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
3D Models
Annotations
Publications
The Fourier
Duck
Fourier
Transform
Back
Transform
Back
Transform
Light Diffraction
Henry S. Lipson Crystals and X-rays Taylor & Francis 1970
Fourier Analysis in Microscopy
X-ray Diffraction
Gale Rhodes, Crystallography Made Crystal Clear: A Guide for Users of Macromolecular Models,
Academic Press, 1993
X-ray Crystallography
X-ray Diffraction Photograph
Rosalind Franklinʼs diffraction photo of DNA
Another X-ray Photo
The Steps in the Process
•  Isolation,
•  Expression,
Target •  Purification,
Data
Selection
•  CrystallizationCollection
Structure Structure Functional Solution Refinement Annotation
Publication
Protein Preparation
Cloning
Expression
Purification
Crystallization Method
Common precipitants:
– Polyethylene glycol
– Salts
•  ammonium sulfate
•  sodium chloride
–  Alcohols
•  Isopropanol
•  Methylpentanediol (MPD)
Cover
Slip
Precipitant
Solution
Protein
+
Precipitant
Crystallization Techniques
Crystallization Strategy
•  Sparse Matrix Screening
– Examine wide range of conditions
•  Optimization
– Fine screening around “initial hit” conditions to
improve crystal quality
– Typical variables: precipitant concentration,
buffer composition, pH, temperature, ligands
Hampton Screen
Results
isopropanol
PEG
Ammonium sulfate
Sodium phosphate
4 crystal forms of E. coli trp repressor
Data Collection
Crystal Mounting for Diffraction Trials
•  Transfer crystal briefly to cryoprotectant solution
–  Xtalln solution + glycerol, PEG, sugars, salts, or
alcohols
•  Scoop up crystal with nylon loop
•  Plunge into liquid nitrogen (LN2)
•  Store in LN2
•  Labeling/tracking very important!
Crystal mounting movie: http://www.youtube.com/watch?v=J4OD_b9XKh4
Data Collection Instrumentation
–  X-ray generation (decelerating electrons)
–  Optics to select single wavelength
–  Crystal position control (centering, precise rotation)
–  Detector
–  Beamstop
–  Gas N2 stream (100oK)
Crystal Diffraction
High Resolution
(large angle)
Water Ring
~3-5 Å
Beam Stop
Shadow
Low Resolution
(small angle)
Jeff Dahl, Sars protease, http://en.wikipedia.org/wiki/File:X-ray_diffraction_pattern_3clpro.jpg
Rotating Anode Diffractometer
Synchrotron Beamline Diffractometer
NSLS
Beamline
X12C
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!
•  Different crystal forms of the same protein
yield different diffraction patterns
trp repressor, sodium phosphate
trp repressor, ammonium sulfate
Data Collection Strategy
•  The American Method
– shoot first, ask questions later
•  Special cases:
– Radiation Decay
– High mosaicity
– Anisotropy
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
1
0
1
0
...etc.
L
12
18
24
30
3
4
5
6
7
8
9
10
11
12
13
14
intensity error
6714.3
347.2
-8.9
16.3
979.5
62.4
4136.4
272.5
3035.4
70.2
0.0
0.7
0.1
0.6
838.4
20.4
14903.0
535.6
2759.4
64.7
1403.5
31.0
109.4
5.6
31739.5 1611.5
231.9
7.6
5433.0
94.3
12392.7
211.4
Initial Phase Determination
Electron Density Calculation
•  The electron density at (x,y,z) is the sum of
contributions of all structure factors Fhkl
Ρ(x,y,z) = Σ F hkl e -2πi (hx + ky +lz)
Structure Factor
(complex number)
•  The electron density provides an image that is
averaged :
•  over all molecules in the crystal
•  over the time of the diffraction experiment
Phase Problem
•  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
Phasing Methods
•  Direct Phasing
–  Isomorphous replacement
–  Anomalous Dispersion
•  Molecular Replacement
•  Density Improvement
Experimental/Direct Phasing
•  Add or incorporate atoms yielding small
changes in reflection amplitudes
•  Can estimate phase by solving for heavy
(or anomalous atom) substructure
Anomalous Phasing
•  MAD:
–  Multiple wavelength anomalous dispersion
–  F+ vs. F- and X-ray wavelength dependence
•  SAD
–  Single wavelength anomalous dispersion
–  F+ vs. F- at single wavelength
•  Selenium, Bromine, Mercury…
Molecular Replacement (MR)
•  New structure expected to resemble one
previously determined
•  Use Patterson-based methods to find
the orientation of known model in new
crystal lattice
Orient
Adapted from Acta Cryst D Aug. 2006 cover image
Density Modification
  Improve experimental or
MR map by adding
additional “knowledge”
  Typical modifications:
  Molecular averaging
  Solvent Flattening
  Histogram Matching
Model Building and
Refinement
Starting Model to Final Structure
Calculating Electron Density
•  Type of maps
– Experimentally phased map: Fobs, Phicalc
– “model” map: (2Fobs – Fcalc), Phicalc
– “difference” map (Fobs – Fcalc) or (Fobs – Fobs),
Phicalc
•  Weighting
– Confidence-based weighting for each Fourier
component amplitude measurement error,
phase estimation error
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
Refinement Decisions
•  Annealing vs. Minimization
•  Rigid body vs. Individual Atom
•  Targets
– (Fobs – Fcalc)
– geometry (bonds, angles, planarity)
•  How many parameters to refine?
– x,y,z
– B-factor
More Refinement
Decisions
•  Restraints
– Geometry
– B-factors
– Noncrystallographic symmetry
•  Detecting Pitfalls
– Model bias (example later)
•  When is refinement complete?
R-factor Equation
Structural Data
-snip-
PDB 3a6b
Validation: Ramachandran Plot
Representative Density
Model Improvement
OLD MODEL
Resolution limit = 3.1 Angstrom
NEW MODEL
Resolution limit= 2.1 Angstrom
Before
old model
r_work = 0.3013
r_free = 0.3503
After
current model
r_work = 0.2649
r_free = 0.3191