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					    Crystallography 101 in 45’

               Deena Oren
Structural Biology Resource Center
       Take Home Message
• Understand the principle of how X-ray
  structure determination works (the physics
  and math, yes the math)
• What the goal is and how to achieve it
• What the pitfalls are and how we try to
  overcome them
• Resolution, Rfactors, Bfactors, oh my!
• Wayne Hendrickson: …not just obtain a
  structure, but obtain one that makes sense,
  that explains other knowledge and that
  predict future results.
X-ray


                  Rotating anode




        crystal
                          Can’t build an X-ray
                          microscope, but we can
                          accurately measure the
                          scattering –
                          X-ray crystallography is
                          essentially determining
                          the structure of the
                          object from the
                          scattering.
                        Crystals
      crystals

• X-ray scattering from a single molecule would be incredibly
  weak and would not be detectable above the noise level
  (scattering from air, water, etc.). A crystal arranges a huge
  number (1015 or more) of molecules in a predictable pattern. In
  this way, scattered X-rays build up and raise the signal to a
  measurable level.
Particles or Waves

Light behaves like a particle (photons) -
Compton Scattering
•Quanta (packets) of energy
•E=h=hc/, h=Plank’s constant
•At synchrotrons keVs are used
(12.39keV, = 1.5 Å wavelength)


But light behaves like a wave
(the Young double-slit experiment)
Diffraction
               Diffraction
• Laser pointer (coherent & monochromatic)




    1) slits       2) array   3) complex pattern
The Math - Bragg’s Law



                             

           }             d
    The Math - As Applied to
           Crystals
          Incident
          X ray beam


               
               
                                 
                                 




                       


                   A        C

          }d           B   Crystal atoms


Diamond
faces
               D=(AB+BC) = 2dsinθ
                   2dsinθ = nλ
          Reciprocal Space
• The farther apart the objects are, the
  closer the diffractions spots are to each
  other
• Reciprocal lattice: the set of points (hkl)
  in the corresponding to the sets of
  lattice planes (hkl) in the real space
  lattice.
    Electromagnetic Wave Math




  Maxwell equations:
E - electric field
B - magnetic field
The solution to the differential equations is a function:
f=Acosx +iBsinx, where i is the imaginary component
resulting from the phase of the wave.
Another way of writing this is:


Where x is a function of space (coordinates) and
time (wavelength) also sometimes written as 2(h.r)
                    The Math
The Fourier Transform
 Electron density



 Inverse
 transform



 General form
          The Phase Problem


MIR/SIRAS, MAD, SAD, MIRAS

•   I = Isomorphous
•   A = Anomalous
•   M = Multiple
•   S = Single
Crystal Symmetry




                   M.C. Escher
Repetitive Symmetry
 7 Linear Classes

        Translation   Combinations


        Glide


       Rotation


       Reflection
17 Plane Groups
230 Space Groups - Unit Cell



               CsCl2: Pm3m




                             Fd3m
     Asymmetric Unit
      and Unit cell

P1                 P2
           Instrumentation
•   Home Source
•   Synchrotron
•   Detectors- Image Plate, CCD, CMOS
•   The experiment
         QC and Statistics
•   Resolution     2dsinθ = nλ
•   B-factors
•   R-factors
•   Geometry
Shabalin,
et. al.,
Actanaturae 3,
89 (2009)
          R-factors




Rfree is for h = hTest
B-Factors
              Objectives
• Electron density good enough to
  correctly place residues/atoms
• Observe interactions between and
  within molecules underpinning the
  biological process
• Be able to predict biological concepts
  based on the structure and design
  experiments to test the hypothesis
                 Pitfalls
•   Missing atoms
•   Waters/ions
•   Poor data
•   Poor R-factors
•   Poor Geometry
•   Over-fitting
              Reference material
• MIT lecture, D. Sadoway http://www.p212121.com/2010/09/21/lecture-on-the-
  x-ray-diffraction-of-crystals/
• http://www.youtube.com/watch?v=zYZNTzviBxs&feature=related
• Dr. Quantum: http://www.youtube.com/watch?v=DfPeprQ7oGc
• Egtechno: http://www.egtecno.com/applets/83/braggs-law-and-diffraction
• Ecole Polytechnique Fédérale de Lausanne, Switzerland:
  http://escher.epfl.ch/fft/
• images-mediawiki-sites.thefullwiki.org: http://images-mediawiki-
  sites.thefullwiki.org/01/2/4/2/566309697200556.gif
• IUCr Computing Commission Newsletter No. 2, July 2003:
  http://cci.lbl.gov/asu_gallery/asu_003.html
• http://www.youtube.com/watch?v=IRBKN4h7u80&NR=1
• UK’s Diamond Light Source: http://www.youtube.com/watch?v=4tpHZwsLB-
  Y&feature=related
  http://www.youtube.com/watch?v=rEK9UPWT9cY&feature=related
• Bernard Rupp’s crystallography 101
  http://ruppweb.dyndns.org/Xray/101index.html

				
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