# PowerPoint Presentation

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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

•   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/
• 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
• UK’s Diamond Light Source: http://www.youtube.com/watch?v=4tpHZwsLB-
Y&feature=related