C7270 Biological X-Ray Crystallography and Cryo-Electron Microscopy Fall 2022 Pavel Plevka, Tibor Füzik, Jiří Nováček, Holger Stark, cryo-EM 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 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 5 •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 6 What is asked of you: •Be present and awake •Participate in discussions •I am here to help, learning is up to you! •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. Not part of this course: •Basic math – mental overload by dealing with simple equations. (Observed before.) • •Reserve time for thinking. 8 Course textbooks: Course plan Can we start at 14:00 or 14:30? 10 Biological X-Ray Crystallography 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? 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” René Just Haüy (1743-1822) “Law of Constancy of Angles” “Law of Constancy of Angles” René Just Haüy (1743-1822) 17 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 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 Wavelength and diffraction amplitude_period_frequency.jpg amplitude_period_frequency.jpg Waves coherent_beam.jpg Coherent beam wave_interactions.jpg Addition of waves particles_and_light_on_slit.jpg Particles & waves Diffraction of light Diffraction of light Wavelength and diffraction amplitude_period_frequency.jpg wavelength_comparison_2.png Wavelength comparison of X-rays and visible light 38l Crystallizing a Protein Protein expression and purification Vapor-diffusion Batch and microbatch Microdialysis Protein crystallization phase diagram Recorded Sound Preparing crystals for diffraction experiment Diffractometer with goniometer Diffractometer with goniometer X-ray sources - sealed X-ray tube Spectrum of copper anode 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 Crystals Recorded Sound A 2D lattice 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 + À Lattice Motif 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 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 If an object is brought into self-coincidence after some operation it said to possess symmetry with respect to that operation. SYMMETRY 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. Recorded Sound Recorded Sound Unit cell selection Alternative unit cell selection (also correct) Positions of twofold symmetry axes Positions of mirror planes Unit cell selection Positions of glide planes Recorded Sound End of lecture #1 in 2022 SIR WILLIAM HENRY BRAGG (1862-1942) SIR WILLIAM LAWRENCE BRAGG (1890-1971) •1915 Nobel Laureates in Physics • for the analysis of crystal structure by means of X-rays wh-bragg wl-bragg nl = 2d sinq Braggs_law.jpg nl = 2d sinq Bragg’s law: There is NO PHASE DIFFERENCE if the path differences are equal to whole number multiplies of wavelength (l) w wave_interactions.jpg coherent_beam.jpg coherent_beam.jpg sinq = w/d 2w = nl nl = 2d sinq Bragg’s law: sinq = w/d 2w = nl There is NO PHASE DIFFERENCE if the path differences are equal to prime number multiplies of wavelength (l) w wave_interactions.jpg Picture 7 Picture 8