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Methods for Structure Determination

Methods for Structure Determination. Chemistry and Chemical Biology Rutgers University. How are macromolecular structures determined?. X-ray (X-ray crystallography). NMR (Nuclear Magnetic Resonance). EM (Electron Microscopy). Protein Data Bank. Download. The Data Pipeline. Isolation,

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Methods for Structure Determination

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  1. Methods for Structure Determination Chemistry and Chemical Biology Rutgers University

  2. How are macromolecular structures determined? X-ray (X-ray crystallography) NMR (Nuclear Magnetic Resonance) EM (Electron Microscopy) Protein Data Bank Download

  3. The Data Pipeline Isolation, Expression, Purification, Crystallization Genomic Based Target Selection Data Collection Structure Determination PDB Deposition & Release X-ray cryst NMR 3D Models Annotations Publications EM

  4. Some Background • Symmetry • Translation, Rotation, Reflection, Inversion • Crystals • Lattice, Unit cell, Asymmetric Unit • Diffraction • Light diffraction, X-ray diffraction

  5. Translation M.C. Escher

  6. Rotation M.C. Escher

  7. Reflection M.C. Escher

  8. ??? M.C. Escher

  9. Mineral Protein Crystals

  10. , , , , Unit Cell 1 , , , , , , , , , , , , , , , , , , , , , , , , Convolution , , , , , , , , , , , , Crystal structure , , , , , , , , Unit Cell 2 Lattice, Crystal and Unit cell lattice . . . . . . . . . . . . . . . . , object

  11. Macromolecular Crystal Lattice Alexander McPherson, Introduction to Macromolecular Crystallography Wiley-Liss, 2002

  12. Unit Cell and Asymmetric Unit

  13. Symmetry in Crystals 1 • 1-fold • 2-fold • 3-fold • 4-fold • 6-fold 2 3 4 5-, 7-, 8- and higher fold symmetries 6 do not pack in a crystal

  14. Crystal Systems Jenny Pickworth Glusker, Kenneth N. Trueblood, Crystal Structure Analysis: A Primer, Oxford University Press, 1985

  15. The International Tables

  16. Diffraction Sunrise through a screened window http://www.flickr.com/photos/fizzix/2458009067/in/photostream/

  17. Light Diffraction Henry S. Lipson Crystals and X-rays Taylor & Francis 1970

  18. Diffraction in Action http://mrsec.wisc.edu/Edetc/supplies/DNA_OTK/images/ABCH.mov

  19. Principles of Microscopy

  20. The Fourier Duck Fourier Transform Reverse Transform Reverse Transform with limited resolution data

  21. Why Use X-rays? http://bccp.lbl.gov/Academy/wksp_pix_1/spectrum.gif

  22. X-ray Diffraction Gale Rhodes, Crystallography Made Crystal Clear: A Guide for Users of Macromolecular Models, Academic Press, 1993

  23. Miller Indices (hkl) • For any plane in the unit cell with intercepts1/h, 1/k and 1/l along the x, y, and z axes the Miller indices are h,k,l • If the resulting indices are fractions, multiply all to get integer numbers Intercepts :   ½ a , a , ∞ Fractional intercepts :   ½ , 1 , ∞ Miller Indices :   (210) http://www.chem.qmul.ac.uk/surfaces/scc/scat1_1b.htm

  24. Bragg’s Law • n = 2d sin • 2 angle between incident • and reflected beams d spacing between planes • wavelength n order of diffraction http://www.bmsc.washington.edu/people/merritt/bc530/bragg/ try the Java Applet! Constructive interference occurs from successive crystallographic planes (h, k, l) in the crystalline lattice

  25. X-ray Diffraction Pattern • Diffraction pattern is in reciprocal space • Size and shape of unit cell determines position of diffraction peaks. • Atomic positions within unit cell determines intensity of peaks. • Experimental data: h,k,l and intensities (with errors) A precession photograph

  26. Ihkl=constant.|Fhkl|2 Structure Factor Structure Factor r(x,y,z) =ΣFhkle-2πi (hx + ky +lz) Electron Density Diffraction Patterns to Structure

  27. Phase Problem • Structure factor is dependent on type and location of atoms in unit cell • The complete Structure Factor Ffor a reflection includes the phase, which cannot be measured directly. Fhkl = |Fhkl|eiϕhkl Structure Factor Phase: must be estimated Amplitude: from experimental measurements

  28. Electron Density • Can be calculated by Fourier transform of diffraction data • Provides an averaged image: • over all molecules in the crystal • over the time of the diffraction experiment Trp in a 4.3 A map Trp in a 1.3 A map Trp in a 2.25 A map

  29. Microscopy vs X-ray Crystallography http://www.iucr.org/education/pamphlets/15/full-text

  30. The X-ray Crystallography Pipeline Crystal growth Data collection Phase determination Model building and refinement Protein preparation

  31. Protein Preparation • Purify from natural sources: e.g. liver, muscle, leaf etc. • Clone in appropriate vector • Express in appropriate host – bacteria, yeast, mammalian cell lines, cell free extracts • Purify target protein from cell lysate

  32. Crystal Growth: Vapor Diffusion Cover Slip Precipitant Solution Protein + Precipitant Common precipitants: • Polyethylene glycol • Salts • ammonium sulfate • sodium chloride • Alcohols • Isopropanol • Methylpentanediol (MPD)

  33. Crystallization Conditions http://www-structmed.cimr.cam.ac.uk/Course/Crystals/ Theory/phase_methods.html Crystallization Phase Diagram

  34. Data Collection Crystal mounted in glass capillary Crystal mounted in nylon loop. Frozen in liquid N2 Rotating Anode Diffractometer

  35. Synchrotron X-ray source http://www.nsls.bnl.gov NSLS Beamline X12C

  36. Crystal Diffraction High Resolution (large angle) Water Ring ~3-5 Å Beam Stop Shadow Low Resolution (small angle) Jeff Dahl, Sars protease, http://en.wikipedia.org/wiki/File:X-ray_diffraction_pattern_3clpro.jpg

  37. trp repressor, sodium phosphate trp repressor, ammonium sulfate Different crystal forms of the same protein yield different diffraction patterns

  38. Data Obtained a = 36.67 Å b = 79.39 Å c = 39.97 Å α = 90.0° ß = 91.25° γ = 90.0° Monoclinic lattice (P2 or P21) H K L intensity error 0 0 12 6714.3 347.2 0 0 18 -8.9 16.3 0 0 24 979.5 62.4 0 0 30 4136.4 272.5 1 0 3 3035.4 70.2 1 0 4 0.0 0.7 1 0 5 0.1 0.6 1 0 6 838.4 20.4 1 0 7 14903.0 535.6 1 0 8 2759.4 64.7 1 0 9 1403.5 31.0 1 0 10 109.4 5.6 1 0 11 31739.5 1611.5 1 0 12 231.9 7.6 ...etc. Crystal unit cell dimensions Lattice type, possible space groups Resolution Limit Merged data set with index, intensity + error for each reflection

  39. Phase Determination • Direct methods • Estimate from probability relationships applied to most intense diffraction peaks • Patterson methods • Multiple Isomorphous Replacement • Anomalous Dispersion • Molecular replacement • Density Improvement • Non-crystallographic symmetry averaging • Solvent flattening

  40. Patterson Function • Convolution of electron density with itself • Evaluated at points u,v,w throughout unit cell • Map of vectors between scattering atom in the real crystal cell (translated to Patterson origin) Patterson map crystal http://www.ruppweb.org/Xray/Patterson/Native_Patterson.htm

  41. Isomorphous Replacement • Derivative – native crystal = heavy atom • Deriv. diffn – native diffn = heavy atom diffn • Patterson synthesis > peaks based on distance between heavy atoms in structure gives initial phase. Real space Reciprocal space http://www.ruppweb.org/Xray/Phasing/Phasingt.html

  42. Anomalous Dispersion • Friedel’s Law: Ihkl = I-h-k-l • Members of a Friedel pair have equal amplitude and opposite phase • In anomalous scattering crystals Friedel’s law is not obeyed http://www.xtal.iqfr.csic.es/Cristalografia/parte_07_2-en.html http://skuld.bmsc.washington.edu/scatter/AS_wavechoice.html

  43. Molecular Replacement • New structure expected to resemble one previously determined • Use Patterson-based methods to find the orientation of known model in new crystal lattice (i.e. find rotation R and translation T) http://reference.iucr.org/dictionary/Molecular_replacement

  44. Density Modification • Improve map by adding additional “knowledge” • Typical modifications: • Molecular averaging • Solvent Flattening • Histogram Matching Image from C. Lawson

  45. Model Building-Refinement Cycle Final Model

  46. Myoglobin Hemoglobin CrystalStructures Lysozyme Ribonuclease Myoglobin: Kendrew, Bodo, Dintzis, Parrish, Wyckoff, Phillips, Nature 181 662-666, 1958.Hemoglobin: Perutz, Proc. R. Soc. A265, 161-187,1962. Lysozyme: Blake, Koenig, Mair, North, Phillips, Sarma, Nature 206 757, 1965. Ribonuclease: Kartha, Bello, Harker, Nature 213, 862-865 1967. Wyckoff, Hardman, Allewell, Inagami, Johnson, Richards. J. Biol. Chem. 242, 3753-3757, 1967.

  47. -snip- Structural Data PDB 3a6b

  48. Types of Electron Density Maps • Experimentally phased map: • Fobs, Phicalc • “model” map: • (2Fobs – Fcalc), Phicalc • “difference” map • (Fobs – Fcalc) or (Fobs – Fobs), Phicalc

  49. R-factor Equation

  50. R versus Rfree

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