SAXS data reduction and processing - EMBL Hamburg...Ln I(s) s 2 • Estimate of the overall size of...
Transcript of SAXS data reduction and processing - EMBL Hamburg...Ln I(s) s 2 • Estimate of the overall size of...
Data reduction and processingAl Kikhney
Outline
• SAXS experiment setup• 3D → 2D → 1D• Background subtraction• High vs. low concentration• Rg, MM• Volume• Distance distribution function p(r)
solution
Small Angle X-ray Scattering
|s| = 4π sinθ/λ
s – scattering vector2θ – scattering angleλ – wavelengthI(s) – intensity
Synchrotron Radiation →
X-ray detector
2θ s
Homogeneous andMonodisperse solution
solvent
1-2 mg purified materialconcentration from 0.5 mg/ml, exposure times: a few seconds/minutes
Beambeamstop
higher angle
lower angle
Beam
Small Angle X-ray ScatteringExposure
X-ray detector
Small Angle X-ray ScatteringExposure
X-ray detector
Beam
X-ray detector
beamstop
Small Angle X-ray ScatteringExposure
X-ray detector
Normalization against:• data collection time,• transmitted sample intensityLog I(s),
a.u.
s, nm-1
Small Angle X-ray ScatteringRadial averaging
Log I(q),a.u.
q, nm-1
|q| = 4π sinθ/λ
2θ – scattering angleλ – wavelength
Small Angle X-ray ScatteringNotations and units
Log I(s),a.u.
s, nm-1
|s| = 4π sinθ/λ
2θ – scattering angleλ – wavelength
Small Angle X-ray ScatteringNotations and units
1 2 3
Log I(s),a.u.
s, Å-1
|s| = 4π sinθ/λ
2θ – scattering angleλ – wavelength
Small Angle X-ray ScatteringNotations and units
0.1 0.2 0.3
Log I(s),a.u.
s, nm-1
|s| = 2 sinθ/λ
2θ – scattering angleλ – wavelength
Small Angle X-ray ScatteringNotations and units
Log I(s),a.u.
s, nm-1
|s| = 4π sinθ/λ
2θ – scattering angleλ – wavelength
Small Angle X-ray ScatteringNotations and units
Data qualityRadiation damage
s, nm-1
RADIATION DAMAGE!
Log I(s), a.u.
samplesame sample again
Data quality
s, nm-1
sample
Log I(s), a.u.
same sample againaverage
Buffer and sampleSolution and Solvent
I(s), a.u.
s, nm-1
Buffer and sampleSolution and Solvent
I(s), a.u.
s, nm-1
Looking for protein signals less than 5% above background level…
(zoom in)
Background subtraction
samplesamplebuffer sample – buffer
(subtracted)
Log I(s),a.u.
s, nm-1
Log I(s),a.u.
s, nm-1
Solution minus Solvent
Normalization against:• concentration
Data quality“Can I use this data for further analysis?”
Log I(s)
s, nm-1
lysozymeLog I(s)
s, nm-1
AGGREGATED!
Dilution seriesLow and High Concentration
Log I(s)
s, nm-1
LytA protein, 60 kDa , 1 mg/ml10 mg/ml
Dilution seriesLow and High Concentration
Log I(s)
s, nm-1
Merging dataLow and High Concentration
Log I(s)
s, nm-1
Merging dataLow and High Concentration
Log I(s)
s, nm-1
Merging dataLow and High Concentration
Log I(s)
s, nm-1
Data analysis
Shape
s, nm-1
0.0 0.1 0.2 0.3 0.4 0.5
lg I(s), relative
-6
-5
-4
-3
-2
-1
0
Solid sphere
Long rod
Flat disc
Hollow sphereDumbbell
s, nm-1
0.0 0.1 0.2 0.3 0.4 0.5
lg I(s), relative
-6
-5
-4
-3
-2
-1
0
s, nm-1
0.0 0.1 0.2 0.3 0.4 0.5
lg I(s), relative
-6
-5
-4
-3
-2
-1
0
s, nm-1
0.0 0.1 0.2 0.3 0.4 0.5
lg I(s), relative
-6
-5
-4
-3
-2
-1
0
s, nm-1
0.0 0.1 0.2 0.3 0.4 0.5
lg I(s), relative
-6
-5
-4
-3
-2
-1
0
s
SizeLog I(s)
s, Å-1
Shape and size
lysozyme
apoferritin
Log I(s)a.u.
s, nm-1
Crystal solutionsolutionvs.
Data range
Atomic structure
Fold
Shape
0 5 10 15
Log I(s)
5
6
7
8
Resolution, nm2.00 1.00 0.67 0.50 0.33
Size
s, nm-1
© Dmitri Svergun
Radius of gyration (Rg)Definition
Average of square center-of-mass distances in the molecule
weighted by the scattering length density
Measure for the overall size of a macromolecule
Log I(s)
s
Guinier plotRadius of gyration (Rg)
Ln I(s)
s2
Guinier plotRadius of gyration (Rg)
Log I(s)
s
Normal Log plot
Ln I(s)
s2
• Estimate of the overall size of the particles
Guinier approximation:
I(s) = I(0)exp(-s2Rg2/3)
sRg≲1.3
Guinier plot
y = ax + bRg = sqrt(-3a)
André Guinier1911-2000
Radius of gyration (Rg)
Ln I(s)
s2
• Estimate of the overall size of the particles
• Quality of the data– aggregation– polydispersity– improper background
substraction
• Zero angle intensity I(0)• First point to use
Guinier approximation:
I(s) = I(0)exp(-s2Rg2/3)
sRg≲1.3
Guinier plot
y = ax + bRg = sqrt(-3a)
Radius of gyration (Rg)
s, 1/nm
Bovine serum albumin (BSA)
Log I(s)
Radius of gyration (Rg)
Ln I(s)
s2
Guinier plotRadius of gyration (Rg)
Ln I(s)
s2
Guinier plotRadius of gyration (Rg)
y = ax + b
Rg = sqrt(-3a)
Ln I(0)
Rg ± stdev
Forward scattering I(0)
Data quality
Data range
lysozymeapoferritin
Log I(s), a.u.
s, nm-1
Guinier approximationMolecular mass
Log I(0)lys
Log I(0)apo
I(0) and Molecular MassMMsampleMMBSA
I(0)sampleI(0)BSA
=
Rg = 1.46 nmI(0) = 3.66MM = 20.6 kDa
MMsample = I(0) sample* MMBSA / I(0)BSA
Rg = 6.81 nmI(0) = 79.45MM = 448.2 kDa
Rg = 3.1 nmI(0) = 11.7MMBSA = 66 kDa
BSA
Porod law
I(s) ~ s-4
Intensity decay is proportional to s-4 at higher angles (for globular particles of uniform density)
I(s)*s4
s
Porod law
Porod lawExcluded volume of the hydrated particle
∫∞
−=
0
24
2
])([
)0(2
dssKsI
IVPπ
K4 is a constant determined to ensure the asymptotical intensity decay proportional to s-4 at higher angles following the Porod's law for homogeneous particles
Porod plot
974 nm3
14 nm3
I(s)*s4 I(s)*s4
s s
Primus
Excluded volume of the hydrated particle
~9 kDa
~610 kDa
Natively unfolded
Globular
Multidomain with flexible linkers
Kratky plotPatterns of globular and flexible proteins
Sasplot
© Stratos Mylonas
I(s) s2
Distance distribution function
r, nm
γ(r)
Distance distribution function
r, nm
γ(r)
p(r) = r2 γ(r)
Distance distribution function
r, nm
p(r)
p(r) functionDistance distribution function
p(r) functionDistance distribution function
drsr
srrpsID
∫=max
0
)sin()(4)( π dssr
srsIsrrp ∫∞
=0
2
2
2 )sin()(2
)(π
Indirect Fourier Transform
p(r) p(r)I(s) I(s)
p(r) plotDistance distribution function
r, nm r, nm
p(r) p(r)
Gnom
DmaxDmax
r, nm
p(r)
Dmax
Data qualitysmin ≤ π/Dmax
I(s)
s, 1/nmsmin
Yeast bleomycin hydrolase 3GCB
50 kDa MonomerCompact dimer
Extended dimer
Hexamer
p(r) plots50 kDa Monomer Compact dimer Extended dimer Hexamer
Yeast bleomycin hydrolase 3GCB
GoodBad
Summary• Exposure 3D → 2D• Radial averaging → 1D• Normalization• Background subtraction• Analysis
• Log plot
• Guinier plot (Rg, MM)
• Porod plot
• Kratky plot (flexibility)
• p(r) plot
s
Log I(s)
s2
Ln I(s)
s
I(s)*s4
r
p(r) s
I(s)*s2
Thank you!
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After questions: group photo!