Data reduction and processing
Al Kikhney
Outline
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SAXS experiment setup
3D → 2D → 1D
Background subtraction
High vs. low concentration
Rg, MM
Volume
Distance distribution function p(r)
Small Angle X-ray Scattering
solution
Synchrotron Radiation →
2θ
Homogeneous and
Monodisperse solution
s
X-ray detector
solvent
|s| = 4π sinθ/λ
1-2 mg purified material
concentration from 0.5 mg/ml,
exposure times: a few seconds/minutes
s – scattering vector
2θ – scattering angle
λ – wavelength
I(s) – intensity
Small Angle X-ray Scattering
Exposure
beamstop
Beam
lower angle
Beam
higher angle
X-ray detector
Small Angle X-ray Scattering
Exposure
beamstop
Beam
X-ray detector
X-ray detector
Small Angle X-ray Scattering
Exposure
X-ray detector
Small Angle X-ray Scattering
Radial averaging
Log I(s),
a.u.
Normalization against:
• data collection time,
• transmitted sample intensity
s, nm-1
Small Angle X-ray Scattering
Notations and units
Log I(q),
a.u.
|q| = 4π sinθ/λ
2θ – scattering angle
λ – wavelength
q, nm-1
Small Angle X-ray Scattering
Notations and units
Log I(s),
a.u.
|s| = 4π sinθ/λ
2θ – scattering angle
λ – wavelength
1
2
3
s, nm-1
Small Angle X-ray Scattering
Notations and units
Log I(s),
a.u.
|s| = 4π sinθ/λ
2θ – scattering angle
λ – wavelength
0.1
0.2
0.3
s, Å-1
Small Angle X-ray Scattering
Notations and units
Log I(s),
a.u.
|s| = 2 sinθ/λ
2θ – scattering angle
λ – wavelength
s, nm-1
Small Angle X-ray Scattering
Notations and units
Log I(s),
a.u.
|s| = 4π sinθ/λ
2θ – scattering angle
λ – wavelength
s, nm-1
Data quality
Radiation damage
Log I(s), a.u.
sample
same sample again
RADIATION DAMAGE!
s, nm-1
Data quality
Log I(s), a.u.
sample
same sample again
average
s, nm-1
I(s), a.u.
Buffer and sample
Solution and Solvent
s, nm-1
I(s), a.u.
Buffer and sample
Solution and Solvent
(zoom in)
s, nm-1
Looking for protein signals less than 5% above background level…
Background subtraction
Solution minus Solvent
Log I(s),
a.u.
Log I(s),
a.u.
sample
buffer
sample – buffer
(subtracted)
Normalization against:
• concentration
s, nm-1
s, nm-1
Data quality
“Can I use this data for further analysis?”
Log I(s)
Log I(s)
lysozyme
AGGREGATED!
s, nm-1
s, nm-1
Dilution series
Log I(s)
Low and High Concentration
LytA protein, 60 kDa , 1 mg/ml
10 mg/ml
s, nm-1
Dilution series
Log I(s)
Low and High Concentration
s, nm-1
Merging data
Log I(s)
Low and High Concentration
s, nm-1
Merging data
Log I(s)
Low and High Concentration
s, nm-1
Merging data
Log I(s)
Low and High Concentration
s, nm-1
Data analysis
Shape
lg I(s), relative
0
Long rod
-1
-2
-3
Solid sphere
-4
-5
-6
0.0
0.1
0.2
0.3
0.4
s, s
nm-1
Hollow sphere
Dumbbell
0.5
Flat disc
Size
Log I(s)
s, Å-1
Shape and size
Log I(s)
a.u.
lysozyme
apoferritin
s, nm-1
Crystal
vs.
solution
Data range
2.00
1.00
0.67
0.50
0.33
Resolution, nm
Log I(s)
8
Atomic
structure
7
Shape
6
Size
5
Fold
0
5
10
15
s, nm-1
© Dmitri Svergun
Radius of gyration (Rg)
Definition
Measure for the overall size of a macromolecule
Average of square center-of-mass
distances in the molecule
weighted by the scattering length density
Log I(s)
Radius of gyration (Rg)
Guinier plot
s
Radius of gyration (Rg)
Guinier plot
Log I(s)
Ln I(s)
s2
Normal Log plot
s
Radius of gyration (Rg)
Guinier plot
Ln I(s)
y = ax + b
Rg = sqrt(-3a)
• Estimate of the overall size
of the particles
Guinier approximation:
I(s) = I(0)exp(-s2Rg2/3)
sRg≲1.3
s2
André Guinier
1911-2000
Radius of gyration (Rg)
Guinier plot
Ln I(s)
y = ax + b
Rg = sqrt(-3a)
• Estimate of the overall size
of the particles
Guinier approximation:
I(s) = I(0)exp(-s2Rg2/3)
sRg≲1.3
• Quality of the data
– aggregation
– polydispersity
– improper background
substraction
• Zero angle intensity I(0)
• First point to use
s2
Radius of gyration (Rg)
Log I(s)
Bovine serum albumin (BSA)
s, 1/nm
Radius of gyration (Rg)
Guinier plot
Ln I(s)
s2
Radius of gyration (Rg)
Guinier plot
Ln I(s)
Rg ± stdev
Ln I(0)
Forward scattering I(0)
Data quality
Data range
y = ax + b
Rg = sqrt(-3a)
s2
Log I(s), a.u.
Log I(0)apo
Molecular mass
Guinier approximation
Log I(0)lys
lysozyme
apoferritin
s, nm-1
I(0) and Molecular Mass
MMsample
I(0)sample
= I(0)
MMBSA
BSA
MMsample = I(0) sample* MMBSA / I(0)BSA
BSA
Rg = 3.1 nm
I(0) = 11.7
MMBSA = 66 kDa
Rg = 1.46 nm
I(0) = 3.66
MM = 20.6 kDa
Rg = 6.81 nm
I(0) = 79.45
MM = 448.2 kDa
Porod law
I(s) ~
-4
s
Intensity decay is proportional to s-4 at higher angles
(for globular particles of uniform density)
Porod law
I(s)*s4
s
Porod law
Excluded volume of the hydrated particle
VP =
2π 2 I (0)
∞
2
[
I
(
s
)
−
K
]
s
ds
4
∫
0
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
Primus
Porod plot
Excluded volume of the hydrated particle
I(s)*s4
I(s)*s4
14 nm3
~9 kDa
974 nm3
s
s
~610 kDa
Sasplot
Kratky plot
Patterns of globular and flexible proteins
I(s) s2
Natively unfolded
Globular
Multidomain with
flexible linkers
© Stratos Mylonas
γ(r)
Distance distribution function
r, nm
γ(r)
Distance distribution function
p(r) = r2 γ(r)
r, nm
Distance distribution function
p(r)
r, nm
p(r) function
Distance distribution function
p(r) function
Distance distribution function
( s ) = 4π
II(s)
Dmax
∫
0
sin( sr )
dr
(r )
pp(r)
sr
2
r
p
r
=
(
)
p(r)
2π 2
Indirect Fourier Transform
∞
s 2 I(s)
I ( s ) sin( sr )
ds
∫0
sr
Gnom
p(r) plot
Distance distribution function
Dmax
Dmax
p(r)
p(r)
r, nm
r, nm
Data quality
Dmax
smin ≤ π/Dmax
I(s)
p(r)
r, nm
smin
s, 1/nm
Yeast bleomycin hydrolase 3GCB
Compact dimer
50 kDa Monomer
Hexamer
Extended dimer
p(r) plots
50 kDa Monomer
Compact dimer
Extended dimer
Bad
Yeast bleomycin hydrolase 3GCB
Hexamer
Good
Summary
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•
•
•
•
Exposure 3D → 2D
Radial averaging → 1D
Log I(s)
Normalization
• Log plot
s
Background subtraction
Analysis
• Guinier plot (Rg, MM)
• Porod plot
s2
I(s)*s4
• Kratky plot (flexibility)
• p(r) plot
Ln I(s)
p(r)
s
I(s)*s2
s
r
Thank you!
After questions: group photo!
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