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