X-ray Crystallography: Diffraction, Symmetry, and Data Collection

X-ray Crystallography: Diffraction, Symmetry, and Data Collection PowerPoint PPT Presentation

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Outline of Today's Lecture. Crystal growth and handlingDiffraction and how it encodes spatial informationCrystal symmetry and how it affects data collection. Power and Limitations of X-ray Diffraction. POWERPicture of molecule with almost no assumptions: r(x,y,z)No size limitations: Mr > 107Rapid structure determination (high throughput) now a reality.

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1. X-ray Crystallography: Diffraction, Symmetry, and Data Collection MBIC 709 Eric A. Toth, Ph.D. 02/18/10

2. Outline of Today’s Lecture Crystal growth and handling Diffraction and how it encodes spatial information Crystal symmetry and how it affects data collection

3. Power and Limitations of X-ray Diffraction POWER Picture of molecule with almost no assumptions: r(x,y,z) No size limitations: Mr > 107 Rapid structure determination (high throughput) now a reality LIMITATIONS Full detail (X-ray crystallography) requires a crystal. Otherwise, less information (e.g. DNA fibers) Each picture is static Resolution often limited

4. What can this information tell you? information ranges from broad perspective of macromolecular complex arrangement to important atomic interactions examples: hemoglobin and myoglobin KcsA K+ channel p53 the ribosome saga

5. Getting Diffraction-Quality Crystals still a huge stumbling block in x-ray crystallography requires three very non-trivial things: obtain sample of superior quality induce the sample to form single crystals manipulate the crystals such that they yield useful data

6. A Sample of "Superior Quality" purity is first check - SDS-PAGE, either Coomassie or silver staining should be a single band when overloaded on Coomassie-stained gel this is not enough

7. Biophysical Characterization not only must be pure, must be monodisperse (i.e. a single, homogenous population of molecules) and at high concentration (10 mg/ml is a typical starting point) buffer system, salt, reducing agents, ligands, can have drastic effect on protein happiness gel filtration native gel dynamic light scattering

9. Example of Good DLS Profile

10. Growing Crystals = Voodoo try to induce complex molecules to make a number of weak contacts that force it to form a three-dimensional lattice crystals grow from a supersaturated solution nucleation is the initial event in the process want this to occur a limited number of times after nucleation, want crystals to grow to a reasonable size (0.1mm at a minimum) need them to be single crystals

11. Crystals alter the solution environment such that proteins are forced to aggregate mostly leads to junk, but every so often crystal formation occurs common precipitants: polyols: typically polyethyleneglycol of varying molecular weights (400-20,000) salts: ammonium sulfate, NaCl, etc. alcohols: ethanol, isopropanol, etc. other: jeffamine, methylpentane diol

12. Methods of Crystallization

13. Key Considerations during the crystallization process, the protein must remain in its native state and monodisperse huge number of variables (precipitant concentration, pH, additives, temperature, etc.) to screen) crystallization space is most often sampled semi-randomly, by "sparse matrix" methods membrane proteins are trickier because they need a lipid in order to keep them solubilized nature of lipid as important as conditions screened

15. Crystal Handling almost as capricious as crystal growth must get small crystal from drop into either a capillary or rayon loop for data collection without damaging it might require solutions vastly different than crystallization conditions (and serial transfers too) collection at 100K also requires that the solution form a glass and not destroy the crystal

17. Cryoprotection idea is to prevent ice formation (ice crystals diffract very well), form a glass usually glycerol or MPD or ethylene glycol is incorporated into the crystallization conditions can be done gradually or suddenly, depending on what the crystal will take some saturated salts also form a glass at 100K oils, like paratone-N and mineral oil can also work

18. Diffraction

19. The Phenomenon of Diffraction Diffraction occurs when waves encounter an obstacle

20. Waves

21. Waves continued basic wave equation: frequency of light ranges from one cycle every 10-14 to 10-19 seconds can't detect time-dependent phase shift diffraction measurements independent of time:

22. Diffraction contains information about the obstacle that caused it observed only if obstacle used not too much larger than wavelength of radiation x-rays 1.54Å, similar to bond lengths diffracted waves distinct from incoming radiation wave vector k contains spatial information

23. Information "Encoded" in Diffraction Pattern wave vectors k vary in direction—spatial info

24. Encoding, continued diffraction from each volume element: Since = 0 outside the obstacle, can recast as Now cast as a Fourier transform : diffraction pattern is Fourier transform of amplitude function ( ) of obstacle

25. varies with k exponential describes phase relationship between scattering centers and arbitrary origin (very important info) How to go diffraction pattern ? obstacle? Fourier transform (T) T(T(a)) = a

27. What Information Resides in a Diffraction Pattern? how to break down info into its components start with simple objects and expand to diffraction from a 3-D crystal measure not the complex amplitude, but the intensity want to reconstruct the obstacle

28. Diffraction Summary

29. Diffraction from a Crystal infinite crystal = infinitely sharp peaks position of main peaks determined by lattice shape of the peaks determined by shape of the obstacle intensity of the peaks determined by the motif under study

30. More Diffraction from a crystal finite crystal equivalent to multiplying infinite lattice by a shape function crystal contains three types of structural info: Lattice Shape of Crystal (not important in practice) Motif determine lattice, then motif

31. Still More Diffraction from a Crystal if the obstacle of interest is a protein, why a crystal? crystal acts as an amplifier S/N for single protein molecule would be too low for detection

32. Real lattice = actual crystalline lattice Reciprocal lattice = T(crystal lattice) reciprocal relationship between the two smaller motif, wider spacing of diffraction maxima and vice versa simple geometric relationship between the two This relationship helps you determine the lattice and eventually the structure

33. Interference most radiation is lost due to destructive interference diffraction only observed when waves constructively interfere exactly same pathlength (qincident = qreflected):

34. Bragg's Law and Diffraction path difference = multiple of wavelength nl = 2d x sinq

35. Scattering Vector useful construct accounts for difference in angle between incident and scattered waves

36. phase of diffracted wave from an electron at position is: to be in phase, must be an integer results in phases of 0, 2p, 4p, etc. otherwise, any phase is possible, leading the integral to go to 0

37. Laue Conditions position in 3D: total scattering from crystal: Laue conditions -- , , integers

38. Ewald Construction (2D)

39. More Ewald Construction (2D)

40. Limiting Circle Ewald construction can't sweep out area larger than its diameter (2/l) can get directly from Bragg's Law (sinq=1) visible light wouldn't give useful data

41. Ewald Sphere for any orientation of the crystal, a limited number of lattice points will fall on the surface of the sphere can determine what the lattice looks like based on a few frames of data will know where all of the spots should be, then measure their intensities Example

43. Symmetry and Data Collection

44. Crystal periodic array of molecules:

45. Lattice lattice is conceptual array of points in space that define geometrical relationship between motifs in structure ƒ(crystal) = ƒ(motif)?ƒ(lattice) nature of lattice (i.e. its symmetry) tells us where to expect diffraction data finite number possible basic components = unit cell and asymmetric unit

46. Unit Cell basic repeating unit of crystal (origins of the unit cells form the lattice) basis vectors , , and describe boundaries

47. by convention (usually) lies along x, along y, and along z a, b, and g are angles between vectors choice of unit cell arbitrary, so enforce conventions right-handed coordinate system unit cell axes coincide with highest symmetry smallest cell that obeys above

48. depending on the situation, one might choose different unit cells encompassing one or more lattice points:

49. Types of Cells Primitive (P), Plane-centered (A, B, or C), Body-centered (I), Face-centered (F)

50. Asymmetric Unit definition: smallest part of the unit cell which will generate the whole cell if all symmetry operators are applied to it abbreviated ASU in protein crystallography, ASU is one or more protein chains

51. Symmetry determines the details of how we solve the structure definition: a symmetry element (or operator) when applied to an object leaves that object unchanged most trivial is identity operator (I), which does nothing primarily rotations and translations in protein crystallography exception is center of inversion inherent in reciprocal lattice mirrors and glide planes incompatible with chiral molecules

52. Basic Symmetry Operators: Rotation 180º about an axis is called a "2-fold" rotation

54. Screw Axes combine rotation and translation mn ("m sub n"): translate n/m of a unit cell, then rotate by an m-fold 21 screw denoted by other screw axes: 31, 32, 41, 42, 43, 61, 62, 63, 64, 65,

56. Rotations compatible with a lattice

57. Groups symmetry elements that describe a lattice must make up a group must contain I combination of any two elements of a group results in another element of the group (closure) #elements = #objects repeated = order of group every element must have an inverse

58. Point Groups That Can Exist in Crystals

59. Space Groups we're interested in 3D groups (e.g. P2):

61. Seven Crystal Systems

63. Space Groups 230 possible 65 contain only rotational symmetry elements ? relevant for chiral molecules

64. Data Collection seek to measure all available Bragg peaks for the crystal under study nature of reciprocal lattice needs to be determined orientation of reciprocal lattice relative to laboratory reference frame also unknown properties of crystal (including symmetry) determine how data collection proceeds

65. Some Factors Affecting Data Collection unit cell size – must resolve spots dmax – influences where we place detector mosaic spread takes into account that neither the beam (divergence) nor the crystal ("mosaic blocks") are perfect can limit rotation range of each frame

66. Mosaic Blocks

67. Symmetry and Diffraction Data Friedel's Law: reflection from back of plane is the same as from the front

68. Systematic Absences 2-fold screw axis along y: x,y,z ? -x,y+½,-z

70. Laue symmetry the diffraction pattern will contain symmetry that is related to the symmetry of the crystal rotational symmetry plus Friedel's Law (inversion center) Laue symmetry plus systematic absences in almost all cases gives an unambiguous space group determination

71. Symmetry and Data Collection data are complete if all reflections or their symmetry mates have crossed the Ewald sphere higher symmetry ? more symmetry mates ? smaller rotation range needed to access all unique reflections

73. Why do we care? most crystals are radiation-sensitive proper orientation can make the difference between complete and incomplete data incomplete data "redundancy"—the more times you measure a reflection, the more accurate that measurement is (duh) low symmetry can make collection of highly redundant data impractical (time) or impossible (radiation damage)

74. Evaluation of Data Quality how well multiple observations of a reflection and/or its symmetry mates agree unweighted statistic, subject to manipulation

75. Evaluation of Data Quality I/s—observed intensity divided by its error "signal-to-noise" ratio, tells how much information is in a measured reflection or group of reflections (i.e. within a certain resolution range, etc.) better indicator of data quality than Rmerge

76. OK, so I've figured out my lattice and space group, I've measured all of the intensities I am able to measure, and I'm satisfied with their quality. Where's my structure?!?

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