Methods for Structure
Determination
Chemistry and Chemical Biology
Rutgers University
How are macromolecular
structures determined?
X-ray
(X-ray crystallography)
NMR
EM
(Nuclear Magnetic Resonance)
(Electron Microscopy)
Protein Data Bank
Download
The Data Pipeline
Genomic
Based Target
Selection
Isolation,
Expression,
Purification,
Crystallization
Data
Collection
Structure
Determination
PDB Deposition
& Release
X-ray
cryst
NMR
EM
3D Models
Annotations
Publications
Some Background
• Symmetry
– Translation, Rotation, Reflection, Inversion
• Crystals
– Lattice, Unit cell, Asymmetric Unit
• Diffraction
– Light diffraction, X-ray diffraction
Translation
M.C. Escher
Rotation
M.C. Escher
Reflection
M.C. Escher
???
M.C. Escher
Crystals
Mineral
Protein
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lattice
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Convolution
Lattice, Crystal and Unit cell
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Crystal structure
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Unit Cell 1
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Unit Cell 2
Macromolecular Crystal Lattice
Alexander McPherson, Introduction to Macromolecular Crystallography Wiley-Liss, 2002
Unit Cell and Asymmetric Unit
Symmetry in Crystals
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•
•
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1-fold
2-fold
3-fold
4-fold
6-fold
1
2
3
4
5-, 7-, 8- and higher fold symmetries
6
do not pack in a crystal
Crystal Systems
Jenny Pickworth Glusker, Kenneth N.
Trueblood, Crystal Structure Analysis: A
Primer, Oxford University Press, 1985
The International Tables
Diffraction
Sunrise through a screened window
http://www.flickr.com/photos/fizzix/2458009067/in/photostream/
Light Diffraction
Henry S. Lipson Crystals and X-rays Taylor & Francis 1970
Diffraction in Action
http://mrsec.wisc.edu/Edetc/supplies/DNA_OTK/images/ABCH.mov
Principles of Microscopy
The Fourier
Duck
Fourier
Transform
Reverse
Transform
Reverse
Transform
with limited
resolution
data
Why Use X-rays?
http://bccp.lbl.gov/Academy/wksp_pix_1/spectrum.gif
X-ray Diffraction
Gale Rhodes, Crystallography Made Crystal Clear: A Guide for Users of Macromolecular Models,
Academic Press, 1993
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
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
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.
A precession photograph
• Experimental data: h,k,l
and intensities (with
errors)
Diffraction Patterns to Structure
Ihkl = constant.|Fhkl|2
Structure Factor
Structure Factor
r(x,y,z) =
Σ Fhkl e -2πi (hx + ky +lz)
Electron Density
Phase Problem
• Structure factor is dependent on type and
location of atoms in unit cell
• The complete Structure Factor F for a
reflection includes the phase, which cannot
be measured directly.
F hkl = |F hkl| e
Structure Factor
Amplitude:
from experimental
measurements
iϕhkl
Phase:
must be estimated
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
Microscopy vs X-ray Crystallography
http://www.iucr.org/education/pamphlets/15/full-text
The X-ray Crystallography Pipeline
Protein preparation
Crystal growth
Data collection
Phase determination
Model building and refinement
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
Crystal Growth: Vapor Diffusion
Common precipitants:
– Polyethylene glycol
– Salts
• ammonium sulfate
• sodium chloride
– Alcohols
• Isopropanol
• Methylpentanediol (MPD)
Cover Slip
Precipitant
Solution
Protein +
Precipitant
Crystallization Conditions
http://www-structmed.cimr.cam.ac.uk/Course/Crystals/
Theory/phase_methods.html
Crystallization Phase Diagram
Data Collection
Crystal mounted in glass capillary
Crystal mounted in nylon loop.
Frozen in liquid N2
Rotating Anode Diffractometer
http://www.nsls.bnl.gov
Synchrotron X-ray source
NSLS Beamline
X12C
Crystal Diffraction
Water Ring
~3-5 Å
High Resolution
(large angle)
Beam Stop
Shadow
Low Resolution
(small angle)
Jeff Dahl, Sars protease, http://en.wikipedia.org/wiki/File:X-ray_diffraction_pattern_3clpro.jpg
• Different crystal forms of the same protein
yield different diffraction patterns
trp repressor, sodium phosphate
trp repressor, ammonium sulfate
Data Obtained
• Crystal unit cell
dimensions
• Lattice type, possible
space groups
• Resolution Limit
• Merged data set with
index, intensity + error for
each reflection
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
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
...etc.
L intensity error
12 6714.3
347.2
18
-8.9
16.3
24
979.5
62.4
30 4136.4
272.5
3 3035.4
70.2
4
0.0
0.7
5
0.1
0.6
6
838.4
20.4
7 14903.0
535.6
8 2759.4
64.7
9 1403.5
31.0
10
109.4
5.6
11 31739.5 1611.5
12
231.9
7.6
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
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)
crystal
Patterson map
http://www.ruppweb.org/Xray/Patterson/Native_Patterson.htm
Isomorphous Replacement
• Derivative – native crystal = heavy atom
Real space
• Deriv. diffn – native diffn = heavy atom diffn
Reciprocal space
• Patterson synthesis > peaks based on distance
between heavy atoms in structure gives initial
phase.
http://www.ruppweb.org/Xray/Phasing/Phasingt.html
Anomalous Dispersion
• Friedel’s Law: Ihkl = I-h-k-l
• Members of a Friedel pair
have equal amplitude and
http://www.xtal.iqfr.csic.es/Cristalografia/parte_07_2-en.html
opposite phase
• In anomalous scattering
crystals Friedel’s law is
not obeyed
http://skuld.bmsc.washington.edu/scatter/AS_wavechoice.html
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
Density Modification
• Improve map by
adding additional
“knowledge”
• Typical modifications:
• Molecular averaging
• Solvent Flattening
• Histogram Matching
Image from C. Lawson
Model Building-Refinement
Cycle
Initial Model
Refine
Experimental
Data
Stereochemical
Knowledge
Calculate
Map
Edit model
Final Model
Myoglobin
Hemoglobin
Lysozyme
Ribonuclease
Crystal
Structures
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.
Structural Data
-snip-
PDB 3a6b
Types of Electron Density Maps
• Experimentally phased map:
– Fobs, Phicalc
• “model” map:
– (2Fobs – Fcalc), Phicalc
• “difference” map
– (Fobs – Fcalc) or (Fobs – Fobs), Phicalc
R-factor Equation
R versus Rfree
Typical
Statistical
Table
Validation: Ramachandran Plot
Graphical Display and Model Fitting
• View maps and model together to:
– Look at crystal contacts
– assess map regions with unassigned density
– assess model geometry problems
– Build missing polymer residues
– Add waters, ligands
Image from C. Lawson
Some Movie Links
• Crystal Mounting Robot
– http://www.youtube.com/watch?v=J4OD_b9XKh4
• Crystal Diffraction
– http://ucxray.berkeley.edu/~jamesh/movies/
• Optical diffraction
– http://mrsec.wisc.edu/Edetc/supplies/DNA_OTK/in
dex.html
Enjoy!
References
• IUCr Online dictionary of Crystallography
– http://reference.iucr.org/dictionary/Main_Page
• Educational web sites and resources
– http://www.iucr.org/education/resources
• An interactive SF tutorial
– http://www.ysbl.york.ac.uk/~cowtan/sfapplet/sf
intro.html