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!