1 C7270 Biological X-Ray Crystallography and Cryo-Electron Microscopy Fall 2020 Pavel Plevka, Tibor Füzik, Jiří Nováček, Holger Stark, Recorded Sound 2 Class rules •Please keep your microphone muted. •When you want to ask question or comment, please unmute your microphone and speak directly. •I would appreciate if you keep your video on. It is not much fun to lecture to black boxes. •Ask questions - it will help to clarify the issue not only for you but for your peers as well! •In class discussions, be respectful of other students' opinions. Recorded Sound cryo-EM Recorded Sound virus_purif_gradient_syringes_cut.jpg protein_crystal.jpg virus_crystal_AFM_cut.jpg protein_diffraction.jpg example_electron_density_phiCB5.jpg 1. Expression & purification 2. Crystallization 3. Diffraction data ESRF.jpg 4. Solve structure Recorded Sound electron_microscope.jpg virus_purif_gradient_syringes_cut.jpg 3. cryo-EM data 4. Reconstruction apply_sample_to_grid.jpg grid_freezing_auto_cut.jpg 2. Grid preparation EM_grid.jpg holey_carbon_2.jpg holey_carbon.jpg cryo_of_EV71.jpg EV71_E18_whole.jpg 1. Expression & purification Recorded Sound 6 •Diffraction of light Aims of the course •Approaches to resolve phase problem in crystallography •Use of electrons to display objects with high magnification and fine detail •Calculation of three-dimensional reconstruction from two-dimensional projections Recorded Sound 7 What is asked of you: •Be present and awake •Participate in discussions •Do voluntary homeworks •I am here to help, learning is up to you! Recorded Sound Levels of passing the course: “Sitter” – hand in homework, participate in discussions => grade E “Student” – sitter + take theoretical part of the exam (will include symmetry and equations) Recorded Sound Not part of this course: •Basic math – mental overload by dealing with simple equations. (Observed before.) • •Reserve time for thinking. You will never have more time than now. Recorded Sound 10 Course textbooks: Recorded Sound Course plan Recorded Sound Recorded Sound Recorded Sound sunstone Johannes Kepler (1571-1630) Why do single snowflakes, before they become entangled with other snowflakes, always fall with six corners? Why do snowflakes not fall with five corners or with seven? Recorded Sound Niels Stensen (1638-1686) Although crystals of quartz and hematite appear in a great variety of shapes and sizes, the same interfacial angles persisted in every specimen. “Law of Constancy of Angles” Recorded Sound René Just Haüy (1743-1822) “Law of Constancy of Angles” Recorded Sound René Just Haüy (1743-1822) “Law of Constancy of Angles” Recorded Sound 18 History of fundamental discoveries WILHELM CONRAD RÖNTGEN (1845-1923) Wilhelm_Conrad_Rontgen.jpg •1901 Nobel Laureate in Physics discovery of the remarkable rays subsequently named after him Recorded Sound MAX VON LAUE (1879-1960) •1914 Nobel Laureate in Physics • for his discovery of the diffraction of X-rays by crystals laue img59 Friedrich and Knipping Recorded Sound Wavelength and diffraction amplitude_period_frequency.jpg Recorded Sound amplitude_period_frequency.jpg Waves Recorded Sound coherent_beam.jpg Coherent beam Recorded Sound wave_interactions.jpg Addition of waves Recorded Sound particles_and_light_on_slit.jpg Particles & waves Recorded Sound Diffraction of light Recorded Sound Diffraction of light Recorded Sound Wavelength and diffraction amplitude_period_frequency.jpg Recorded Sound wavelength_comparison_2.png Wavelength comparison of X-rays and visible light 38l Recorded Sound Crystallizing a Protein Recorded Sound Protein expression and purification Recorded Sound Vapor-diffusion Recorded Sound Batch and microbatch Recorded Sound Microdialysis Recorded Sound Protein crystallization phase diagram Recorded Sound Recorded Sound Preparing crystals for diffraction experiment Recorded Sound Recorded Sound Diffractometer with goniometer Recorded Sound Diffractometer with goniometer Recorded Sound X-ray sources - sealed X-ray tube Recorded Sound Spectrum of copper anode Recorded Sound Synchrotron -Bending magnet -Wavelength shifter -Wiggler -Undulator Recorded Sound X-ray detectors Single photon counter Film Image plates Area detectors: - CCDs - Direct X-rays detectors - Pilatus Recorded Sound Crystals Recorded Sound Recorded Sound Recorded Sound A 2D lattice Recorded Sound Translationally periodic arrangement of motifs Crystal Translationally periodic arrangement of points Lattice Lattice Ø the underlying periodicity of the crystal Motif Ø atom or group of atoms associated with each lattice point Crystal = Lattice + Motif Recorded Sound + À Lattice Motif Recorded Sound À À À À À À À À À À À À À À À À À À À À À À À À À À À À À À À À À À À À À À À À À À À À À À À À À À À À À À À À Crystal = Courtesy Dr. Rajesh Prasad Recorded Sound § A cell is a finite representation of the infinite lattice § A cell is a parallelogram (2D) or a parallelopiped (3D) with lattice points at their corners. § If the lattice points are only at the corners, the cell is primitive. § If there are lattice points in the cell other than the corners, the cell is nonprimitive. Unit cells Instead of drawing the whole structure I can draw a representative part and specify the repetition pattern Recorded Sound Primitive cell Primitive cell Nonprimitive cell Courtesy Dr. Rajesh Prasad Recorded Sound Recorded Sound Arrangement of lattice points in the unit cell No. of Lattice points / cell Position of lattice points Effective number of Lattice points / cell 1 P 8 Corners = 8 x (1/8) = 1 2 I 8 Corners + 1 body centre = 1 (for corners) + 1 (BC) 3 F 8 Corners + 6 face centres = 1 (for corners) + 6 x (1/2) = 4 4 A/ B/ C 8 corners + 2 centres of opposite faces = 1 (for corners) + 2x(1/2) = 2 Recorded Sound If an object is brought into self-coincidence after some operation it said to possess symmetry with respect to that operation. SYMMETRY Recorded Sound Primitive unit cell For each crystal structure there is a conventional unit cell, usually chosen to make the resulting lattice as symmetric as possible. However, the conventional unit cell is not always the smallest possible choice. A primitive unit cell of a particular crystal structure is the smallest possible unit cell one can construct such that, when tiled, it completely fills space. Primitive cell Non-primitive centered cell 4- fold axes a b Recorded Sound Bravais Lattice A lattice is a set of points constructed by translating a single point in discrete steps by a set of basis vectors. In three dimensions, there are 14 unique Bravais lattices (distinct from one another in that they have different space groups) in three dimensions. All crystalline materials recognized till now fit in one of these arrangements. 14 Bravais lattices are divided into seven crystal systems Crystal system Bravais lattices 1.Cubic P I F 2.Tetragonal P I 3.Orthorhombic P I F C 4.Hexagonal P 5.Trigonal P 6.Monoclinic P C 7.Triclinic P Courtesy Dr. Rajesh Prasad Recorded Sound Recorded Sound Recorded Sound 230 space groups Recorded Sound Recorded Sound Recorded Sound Recorded Sound Recorded Sound Recorded Sound Recorded Sound Unit cell selection Alternative unit cell selection (also correct) Positions of twofold symmetry axes Positions of mirror planes Recorded Sound Unit cell selection Positions of glide planes Recorded Sound