisier JR
87. f a protein lysozyme B Image processing and computing methods are essential for solving structures of macromolecules Both X ray crystallography and the NMR require the power of computing Images from electron microscopy Figure 3 also need image processing to reconstruct the 3D structure For EM images computing methods for 3DEM single particle reconstruction is still developing rapidly They utilize many computer image processing techniques In image mode TEM is affected by the instrumental aberration problem and the image is distorted by the contrast transfer function CTF Aberration correction of the CTF is one of the major tasks of image processing in 3DEM In diffraction mode diffraction patterns from electron microscopy actually represent a Fourier lattice Analysing this Introduction data also needs complicated procedures of image processing and computing Electron crystallography of 3D crystals is not new in inorganic chemistry and material science but it is a new in biochemistry There is no existing way to obtain a 3D structure from the diffraction images of 3D protein crystals though there are a few successful cases with 2D and 1D crystals But in theory a set of random diffraction images from one species of 3D protein crystals may include sufficient information to reconstruct their atomic structure No matter which methods are to be used complicated image processing procedures and time consuming computing are in
88. f the ribosomal proteins can be recognized while the result of normal full CTF correction left model is generally over corrected Using even odd tests and FSC with 0 5 criterion we calculated the resolution of each model respectively The model obtained using the direct CTF deconvolution has a resolution of 10 1 A The model of filtered CTF correction has an even slight better resolution of 9 8 A In both cases the resolution improved by more than 1A compared to the conventional full CTF correction using the same data and starting model The differences between the results on the ribosome compared to the results of GroEL suggest it is better to use the filtered CTF correction algorithm when the experimental data are very noisy e g images with a defocus of less than lum Although the data are noisy the algorithm stably suppresses the noise The filtered CTF correction algorithm suppresses the noise more strongly but doesn t prohibit the 3D reconstruction On the contrary Using only four iterative cycles the new algorithms are capable of producing a 3D structure with a better resolution while converging to the optimal resolution more quickly 3 4 Discussion The direct CTF deconvolution algorithm provides a novel approach to full CTF correction without using a Wiener filter Although it is an approximation approach in our tests it gave better results in practice than current methods Especially when we have
89. f them containing seven identical subunits The rings have an outer diameter of 13 7 nm and inner diameter of 4 5 nm each monomer has a molecular weight of 58 kDa Braig et al 1994 Hartl 1996 GroEL is one of the typical test beds for methods research in the field of 3DEM reconstruction Ludtke et al 2008 Stagg et al 2008 A total 4169 particles 128 by 128 pixels in size 2 08 A pixel were selected from 12 micrographs with defocus ranging from 1 9 2 3 um D7 symmetry 14 fold symmetry is imposed in the reconstruction thus 58366 asymmetric subunits are used The algorithms were all tested using the same particle data set and starting model The same set of projections was used as class references The classification required for making the averaged images was imported from one single reference supervised classification procedure Only the algorithms for making the average image including full CTF correction Figure 3 were different The three models shown in Figure 4 were reconstructed from the same reference model and classification 52 A novel method of CTF correction Projection Class averages obtained using different algorithms Figure 3 Representative class averages of GroEL generated by different CTF correction algorithms The second column is generated by the conventional full CTF correction algorithm The third column is generated by the new direct CTF deconvolution algorithm The last column is generated by the new
90. ficiently high to fit atomic models of the individual components 50S tRNA and Hsp15 into the EM density maps We confirmed our results with puromycin nascent chain release assays We identified the binding site of Hsp15 on the large ribosomal subunit and its contacts with the P site tRNA The conserved aL RNA binding domain of Hsp15 contacts helix H84 of 23S rRNA which is positioned close to the 30S 50S interface and it lines the cleft above the P site The D T loops of the P site tRNA within the 50Senc tRNA Hsp15 complex bind the positively charged C terminal a helix of 68 Recycling of aborted ribosomal 50S complex by Hspl5 Hsp15 Based on these findings we suggest a mechanism for the recycling of aborted 50S subunits during heat shock Initiation amp Elongation Hsp15 tRNA Nascent chain Heat shock amp Erroneous issociation Hydrolysis er Release factor 7 Translocation Q Hsp15 Figure 1 Rescue cycle of the stalled ribosomal 50S subunit Heat shock can erroneously dissociate a translating ribosome into a 30S subunit and a blocked 50S subunit carrying a tRNA linked to the unfinished nascent chain upper left Here we show that in these stalled 50Senc tRNA complexes the tRNA is located at the A site bottom left and that the small heat shock protein Hsp15 translocates the tRNA to the P site bottom right where it can be liberated by a release factor top right 69 Chapter 4 4
91. fore in uniform polar angle sampling orientations around K 0 and w r 2 are overrepresented again resulting in a non uniform distribution of orientations in 3D rotation space Sampling of amp and w does not have to be linear but is also possible to use platonic solids like the dodecahedron and the icosahedron Here the vertices of the polyhedron can be used as sampling points covering the sphere uniformly The sampling density of and y may be increased by subsampling the triangular or pentagonal faces of the polyhedron Yershova and LaValle 2004 This sampling however only describes a rotation with 2 degrees of freedom 2D The in plane rotation j still needs to be sampled in a separate step and the same objections remain orientations crowd around k 0 Orientations can also be defined by quaternions which do allow uniform sampling of rotational space Quaternions are 4D complex numbers of the form q atxit yj zk where i j k 1 jk kj i ki ik j 26 Automated carbon masking and particle picking ij ji k Rather than a real axis and a single imaginary axis as in ordinary 2D complex numbers quaternions have a real axis and three orthogonal imaginary axes The orthogonal directions of these axes are defined by the unit quaternions i j and k Arithmetic with quaternions is straightforward but multiplication does not commute e g jk kj In analogy to complex numbers the following properties of a
92. g from the edge detection result of the second step using a lower threshold in order to construct a new binary map This allows the regions already masked to grow and holes in the mask to be filled leading to better segmentation Fig 1c Next an initial mask image is created by binning the binary map by a large factor 10 X 10 pixels Fig Id In the last step a closing process for the mask image is performed In the primary mask image some holes are present in carbon regions and some false positive points in non carbon regions A new algorithm is used to close and smooth the image Fig le h The basic idea is that the edge of the carbon region is continuous and smooth and doesn t have sharp turns A masked point on the edge of a carbon region should have at least four masked neighbors or the mask at this pixel will be removed A similar rule for unmasked points is applied After several normally 5 6 of these iterative closing operations the mask map will converge to a nice map with smooth edges By default five iterations are performed but this value may be changed by the user The plug in produces mask images for carbon regions of the EM micrographs but large ice aggregates and over crowded blocks are masked out as well In our experience the module works well for most EM images producing adequate masks in 95 of cases 2 2 2 Even sampling of 3D rotation space We define the angular distance to be the angle about a common ro
93. g state as a result of the crystal constraints Difficult to solve in presence of disorder Advantages of 3DEM No need to crystallize No phase problem Introduction Small amount of materials needed Easy for large molecules up to 2000 A All native functional states in solution can be captured in principle Disadvantages of 3DEM large computational cost limited resolution highest resolution thus far 4 A Yu et al 2008 less developed for different conformational states Advantages of electron diffraction Can handle nano size crystals Growing nano crystals is relative easier Small amount of materials needed Strong diffraction with matter at an atomic resolution Share lots of common knowledge with well developed X ray diffraction techniques Disadvantages of electron diffraction Dynamic scattering Electron beam damage Manual data acquisition is less automated Other technologies such as powder diffraction and tomography are also relevant for structure determination but only have limited applications due to the low resolution that can be achieved 1 3 Basics of 3DEM single particle reconstruction 3DEM single particle reconstruction is the reconstruction of a macromolecular 3D structure from a set of cryo EM projection images In a micrograph e g Figure 3A the molecules exist in the form of single isolated particles randomly distributing in a layer of vitreous ice Thousands t
94. gements This work was in part supported by Cyttron www cyttron org and by the Swiss National Science Foundation SNSF and the National Center of Excellence in Research NCCR Structural Biology program of the SNSF to NB We would like to thank Sascha Gutmann for Hsp15 purification Ronald Limpens for doing part of the image acquisition and Daniel Boehringer for critically reading the manuscript 86 Recycling of aborted ribosomal 50S complex by Hsp15 Supplement Figure S1 Particles of the 50S tRNA Hsp15 complex selected from the Cryo EM micrographs size 120 120 pixels 2 54A pixel defocus 2 5um 1 0 9 0 8 0 7 0 6 0 5 0 4 Fourier Shell Correlation 0 3 0 2 0 1 1 1 1 f f 1 1 0 0 02 0 04 0 06 008 O1 012 0 14 016 0 18 0 2 Spatial Frequency 1 A Figure S2 Fourier shell correlation of the even odd test of the last iterative refinement reconstruction of the complex of 50S tRNA Hsp15 50S Ribosomal Complex The reconstruction of the free 50S ribosomal large subunit had a resolution of 22 A based on the 50 FSC criterion The resolution is relatively low because only 8681 particles from 37 micrographs were used and because we did not collect defocus pairs It conforms to the known global shape of the 50S particle Matadeen et al 1999 87 Chapter 4 References Baranov PV Vestergaar B Hamelryk T Gesteland RF Nyborg J Atkins JF 2006 Divers
95. gorithm for unit cell determination from randomly oriented electron diffraction patterns of different but similar crystals These diffraction patterns may be noisy their centre may be poorly defined and their low resolution reflections which are of prime importance for cell determination may be obscured by a beam stop or be outshone by the central beam To deal with these problems we first calculate the autocorrelation pattern of the diffractograms Because of the low curvature of the Ewald sphere the spots of the diffractogram overlap with all spots of the autocorrelation pattern but not vice versa see also fig 1 Furthermore autocorrelation patterns have an inversion centre whereas the beam centre of a diffractogram may be unknown Identifying the peak positions in the autocorrelation pattern is similar to the approach taken by the indexing program Refix Kabsch 1993 which calculates the low resolution spacings between observed spots 93 Chapter 5 A B C Figure 1 A Electron diffraction pattern of lysozyme electron energy 300 keV B Diffraction pattern after removing the central beam and subtracting the radial background C Auto correlation pattern of B The diffractogram in Figure 1 A shows a regular point symmetrical pattern The flatness of the Ewald sphere the wavelength of 300 keV electrons is approximately 0 019 A causes this regularity The low resolution peaks in the autocorrelation pattern form a 2D la
96. he functions may also differ slightly in the different software packages Once estimates of the CTF and noise parameters are available estimates of the functions of CTF and noise will be known There are several solutions to use these in correcting the measured image data in 3D reconstruction software packages 1 Filtering at the first zero of the CTF by truncating the high resolution part after the first zero No actual CTF correction is applied in this case Usually it is suggested to use this procedure only for making the first prototype model and in other early stages of the structure determination 2 Applying phase correction only as it is for instance done in IMAGIC van Heel et al 2000 This is achieved by flipping phases of structure factors at spacings where the CTF dips below zero whilst keeping the amplitudes intact The 43 Chapter 3 rationale of flipping the phases is that the phase plays a much more important role in the structure determination than the amplitude Ramachandran amp Srinivasan 1970 The rationale for not correcting the amplitudes is that boosting low level amplitudes close to the CTF zeroes will deteriorate the overall signal to noise ratio in rings in Fourier space Hence only applying phase correction without bothering about the amplitudes also has practical advantages 3 Do both phase and amplitude correction Complete CTF correction or full CTF correction is normally performed in two sepa
97. hematical equivalence between phased electron diffraction patterns and their corresponding projection structures are compromised by the multiple scattering of electrons dynamic diffraction Even when the thickness of the sample is less than 100 nm dynamic diffraction still affects the data ii Protein crystals are susceptible to radiation damage caused by the electron beam Some researchers are trying to solve the structure of 3D nano crystals by using tilt series which is similar to the technique of tomography in diffraction mode as is prevalent in X ray crystallography Unfortunately this is not yet suitable for the beam sensitive protein crystals with current electron detection methods iii Electron diffraction in TEM still needs lots of manual intervention For example locating the crystals in image mode and tilting the sample manually are time consuming operations Compared to highly automated X ray diffraction experiments electron diffraction is still extremely tedious In the research described in chapter 5 nano crystals and the new technique of precession of the electron beam were used to reduce the dynamic diffraction problem Clear electron diffraction patterns could be acquired for structure determination To solve the atomic structure from the electron diffraction patterns of protein nano crystals following steps are required 1 Background removal and spot location Firstly center the diffraction images and remove the
98. ic axis and recording a set of oriented diffraction patterns a tilt series at various preferably main crystallographic zones Vainshtein Vainshtein 1964 proposed a simple 2D lattice reconstruction methods based on tilt series where the d values for the non tilt axis were plotted against the tilt angle Recently a method of cell parameter determination based on a tomography tilt series of diffraction patterns was presented Kolb et al 2008 A different algorithm is implemented in the programme TRICE Zou et al 2004 which determines the unit cell in two steps First the position and the intensities of each diffraction reflection in the individual electron diffraction patterns from the tilt series are determined and refined For the purpose any three reflections that do not lie in the same line are selected and are assigned a 2D index assuming a primitive cell Then the positions of diffraction spots and the angles between the diffraction patterns are used to identify the shortest 3D vectors defining the unit cell parameters and the crystal orientation The angle between two electron diffraction patterns of a single crystal oriented with a double tilt holder at the angles a 6 and as 22 is given by 92 Unit cell determination from randomly oriented electron diffraction patterns 0 cos cos a7 cos f cos a2 cos fz cos a sin f cos a2 sin B sin a sin a The concept of the Niggli cell and the cell redu
99. ical problems can be solved electron diffraction on protein nano crystals can be of immense importance in the foreseeable future and cryo EM will be as important as synchrotrons for protein crystallography 140 Summary With the help of modern techniques of imaging processing and computing image data obtained by electron cryo microscopy of biomolecules can be reconstructed to three dimensional biological models at sub nanometer resolution These models allow answering urgent problems in life science for instance the pathways directing the self recovery system of cell which certainly has great significance for all our lives To determine these models there are two main electron microscopic methods available corresponding to its two main modes of operation 3DEM single particle reconstruction and electron diffraction This thesis focuses on the research and methods of 3DEM chapter 2 and 3 and electron diffraction and its practical application in solving the structure of a 50S ribosomal complex which clarifies the mechanism of cell recovery in heat shock stress chapter 4 Preliminary research on a novel structure determination method by using nano crystals resulted in a novel software suite EDiff which is a program for unit cell parameter determination and indexing chapter 5 and 6 The first chapter of this thesis introduces the background of some methods in structural biology specifically emphasizing the relationship between
100. iform Eulerian or polar angle sampling produces a non uniform set of orientations in which certain orientations occur far more often than others we developed an algorithm that generates such a uniform set of orientations using unit quaternions We also discuss this new algorithm below 2 2 Methods The new methods of automated carbon masking and uniform sampling of rotational space for a model based particle selection have now been implemented as plug ins in Cyclops software 2 2 1 Automated carbon masker Fully automated particle picking requires a masking procedure that identifies the areas of the micrograph that contain the useful data Usually the microscopist is only interested in particles within the holes of the carbon layer One way of finding the proper regions is to use a carbon layer with a regular grid of circular holes These layers however are not yet being used routinely and most of the times the holes are irregular in both size and spacing Currently no other automatic carbon masking algorithm for EM image processing exists Traditional edge detection and segmentation algorithms do not work due to the extreme high noise in this type of cryo EM image Here we present a new masking algorithm which is based on the relatively high variance within carbon regions Since this is also a property of regions containing aggregates these are also masked by the method The method consists of a series of image processing steps which t
101. igure 5B to generate all possible solutions and pick a better fitting facet The RefineOrient procedure is based on this fitted facet If this fitting is not correct the orientation refinement and indexing will be meaningless 2a Select RefineOrient Select the Resolution range from which No of pairs facets are used for the refinement 4 5 7 11 in figure 5B need to be set The RefineOrient procedure will select pairs of high resolution reflections fitting and indexing these high resolution facets to find a more accurate orientation of the diffraction pattern using the known or inferred unit cell parameters If 136 User manual of EDiff ckV1V2hk 20 in figure 5B is checked the procedure will ensure that V1 amp V2 together with their indices are present in the simulated pattern when indexing the high resolution reflections If yow re uncertain of the correctness of the indices of V1 amp V2 click the radio button checkV1V2 21 in figure 5B to ensure the existence of two reflections shown on the positions of V1 amp V2 but without fixing their indices so in this case other orientations that change the indices of V1 amp V2 are also allowed 2b Alternatively to RefineOrient the algorithms RF and RF3 can be selected Some parameters for RefineOrient 4 5 7 11 20 21 options in figure 5B are not used by RF2 and RF3 Other parameters MosaicType
102. images in one class K s are given by _ 1 RO GOEG COE R YC 5 E K s 6 Where the subscript n denotes particle number and m denotes the total amount of particles in the class The term 1 C s E s is the inverse of CTF the same function as the term 1 H s of the Wiener filter Ra s C s En S N s is used as the relative signal to noise ratio SNR for each particle N s is left out assuming it to be approximately equal in different micrographs If an estimate of the solution structure factor curve is known the absolute SNR can be calculated and used instead of the relative SNR In this case this method actually acts as a Wiener filter An additional Wiener filter or a low pass Gaussian filter may still be applied to smooth the final model If there are only a few defocused images this procedure may run into trouble of coincident zeros and in practice EMAN calculates the direct average C Other methods Other ways of doing a full CTF correction have been tried as well such as the iterative method given by Penczek Penczek et al 1997 the Iterative Data Refinement IDR technique Sorzano et al 2004b and Chahine s method Zubelli et al 2003 Differing in important details these methods all attempt finding an approximation of the original image by iterative refinement or minimization of a residual function Their 47 Chapter 3 penalty is that they increase the time consumed by
103. ing 3D rotations can be reduced to the more straightforward task of uniformly sampling the 4D hypersphere of unit quaternions To uniformly sample the 4D quaternions a subdivision procedure is performed i Select one of the regular 4 polytopes as the base of sampling e g the simplex ii Then construct a stack in the program and push the known quaternions of the 4 polytope onto the stack e g the 5 vertices of Simplex are pushed onto the stack iii Calculate the geometric mean of each two quaternions vertices in the stack until all the combinations are used then push the medians to the stack Not all combinations of quaternions are allowed only those combinations which result in a new quaternion with a length that is close to 1 are included In the algorithm this is optimized by a specific selection process but it goes too far to describe it here in great detail 33 Chapter 2 iv This subdivision step can be done iteratively until the precision of sampling the angular distance A 2 between two neighbor vertices reaches the user requirement Subdivision into edges faces and cells of certain regular polytopes may result in a series of discrete number of quaternions in the stack 5 8 15 16 24 32 5880 6120 26520 30360 as showing in Table 1 Basic Simplex Cross Hypercube 24 Cell 600 Cell 120 Cell platonic polytope Basic 5 8 16 24 120 600 vertices no Subdivis
104. ion matrices sorted according to their quality of fit You can inspect all these orientations and check how well they match the diffraction pattern by selecting their sequence number in the Rotation Matrix spin box 6 in figure 5B Most of the time the orientation at the top of the list fits best One way of picking the best indexing solution is e Clicking ShowMosaic to show the indexed mosaic pattern all the model reciprocal lattice spots that are close to the Ewald sphere e then go through all the possible orientations in the Rotation Matrix spin box starting from the most likely fitting sequence number zero to find the best fit For certain unit cells in certain orientations it may be that more than one orientations 137 Chapter 6 indexing solution fits well This depends on the unit cell parameters and unfortunate combinations can exist in which it is not possible to distinguish on the basis of the positions of the diffraction spots alone In this case you would also need to include intensity information and 3D merging of the diffraction data This is beyond the current scope of EDiff In these rare cases you have to judge for yourself which is the most reasonable indexing 6 9 Conclusion The program EDiff will allow you to determine the unit cell of a crystal type even if you can only collect single shots from randomly oriented crystals It will index the diffraction images and allows considerable use
105. ion 15 32 40 120 840 1320 1 iter Subdivision 65 176 168 600 5880 6120 2 iter Subdivision 285 848 712 2712 30360 26520 3 iter Table 1 Numbers of uniform quaternions generated by iterative subdivision of regular 4 polytopes It means that we can not randomly select any number of quaternions for uniformly sampling 3D rotation space but we can certainly select a sampling with the precision that is higher than what we need To use the quaternions we need to convert the 4D quaternions to Euler angles triples which are accepted by most other programs to represent rotations An equivalent problem in 3D space can be solved by sampling the unit sphere using platonic solids like the dodecahedron and the icosahedron The subdivision procedure was degraded to sampling 3 dimensional regular polytopes regular 3 polytopes generating uniform distributions on the 3D unit sphere It is worth mentioning that although this distribution evenly samples rotation axes e g Fig 5 it does not evenly sample rotation space as no in plane rotation is included Nevertheless also this result is still very useful in current popular 3DEM reconstruction software packages 34 Automated carbon masking and particle picking 0 5 z axis Qo 0 5 y axis x axis Figure 5 Uniform sampling on the surface of 3D unit sphere based on subdivision of icosahedron 1002 sampling points with 6 angular distance There
106. is still under control and the algorithm is stable Two new algorithms that apply the proposed function of G s have been implemented for calculating a class average image Algorithm of direct CTF deconvolution A class average image can be calculated by aligning and straightforward averaging of all the G s filtered images within a class To distinguish our method from other conventional methods we refer to it as direct CTF deconvolution as its filter G s can be used for calculating the class average image A 1 N without a Wiener filter which in a formula is F s LEM s A wide 1 low pass Gaussian filter can still be used to erase the limited noise at high resolution A Wiener filter or other filter can be an optional choice for the later processing stages but by omitting it at this early stage we can also circumvent some of its more problematic aspects see above Algorithm of filtered CTF correction The proposed function of G s can also be used in combination with other full CTF correction methods since most of them have an inverse term in the algorithm For example in the weighted average method which is used by the ctfc or ctfcw options of EMAN software the new function of G s can be used instead of the first term 1 C s E s of the weight factors in averaging the images In this case the implemented algorithm works like a selective filter suppressing the noise only at regions near zero
107. ise and Tom de Kruijff for technical support Dr S Nikoloupulos and Prof C Giacovazzo for providing the pharmaceutical powders for the electron diffraction experiments M W A Kok for making the figure 3 B Prof X Zou and Eleni Sarakinou for help with the programme PhIDO and Dr Rag de Graaff Vikas Kumar and Qiang Xu for the fruitful discussions 106 Unit cell determination from randomly oriented electron diffraction patterns References Biswal B K Sukumar N and Vijayan M 2000 Acta Cryst D56 1110 1119 Boysen H Lerch M Stys A and Senyshyn A 2007 Acta Cryst B63 675 682 Clegg W 1981 Acta Cryst A37 913 915 Dexter D D and van der Veen J M 1978 J Chem Soc Perkin Trans 1 185 Georgieva D G Kuil M E Oosterkamp T H Zandbergen H W and Abrahams J P 2007 Acta Cryst D63 564 570 Gibon V Norberg B Evrard G and Durant F 1988 Acta Cryst C44 652 654 Grosse Kunstleve R W Sauter N K and Adams P D 2004 Acta Cryst A60 1 6 Henderson R 1995 QO Rev Biophys 28 171 93 Kabsch W 1993 J Appl Cryst 26 795 800 Kolb U Gorelik T and Otten M T 2008 Ultramicroscopy 108 763 772 Plaisier J R Jiang L and Abrahams J P 2007 Journ Struct Biol 157 19 27 PhIDO Phase identificarion and indexing from ED patterns Calidris Solentuna Sweden 2001 www calidris em com Saijo S Yamada Y Sato T Tanaka N Matsui T Sazaki G Nak
108. itFacets 17 FitFacets find all the potential facets that fit V1 amp V2 3 ShowIndex show turn off the fitted pattern and its index 15 GenMosaic generate a diffraction pattern using the mosaic parameters described below 4 amp 5 Resolution range from which select No of pairs facets 11 for refining the orientation using RefineOrient 10 fitting and indexing the high resolution reflections in order to find a more accurate orientation of the diffraction image Don t forget to press lt enter gt after having inserted a value The resolution range will show up as blue circles Be sure this resolution is within the global ResolutionRange show as black circles set on EDiff main interface figure 2 7 Tolerance maximum index error tolerance used for indexing high resolution reflections in RefineOrient 11 Maximum No of pairs facets for refining the orientation using RefineOrient 20 ckV1V2hkl check the existence of V1 amp V2 with their indices when indexing the high resolution reflections in RefineOrient Only useful when the MainVectorMatching algorithm was selected V1 amp V2 must exist for this option to be meaningful 21 checkV1V2 check the existence of the two reflections V1 amp V2 and show their positions when indexing the high resolution reflections in RefineOrient Only useful when the MainVectorMatching algorithm was selected V1 amp V2 must exist for
109. ize 148
110. kground Rotation Mati 1 RefineOren RF2 RF3 shower MosaicType 2 2 Threshold 0 004 ShowMosaid Rotation Matrix 1 0 Fitted Main Facet 0 0 E Zelectrondif lyso ilt serials bakup 040708_12 atc plt V1 53 31 1 4 V2 32 56 1 A Ratio 1 64 Angle 89 58 degree A Images No EE a Unit Cell Edges Angles CloseZone RMSE AngErr OverallRMSE Diitracets Fitted_facets 16 are Benosa RefineOrient Resolution D gt Tolerance QBs No of pai DS 20 ck 1 2hkI 8 AtcBackground rotation Matic QT Memorie Oro MosaicT ype Threshold Drowmosaic ca B Figure 5 A Pattern fitting of the main facet and the peaks of the autocorrelation image to unit cell parameters Crosses mark the peaks of the spots of the 132 User manual of EDiff autocorrelation image blue circles mark the best fitting diffraction simulation of a given unit cell B Control Panel of the Pattern Fitting and Indexing Refinement window in EDiff V1 0 all options highlighted and described below 1 Slide bar to select an image its sequence number will be shown on the right When the bar is active the left and right arrow key can also be used for controlling the bar 2 Search box locate a file using its name and pressing enter if more files match the name press enter to switch between them 16 Fitted_facets spinbox select a specific facet if more than one facet was generated by F
111. level is an important and often vital strategic step to find the reasons behind many human diseases This step can help us clarifying the role of the shape of proteins and their complexes including viruses in health and disease Structure determination of viruses is thus a persistent hot topic of research Figure 1 shows an example of the structure of cytoplasmic polyhedrosis virus CPV Biomolecules even the so called macromolecules normally have a tiny size measured in tens of nanometers or less Such molecules are too small to see with the light microscope The techniques that can reach atomic resolution mainly include X ray crystallography nuclear magnetic resonance NMR spectroscopy and electron cryo microscopy cryo EM X ray crystallography has been able to tackle large complexes but is limited to complexes that can form crystals and NMR is only suitable for smaller macromolecules and complexes This leaves a large number of Chapter 1 challenging structures that cannot be resolved using the X ray and NMR techniques Especially for large complexes that resist crystallogenesis electron cryo microscopy cryo EM or cryo electron microscopy is a viable alternative This technique is a combination of transmission electron microscopy TEM and cryo equipment Figure 1 Structure of cytoplasmic polyhedrosis virus CPV with a resolution of 3 88A obtained by using cryo EM single particle reconstruction EMDataBank id EMD 1508 Yu
112. lution 4A result of GroEL using cryo EM reconstruction Ludtke et al 2008 also excludes the possible existence of additional ordered density in the inner channel of live GroEL in solution All this confirms the validity of the new CTF correction algorithms We will further address the correctness of the EM models in the discussion In order to compare the convergence of different algorithms we also calculated the Fourier Shell Correlation using the 0 5 criterion between the results and the starting model for a rough comparison of the inter models differences Table I Here the FSC value between models can be considered as a measure of inter model similarity From the comparison we can see that M2 is 6 7A similar to the starting model while M1 is at 5 3A It shows that the direct CTF deconvolution method has better convergence properties less model bias it is more different from the starting model smaller internal divergence better resolution more consistency between the models of even and odd numbered particles The test shows the two new algorithms to be feasible alternatives for other CTF correction algorithms and suggests they have better convergence properties than the normal full CTF correction 3 3 2 Asymmetrical particles the stalled ribosomal 50S complex The complex of a large ribosome subunit 50S with tRNA and heat shock protein 15 was used to test the new algorithms The complex has a diameter of
113. lutionRange allows entering the resolution range manually Don t forget to press lt Enter gt to validate it If the values of resolution range are changed here they will also be changed in the main window of EDiff 17 ShowRange shows the resolution range as two black circles in the pattern 25 AtcBackground shows the autocorrelation image or background removed diffraction pattern as background By default the autocorrelation pattern is shown 26 ImageSpots show the peaks of the background removed diffraction pattern as dark blue crosses or show the peaks of autocorrelation pattern as black crosses or show both 27 V1V2 gt Aff add V1 and V2 to An affiliate spots list 28 ClearAff delete all the spots in the affiliate spots list 29 SetAff if this button is checked V1V2 gt Aff and ClearAff operations will only apply to the current image When clicking in the image with this button selected a new affiliate spot will be added to the affiliate spots list 23 BrightV1V2 find the brightest two spots in the diffraction pattern and select these as the main facet 22 All do the BrightV1V2 search for all the images not only for the current one 7 An affiliate spots list is a list of reflections that is used for checking a simulated 2D lattice Every diffraction simulation of a potential unit cell must contain the main facet V1 amp V2 spots and all the affiliate spots in the same time otherwise
114. m 3 Full Vector Matching To the user the Full Vector Matching algorithm appears very similar to the Unique Facet Matching algorithm but its inner workings are different Normally it s rather slow and we advise you to only use it for comparison and verification On the other hand as it uses more data it can be more accurate Main steps Set the basic microscope and diffraction parameters in the graphic interface figure 2 127 Chapter 6 Choose a data directory with SetDataDir If you know the crystal system or want to test out whether your assumption of the crystal system is reasonable select it otherwise select Triclinic Set the search range of edges and angles Set the SearchAlgorithm to Full VectorMatching 2 Find the proper ResolutionRange click CheckData and adjust the resolution range to cover all the main vectors in different images It is important to set the resolution range as narrow as possible as this solution is very time consuming since it uses all the vectors in the resolution range in its calculations Close the window of CheckData Save V1V2 is NOT necessary 3 Click the DoSearch button to perform unit cell parameters search The console window running in the background will indicate progress 4 The best fitting unit cell parameters will be displayed in the BestFit UnitCell column and the best five results will be shown in the console window
115. master degree cum laude he joined the Cyttron research project as a Ph D candidate in the department of Biophysical Structural Chemistry Leiden University He devoted himself to the research of new methods and their applications in solving the structures of macromolecules which resulted in this thesis 146 A Special Word of Thanks To end my thesis I would like to express my sincere gratitude to all the people who helped me and supported me during the last four years First I would like to thank Prof Dr Jan Pieter Abrahams for his guidance support and encouragement during my research period I found great enlightenment from his remarks Lots of original ideas resulted from the fruitful discussions with him With his support I had so many opportunities of advanced traineeship e g in Houston USA Madrid Spain and Antwerpen Belgium I would also like to thank my supervisor Dr Jasper R Plaisier for his great help in starting my research of single particle reconstruction I really appreciate the happy time that we work together and our journey to the USA for an international conference near Lake Tahoe Many thanks to my collaborators who helped me and contributed in the project of ribosomal reconstruction Prof Dr Nenad Ban Dr Christiane Schaffitzel Dr Roman I Koning Dr Rouven Bingel Erlenmeyer Dr Philipp Korber Dani l C de Geus And also in the project of electron crystallography Prof Dr Henny W Zandbergen Dr Stavr
116. n facet old V1 amp V2 as affiliate spots Buttons 22 23 27 29 of the CheckData window see figure 4 allow these actions Button 27 V1V2 gt Aff must be used to add V1 and V2 to the affiliate spots list Button 23 BrightV1V2 will find the brightest two spots in the diffraction image and reset V1 amp V2 to them The user can switch the background from the autocorrelation pattern to centered diffraction pattern for verification by turning off the radio button 25 AtcBackground This solution proved also valid and reliable in various test cases in which the experimental data were very noisy and lots of miss tilted diffractions were collected We encourage all experienced users to try this method at least once Main steps 1 Set the basic microscope and diffraction parameters in the graphic interface figure 2 Choose a data directory with SetDataDir If you know the crystal system or want to test 129 Chapter 6 out whether your assumption of the crystal system is reasonable select it otherwise select Triclinic Set the search range of edges and angles Set the SearchAlgorithm to BrightestSpotsMatching Click CheckData and set a large resolution range to cover most of the brightest spots in different images In the window of CheckData visually check the main facet V1 amp V2 Button 20 Refine in figure 4 can be used to refine the position of VI amp V2 Button 27 V1V
117. n the X ray films were quantified densitometrically 4 4 5 Specimen preparation and cryo electron microscopy For grid preparation a 20 fold molar excess of Hspl5 was added to 150 nM 50Senc tRNA complexes Glow discharged carbon coated lacey Formvar grids 300 mesh Ted Pella were loaded with 3 ul sample approximately 150 nM of ribosomal complex Grids were blotted and plunged into liquid ethane using a fully automated home built environmental chamber and vitrification device operating at 100 humidity and 25 C Micrographs were recorded on film at a magnification of x50 000 under low dose conditions lt 10e A with a FEI Tecnai F20 electron microscope operated at 200 kV using a defocus range of 1 5 to 4 8 um taking focal pair images Images were recorded on Kodak SO 163 film and developed for 12 minutes in full strength KODAK D19b developer Micrographs were scanned with a scan step of 4000 dpi on a Nikon super coolscan 9000 scanner corresponding to a pixel size of 1 27 A on the object scale 83 Chapter 4 4 4 6 Image Processing and 3D Reconstruction Single particles were selected from the EM micrographs using Cyclops Plaisier et al 2007 We also used Cyclops to create the particle sets and manage Cryo EM micrographs We used the unique features of Cyclops to generate masks for removing the carbon layer large ice regions over crowed regions and aggregates In order to speed up the processing we rescaled the original photos to 1
118. nally active again 81 Chapter 4 4 4 Materials and Methods 4 4 1 Preparation of 50S nc tRNA complexes The plasmid pUC19Strep3FtsQSecM was transcribed in vitro and translated in a membrane free E coli cell extract as previously described Schaffitzel amp Ban 2007 The translation mix was loaded directly onto a 38 ml sucrose gradient 10 50 sucrose in 50 mM Hepes KOH 100 mM KOAc 0 3 mM Mg OAc 2 pH 7 5 and centrifuged for 15 hours at 23000 rpm 4 C in a SW32 Ti rotor Beckman Coulter The 50S fraction was loaded onto a 300 ul Strep Tactin sepharose column IBA G ttingen Germany equilibrated with buffer 1 20 mM Hepes KOH 150 mM NH4CI 1 mM Mg OAc s 4 mM B mercaptoethanol pH 7 5 at 4 C eluted with 2 5 mM desthiobiotin in buffer 2 20 mM Hepes KOH 150 mM NH4CI 12 mM Mg OAc 4 mM B mercaptoethanol pH 7 5 and pelleted by ultracentrifugation 3 h 55000 rpm 4 C TLA 55 rotor Beckman The 50Senc tRNA 50S nc pellet was dissolved in buffer 2 by gentle shaking on ice 4 4 2 Purification of Hsp15 The plasmid pTHZ25 Korber et al 1999 was transformed in E coli BL21 DE3 and the cells were cultured as described Cells were ruptured by two passages through an EmulsiFlex C5 homogenizer Avestin at 15000 psi and the lysate cleared by ultracentrifugation 1h 18000 rpm 4 C Ti70 rotor Beckman The supernatant was loaded onto a Q sepharose FF column GE Healthcare and a phenyl sepharose column GE Healthcar
119. nd important Aberration correction of the CTF is important and different correction methods affect the resolution of the final model The newly implemented method yielded higher resolution models with data sets from both highly symmetric GroEL and asymmetric structures 50S ribosomal complex The tests also proved to be an efficient correction method that allowed quick convergence of the 3D reconstruction and had a high tolerance for noisy images In Chapter 4 with the single particle analysis of stalled 50S ribosome structures I discovered the mechanism of how the heat shock protein Hsp15 recovers the aborted ribosomal elongation cycle under cellular stress When thermal stress dissociates the 50S and 30S particles of translating ribosomes a 50S particle with a tRNA carrying a nascent chain can result Because the nascent chain is threaded through the 50S particle the tRNA does not readily dissociate and hence the 50S particle is rendered useless However upon binding of the Hsp15 to such stalled 50S particles the tRNA is translocated from A site to P site and stabilized in a discrete conformation The A site is then freed up for a release factor to dissociate the tRNA and the 50S subunit regains its translational activity We determined the structure of the complex of the 50S ribosome carrying Hspl5 and a nascent chain tRNA to a resolution of 1 0 nm This resolution approaches the highest resolutions obtained so far for asymmetric 3DEM
120. noise ratio SNR images Firstly edge detection with a large Prewitt operator There are lots of known edge detectors such as the Roberts operator Sobel operator Laplacian or Gaussian etc Here 9 9 size Prewitt operator see below Prewitt H1 amp H2 was selected because it can also suppress noise by averaging For instance if every pixel is 12 7A a 9 9 size Prewitt operator covers 114 3A 9 12 7 width height in real space which is comparable to single particle size of 200 250 A Edge detector Prewitt H1 l 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0O 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 30 Automated carbon masking and particle picking Edge detector Prewitt H2 The filtering result Fig 1b clearly shows the edge of carbon region block ice and 50S particles Secondly binarize image with selft adaptive threshold When transferring grayscale images to binary images only white and black colors we can hardly find a fixed threshold which works well for all of the images To solve this problem an adaptive threshold needed to be implemented which was realized here according to the statistic attributes of each of the images We chose Threshold Average Average is the averaged grayscale value of all pixels Clearly the threshold is adaptive it changes for every different image that has differen
121. o hundreds of thousands of noisy images of individual molecules are needed to calculate the 3D structure Chapter 1 Biomolecules are highly susceptible to radiation damage when exposed to the electron beam In order to decrease the damage images are obtained with a low dose of exposure and by using electron cryo microscopy Nevertheless the technique results in extremely noisy images Averaging method is needed to calculate a high signal to noise ratio SNR structure from these noisy images All the molecules must have the same inner conformation to within the resolution limit of the reconstruction otherwise the averaging is meaningless To start a single particle reconstruction all we need is cryo EM micrographs of randomly distributed particles and reconstruction software e g IMAGIC SPIDER EMAN A typical reconstruction process shows as Figure 4 Cryo electron Microscop Figure 4 The diagram of single particle reconstruction process of IMAGIC van Heel et al 2000 Generally speaking image processing of 3DEM includes several steps 1 Single particle selection Introduction Normally only about 500 particles can be selected from a single EM micrograph but a typical 3DEM reconstruction needs more than tens of thousand of particles The micrographs are very noisy images due to the low dose exposure of cryo EM It is too difficult for a person to select large amount of particles required for 3DEM manually Automated
122. ocess which is the most time consuming step in the reconstruction Software packages for iterative refinement and pushing the 3D models to atomic resolution are still in continuous development For electron diffraction of 3D protein nano crystals lots of work is still needed to determine atomic structures such as intensity integration recovering the phase and refinement The work described in this thesis is only the first step in a series of many that may lead up to a general method for solving structures with diffraction data of 3D protein nano crystals In X ray crystallography scientists invest major efforts into growing protein crystals which in many cases do not grow beyond a size of several micrometers Solving structures using such protein crystals requires the most advance and expensive third generation synchrotron beam lines However electron crystallography can deal with even smaller crystals of nanometer size which are beyond the reach for X rays but ideal for electron diffraction Chapter 7 Electron crystallography has already been successful for a number of complicated inorganic compounds in material science Organic and protein crystals are now also being studied by several research groups There is no theoretical obstacle to solving atomic structures by using electron diffraction But technical problems do exist for example protein crystals suffer from the serious and limiting factor of radiation damage If these pract
123. on of the algorithm see chapter 5 EDiff has several variations of the general algorithm for identifying unit cell parameters which are discussed below 6 6 1 Algorithm 1 Unique Facet Matching This algorithm is the most straightforward one It is a good idea to try this method first especially for first time users Below we walk you through the procedure 125 Chapter 6 Main steps 1 Set the basic microscope and diffraction parameters in the graphic interface figure 2 Choose a data directory with SetDataDir If you know the crystal system or want to test out whether your assumption of the crystal system is reasonable select it otherwise select Triclinic Set the search range of edges and angles Set the SearchAlgorithm to UniqFacetMatching 2 Find the proper ResolutionRange click CheckData and adjust the resolution range to cover all the main vectors in different images Close the window of CheckData Save V1V2 is NOT necessary 3 Click the DoSearch button to perform unit cell parameters search The console window running in the background will indicate progress 4 The best fitting unit cell parameters will be displayed in the BestFit UnitCell column and the best five results will be shown in the console window Use Show Fitting to check whether the result is reasonable or not This algorithm is the most automated one After the user has clicked the Do
124. on ranges can be limited to ensure that the relative topology of the fragments is maintained We started with a few segments checking intermediate results and ultimately fitted 57 separate rigid fragments 23S RNA was segmented into 29 fragments based on the secondary structure 5S RNA was segmented into 2 fragments and every ribosomal protein was treated as a single rigid body Difference maps were generated by subtracting the fitted density of 50S subunit form the EM maps To fit tRNA and Hsp15 in the difference map we first placed the tRNA and Hspl5 manually and then improved them respectively as rigid bodies with 85 Chapter 4 LOCALFIT We use the atomic model of tRNA as there is no structure known of tRNA the tRNA present in the 50S complex The fit of the tRNA could be slightly improved by segmenting it into two fragments Different types of tRNA can have different angles between the anticodon and D arm and the arm containing the acceptor stem and T WC stem Moras et al 1980 Accession codes The three dimensional EM maps of the 50Senc tRNAsHsp15 and 50Senc tRNA complexes were deposited in the European Bioinformatics Institute Macromolecular Structure Database with accession codes EMD 1456 and EMD 1455 respectively The fitted atomic structures of 50Senc tRNA Hsp15 were deposited in the Research Collaboratory for Structural Bioinformatics Protein Data Bank with IDs 3BBX 50S 3BBV P site tRNA and 3BBU Hsp15 Acknowled
125. ons providing a set of reference images Chapter 2 of my thesis describes an optimal sampling of rotational space to generate a minimal set of reference images with a maximal covering of potential orientations The set of reference images is used in the subsequent iterative alignment and classification steps Refinement is the most time consuming step in 3DEM For instance on Pentium 4 1 6G Linux PC 1500 particles need 5 hours per iteration 2500 particles need 11 hours per iteration So how about 100 000 particles And more particles if an even higher resolution is required It may need days weeks or even longer So most state of art reconstructions are carried out on a parallel computing facility such as a supercomputer or a computer cluster Although there is a reasonably wide choice in software for 3D reconstruction such as EMAN SPIDER IMAGIC etc the method of 3DEM is still developing rapidly since the cryo EM technique started booming in the most recent 10 years The main difficulties of this method are low resolution high noise time consuming calculations and semi automated software still leave enough space for improvement 14 Introduction 1 4 Basics of electron diffraction and structural reconstruction When the electron beam in a TEM passes through a thin e g lt 100 nm crystalline layer the electrons scatter and interfere with each other and if the microscope is set to the proper mode a diffraction patt
126. or MainVectorPair in lattice Lattice2FacetTri_BEval 6 5 Checking the Data After having run AMP to prepare the data for EDiff the data can be checked by entering the data directory in EDiff SetDataDir button 27 and clicking the CheckData button 28 This opens the window shown in Figure 4 The purpose of checking the data is to allow the user to verify that the peak positions of the auto correlation images and peaks positions of the background removed diffraction patterns coincide It also automatically finds the main facet also called main vectors V1V2 for each autocorrelation image Here the peaks of the spots within the resolution range are visualized as crosses the points of simulated lattice generated from this main facet are indicated by small circles Normally if the crosses Lattice2MainFacet BEval is a function to generate main facets from electron diffraction images for the Unique Facet Matching algorithm calculation The angle of the facet is limited in between AngleLowerBoundary and AngleUpperBoundary of Find UniqFacet in Pattern Lattice2FacetTri_ BEval is a function to generate main facets from electron diffraction images for the Main Vector Matching algorithm calculation The angle of the facet is limited in between AngleLowerBoundary and AngleUpperBoundary of Find MainVectorPair in Pattern 121 Chapter 6 overlap the circles very well then that means the
127. or semi automated software was created in need to accelerate this task The software Cyclops designed in our group Plaisier et al 2007 includes an automated function to select single particles Different methods are available in the software to locate the potential particles such as the methods of local average local variance and cross correlation In this thesis I describe my contribution to this program in chapter 2 2 Filtering amp centering An optional pre processing step is to filter the particle images with a low pass filter erasing the high frequency noise as well as a little information detail Mislocated intensities caused by the contrast transfer function CTF of the electron microscope have to be phase corrected at this step That is so called CTF phase correction Further amplitude correction will be needed in a later step for full CTF correction In chapter 3 of this my thesis I discuss a novel approach to these corrections Particles are centered in several alignment cycles in which the cross correlation between each individual image and the overall average image of a given data set is calculated 3 Classifying amp averaging A classification step is required to assign particles to different classes in which the projections are assumed to be taken from the same view angle One of the classification methods is Multivariate Statistical Analysis MSA van Heel et al 2000 In this method Principal Componen
128. os Nikolopoulus and Dr Dilyana Georgieva I am really impressed by Dilyana for working so hard and spending so much time in collecting perfect electron diffraction data and help me testing the EDiff software We successfully collaborated in determining the unit cell of several types of nano crystals I also acknowledge the contributions of the master students Maurits W A Kok and K I M IJspeert in this project I am very grateful for the help from other teachers and colleagues Dr RAG de Graaf Dr Maxim Kuil Dr Navraj S Pannu Prof Dr Mathieu Noteborn Dr Irakli Sikharulidze Dr Pavol Skubak Dr Zunfeng Liu Dr Pavol Skubak Dr Ellen Thomassen Jan de Sonneville Francoise Grenouilleau and others Particularly thanks to Dr RAG de Graaf for translating the summary to Dutch Samenvatting 147 Special thanks to my wife Hua Pan She abandoned a nice job and easy life in Shanghai to accompany me She always understands me and supports me and has even helped me with producing drawings and documentation for my thesis Without her I would not have such a lovely son Hauer Jiang who was born in May 2008 She works so hard and is such a good unselfish mother in our small home Last but not the least I would like to acknowledge my families in China my parents parents in law brother and sisters Though they are far away they always contact me and give me encouragement and confidence To those whom I forgot to mention I apolog
129. our data also indicate why Hspl5 does not have a marked affinity for translating 70S ribosomes the presence of the 30S subunit partially blocks access of Hsp15 to its binding site on the 50S subunit and the conformation of the tRNA interacting simultaneously with the peptidyl transferase center on the 50S subunit and the decoding center on 30S subunit would not allow it to rotate into the position necessary for Hsp15 binding as observed in the EM reconstruction of the 50Senc tRNA Hsp15 complex Which release factor cleaves the aminoacylester bond between tRNA and nascent chain in the 50Senc tRNA Hsp15 complex All well characterized release factors interact with translating ribosomes and mimic a tRNA molecule They all have a stop codon recognizing domain at one end and a GGQ peptidyl hydrolase domain at the other end which interacts with the peptidyl transferase center of the ribosome Baranov et al 2006 Petry et al 2005 Klaholz et al 2003 Rawat et al 2003 In the blocked 50Senc tRNA Hsp1I5 complex there is no need for a stop codon recognizing domain The putative 15 kD 140 aminoacid protein with unassigned function encoded by the yaeJ gene in E coli is a likely candidate for this role In coli yaeJ is transcribed immediately ahead of cutF nplE a factor involved in the extracytoplasmic stress response both apparently belong to the same stress induced operon Connolly et al 1997 YaeJ contains the conserved GGQ peptidyl hydrolase
130. p15 at this Mg concentration The experiments were performed in duplicate 78 Recycling of aborted ribosomal 50S complex by Hsp15 4 3 Discussion Translational reactivation of a heat shock aborted 50Senc tRNA complex requires removal of the nc tRNA by severing of the aminoacyl ester bond between these moieties In the cell this hydrolysis requires the tRNA to be located in the P site and a release factor to bind at the vacant A site In the absence of Hsp15 the tRNA moiety of nc tRNA although being somewhat disordered was clearly located in the A site Fig 3a The A site location of the tRNA moiety was further corroborated by a puromycin assay Fig 7 At first sight this is a surprising result as in the complete 70S ribosome peptidyl tRNA has a preference for the P site However in the 70S complex peptidyl tRNA is stabilized at the P site by extensive contacts with the mRNA 16S RNA and protein residues of the 30S subunit e g Ref Noller et al 2005 and these interactions are obviously absent in the 50Senc tRNA complex On the other hand the A site location of the tRNA is stabilized by additional interactions with residues of the 50S subunit that lie outside the peptidyl transfer center e g helix 38 of the A site finger Stark et al 1997 Apparently in the absence of the 30S subunit these interactions are strong enough to direct the tRNA moiety in the 50S nc tRNA complex to the A site Our observation explains wh
131. plt Images No 9J ad Fitting Threshold lt refine Well pas R Find Next gt gt Wyeark Bad SaMark Normal hark Gooch nportant get ResolutionR ange Angstrom A ShowRange rave VIV2 AtcBackground f nageSpots Fiv2 gt Aff Clearaft el pave As Bright V1v2 eek ShowSimu ShowV 1 2 Reset 1 Reset 2 SetAff Close J Figure 4 Check data window in EDiff V1 0 all options highlighted 1 Slide bar to select an image for checking the sequence number will show on the right 123 Chapter 6 When the bar is active the left and right arrow keys can also be used to slide the bar 2 Search box used for locating a file by typing in the filename and pressing enter If more files match the name pressing enter switches between them 3 Slide bar to set the fitting threshold show on the right which is used in the Find Next function 4 Find Next gt gt click this button to find the next pattern that has a fitting value larger or smaller than the Fitting Threshold Fitting value is a measure of how well the simulated lattice fits with the experimental autocorrelation pattern 5 7 Mark the quality of the image as Bad Normal Good or Important This is used to weigh the images as sometimes certain orientations are rare but give vital information on one of the cell parameters Only in such cases and provided the image is nice it should be marked as Important 16 Reso
132. quaternion are defined Conjugation q a xi yj zk Sum qi q2 qi q2 e Product q1q2 qo qi e Magnitude lal V qa Real part q q 2a Quaternions are attractive for describing orientations If qq 1 q is a unit length quaternion p p 0 the real part of p is zero p qpq then p is related to p by a 3D rotation in imaginary quaternion space The axis about which p is rotated to generate p is xi yj zk and the angle of rotation is 2acos a Another useful notation of a unit length quaternion therefore is q cos k 2 xi yj zk where is the angle of rotation and x y z is the positive direction of the rotation axis Suppose q and qz are unit quaternions then both define a 3D rotation of a volume V generating two copies V and Vs respectively This being the case the operation that rotates V onto Vs is defined by the quaternion product q2 q1 The angular distance A12 between the two objects is given by the real part of the quaternion qo qi according to cos Ay 2 2 q2q1 qoqi 2 27 Chapter 2 qoqi t qiqo 2 1 The orthogonal distance between q and qz is given by lqi qol q q2 qi qz qi q2 q1 q2 qiqi qigo qoqi q2q2 l qiqo qoq 1 2 Substitution of Eq 1 in Eq 2 shows that the orthogonal distance between two unit quaternions q and qp is strictly related to the angular distance A12
133. r interaction in determining verifying and assessing the results This is required as every crystal may have its own peculiarities and only by understanding the way in which the program its results can you truly appreciate the relevance of the suggested solution Next steps include integration of the data determining the intensities of the diffraction spots and phasing These are currently beyond the capacities of EDiff and I am working towards these additional options 138 Chapter 7 Conclusions and Perspectives The research described in this thesis includes new methods for 3DEM single particle reconstruction new software modules for particle picking and a more efficient CTF correction method These new methods were used to solve an important biological question how does the recovery system of heat shock disrupted 50S ribosomal complexes work Preliminary research on electron diffraction of nano crystals allowed unit cell determination and resulted in the EDiff software suite Combined with image processing techniques electron microscopy is powerful enough to investigate the atomic structure of bio molecules The potential of electron diffraction is still developing 3DEM will allow investigations at near atomic resolution and can become as powerful as the X ray diffraction method in the foreseeable future The method of 3DEM still has scope for further research and improvement For instance for speeding up the Multi Reference Alignment pr
134. rate steps first flipping the phase and then applying amplitude correction Due to it being theoretically optimal the problem of full CTF correction is frequently addressed in the community of 3DEM methods research e g Frank amp Penczek 1995 Zhu et al 1997 Ludtke et al 1999 Zubelli et al 2003 Wan et al 2004 Sorzano et al 2004b Grigorieff 2007 A general approach to do full CTF correction is to find a deconvolution filter function G s so that we can estimate F s as follows F s G s M s 2 To recover the amplitude of the object F s a simple attempt is F s 1 CTF s M s 3 Here G s 1 CTF s However this attempt is not feasible in practice due to the problems of random noise and zeros of the CTF The random noise cannot be removed directly It is expected to be reduced by averaging multiple images in one class The We do not discuss approaches that reduce noise by improved detectors or other experimental aspects of data collection Medipix a photon counting pixel detector Plaisier et al 2003 as these approaches are fully compatible with the improvements in data analysis discussed here With class we mean the result of references projections supervised classification or an automatic classification In a class images are assumed to be the projections from the same view of a 3D model and they are used to calculate a class average image 44 A novel method of CTF correction C
135. rocedure Show Fitting fit each auto correlation image with the Refined UnitCell model if there is no refined unit cell it uses the BestFit UnitCell instead Used for indexing an auto correlation pattern and verifying the search result of the unit cell parameters Indexing index the centered background removed diffraction image EDMosaic simulating a diffraction pattern for testing By selecting the Tool Config menu a window opens that allows detailed configuration of some global parameters see Figure 3 The default parameters are empirical settings they work well with most of the data used for testing Don t change them unless you do really know the meaning of each parameter and know what you re doing 119 Chapter 6 W Global Params Configuration Files 1 0 MaxFilesReadin Facet VectorPair Fitting ScaleT olerance Full ector Matching VYectLengthT olerance VectAngleT olerance Find UnigFacet in Pattern AngleLowerB oundary Diffraction Patterns Fitting MinPattsFitR atio MinSpotsFitRatio MaxFitError Pixels Main ector Matching VectLengthT olerance 0 15 VectAngleT olerance 5 Find MainVectorPair in Pattern AngleLowerB oundary AngleU pperB oundary 30 Cancel AngleUpperB oundary Figure 3 More detail global technique parameters configuration of EDiff V1 0 If you re really interested a brief description of each variable is MaxFilesReadIn Maximum
136. ry to keep the edge information of EM images as much as possible while dealing with the high 23 Chapter 2 noise levels e Figure 1 Intermediate results of the carbon masking algorithm on a micrographs of 50S ribosomal subunits showing a original image b result of edge detection c removal of sparse points and growth of masked regions d initial mask e h iterative closing of the scaled down initial mask The algorithm for automated masking of the carbon comprises the following steps First the image is scaled down to a smaller size by binning n X n pixels where n is an integer number thus speeding up processing and suppressing the noise level by averaging Fig la Second edge detection with a large size Prewitt operator Prewitt 1970 is applied and the result is converted to a binary map using a self adaptive threshold based on the statistics of the gray scale distribution of the image Chang et al 1995 Fig 1b Next sparse points usually located outside the carbon layer are removed from the binary map The amount of pixels with value 1 within a given distance of the pixel examined must exceed a threshold otherwise the pixel is set to 24 Automated carbon masking and particle picking zero This leaves most of the points in a carbon region whereas the sparse points in regions with just vitreous ice are erased Subsequently the regions near every none zero pixel are searched in the map resultin
137. s it is fairly robust Because our algorithm uses autocorrelation patterns rather than the original data precise knowledge of the position of the beam center is not required as autocorrelation patterns are always cantered by definition Using autocorrelation patterns for unit cell determination would fail at higher diffraction angles but since the wavelength of the electrons used approximately 0 013A was 2 to 3 orders of magnitude smaller than the highest resolutions we used for our analyses between 1 and 4A this did not impose any serious problems in practice For the small molecule crystals which belonged to orthorhombic or cubic space groups and hence had 3 or less degrees of freedom in their unit cell parameters the algorithm performed well reproducing literature values within a few percent We do not expect a higher level of accuracy as the method is based on the low resolution spacings In a subsequent indexing and unit cell refinement step which will use the original diffraction pattern we assume that these small errors can be reduced Somewhat surprising was the unit cell we found for orthorhombic lysozyme which had a significantly shorter b axis and a significantly longer c axis than unit cells reported in literature The unit cell volume of largest known orthorhombic polymorph of hen egg lysozyme was about 13 smaller than that of our nano crystals table 2 Unfortunately our nano crystals could not be grown to a larger size
138. s a starting model for the reconstruction of the two 50S nascent chain tRNA complexes Statistics of the reconstructions are given in Table I We examined the uniformity of the ribosomal complexes present in the sample by re analyzing the data using supervised classification As starting models we used empty 50S and 50Senc tRNA The vast majority gt 80 of ribosomal complexes correlated best with the 50Senc tRNA starting model indicating the sample was essentially uniform 84 Recycling of aborted ribosomal 50S complex by Hspl5 Table I Statistics of the three dimensional reconstructions 50S 50Senc tRNA 50Senc tRNA Hsp15 Numbers of particles 8 681 10 731 defocus 33 922 defocus pairs picked pairs Particles used in the 92 84 85 final 3D reconstruction Resolution 0 5 FSC 22 14 10 Numbers of micrographs 37 42 112 Defocus range um 2 5 3 5 1 5 4 1 0 6 3 5 FSC Fourier shell correlation 4 4 7 Fitting X Ray structures into the EM density maps generation of an atomic model We used the Colores subroutine of SITUS Wriggers et al 1999 to fit the high resolution model of the 50S subunit of the 70S E coli ribosome Schuwirth et al 2005 into our EM density Subsequently we segmented the 50S model and fitted the segments in the density map using multi rigid body refinement For this purpose we used our program LOCALFIT which is a 6D searching tool in Fourier space within which the translation and rotati
139. s and the high resolution end in a manner adapted to each image These two new algorithms were implemented and tested in EMAN 1 6 and it also works for the newer version of EMAN 1 8 The algorithm of filtered CTF correction is implemented as a combination of the new function with the weighted average method of the EMAN refinement program which also applies a Wiener filter We have tested and compared the new algorithms using a data set from a highly symmetric structure and one obtained from a structure with no internal symmetry 51 Chapter 3 3 3 Results Two sample data were used to test the algorithms First we demonstrate the feasibility of the two new algorithms Then by comparing the results from conventional full CTF correction to the new algorithms we show the new algorithms both have the advantage of better convergence while both are stable in the reconstruction process of asymmetric macromolecules 3 3 1 Highly symmetrical particles a test with GroEL The high resolution EM data of native free GroEL that we used were kindly provided by Ludtke and Chiu for testing the algorithms The data were first made available course material for the participants of the workshop on Single Particle Reconstruction and Visualization 2007 in Houston USA Sample preparation and data acquisition were described elsewhere Ludtke et al 2004 GroEL is a homotetradecameric protein consisting of two back to back stacked rings each o
140. s randomly oriented electron diffraction patterns with unknown angular relationship is presented here The algorithm determined unit cells of mineral pharmaceutical and protein nano crystals in orthorhombic high and low symmetry space groups allowing well oriented patterns to be indexed Chapter 5 5 1 Introduction Elastic diffraction provides the information for atomic structure determination However the majority of electrons or X rays impinging on a sample scatter inelastically and these inelastically scattered quanta induce radiation damage Relative to the total elastic diffraction high energy 300 keV electrons deposit approximately 1000 times less energy in thin biological samples than X rays and hence induce less radiation damage after normalising for the elastically diffracted quanta In theory electrons should therefore be more suited for structure determination if radiation damage is the limiting factor Henderson 1995 However practical problems in data collection and data processing prevent the use of electrons for 3D crystallographic structure determination of organic molecules like proteins and pharmaceuticals Here we address one of these practical problems determining an unknown unit cell from random diffraction patterns In electron crystallography the unit cell is determined from electron diffraction tilt series For this purpose 3D diffraction data are collected by tilting a crystal about a selected crystallograph
141. s the microscope allows Moreover if the unit cell is large the reflection spots will often be elongated in the direction normal to the plane of the crystal due to the wide spike function or rocking curve in X ray terms in this particular direction This can be caused by the limited number of unit cells in this direction As a result of this elongation the positions of the reflections present on the diffraction patterns may not represent the centroid of the reflection As this is an implicit assumption of the algoritms discussed previously they may not be reliable any more for thin plate like nano crystals with a large unit cell This may be compounded by missing information on the unit cell dimension normal to the plane a few ultra high tilted diffraction images may still have some useful information but may have a very poor quality due to the high tilt This algorithm abandons the idea of using the main facets and instead uses the two brightest spots in the diffraction image not the autocorrelation image The brightest spots are most likely to have their centroids closest to the Ewald sphere and can be further from the center thus containing higher index information also in the direction normal to the plane of the crystal The main practical difference from the users perspective is that the two brightest spots are set as the new main facet V1 amp V2 in CheckData tool It is strongly advised to set the original mai
142. selectie door het automatisch maskeren van koolstof gebieden in de foto zowel als meer nauwkeurige plaatsbepaling bij gebruik van een beginmodel In hoofdstuk 3 wordt een nieuwe methode van benadering gepresenteerd waarmee de amplitude modulatie die het gevolg is van de contrast transfer functie CTF van het gebruikte microscoop gemodelleerd kan worden Hierdoor kan de resolutie die verkregen kan worden met 3DEM worden verbeterd tot in het subnanometer gebied De nieuwe benadering bevordert tevens een spoedige convergentie van het iteratieve reconstructieproces waarbij een hoge tolerantie voor beelden met veel ruis opvalt Een praktische toepassing het bepalen van de structuur van een 50S ribosomaal complex wordt beschreven in hoofdstuk 4 De verkregen resultaten zijn verhelderend voor het begrip van het herstelmechanisme van cellen die te lijden hebben gehad van hitte shock Wanneer ten gevolge van hitte shock dissociatie optreedt van de 50S en 30S deeltjes van transcriptieribosomen is het mogelijk dat een 50S deeltje ontstaat met een gedeeltelijk getranscribeerd tRNA Wanneer Hspl5 bindt aan zo n stalled 50S deeltje verhuist het tRNA van de A site naar de P site en is daar stabiel in een gegeven conformatie De A site is dan vrij voor een release factor waardoor het tRNA kan 144 dissoci ren en het 50S deeltje zijn activiteit herwint Verkennend onderzoek naar een structuurbepalingsmethode gebaseerd op diffractie
143. setting the center 10 Instead of setting the value to 0 one can also chose to use the beam stop removal tool for any given shape of beam stop This comes in handy when the user suspects that the center is found far from its actual position 11 Allows the user to smooth the image This option is only advised when salt and pepper noise is present because this type of noise is not removed well with the standard background removal tools The user is notified that using this option might result in a minor loss of data 12 Allows the user to decide which intermediate output images are shown while running the program This output consumes large amounts of memory so when you process more than ten images you would better not choose this option 13 Selects the directory that contains the original images jpeg tiff 14 amp 15 Selects the directory that will be used to store the plt files and autocorrelation images 16 Quits the program The program processes all images in one directory One can chose to work with jpeg tiff or both file types simultaneously The program takes about 2 minutes to process a single image In the current version we strongly advise against dragging or changing any windows that are related to the GUI during image processing or you might crash the program Currently AMP is a single thread program which means that it can t handle more than one job at a time Furthermore there is a limited amount of virtual
144. stically 1 N smaller whereas the length of the indices vectors of fitted facet is N times bigger so the weighting factor of the square of indices length in 4 corrects the over fitting problem of oversampling 5 3 Results 5 3 1 Unit cell determination of mayenite from electron diffraction data The algorithm was tested on randomly oriented electron diffraction data from mayenite Caj2A1 4033 a cubic inorganic mineral fig 3 Our algorithm suggested a cell parameter of 11 9 A which is in line with a reported value from literature of 11 98 A Boysen et al 2007 We could index the diffraction patterns of certain zones satisfactory fig 3 with RMSD s between observed and predicted spot positions of about 0 5 We considered data from 8 diffractograms in this analysis In order to test the accuracy of our method and the potential for false minima we performed a fine grid search fig 3B Here we found a broader second minimum around 17 A This is within a few percent a factor V2 times larger than the known unit cell of about 12 A and hence represents an oversampling of exactly the same lattice 99 Chapter 5 J A 8 ey fs ver ey C ke e Q ie 9 g b 0 2 5 5 015 o x 0 1 0 05 0 12 0 5 10 15 20 B Unit cell A Figure 3 A Examples of autocorrelation patterns from experimental electron diffractograms of mayenite Crosses indicate the centroids of the peaks of the autocorrelation image used for
145. stop remove tool Smooth image jefe tet fe BaF Stine Y atlab figure output C Original Image C Removed beamstop C Autocorrelation map C pit output Save directory of autocorrelation map ER S N ey 5 th Na Save directory of plt file 4 Original_Image J 3 se 5 Information Box Directory containing images 5 J New Guide Matlab JPG Ga B File currently processed 6 Ns Figure 1 Graphical User Interface of pre processing program AMP V1 2 with all options highlighted 1 Run button to start the program with the desired settings Selection of images types that will be processed Image window Slider to select current image in directory Change to original pattern Autocorrelation pattern png output pattern Progress tracker Information box containing error messages and help files GO ON OA Eer 9e Parameter input allowing the user to change area of the center beam that needs to be removed 112 User manual of EDiff 9 Allows the user to make the program more or less flexible in finding the center of the diffraction pattern automatically The number indicates the allowed error that is based on the difference in length between two different independent calculations of the beam center Setting it to a higher value allows the program to accept more elliptic or irregular shapes of the central beam whereas setting it to 0 automatically redirects the user to a window for interactively
146. suggested for indexing refinement 135 Chapter 6 m Indexing Refinement i Ce Images No i Unit Cell Edges 32 0137 53 2363 63 9863 Angles 90 30 90 CloseZone 0 0 1 RMSE 1 25 AngleEn 0 21 OverallAMSE 13 32 FitFacets Fitted_facets 0 4 ShowlIndex GeniMasaic RefineDrient Resolution 6 2 68 Tolerance 08 No otpairs f3 3 K I okV1V2hkl T__AtcBackground Rotation Matrix 0 El RefineOrient RF2 RF3 ShowRF MosaicType 1 amp Threshold 10 03 ShowMosaid Rotation Matrix 0 5 Fitted Main Facet 0 0 E electrondiff lyso tit serials bakup 040708_12 ctr pks W1 13 30 1 A V2 8 1511 A Ratio 1 63 Angle 89 79 degree Figure 6 Indexing of a background corrected diffraction pattern using unit cell parameters that were inferred in earlier steps Crosses mark the peak positions of the reflections of the diffraction image Small blue circles are the best fitted diffraction simulation of the selected unit cell Here the unit cell was determined using the Bright Spots Matching algorithm VI amp V2 are the two brightest spots of the diffraction pattern AO and Al are the affiliate spots of the autocorrelation image The control panel of this window shares its interface with the Pattern Fitting window fig 5B Steps of orientation refinement and indexing 1 Visually check whether the main facet V1 amp V2 fits well and is reasonable indexed If not click FitFacets 17 in f
147. t total mean grayscale value The parameter J can be changed by the user The default value by experience is 2 3 which is stable for most of EM images For EM photos taken in different facilities it may need to be slightly adjusted The other techniques generating a primary mask image and iterative closing of the final mask have already been presented in the methods section In conclusion the abundant variance information is well used in the algorithm of automated carbon masking It relies on the fact that the carbon region and white ice region always have higher variance than the vitreous ice region In a few cases when the variance of the carbon region is very low for example insufficient exposure of the 31 Chapter 2 carbon region may cause wrongly classifying carbon regions as vitreous ice In these cases the failed data normally have lower quality and should be excluded in later processing 2 3 2 Implementation of even sampling of 3D rotation space Regular polytopes of 4D quaternion Regular polytopes also called platonic solids are convex solids where all the building blocks vertices edges faces hyperfaces have the same characteristics That is vertices have the same number of neighbours edges are all the same length polygons are all the same shape and area and hyperfaces have the same volume Bourke 1993 In 2 dimensions the type of regular polytopes is infinite E g regular triangle 3 edges square 4 edg
148. ta except perhaps for setting the proper ResolutionRange and it gives quick results e Main Vector Matching requires running CheckData to select verify and save the facets of each diffraction image that are to be used in the calculation This option is 29 30 31 33 36 39 53 52 User manual of EDiff useful for very noisy and or marginal data e Full Vector Matching does not require running CheckData as it uses all vectors within the resolution range It can be rather slow but it is useful for refinement and comparison e Brightest Spots Matching a variation of Main Vector Matching especially useful for thin nano crystals with a large unit cells For more details please see the chapter on Unit cell Parameters Determination SaveParms save all the parameters in a file so that the parameters can be loaded next time by select File Open menu DoSearch to start unit cell parameter determination The result will show on the console window and the BestFit UnitCell column DoRefine refine the unit cell parameters refinement edge parameters steepest descend refinement with decreasing step size starting from the BestFit UnitCell and reporting the result in Refined UnitCell BestFit UnitCell reports the best fitting unit cell parameters found by DoSearch procedure Refined UnitCell reports the refined unit cell parameters generated by DoRefine p
149. target function as closely as possible The squared difference function is used to calculate the least square error of fitting two facets If we assume that po and p define the 2D vector pair of the observed facet and qo and q define the simulated facet then the square error is defined as r po qR pi qR 3 Where R is the rotation matrix that minimises r This function can be solved analytically for R thus speeding up its computation In order to improve accuracy but at the expense of computational speed multiple vectors of the autocorrelation image can also be matched However it is not sufficient to accumulate the residual defined in 3 for all observed facets We need to take into account that by choosing an arbitrarily large unit cell resulting in a very dense modelled reciprocal lattice this residual can be decreased at will We tested several weighting schemes and found that the one which most consistently produces good unit cells is 98 Unit cell determination from randomly oriented electron diffraction patterns r po goR hgal pi qR hg 4 Where the weighting factors Ago and Aq are the integral indices vectors h k 1 of go and q of simulated facet For instance the indices of go and q of a facet might be 0 1 1 1 0 0 in which case haol would be 2 and Mai would be 1 If a simulated dense lattice is N times oversampling the observed lattice the r value in 3 is stati
150. tation axis that maps one object onto another The centres of mass of both objects are superimposed and the rotation axis goes through this joint centre of mass Orientation space is sampled by a discrete set of 3D orientations with a precision of A if the angular distance between any orientation from the continuum of possibilities and at least one orientation from the sampled set is smaller than A 25 Chapter 2 There are many ways to sample orientations with a given angular distance One example is Eulerian sampling where each of the Euler angles is sampled by A and all possible combinations of a B y are generated There are many definitions of the Eulerian rotation angles and here we use the convention of a rotation by a about the Z axis then a rotation of B about the new Y axis and finally a rotation of y about the new Z axis Clearly when B 0 only the sum of a and y is defined a property also known as a gimbal lock At even sampling of Euler angles rotations with a final rotation axis close to the Z axis are therefore overrepresented resulting in a non uniform distribution of orientations in 3D rotation space Polar angle sampling suffers from similar problems Here the orientation is defined by the angles b y x where x is the right handed rotation about an axis with polar coordinates and y Uniform sampling of the polar angles is also inefficient as at k 0 b and y are undefined and at w 7 2 b is undefined There
151. tations or unexpected failures to index the pattern properly Only an experienced eye can tell However don t be fooled into certainty when the information of one unit cell dimension is missing in the original data some crystals have a preferred orientation and if you haven t tilted the diffraction grid you may not have sampled the reciprocal lattice well enough If you don t believe a certain indexing click FitFacets 17 in figure 5B to go through all potential fittings in a spin box 16 in figure 5B The fitted facets are sorted and a smaller number should give a better fitting The buttons and options in RefineOrient group box are not originally designed for this Pattern Fitting window but for refining the orientation of diffraction image in the Indexing Refinement window However if you really want to you can use this RefineOrient operation to index the autocorrelation pattern for testing and comparing even though some buttons to do with refining diffraction patterns may be not fully functional for refining autocorrelation images 131 Chapter 6 m Pattern Fitting with Auto Correlation Image Images No Unit Cell Edges 32 0137 53 2363 63 9863 Angles 90 90 90 CloseZone 0 0 1 RMSE 0 86 AngleE rr 0 42 OverallRMSE 5 21 FitFacets Fitted facets 0 Showindex GenMosaid RefineDrient Resolution 4 2 46 Tolerance 0 8 No of pairs 10 3 Vv I ckVTV2hkl I AtcBac
152. ter et al 1978 Gibon et al 1988 On the basis of these unit cells we could index two main zones 001 and 011 in the case of potassium penicillin G using the program PhIDO Phase identification and indexing from ED patterns 2001 see fig 4 We considered data from 13 diffractograms for potassium penicillin G and 11 for sodium oxacillin in the analysis 101 Chapter 5 b h Figure 4 4 Crystals of potassium penicillin G scale bar 2 um B E Electron diffraction patterns and corresponding autocorrelation patterns of potassium penicillin G from two main crystallographic zones Crosses indicate the centroids of peaks in the 102 Unit cell determination from randomly oriented electron diffraction patterns autocorrelation image circles indicate predicted the peak positions The root mean square deviation RMSD of the experimental and simulated patterns for the different zones diffraction patterns is between 0 6 and 1 7 5 3 3 Unit cell determination of orthogonal lysozyme In the case of orthogonal nano crystals of hen egg lysozyme our algorithm did not produce a unit cell that is known from literature Saijo et al 2005 Biswal et al 2000 see fig 1 for an example of a diffractogram and corresponding autocorrelation pattern see table 2 for reported unit cells and the unit cell determined by our algorithm For this calculation we used 19 different crystals The crystals adopt preferred orientations on the EM
153. terms of computer resources as every distinctive view and orientation of the low resolution 3D structure requires a separate search There are several ways of speeding up such model inspired particle picking Most importantly use is made of the correlation theorem which states that the product of the Fourier transform of one function with the complex conjugate of the Fourier transform of another is the Fourier transform of their correlation Proper local and resolution dependent scaling are essential to avoid false positives but in general this is fairly straightforward As discrete Fourier transforms are calculated using FFT routines numerically efficient algorithms result However additional optimizations are still required including two optimizations we designed and implemented in Cyclops First when dealing with samples deposited on holey carbon it often is important to select only those particles that are suspended in the film of vitreous ice and exclude particles that have attached themselves to the carbon In order to automate recognition 22 Automated carbon masking and particle picking of the carbon region so that it can be excluded from computerized particle searches we developed a new algorithm that is discussed below Second efficiency can be increased if the list of 3D projections of the low resolution model used for automated correlation searches is sampled as sparsely as possible implying uniform sampling As un
154. the 3D reconstruction CTF correction is a vital prerequisite for effective 3D reconstruction using 2D images obtained by electron microscopy This explains why so many researchers are continuously trying to improve existing methods and developing new ones Here we introduce a novel approximation filter for CTF correction It is easily implemented and shows good convergence properties in iterative reconstruction refinement Application of the filter proposed clearly improves the resolution and it is robust in tests with noisy close to focus data sets 3 2 Method We propose a novel approach we constructed continuous and differentiable function which allows direct application of an inverse CTF filter in 3D reconstruction The function contains no singularities in its approximation to the CTF Since the simple attempt of G s 1 CTF s fails because of CTF s having zeros and other small values the CTF curve is partially modified avoiding zeros and preventing divisions by small values at high spatial frequencies The modified curve must be continuous to avoid edge effects in Fourier filtering The reasons for trying this new approach are There is no need to separately estimate the true structure factor without the noise so it can even be applied to a single image Ifthe CTF is not known very accurately the method includes integration over the uncertainties of the CTF Continuous differentiable functions in general produce f
155. the inverse deconvolution method feasible figure 2 shows the curve of the approximation to the CTF the numerator of G s At the high frequency region the numerator of G s still tends to zero however the estimation of E s E s tends to be of the same order as N s After filtering by G s the intensity of the signal and the noise at high frequencies are only multiplied by a small number pnyjduy 008 01 O12 014 O16 018 02 Spatial frequency 1 A 0 002 004 0 06 Figure 2 Blue Theoretical CTF curves after phase flipping Red The approximation of the CTF 1 G s used in the inverse filter after phase flipping The proposed function of G s is an approximation assuming noise and small uncertainties in the CTF parameters In the absence of noise and full knowledge of the CTF a better function can be formulated In the 3D reconstruction noise is decreased in two stages of averaging first in generating each of the class average images then in 3D reconstruction when thousands of class average images are combined to form a 3D model By applying the new inverse filter the noise is amplified somewhat for a single particle image but by a limited factor only a maximum around 3 4 times at zeros in low frequency region 50 A novel method of CTF correction Despite the new filter increasing both the signal and noise near zeros of the CTF we show the averaging procedure to reduce the noise efficiently the noise
156. tical 3DEM reconstruction of the macromolecular model of a 50S ribosomal complex In chapter 2 new modules in cryo EM automated carbon masking and quaternion based rotation space sampling are presented The new modules were implemented and tested in Cyclops software In chapter 3 a novel approximation method of CTF amplitude correction for 3D single particle reconstruction is described This new method yields higher resolution models compared with to traditional CTF correction methods and shows better convergence in practice Chapter 4 reports 3DEM reconstructions with a highest resolution of 10A of macromolecular ribosomal complexes of stalled 50S ribosomal particles They sow how Hsp15 rescues heat shocked prematurely dissociated 50S ribosomal particles This 3DEM reconstruction project the first 17 Chapter 1 project in my Ph D research period required reconstructing multiple asymmetric macromolecules Until now it is still very challenging work to determine EM models of asymmetric complexes at such resolutions In chapter 5 and 6 I describe progress in analysing the random electron diffraction images of 3D protein crystals In chapter 5 the second main topic of my Ph D research discusses a brand new approach to structure determination compared to the traditional X ray and NMR technologies A new algorithm to determine unit cells from a set of randomly oriented diffraction patterns is presented here Unit cell determination is th
157. ting rdering ovosac Figure 2 Main graphical user interface of the program EDiff V1 0 with all options highlighted 1 Voltage in KeV of the electron microscope The wave length 4 will be automatically calculated from the voltage 2 Alternatively the user can enter the wave length and ignore the voltage In the final calculation the wave length is used rather than the voltage 5 ScaleBarParam the Scale Bar Parameter defines the scale of the diffraction pattern in A per pixel 8 Alternatively the Digitization parameter can be entered defining the step size in millimeter per pixel when scanning films or the resolution of the CCD digital camera In this case the user also needs to set the ED Constant parameter 9 or the CameraLength and WaveLength parameters 11 and 4 from which the ED Constant is calculated The ScaleBarParam 5 is calculated from the ED Constant 9 and the 116 User manual of EDiff Digitization parameter 42 amp 43 Image center of the autocorrelation image in pixels this is also the center of centered background corrected electron diffraction pattern For files generated by the pre processing program AMP these two values are always 513 corresponding to the center of a 1024 by 1024 size image 44 MissingSpots indicates how many spots are allowed to be absent between the spots of main vector and the center This parameter is used in MainVectorMat
158. tional CTF correction algorithm blew up Average images in the left panel are generated with the conventional full CTF correction Average images in the middle panel are generated with direct CTF deconvolution algorithm Average images in the right panel are generated with filtered CTF correction algorithm 57 Chapter 3 Resolution 11 2A FSC at 0 5 Figure 6 3D models reconstructed with different CTF correction algorithms Column Left the result of conventional full CTF correction as implemented in most used reconstruction software after four iterations of refinement from a starting model Middle amp Right the results of direct CTF deconvolution and filtered CTF 58 A novel method of CTF correction gt correction algorithms after four iterations of refinement using the same starting model and the same data set as used for the left model A Front view of ribosomal 50S complex B Back view of ribosomal 50S complex The black dash line boxes indicate representative regions C Views zoomed in for the indicated regions in B Figure 5 shows some selected representative average images from classes having relative many particles Comparison of the projections and class average images with the results obtained from the GroEL samples in Figure 3 show the ribosome projections to be more blurred and have less contrast The reasons are mainly e The GroEL data set of 4 169 particles contains the highest
159. tions The angular distance is about 7 59 As a plug in Cyclops we implemented rotational sampling using all 4D platonic solids and their sub sampled approximations The user has the choice of generating sets of between 5 and 5880 orientations corresponding to an angular precision of sampling that ranges between 2 1 5 and 2 1 30 In the current application the generated projections are used by a plug in for particle picking using template matching Fig 6 shows a typical example of the result of template matching when picking 50S particles using 16 projections Clearly the plug in detects the particles but at these low sampling densities the advantages versus Euler sampling for projection generation are fairly small More significant improvement is achieved in for instance projection matching for orientation assignment 29 Chapter 2 2 3 Implementation In the methods section the principles and general methods have been described Here we will focus on some technique details for implementation 2 3 1 Implementation of automated carbon masking To mask the carbon region block ice and over crowded particles special image processing methods are needed for the micrographs with extremely high noise Not all the known image processing operators are suitable to deal with high noise though they may work very well in most other cases We have to select and customize the operators to make them be really functional with lower signal to
160. trix R and from these matrices R and C a matrix M CR is constructed The position of any reflection point p of the 3D reflection lattice in Fourier space for a given unit cell and crystal orientation can be calculated using the equation p hM 1 Here h h k 1 is an index vector containing the integral indices of p M is defined by the unit cell parameters and the crystal orientation The indices that satisfy p for a chosen resolution range can be found by imposing the boundary conditions l dmin gt p 1 dmax 2 97 Chapter 5 Where dyin is the lower boundary of the resolution range and dmax the upper boundary resolution Given these equations and boundary conditions we implemented an algorithm to quickly generate all possible positions of reflection spots in 3D Fourier space From this collection of simulated 3D spot positions we generated a list of all unique model facets i e model facets differing from all other by less than a specified tolerance 5 2 4 Calculating residuals In the ideal case all facets from the experimental data exactly match the facets of one specific model unit cell In practice however limited accuracy of determining centroids of autocorrelation peaks small variations in unit cell parameters of different crystals and the uncertainty of the crystal orientation prevent such ideal fits Therefore function approximation needs to be performed in which a function is selected that matches a
161. ts Analysis PCA is applied to solve the problem caused by high noise in the images after a time consuming procedure named multi reference alignment or reference supervised alignment Another classification method is reference supervised classification if coarse starting model is available A particle image is compared with all the reference images and is then assigned to the class corresponding to the most similar reference image Subsequently an average image is calculated for each class to get high signal to noise ratio image CTF amplitude correction is normally performed in this stage 13 Chapter 1 4 3D reconstruction According to the common line projection theorem two different 2D projections of the same 3D object must have a 1D line projection in common Relative Euler angles can be assigned for each average image in an angular reconstruction Once the Euler angles are assigned average images are back projected to get a 3D model This procedure is normally done in Fourier space because every projection image is a section of 3D model in Fourier transform Back projection can be conveniently implemented by inserting the image in Fourier space and then transferring back to get the real space model 5 Refinement The reconstructed 3D model resulting from the first iteration usually has a sub optimal resolution An iterative refinement aiming at higher resolution is then necessary The rough model is re projected in many directi
162. ttice fig 1 which is defined by a pair of independent vectors From this vector pair we construct a facet which is characterised by three numbers the lengths of both basis vectors and the angle between them A facet is a rotation invariant feature of a 2D lattice Each planar intersection of a 3D lattice along a principal zone also generates a 2D lattice and hence defines a corresponding facet Our algorithm is based on matching the observed crystal facets to model facets extracted from a simulated 3D lattice Briefly our procedure involves the following steps see also fig 2 1 foreach observed electron diffraction pattern we determine its crystal facet by a removing the central beam and overall background of the image b calculating the autocorrelation pattern of each corrected diffraction pattern c identifying the principal facet of the autocorrelation pattern and adding it to List 94 Unit cell determination from randomly oriented electron diffraction patterns 2 for each potential unit cell we determine its fit to the experimental data by a calculating all unique low resolution model facets that can be extracted from the corresponding simulated 3D lattice and storing these in ist2 b for each crystal facet of list selecting the best matching model facet from J ist2 calculating a residual and accumulating the residuals 3 finally we select the potential unit cell with the lowest accumulated residual The
163. tus information and results of the EDiff program will show up here 13 amp 14 ResolutionRange A The resolution range in Angstrom is used for finding the unit cell parameters and for indexing Only peak positions within the specified resolution range will be used for the calculation When the user starts CheckData only reflections spots within the resolution range will show up If a very large resolution range is selected a large number of spots is used in the calculation and this may cost too much computing time If the resolution range is too narrow the absence of essential of information may prevent finding the right answer In practice a resolution range that is a 117 Chapter 6 118 bit wider than that defined by the main facet is fine As a rule of thumb a reasonable resolution range is from half of the estimated smallest unit cell dimension to double of the largest unit cell dimension For example if the smallest unit cell dimension is expected to be around 30 Angstrom and the largest dimension is around 80 Angstrom it is reasonable to set the resolution range between 15 and 160 Angstrom 15 CrystalSystem all seven different crystal systems are supported in the unit cell parameters determination If we know the crystal system beforehand we can apply its constraints in the exhaustive search of edges and angles sometimes dramatically speeding up the calculations and improving their precision If we don t know the
164. ual Montano A 2004a XMIPP a new generation of an open source image processing package for electron microscopy J Struct Biol 148 194 204 Sorzano C O S Marabini R Herman G T Censor Y Carazo J M 2004b Transfer function restoration in 3D electron microscopy via iterative data refinement Phys Med Biol 49 509 522 Stagg S M Lander G C Quispe J Voss N R Cheng A Bradlow H Bradlow S Carragher B Potter C S 2008 A test bed for optimizing high resolution single particle reconstructions J Struct Biol 163 29 39 Thon F 1966 Zur defokussierungsabh ngigkeit des phasenkontrastes bei der elektronen mikroskopischen abbildung Z Naturforsch 21a 476 478 Thon F 1971 Phase contrast electron microscopy Electron Microscopy in Materials Science Ed U Valdre Academic Press N Y 570 625 van Heel M 1979 IMAGIC and its results Ultramicroscopy 4 117 van Heel M Harauz G 1986 Resolution Criteria for 3 Dimensional Reconstruction Optik 73 119 122 van Heel M Harauz G Orlova E V Schmidt R Schatz M 1996 A new generation of the IMAGIC image processing system J Struct Biol 116 17 24 65 Chapter 3 van Heel M Gowen B Matadeen R Orlova E V Finn R Pape T Cohen D Stark H Schmidt R Schatz M Patwardhan A 2000 Single particle electron cryo microscopy towards atomic resolution Q Rev Biophys 33 307 69 van Heel M Schatz M 2005
165. will pass the input parameters to the program Cyclops Module Carbon masker Job title Carbon Removal Input File s Input micragraph s 22604m32s img l Start job Cancel Figure 7 Dialog window for entering the input parameters for the module of automated carbon masker These applications are now routinely used through the Cyclops interface Due to the 37 Chapter 2 modular structure of Cyclops software the plug in applications can be easily extended and updated 2 4 Conclusions Two new algorithms dealing with the automation of particle selection are presented The automated carbon masking routine allows automated removal of carbon region and only searching particles in the vitreous ice region of micrographs The algorithm of even sampling of 3D rotation space can be used to generate uniform projections from a starting model and a set of rotational equal distance vectors These projections are further used in a template matching procedure for particle picking Both algorithms boost the automation and efficiency of particle selection in the step of data preparation These algorithms greatly assisted in the structure determination of the stalled 50S ribosomal complexes described in chapter 4 Acknowledgements Thanks to Jasper R Plaisier for his great help in embedding the new algorithms in Cyclops software suite Cyclops is available under a GPL license and can be downloaded from http www bfsc
166. y the 50Senc tRNA complex cannot be recycled a tRNA moiety in the A site prevents release factors from binding and severing the aminoacyl ester bond between the tRNA and the nascent chain Hspl5 located the tRNA in the P site by bridging it to helix 84 of the central protuberance of the 50S subunit the aL RNA binding motif of Hsp15 bound to helix 84 while its positively charged C terminal tail bound to the D T loops of the nc tRNA Locked in the P site the CCA end of the nc tRNA is optimally positioned in the peptidyl transferase center for hydrolytic attack of its aminoacyl ester bond by a release factor The translocation of the tRNA to the P site in the Hsp15 containing complex is in full agreement with the puromycin assay Fig 7 and with puromycin sensitivity of dissociated translating ribosomes in cell lysates Korber et al 2000 Translocation of the nc tRNA from the A site to the P site would allow a release factor to bind in the A site In the 70S ribosome this translocation requires energy EF G hydrolyzes GTP in the process Our results indicate that in the absence of interactions with the 30S subunit the binding energy of the Hsp15 to the 50S nc tRNA complex is sufficient to induce translocation 79 Chapter 4 Our data explain why Hsp15 has a reduced affinity for translationally active 50S subunits its binding energy is reduced because the interaction between the C terminus of Hsp15 and the P site tRNA is missing Furthermore

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