Protein x-ray crystallography
Two truths of x-ray crystallography
(1.) Models, not structures. Corroborating results suggest that the models are
close to biological reality.
(2.) No matter how carefully performed, any experiment will have errors associate
with it. Errors in the fitting of the (sparse) electron density maps are some of the
most common.
Steps in protein x-ray crystallography
•
Molecular biology: over-express protein in
expression system.
•
More art than science (and more luck
than art): Grow crystals of the protein that
diffract well (difficult step, can take from
weeks to years!).
•
Physics: Obtain the X-ray diffraction data.
•
Computation: Compute electron density
maps.
•
Computation again: Refinement --calculate an atomic model to fit electron
density; compare the diffraction data
computed from the model with the actual
data; refine the model to fit the data (iterate).
Protein crystals are “liquid crystals”
Look like normal crystals, but are actually more like gels (20 to 80% solvent).
Crystallization energy diagram
Unit cell
Experimental set-up
Diffraction pattern
Bragg’s law explains why cleavage faces of crystals reflect
x-ray beans at certain angles of incidence (diffraction)
d = spacing between molecules in the lattice
2d (sin) = n
 = angle of observed diffraction
= wavelength of x-rays
n = integer for first order, second order, etc.

X-rays
Crystal
Detector
Resolution is directly proportional to 
In x-ray crystallography, the
phrase “2 Å model” means that
the analysis included reflections
out to a distance of 1/(2 Å) from
the center.
Diffraction to electron density
(which is not the same as the final model structure)
Fourier Transform
To get from the diffraction pattern to the electron
density, you have to use a Fourier Transform.
Note: This process is largely done automatically by a computer.
Phases critically impact model quality
Methods to resolve the phase problem
(largely outside our scope)
• Isomorphous Replacement
– Single Isomorphous Replacement (SIR)
– Multiple Isomorphous Replacement (MIR)
• Anomalous Dispersion
– Single Wave-Length Anomalous Dispersion (SAD)
– Multiple Wave-Length Anomalous Dispersion (MAD)
• Selenomethionine is commonly used for MAD
• Molecular Replacement
• Direct Methods
From electron density to model
Note: While some manual fitting still occurs, this process is largely done
automatically by a few different computer programs.
Final models are determined from a combination of
electron density overlap and MM energies
Note: due to the wavelength of x-rays, hydrogen atoms are
only resolved in the absolute highest resolution structures.
Key x-ray crystallography model quantities
Quality: Resolution (in Å) and R-factor (values = 0 to 1).
Atom coordinates: Define the mean coordinates of the (heavy) atoms.
B-factors (aka, temperature factors): Describes the apparent disorder about the
mean. Disorder is spatial (crystal heterogeneity) and temporal (protein flexibility).
However, in reality, B-factors are in protein crystallography are NOT pure DebyeWaller factors (mobilities). Instead, B-factors are most often best characterized as
“fudge factors” uses to fit the electron density maps.
Occupancies: Occasionally, a better fit to the electron density can often by
obtained by assuming that certain atoms can be in more than one location, due to
alternate conformations.
Resolution
Resolution statistics
R-factor
R-factor (aka, residual factor or agreement factor) is a measure of the difference
between the observed and computed intensities. Note that the structure factor F is
related to intensities from the diffraction pattern.
A similar quality criterion is Rfree, which is calculated from a subset (~10%) of
reflections that were not included in the structure refinement.
0.6: Very bad
||Fobs| - |Fcalc||
R = -----------------|Fobs|
0.5: Bad
0.4: Recoverable
R values:
0.2: Good for Protein
0.05: Good for small
organic models
0.0: Perfect
Rfree statistics
Common rules of thumb
A good rule of thumb for defining an acceptability threshold is based on resolution
and R-factor. A resolution of 2.0 Å or lower and a R-factor of 0.20 or lower is a
commonly used threshold in structural bioinformatic analyses.
It is important to remember though, that there is no such thing as a single
structure. Proteins are best described by ensembles.
In the past, NMR structures were considered to be of lower quality than x-ray
structures. However, they are increasingly accepted, especially since the
environmental conditions (solvent vs. liquid crystal) have been argued to be more
biological. Unfortunately, there is no magic number that can be used to assess
NMR structure quality, or lack thereof.
An example of occupancy != 1.00
Common methods for model evaluation
(you will cover this more in Dr. Guo’s class)
Model evaluation via MM force fields
(you will cover this more in Dr. Guo’s class)
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For more info on x-ray crystallography
I strongly recommend this book to anyone doing structural bioinformatics!
Protein NMR
A few comments about protein structure
determination via NMR
(HSCQ + others)
Introduction of a magnetic field will orient
the random spins along the external field
The basics of NMR
The extent of the chemical shift is related to local
environment (e.g. chemical shifts in 1H NMR)
Chemical shifts
Chemical shifts are determined relative to a reference state --- frequently
tetramethalsilane (TMS).
TMS is great for several reasons...
(1.) Twelve chemically equivalent protons means lots-o-signal
(2.) Electronegativity of Silicon << electronegativity of Carbon, thus signal
shouldn’t effect things.
(3.) Low boiling point, so can be easily removed via heating.
J-Coupling
Q: What is the output of multidimensional protein NMR
experiment?
Distance restraints, angle restraints, and orientation restraints.
Distance comes from HSQC’s (NOESY, etc.).
A series of protein structure models is built that attempt to satisfy as many of the
restraints as possible, in addition to general properties of proteins such as bond
lengths and angles.
The algorithms convert the restraints and the general protein properties into
energy terms, and thus tries to minimize the energy.
The process results in an ensemble of structures that, if the data were sufficient to
dictate a certain fold, will converge.
Q: What is the output of multidimensional protein NMR
experiment?
Answer: A series of models that
satisfy the experimental
constraints, while still obeying the
chemical rules that govern protein
structure (as we understand it).
Also: While other NMR
experiments do directly quantify
flexibility through NMR order
parameters (i.e., S2), which is
beyond the scope of this class,
NMR protein structures do not
directly quantify flexibility.
Nevertheless, regions where
models vary is frequently used to
indirectly identify flexible regions.
Sometimes NMR spectra are informative
even when they can’t be resolved
Heteronuclear single quantum correlation
Brief aside: Magnetic resonance imaging (MRI)
Other methods to determine macromolecular structure:
Examples from (cryo)-electron microscopy
Other methods to determine macromolecular structure:
Small Angle X-Ray Scattering (SAXS)
Current PDB Holdings (as of 4/11/12)
Method
Proteins
Nucleic
Acid
Prot/NA
Complex
Other
Total
X-ray
66098
1348
3266
2
70714
NMR
8190
979
186
7
9362
Electron
microscopy
284
22
116
0
422
Hybrid
44
3
2
1
50
other
140
4
5
13
162
Total
74756
2356
3575
23
80710