X-ray crystallograp
How do we obtain the crystal structure of a protein phy course 2
the crystal structure of a protein from the diffraction data |Fhkl|?
007, Karstenn Theis, U
Mass A
mherst
Protein structure from X-ray diffraction
X-ray
y
Crystallize a protein with knownRaw data: Diffraction images
crystallograp
Crystallize a protein with knownchemical structure:MSALEFGPSLKMNE… phy course 2
CRYST1 221 200 73 600 80 900 90 00 90 00 90 00 P 21 21 2 4
Conformation, 3D-structure:
007, Karsten
CRYST1 221.200 73.600 80.900 90.00 90.00 90.00 P 21 21 2 4 ATOM 1 N ILE A 6 97.764 18.390 39.211 1.00 84.23ATOM 2 CA ILE A 6 97.130 18.979 37.983 1.00 84.74ATOM 3 C ILE A 6 96.655 17.885 37.031 1.00 84.98ATOM 4 O ILE A 6 97.460 17.052 36.605 1.00 85.82ATOM 5 CB ILE A 6 98.139 19.855 37.248 1.00 99.99ATOM 6 CG1 ILE A 6 99.043 18.979 36.389 1.00 99.99ATOM 7 CG2 ILE A 6 98.984 20.617 38.263 1.00 99.99ATOM 8 CD1 ILE A 6 100 297 18 614 37 178 1 00 99 99
n Theis, UM
a
ATOM 8 CD1 ILE A 6 100.297 18.614 37.178 1.00 99.99ATOM 9 N ALA A 7 95.359 17.896 36.702 1.00 84.56ATOM 10 CA ALA A 7 94.757 16.906 35.795 1.00 83.75ATOM 11 C ALA A 7 95.816 16.303 34.876 1.00 83.47...ATOM 7604 O2* G R 3 73.810 43.517 21.774 1.00 62.48 ss A
mherst
Reciprocal space Real space
: Fourier transformX
-ray Diffraction: real space vs. reciprocal space crystallograp
p p p
phy course 2007, Karsten
pulsed NMR, FT-IR and other spectroscopic methods:time series vs frequencies n Theis, U
Ma0.6
0.8
1
plitu
de
time series vs. frequencies
0
0.5
1
1.5
2
nal ss A
mherst
0
0.2
0.4
0 2 4 6 8 10 12
frequency/Hz
Am
-2
-1.5
-1
-0.5
00 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
time/sec
Sign
Fourier tour in two dimensions
X-ray Light/dark:ρ(r) F(q)
crystallograp
Light/dark:Intensities
ρ( )
phy course 2
Colors:Phases
007, Karsten
Molecule Fourier transforme--density n Theis, U
Ma
e density
“reciprocal space”“real space” ss Am
herst
p
This tour is from Kevin Cowtan’s picture book of Fourierat www.ysbl.york.ac.uk/~cowtan/fourier/fourier.html
Crystals amplify the scattering signal
X-ray
y p y g g
F(h,k,l)ρ(r)
crystallograpCrystalFourier
f
phy course 2
Crystal transform
007, Karsten
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 n Theis, UM
a
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) ss A
mherst
empty areas (another level of signal/noise increase)
Flipside: diffraction image represents average structure (over time and crystal)
The Fourier transform is reversible
X-ray crystallograpphy course 2
Fourier analysis Fourier synthesis 007, Karsten
Fourier analysis Fourier synthesis
n Theis, UM
ass Am
herst
Questions: X-ray diffraction
X-ray
Q y
1) Why don’t we see a diffraction pattern in a crystallograp
1) Why don t we see a diffraction pattern in a medical X-ray image?
2) Why can we distinguish between bones phy course 2
2) Why can we distinguish between bones and soft tissue in a medical X-ray image?
3) Wh d ’t diff ti tt 007, Karsten
3) Why don’t we see a diffraction pattern when observing crystals under the light
i ?
n Theis, UM
a
microscope?4) In a protein with 10000 atoms, how many
ss Am
herst
atoms contribute to a given diffraction spot?
Wh i l i d i iWhy is solving and interpretinga crystal structure difficult?a crystal structure difficult?
The Phase ProblemThe Phase Problem
Cr stals aren‘t perfect beca se proteins are fle ibleCrystals aren‘t perfect because proteins are flexible
P t i f ti diff t t t d diProtein conformations differ to some extent depending on their environment
Problem: without phases, l t d it
X-ray
no electron densityFourier FourierF(q) crystallograp
analysis synthesis(q)
phy course 2007, Karsten
measureddiffraction patternUnknown structure
F i
n Theis, UM
a
without phases:gibberish
Fouriersynthesis
|F(q)|
ss Am
herst
g bbe s
Solving the phase problem
X-ray
g p p
1. Direct methods (guessing the phases) crystallograp
(g g p )Works for small molecules (lots of measurements per atom in structure)
phy course 2
2. Patterson methods (inter-atomic vectors)Works for simple structures (4 atom pairs with 2 atoms, 100 atom pairs with 10 atoms 007, K
arsten
3. Model phases; molecular replacementRelies on partial knowledge of the structure n Theis, U
Ma
4. MIR/MAD techniques (ab initio)Prepare crystals that contain Se, Hg, Pt or other heavy atoms at a ss A
mherst
p y , g, yhandful of positions in the crystal and solve that simple structure first using method 1. or 2.
Calculating phases from an atomic model
X-ray
g p
crystallograp
|Fo(hkl)| derived from observed intensities phy course 2
unknown structure measureddiffraction pattern 007, K
arstenn Theis, UM
a
“2Fo-Fc map”|Fc(hkl)| and phasesderived from model ss A
mherst
atomic model of calculatedknown structure diffraction pattern
derived from model
Molecular replacement: unknown structure has a distinct crystal packing
X-ray
has a distinct crystal packing
I i i crystallograp
Intensities
phy course 2
Unknown structure measureddiffraction pattern
Ph
“2Fo-Fc map”
007, Karsten
Phases
n Theis, UM
ass Am
herst
Known structure rotated structure calculateddiffraction pattern
MIR/MAD method
X-ray Solve a simpler problem first: just a couple of atoms crystallograp
Solve a simpler problem first: just a couple of atomsCollect data of crystals multiple times, with slight variations
MAD MIR phy course 2
MADMultiwavelengthAnomalousDispersion
MIRMultiple IsomorphousReplacement
measure identical crystalat 3 different wavelengths near Se absorption edge
soak crystals in differentsubstances and measure
007, Karsten
:-{ :-{ :-{ :-{:-{ :-{
n Theis, UM
aPt derivative Hg derivativeSe scattering is influenced by ss Am
herst
nativechoice of wavelength, scattering by other atoms is not
What is the best method?
X-ray MIR/MAD works for all protein structures crystallograp
MIR/MAD works for all protein structuresbut…
requires additional measurements, experience and
phy course 2
lots of work to place atoms into density
Molecular replacement is fast 007, Karsten
Molecular replacement is fastbut…
large model bias in low-resolution structures n Theis, UM
a
• errors are propagated• new features are overlooked
ss Am
herst
Crystal imperfection (disorder), not l th li it l ti
X-ray
wavelength, limits resolution
The electron density averaged over time and over the crystal is crystallograp
The electron density, averaged over time and over the crystal, is more or less “fuzzy” depending on crystal quality
phy course 2
• electrons have distribution around atom rather than one single location (same for all crystals)
l l i id b di i t l ki (d d 007, Karsten
• molecules move as rigid bodies in crystal packing (depends on crystal contacts)
• atom positions change with time (local dynamic disorder) n Theis, UM
a
p g ( y )• atom positions change from one unit cell to another (local
static disorder)
ss Am
herstDisorder in real space
X-ray
p
Lower resolution Higher resolution
crystallograpphy course 2007, Karstenn Theis, U
Mass A
mherst
File size: 2 Kb 11 Kb 672 Kb
B-factors and disorder
X-ray • Synonyms: Temperature factors, atomic displacement crystallograp
y y p , pfactors
• B-factors describe how the electron density of an i b d d b i d d i di d i
phy course 2
atom is broadened by static and dynamic disorder in the crystal
007, Karsten
B-factor Displacement20 Å2 0.25 Å40 Å2 0 51 Å
Static disorder: distinct atomic positions in different unit cells of the cr stal
n Theis, UM
a
40 Å 0.51 Å80 Å2 1.01 Å
of the crystalDynamic disorder: changes in conformation over time during ss A
mherst
the measurement
Disorder prevents collection of high l ti d t i i l
X-ray
resolution data in reciprocal space
crystallograpphy course 2007, Karsten
3Å
n Theis, UM
a
12Å6Å
4Å
ss Am
herst
Disorder makes data collection
X-ray
(and solving a structure) more difficultThe intensity of the crystallograp
ydiffraction data decreases with resolution
5Å 2.5Å 1.7Å 1.2Å 1Å
phy course 20 Å2
resolution
The higher the fen
sity
)
007, Karsten
0 Åaverage B-factor, the faster the drop-off.sq
rt (in
te
n Theis, UM
a
50 Å2 10 Å2p
This makes it more difficult (impossible)1/res ss A
mherst
difficult (impossible) to collect high resolution data
High resolutionLow resolution
1/res
Low resolution data: loss of detail
X-ray weak signal crystallograp
g
strong signal
phy course 2
Fourier l i
Fourier
007, Karsten
analysis synthesis
n Theis, UM
ass Am
herst
The Fourier transform (in 1D)X
-ray ( )
|F|(h) Color: φ(h) crystallograp
ρ(r)
|F|(h) Color: φ(h)
phy course 2007, Karsten
r0 1
h0 5
n Theis, UM
a
Real space Reciprocal space
Fourier analysis ss Am
herstFourier synthesisFourier analysis
Fourier analysis
X-ray
y1/|qh=1| crystallograp
|F|(h) Color: φ(h)h=1h=2
h=0
phy course 2
h=2h=3h=4h=5 007, K
arsten
ρ(r)
h0 5
h=5
n Theis, UM
a
R l
0 1
Reciprocal space
0 5
ss Am
herst
Real space Reciprocal space
What resolution does h=5 correspond to (please estimate from atomic distances)?
Fourier synthesis r
ρ(r)
h
|F|(h)
X-ray
y r0 1
h0 5
crystallograp
addaddadd
phy course 2
synthesis up to h = 1synthesis up to h = 2
007, Karstenn Theis, U
Mass A
mherst
contribution from h = 0contribution from h = 1contribution from h = 2
Fourier synthesis r
ρ(r)
h
|F|(h)
X-ray
y r0 1
h0 5
crystallograp
addsynthesis up to h = 3 phy course 2
synthesis up to h = 2
synthesis up to h = 3
007, Karstenn Theis, U
Mass A
mherst
contribution from h = 3
Fourier synthesis r
ρ(r)
h
|F|(h)
X-ray
y r0 1
h0 5
crystallograp
addth i t h 3
synthesis up to h = 4
phy course 2
synthesis up to h = 3
007, Karstenn Theis, U
Mass A
mherst
contribution from h = 4
Fourier synthesis r
ρ(r)
h
|F|(h)
X-ray
y r0 1
h0 5
synthesis up to h = 5
crystallograp
add
synthesis up to h = 4
phy course 2
C t 007, Karsten
Contourlevel ≈2 sigma
n Theis, UM
a
0
1
ss Am
herst
Fourier ripplescontribution from h = 5
Low resolution leads to model biasX
-ray crystallograpIntensitiesno tail phy course 2
Real structure measureddiffraction pattern
no tail
007, Karstentail? n Theis, U
Ma
Phases Although the cat has no tail in the real structure, it appears
tail ss Am
herst
Current model calculateddiffraction pattern
in the model-biased density
tail
Disorder makes interpretation diffi lt
X-ray
Shading represents
more difficult
crystallograp
Phosphorous
pnoise due to 1) errors inexperimental data phy course 2Carbon
data 2) errors in phases derived from model
B
007, Karsten
B
n Theis, UM
ass Am
herst
Interpretation of electron density
X-ray
p y
crystallograpphy course 2007, Karstenn Theis, U
Mass A
mherst
Building a model into the electron density i l i t t ti d i k l d
X-ray
involves interpretation and prior knowledge
crystallograp
• Protein/solvent regions• C-alpha trace phy course 2
• main chain, peptide direction• sequence assignment 007, K
arsten
• side chain conformations• disulfides, metals, glycosylation and other n Theis, U
Ma
, , g y ysurprises
ss Am
herst
Problem set 9: interpreting electron density
X-ray
p g y
1) Which pairs of amino acids have very similar electron crystallograp
1) Which pairs of amino acids have very similar electron density and are thus difficult to distinguish crystallographically? Asp/Glu ; Thr/Val ; Leu/Ile ; L /M t A /A L /A Gl /Gl
phy course 2
Lys/Met ; Asp/Asn ; Leu/Asp ; Glu/Gln2) Which amino acids other than histidine have two side
chain conformations resulting in almost identical electron 007, Karsten
chain conformations resulting in almost identical electron density? What could help to distinguish the two possible conformations?
n Theis, UM
aN
NH
ss Am
herst
NH
N
Assessing overall quality of structures
X-ray
g q y
Quality criteria crystallograp
Quality criteriaResolution (related to # of observations per # of atoms)R-factor and free R-factor (compares measured intensities to th l l t d f th t ll hi d l)
phy course 2
those calculated from the crystallographic model)Geometry (Ramachandran plot, bond lengths and angles)Publication date (determines whether certain methods were 007, K
arsten
Publication date (determines whether certain methods were available, i.e. refinement, free Rfactor + other checks)
Wh h k th t ll h ?
n Theis, UM
a
Who checks the crystallographer?The reviewersThe protein data bank ss A
mherst
pCompeting labs working on similar structures
Spotting regions that are problematicX
-ray p g g p
1) Region is absent from the crystallographic model crystallograp
1) Region is absent from the crystallographic modela. unstructuredb. folded but moves independently of rest of protein phy course 2
p y p2) Region has high B-factors3) Region is wrong in the model, i.e. different from true
007, Karsten
conformation in the crystal (check electron density)4) Region is ordered and correctly modeled but…
a Conformation in solution is different n Theis, UM
a
a. Conformation in solution is differentb. Region is flexible in solution but not in the crystalc. Conformation changes upon ligand binding ss A
mherst
c. Conformation changes upon ligand binding
Critical use of diffraction data
X-ray
• The atomic model is an interpretation of the electron density that in turn is based partially on the atomic model (model bias) crystallograp
based partially on the atomic model (model bias)• High resolution and low R-factors → reliable and accurate structures
phy course 2
• Be aware of possible differences between a protein in solution and in different crystal environments
• Expect structural changes upon ligand binding or other cellular events 007, Karsten
– Hydrophobic cores of structural domains do not change much in different environments
– Conformations of surface side chains and the relative orientations of n Theis, UM
a
structural domains connected by flexible linkers might differ from case to case
• Flexibility is expected in regions with high temperature factors ss Am
herst
y p g g p• Look for structural variablity by superimposing atomic models obtained
under different conditions
To reciprocal space and back: For hands-on experience, enroll in the 2008 intensive course
X-ray
p ,
Crystallize a protein with knownRaw data: Diffraction images
crystallograp
Crystallize a protein with knownchemical structure:MSALEFGPSLKMNE… phy course 2
CRYST1 221 200 73 600 80 900 90 00 90 00 90 00 P 21 21 2 4
Conformation, 3D-structure:
007, Karsten
CRYST1 221.200 73.600 80.900 90.00 90.00 90.00 P 21 21 2 4 ATOM 1 N ILE A 6 97.764 18.390 39.211 1.00 84.23ATOM 2 CA ILE A 6 97.130 18.979 37.983 1.00 84.74ATOM 3 C ILE A 6 96.655 17.885 37.031 1.00 84.98ATOM 4 O ILE A 6 97.460 17.052 36.605 1.00 85.82ATOM 5 CB ILE A 6 98.139 19.855 37.248 1.00 99.99ATOM 6 CG1 ILE A 6 99.043 18.979 36.389 1.00 99.99ATOM 7 CG2 ILE A 6 98.984 20.617 38.263 1.00 99.99ATOM 8 CD1 ILE A 6 100 297 18 614 37 178 1 00 99 99
n Theis, UM
a
ATOM 8 CD1 ILE A 6 100.297 18.614 37.178 1.00 99.99ATOM 9 N ALA A 7 95.359 17.896 36.702 1.00 84.56ATOM 10 CA ALA A 7 94.757 16.906 35.795 1.00 83.75ATOM 11 C ALA A 7 95.816 16.303 34.876 1.00 83.47...ATOM 7604 O2* G R 3 73.810 43.517 21.774 1.00 62.48 ss A
mherst
Reciprocal space Real space
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