primary data reduction and analysis - embl hamburg
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Solution scattering from biological macromoleculesPrimary data reduction and analysisAl KikhneyEMBL Hamburg
Outline
• 3D → 2D → 1D• Experiment design and data reduction
• Exposure time• Background subtraction• Dilution series
• Overall parameters:• Guinier analysis:
Rg, I(0), molecular mass• Volume• p(r), Dmax
X-raydetector
solvent
• Few kDa to GDa• Monodisperse and homogeneous• Concentration: 0.5–10 mg/ml• Amount: 10–100 μl
solution
X-ray →
SAXS experiment
Log I(s)a.u.
105
104
103
102
101
2D → 1D
s, nm-1
s, nm-1
Log I(s)a.u.
105
104
103
102
101
Normalization• Transmitted beam• Exposure timeBackground subtraction
nm-1
log I(s)
experimental SAXS pattern
experimental SAXS pattern
SAXS data from macromolecules in solution
nm-1
log I(s)
experimental SAXS pattern
experimental SAXS pattern
calculated from model
SAXS data from macromolecules in solution
SAXS data from macromolecules in solution
nm-1
log I(s)
experimental SAXS pattern
experimental SAXS pattern
calculated from model
X-raydetector
solution
X-ray →2θ
s
solution
X-ray →2θ
s
I(s),a.u.
s, nm-1
Notations and units
|s| = 4π sinθ/λ
2θλs
I(s)
– scattering angle– wavelength– scattering vector– intensity
I(s),cm-1
s, nm-1
Notations and units
|s| = 4π sinθ/λ
2θλs
I(s)
– scattering angle– wavelength– scattering vector– intensity
I(q),a.u.
q, nm-1
|q| = 4π sinθ/λ
2θ – scattering angleλ – wavelength
Notations and units
I(s),a.u.
s, nm-1
|s| = 4π sinθ/λ
2θ – scattering angleλ – wavelength
1 2 3
Notations and units
I(s),a.u.
s, Å-1
|s| = 4π sinθ/λ
2θ – scattering angleλ – wavelength
0.1 0.2 0.3
Notations and units
I(s),a.u.
s, nm-1
|s| = 4π sinθ/λ
2θ – scattering angleλ – wavelength
Notations and units
Exposure time0.05 second
I(s)
s, nm-1
0.1 second
Exposure timeI(s)
s, nm-1
0.2 second
Exposure timeI(s)
s, nm-1
0.4 second
Exposure timeI(s)
s, nm-1
0.8 second
Exposure timeI(s)
s, nm-1
1.6 second
Exposure timeI(s)
s, nm-1
0.05 second0.2 second0.8 second
Exposure timeI(s)
s, nm-1
Exposure time0.05 second0.2 second0.8 second1.6 second
I(s)
s, nm-1
RADIATIONDAMAGE!
I(s)
s, nm-1
frame 1frame 10
Multiple exposures
I(s)
s, nm-1
frame 1frame 2
Multiple exposures
:)
I(s)
s, nm-1
average
Multiple exposures
3.2 mg/ml lysozyme + buffer + cell
Sample and bufferI(s)
s, nm-1
3.2 mg/ml lysozyme
Sample and bufferI(s)
s, nm-1
Background subtractionSolution minus Solvent
I(s)
s, nm-1
Background subtractionSolution minus Solvent
I(s)
s, nm-1
Normalization against:• Concentration
Log I(s)
s, nm-1
Logarithmic plot
Dilution series2 mg/ml
Log I(s)
s, nm-1
Dilution series4 mg/ml
Log I(s)
s, nm-1
Dilution series8 mg/ml
Log I(s)
s, nm-1
Dilution series16 mg/ml
Log I(s)
s, nm-1
Dilution series32 mg/ml
Log I(s)
s, nm-1
Dilution series2 mg/ml
32 mg/ml
Log I(s)
s, nm-1
Inter-particle interactions
No interactions
Inter-particle interactions
Attractive interactions Repulsive interactions
Merging dataLog I(s)
s, nm-1
Merging dataLog I(s)
s, nm-1
Merging dataLog I(s)
s, nm-1
Data analysis
~6 nm 100 nm3
Shape
Log I(s)
100 nm3
s
Shape
Log I(s)
s
1dqi57.5 kDa
3oux57.9 kDa 3odt
65.9 kDa
3zx663.4 kDa
Shape
Log I(s)
100 nm3
50 nm3
25 nm3
200 nm3 Size
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
Rg: 4.7 nm
Rg: 3.0 nm
Myomesin-1 My12-My13, SASBDB: SASDAK5
Radius of gyration (Rg)
6 nm 100 nm3
3.6 nm
6.4 nm
3.4 nm
4.8 nm
2.2 nmRadius of gyration (Rg)
Radius of gyration (Rg)
André Guinier1911-2000
Guinier approximation:
I(s) ≈ I(0) exp(s2Rg2/-3)
s ≲ 1/Rg
Ln I(s)
s2
Guinier plotRadius of gyration (Rg)
Ln I(s)
s2
Guinier plotRadius of gyration (Rg)
y = ax + b
Rg = √-3a
Ln I(0)
sRg < 1.3
Ln I(s)
s2
Guinier plotRadius of gyration (Rg)
Rg ± stdev
Forward scattering I(0)
Data quality
Data range
Log I(s)
s, 1/nm
Log I(s)
s, 1/nm
Aggregation
Monodisperse sample
Aggregated sample
Aggregation
Log I(s)
s, 1/nm
Logarithmic plot
Guinier plotLn I(s)
s2
Guinier plotLn I(s)
s2
0.26 nm-1 0.63 nm-1
Rg = 2.0 nmsminRg = 0.52smaxRg = 1.26 < 1.3
Guinier plotLn I(s)
s2
0.44 nm-1 0.63 nm-1
Rg = 2.3 nmsminRg = 1.01smaxRg = 1.45 > 1.3
I(0) and Molecular Mass
MMsampleMMBSA
I(0)sampleI(0)BSA
=
MMsample = I(0) sample ∙ MMBSA / I(0)BSA
• I(s) on absolute scale (cm-1)
Assuming I(0) is normalized against concentration (mg/ml)
MMsample = 103 I(0)sampleNA / (Δρνsample)2
NA – Avogadro’s numberΔρ – contrast in cm-2
vsample – partial specific volume in cm3/g
• I(s) on relative scale (a.u.)
Porod volumeExcluded 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 volumeExcluded volume of the hydrated particle
∫∞
−=
0
24
2
])([
)0(2
dssKsI
IVPπ
For proteins: MW [kDa] ~ Vp [nm3] / 1.6
69.5 nm369.2 nm3
Excluded volume of the hydrated particle
~43 kDa ~43 kDa
Porod volume
*Simulated data
770 nm323.7 nm3
Excluded volume of the hydrated particle
~14.8 kDa ~480 kDa
Porod volume
SASBDB: SASDA96 SASDA82
SAXS MoW
580 nm313.6 nm3
Determination of protein MW from a SAXS measurement on a relative scale
~11.2 kDa ~480 kDa
H. Fischer et al. (2010) J. Appl. Cryst. 43, 101–109 DATMOW
Volume-of-correlationDetermination of the molecular mass of proteins or RNA
ranging from 10 to 1000 kDa
12.3–14.1 kDa 503–515 kDa
R.P. Rambo and J.A. Tainer (2013) Nature 496(7446) 477–481 DATVC
Distance distribution function
r, nm
γ(r)1
0
Distance distribution function
r, nm
γ(r)1
0
p(r) = r2γ(r)
Distance distribution function
r, nm
p(r)
0
p(r) = r2γ(r)
6 nm
100 nm3
r, nm
p(r)
Dmax= 6 nm
Distance distribution function
Dmax: 18 nm
Myomesin-1 My12-My13, SASBDB: SASDAK5
Maximum intra-particle distance Dmax
Dmax: 18 nm
Dmax: 10 nm
Myomesin-1 My12-My13, SASBDB: SASDAK5
Maximum intra-particle distance Dmax
r, nm
p(r)
Distance distribution function
r, nm
p(r)
Distance distribution function
r, nm
p(r)
Distance distribution function
r, nm
p(r)
Distance distribution function
r, nm
p(r)
Distance distribution function
r, nm
p(r)Log I(s)
s, nm-1
dssr
srsIsrrp ∫∞
=0
2
2
2 )sin()(2
)(π
r, nm
p(r)Log I(s)
s, nm-1
drsr
srrpsID
∫=max
0
)sin()(4)( π
p(r) plotDistance distribution function
r, nm r, nm
p(r) p(r)
DmaxDmax
r, nm
p(r)
Dmax
Data qualitysmin < π/Dmax
I(s)
s, 1/nmsminDmax
I(s)
s
I(s)
s
Ambiguity
I(s)
s
I(s)
s
Ambiguity
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
smin < π/Dmax
Beamline P12
Data range can be adjusted bychanging the wavelength λ or the sample-detector distance
Beamline P12
Detector closer to the sample –collect wider angles (for smallerparticles)
Beamline P12
Detector further from the sample –collect smaller angles (for largerparticles)
Data reduction and analysis steps
Radial averaging
Radiation damage check
Normalization
Background subtraction
Merge multiple concentrations
Rg, molecular weight
Dmax, p(r)
Porod volume
…
Ab initio shape determination
1s 2s
0.5 1.0 2.0
3sX
p(r)
p(r)
Thank you!
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