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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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
nλ = 2d sinθ
2θ angle between incident
and reflected beams
d spacing between planes
λ 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
ρ(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 iϕhkl
Structure Factor
Amplitude:
from experimental
measurements
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
Proteinpreparation
preparation
Crystal
Crystalgrowth
growth
Data
Datacollection
collection
Phase
Phasedetermination
determination
Model
Modelbuilding
buildingand
andrefinement
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
a = 36.67 Å
a = 36.67 Å b = 79.39 Å
b = 79.39 Åc = 39.97 Å
c = 39.97 Å
αα= 90.0°
= 90.0° ßß= 91.25°
= 91.25° γγ= 90.0°
= 90.0°
Monoclinic
lattice
Monoclinic lattice (P2
(P2 or
or P2
P21))
1
• Lattice type, possible
space groups
• Resolution Limit
• Merged data set with
index, intensity + error for
each reflection
HH KK
00 00
00 00
00 00
00 00
11 00
11 00
11 00
11 00
11 00
11 00
11 00
11 00
11 00
11 00
...etc.
...etc.
LL intensity
intensity error
error
12
6714.3
347.2
12 6714.3
347.2
18
-8.9
16.3
18
-8.9
16.3
24
979.5
62.4
24
979.5
62.4
30
4136.4
272.5
30 4136.4
272.5
33 3035.4
70.2
3035.4
70.2
44
0.0
0.7
0.0
0.7
55
0.1
0.6
0.1
0.6
66 838.4
20.4
838.4
20.4
77 14903.0
535.6
14903.0
535.6
88 2759.4
64.7
2759.4
64.7
99 1403.5
31.0
1403.5
31.0
10
5.6
10 109.4
109.4
5.6
11
11 31739.5
31739.5 1611.5
1611.5
12
231.9
7.6
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
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