structure Protein from X-ray diffraction y
X-ray crystallograp course 2007, Karsten Theis, UMass Amherst phy n X-ray crystallograp course 2007, Karsten Theis, UMass Amherst phy n
Raw data: Diffraction images
How do we obtain the crystal structure of a protein from the diffraction data |Fhkl|?
Crystallize a protein with known chemical structure: MSALEFGPSLKMNE... Conformation, 3D-structure:
CRYST1 221 200 221.200 ATOM 1 N ATOM 2 CA ATOM 3 C ATOM 4 O ATOM 5 CB ATOM 6 CG1 ATOM 7 CG2 ATOM 8 CD1 ATOM 9 N ATOM 10 CA ATOM 11 C . . . ATOM 7604 O2* 73 600 73.600 ILE A ILE A ILE A ILE A ILE A ILE A ILE A ILE A ALA A ALA A ALA A 6 6 6 6 6 6 6 6 7 7 7 80 900 90 00 90 00 80.900 90.00 90.00 97.764 18.390 97.130 18.979 96.655 17.885 97.460 17.052 98.139 19.855 99.043 18.979 98.984 20.617 100 297 18 614 100.297 18.614 95.359 17.896 94.757 16.906 95.816 16.303 90 00 P 21 21 2 90.00 39.211 1.00 84.23 37.983 1.00 84.74 37.031 1.00 84.98 36.605 1.00 85.82 37.248 1.00 99.99 36.389 1.00 99.99 38.263 1.00 99.99 37 178 1 00 99 99 37.178 1.00 99.99 36.702 1.00 84.56 35.795 1.00 83.75 34.876 1.00 83.47 4
G R
3
73.810
43.517
21.774
1.00 62.48
Reciprocal space
Real space
: Fourier transform
X-ray crystallograp course 2007, Karsten Theis, UMass Amherst phy n
Fourier tour in two dimensions
X-ray crystallograp course 2007, Karsten Theis, UMass Amherst phy n
Diffraction: real space vs. reciprocal space p p p
( ) (r)
F(q)
Light/dark: Intensities Colors: Phases
pulsed NMR, FT-IR and other spectroscopic methods: time series vs. frequencies vs
2 1.5
Molecule e--density density "real space" p
Fourier transform
1 0.8
Am plitude
1
Sign nal
0.5 0 -0.5 -1 -1.5 -2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0.6 0.4 0.2 0 0 2 4 6 8 10 12
"reciprocal space"
time/sec
frequency/Hz
This tour is from Kevin Cowtan's picture book of Fourier at www.ysbl.york.ac.uk/~cowtan/fourier/fourier.html
Crystals amplify the scattering signal y p y g g
X-ray crystallograp course 2007, Karsten Theis, UMass Amherst phy n
The Fourier transform is reversible
X-ray crystallography course 2007, Karsten Theis, UMass Amherst p n
(r)
F(h,k,l) Fourier transform f
Crystal
Fourier analysis
Fourier synthesis
The signal from a single molecule would be much too weak to detect The signals originating from the molecules in the crystal add up because the molecules are in identical orientation Scattering by a crystal (i.e. diffraction) results in a pattern with discrete spots and empty areas (another level of signal/noise increase) Flipside: diffraction image represents average structure (over time and crystal)
Q Questions: X-ray diffraction y
X-ray crystallograp course 2007, Karsten Theis, UMass Amherst phy n
1) Why don t we see a diffraction pattern in a don't medical X-ray image? 2) Why can we distinguish between bones and soft tissue in a medical X-ray image? 3) Wh d 't we see a diffraction pattern Why don't diff ti tt when observing crystals under the light microscope? i ? 4) In a protein with 10000 atoms, how many atoms contribute to a given diffraction spot?
Why i Wh is solving and interpreting l i di i a crystal structure difficult?
The Phase Problem Crystals Cr stals aren`t perfect because proteins are flexible beca se fle ible Protein P t i conformations differ to some extent depending on f ti diff t t td di their environment
Problem: without phases, no electron density l t d it
X-ray crystallograp course 2007, Karsten Theis, UMass Amherst phy n
Solving the p g phase p problem
X-ray crystallograp course 2007, Karsten Theis, UMass Amherst phy n
Fourier analysis
F(q) (q)
Fourier synthesis
1. Direct methods (guessing the p (g g phases) ) Works for small molecules (lots of measurements per atom in structure) 2. Patterson methods (inter-atomic vectors) Works for simple structures (4 atom pairs with 2 atoms, 100 atom pairs with 10 atoms 3. Model phases; molecular replacement Relies on partial knowledge of the structure 4. MIR/MAD techniques (ab initio) Prepare crystals that contain Se, Hg, Pt or other heavy atoms at a p y , g, y handful of positions in the crystal and solve that simple structure first using method 1. or 2.
Unknown structure
measured diffraction pattern |F(q)| Fourier F i synthesis
without phases:
g bbe s gibberish
Calculating p g phases from an atomic model
X-ray crystallograp course 2007, Karsten Theis, UMass Amherst phy n
Molecular replacement: unknown structure has a distinct crystal packing
X-ray crystallograp course 2007, Karsten Theis, UMass Amherst phy n
Intensities I ii
|Fo(hkl)| derived from observed intensities
unknown structure
measured diffraction pattern
Unknown structure
measured diffraction pattern
"2Fo-Fc map"
Phases Ph
"2Fo-Fc map"
|Fc(hkl)| and phases derived from model
atomic model of known structure
calculated diffraction pattern
Known structure
rotated structure
calculated diffraction pattern
MIR/MAD method
X-ray crystallograp course 2007, Karsten Theis, UMass Amherst phy n
What is the best method?
X-ray crystallograp course 2007, Karsten Theis, UMass Amherst phy n
Solve a simpler problem first: just a couple of atoms Collect data of crystals multiple times, with slight variations MAD
Multiwavelength Anomalous Dispersion
:-{
measure identical crystal at 3 different wavelengths near Se absorption edge
:-{ :-{
MIR
Multiple Isomorphous Replacement
:-{
soak crystals in different substances and measure
MIR/MAD works for all protein structures but... requires additional measurements, experience and lots of work to place atoms into density Molecular replacement is fast but... large model bias in low-resolution structures
errors are propagated new features are overlooked
:-{
:-{
Se scattering is influenced by choice of wavelength, scattering by other atoms is not
Pt derivative native
Hg derivative
Crystal imperfection (disorder), not wavelength, limits resolution l th li it l ti
X-ray crystallograp course 2007, Karsten Theis, UMass Amherst phy n
Disorder in real space p
X-ray crystallography course 2007, Karsten Theis, UMass Amherst p n
The electron density, averaged over time and over the crystal, is density crystal more or less "fuzzy" depending on crystal quality electrons have distribution around atom rather than one single location (same for all crystals) molecules move as rigid bodies in crystal packing (depends l l i id b di i t l ki (d d on crystal contacts) atom positions change with time ( p g (local dynamic disorder) y ) atom positions change from one unit cell to another (local static disorder)
Lower resolution
Higher resolution
File size: 2 Kb
11 Kb
672 Kb
B-factors and disorder
X-ray crystallograp course 2007, Karsten Theis, UMass Amherst phy n
Disorder prevents collection of high resolution d t i reciprocal space l ti data in i l
X-ray crystallography course 2007, Karsten Theis, UMass Amherst p n
Synonyms: Temperature factors, atomic displacement y y p , p factors B-factors describe how the density electron of an atom i broadened by static and dynamic disorder in is b d d b i dd i di d i the crystal
Static disorder: distinct atomic positions in different unit cells of the crystal cr stal Dynamic disorder: changes in conformation over time during the measurement B-factor 20 2 40 2 80 2 Displacement 0.25 0.51 0 51 1.01
3 12 6 4
Disorder makes data collection (and solving a structure) more difficult
X-ray crystallograp course 2007, Karsten Theis, UMass Amherst phy n
Low resolution data: loss of detail
X-ray crystallograp course 2007, Karsten Theis, UMass Amherst phy n
5 sqrt (inte ensity)
2.5
1.7
1.2
1
The intensity of the y diffraction data decreases with resolution The higher the average B-factor, f the faster the drop-off. p
weak signal g strong signal Fourier analysis l i
0 2
Fourier synthesis
50 2
10 2
1/res Low resolution High resolution
This makes it more difficult (impossible) to collect high resolution data
The Fourier transform (in 1D) ( )
X-ray crystallograp course 2007, Karsten Theis, UMass Amherst phy n
Fourier analysis y
X-ray crystallograp course 2007, Karsten Theis, UMass Amherst phy n
|F|(h) (r)
Color: (h)
1/|qh=1|
0 Real space
1
r
0
5 Reciprocal space
h
(r) 0 Real R l space 1
h=0 h=1 h=2 h=3 h=4 h=5
|F|(h)
Color: (h)
0
5 Reciprocal space
h
Fourier analysis Fourier synthesis
What resolution does h=5 correspond to (please estimate from atomic distances)?
|F|(h) h
(r)
|F|(h) r 1
X-ray crystallograp course 2007, Karsten Theis, UMass Amherst phy n
(r) h
0
5
Fourier synthesis y
0
0
5
Fourier synthesis y
0
r 1
X-ray crystallograp course 2007, Karsten Theis, UMass Amherst phy n
add
synthesis up to h = 1 synthesis up to h = 2
add
synthesis up to h = 2
synthesis up to h = 3
contribution from h = 0 2 1
contribution from h = 3
|F|(h) h
(r)
|F|(h) r 1
X-ray crystallograp course 2007, Karsten Theis, UMass Amherst phy n
(r) h
0
5
Fourier synthesis y
0
0
5
Fourier synthesis y
0
r 1
X-ray crystallograp course 2007, Karsten Theis, UMass Amherst phy n
synthesis up to h = 5 synthesis up to h = 4
add
synthesis up t h = 3 th i to
synthesis up to h = 4
add
Contour C t level 2 sigma
0 1
contribution from h = 4
contribution from h = 5
Fourier ripples
Low resolution leads to model bias
X-ray crystallograp course 2007, Karsten Theis, UMass Amherst phy n
Disorder makes interpretation more diffi lt difficult
Phosphorous Shading represents p noise due to 1) errors in experimental data 2) errors in phases derived from model
X-ray crystallograp course 2007, Karsten Theis, UMass Amherst phy n
no tail
Intensities
Real structure
measured diffraction pattern
tail? Phases
Although the cat has no tail in the real structure, it appears in the model-biased density
Carbon B
tail
Current model
calculated diffraction pattern
Interpretation of electron density p y
X-ray crystallography course 2007, Karsten Theis, UMass Amherst p n
Building a model into the electron density involves interpretation and prior knowledge i l i t t ti d i k l d
X-ray crystallograp course 2007, Karsten Theis, UMass Amherst phy n
Protein/solvent regions C-alpha trace main chain, peptide direction sequence assignment side chain conformations , , glycosylation and other disulfides, metals, g y y surprises
Problem set 9: interpreting electron density p g y
X-ray crystallograp course 2007, Karsten Theis, UMass Amherst phy n
Assessing overall q g quality of structures y
X-ray crystallograp course 2007, Karsten Theis, UMass Amherst phy n
1) Which pairs of amino acids have very similar electron density and are thus difficult to distinguish crystallographically? Asp/Glu ; Thr/Val ; Leu/Ile ; Lys/Met A /A L /M t ; Asp/Asn ; Leu/Asp ; Glu/Gln L /A Gl /Gl 2) Which amino acids other than histidine have two side chain conformations resulting in almost identical electron density? What could help to distinguish the two possible conformations?
N H
Quality criteria Resolution (related to # of observations per # of atoms) R-factor and free R-factor (compares measured intensities to those calculated from the crystallographic model) th l l t df th t ll hi d l) Geometry (Ramachandran plot, bond lengt...