SAS data reduction Haydyn Mertens (EMBL-Hamburg) Data reduction - - PowerPoint PPT Presentation

SAS data reduction

Haydyn Mertens (EMBL-Hamburg)

Data reduction steps

Parameters

SAXS invariants

• Rg
• I0 (MM)
• Vp

Acquisition

SAXS instrumentation

• Sample
• Buffer
• Background

Reduction

2D images to 1D profile

• Integration
• Normalisation
• Averaging/Subtract

Data Acquisition

Detection

X-rays, neutrons Detectors

Instrumentation – X-rays

Haydyn Mertens, EMBO 2017 (Singapore)

• 4. December 2017
• Monochromatic and collimated X-ray radiation
• Reduced parasitic scattering
• Calibrated detector with low background

slits slits detector Scattered X-rays

primary beam beamstop

Wavelengths ~ 0.06 nm - 0.15 nm

Haydyn Mertens, EMBO 2017 (Singapore)

• 6. December 2017
• Cf. Al Kikhney (EMBL-Hamburg)

Instrumentation – X-rays

Instrumentation – Neutrons

Haydyn Mertens, EMBO 2017 (Singapore)

• 6. December 2017
• Monochromatic and collimated radiation
• Reduced parasitic scattering
• Calibrated detector with low background

collimator collimator detector Scattered Neutrons

primary beam beamstop

Wavelengths ~ 0.2 nm – 1.0 nm Velocity selector

The small-angle scattering experiment

• X-rays are scattered mostly by electrons
• Thermal neutrons are scattered mostly by nuclei
• Scattering amplitude from an ensemble of atoms A(s) is the

Fourier transform of the scattering length density distribution in the sample r(r)

• Experimentally, scattering intensity I(s) = [A(s)]2 is measured.

Haydyn Mertens, EMBO 2017 (Singapore)

• 4. December 2017

k0 = 2π/λ

2θ

k1 s = k1-k0 =(4πsinθ)/λ

Radiation sources: X-raylaboratory λ = 0.1-0.2 nm X-raysynchrotron λ = 0.03-0.35 nm Neutrontherm λ = 0.2-1 nm

The small-angle scattering experiment

• 2D pattern collected
• Exposure time (ms- sec)
• Transmitted beam intensity (beam-stop)
• Radially averaged (for isotropic scattering) à 1D profile
• Normalisation
• Frames checked for radiation damage and averaged
• Subtraction of buffer/background

Haydyn Mertens, EMBO 2017 (Singapore)

• 5. December 2017

• 1

The small-angle scattering experiment

Haydyn Mertens, EMBO 2017 (Singapore)

• 6. December 2017
• MASKING
• S-AXIS calibration
• AgBeh (d = 5.38 nm)
• Intensity scale calibration
• H2O 0.0163 cm-1

SAS sample measurement

• Subtract scattering from matrix/solvent (also reduces contribution of

background, eg. slits & sample holder)

• Contrast Dr

Dr = <r(r) - rs>, where rs is the scattering density of the matrix, may be very small for biological samples To obtain scattering from particles of interest:

Particle+matrix matrix Difference

What are we really measuring?

Haydyn Mertens, EMBO 2017 (Singapore)

• 4. December 2017
• Contrast and the other things ...
• SAXS intensity profile of “difference” between particle and

matrix/background.

I(q) = ξ dσ (q) dΩ = ξ nΔρ2V 2P(q)S(q)

Number of particles Contrast Particle volume Form factor Structure factor Instrument constant

What are we really measuring?

Haydyn Mertens, EMBO 2017 (Singapore)

• 4. December 2017
• Contrast and the other things ...
• SAXS intensity profile of “difference” between particle and

matrix/background.

I(q) = ξ dσ (q) dΩ = ξ nΔρ2V 2P(q)S(q)

Number of particles Contrast Particle volume Form factor Structure factor Instrument constant

Solute Buffer

Scattering Density Δρ

What are we really measuring?

Haydyn Mertens, EMBO 2017 (Singapore)

• 4. December 2017
• SAXS intensity profile of “difference” between particle and

matrix/background.

• If dilute enough, S(q) = 1.0 (can neglect)
• If n high enough (concentrated sample), we have signal!
• If V is big (eg. large protein), strong signal (even if n is small)
• P(q) defines the shape
• If contrast (Δρ = ρparticle – ρsolvent) is small à see close to nothing!

I(q) = ξ dσ (q) dΩ = ξ nΔρ2V 2P(q)S(q)

Contrast

Haydyn Mertens, EMBO 2017 (Singapore)

• 4. December 2017
• X-ray scattering densities of solvents and macromolecules
• Possible to contrast match in an X-ray experiment but tricky!

Scattering species Scattering density eÅ-3 H2O 0.334 D2O 0.334 50 % Sucrose in H2O 0.40 Protein 0.42 RNA 0.46 DNA 0.55

Adapted from Svergun & Feigin, Structure Analysis by Small-Angle X-Ray and Neutron Scattering, Plenum, 1987

Contrast for X-ray

Haydyn Mertens, EMBO 2017 (Singapore)

• 4. December 2017
• Matching electron density of sub-complex (eg. Protein:DNA)

Standard buffer (aqueous) ~ 50% sucrose

I = IDNA + IDNAIPROT + IPROT I = IDNA + IDNAIPROT + IPROT I = IDNA + IDNAIPROT + IPROT

Characterise your sample & Look at your data!

PAGE/SEC-MALLS/SAXS DATA

Standard situation

Monodisperse non-interacting systems

I(s) = 4π p(r)sin(sr) sr

Dmax

∫

dr

• Observed scattering proportional to

(averaged over all orientations)

• Facilitates size, shape internal structure

investigation (at low resolution)

0.5 1 1.5 2 2.5 3 s, nm

• 1

2 4

ideal

0.5 1 1.5 2 2.5 3 s, nm

• 1

2 4

attractive

0.5 1 1.5 2 2.5 3 s, nm

• 1

2 4

repulsive

• Form factor of each particle in the solution summed
• Monodisperse
• Dilute

Experimental SAS profile

Experimental SAS profile

0.5 1 1.5 2 2.5 3 s, nm

• 1

2 4

ideal

0.5 1 1.5 2 2.5 3 s, nm

• 1

2 4

attractive

0.5 1 1.5 2 2.5 3 s, nm

• 1

2 4

repulsive

Inter-particle distances begin to be of the same order as the intra- particle distances.

• Form factor and structure factor
• Interparticle interference
• Attractive (eg. aggregation)

Experimental SAS profile

0.5 1 1.5 2 2.5 3 s, nm

• 1

2 4

ideal

0.5 1 1.5 2 2.5 3 s, nm

• 1

2 4

attractive

0.5 1 1.5 2 2.5 3 s, nm

• 1

2 4

repulsive

Start to see a set of dominant average inter-particle distances (usually only at high conc.).

• Form factor and structure factor
• Interparticle interference
• Repulsive (eg. ordering)

1 2 3 4 5 s, nm

• 1

I(s), rel. units. 5 10 15 r, nm 0.0 0.5 1.0 p(r), rel. units.

Haydyn Mertens, EMBO 2017 (Singapore)

• 4. December 2017

) s R ) I( I(s)

g 2 2

3 1 exp(

• @

Radius of gyration Rg (Guinier, 1939)

Maximum size Dmax: p(r)=0 for r> Dmax

Dmax

Excluded particle volume (Porod, 1952)

ò

¥

= =

2 2

) ( I(0)/Q; 2 V ds s I s Q p

Parameters from SAS:

Big vs small objects and the scattering angle!

Haydyn Mertens, EMBO 2017 (Singapore)

• 4. December 2017
• Intensity drops off more rapidly for larger particles!

Adapted from: Kratky, O. (1963) Prog. Biophys. Mol. Biol. 13.

2θ Δb Δb = Δa à signal cancellation at lower angles Δa = 1λ àall phases uniformly represented (cancellation of signal) 2θ Δa

Haydyn Mertens, EMBO 2017 (Singapore)

• 4. December 2017

① SAMPLE OPTIMISATION ② DATA COLLECTION ③ DATA REDUCTION ④ PRIMARY ANALYSIS ⑤ MODELING ⑥ VALIDATION

Haydyn Mertens, EMBO 2017 (Singapore)

• 4. December 2017

① SAMPLE OPTIMISATION ② DATA COLLECTION ③ DATA REDUCTION ④ PRIMARY ANLAYSIS ⑤ MODELING ⑥ VALIDATION

Data reduction

1D profiles

Averaging/Subtraction Merging

Data flow

19/06/12

Obtain 1D profiles of frames (sample & buffer) Average frames

(in PRIMUS)

Subtract background/buffer scattering

(in PRIMUS)

Guinier analysis Concentration dependent behaviour? average Merge/extrapolate No Yes IFT (eg. GNOM) Modeling Fitting (eg. CRYSOL)

Data reduction: Averaging of frames in PRIMUS

19/06/12

Concentration series loaded (including buffers)

lin - lin log - lin

Data reduction

19/06/12

Averaging data sets

Sample and two buffer sets Sample VS buffer

Data reduction

19/06/12

Averaging data sets

Average buffers

Data reduction

19/06/12

Subtraction of the background (averaged buffer)

Subtract average buffer from sample

Radiation damage

Frames change

Following exposure

• Intensity increase
• SAS parameters

Concentration dependence!

Concentration dependence

19/06/12

• Difference of low and higher concentration data

Low conc. High conc.

Merging data sets

19/06/12

• Option 1:
• Use lowest conc data for low-s and merge with high-s from high conc

data.

• Option 2:
• If Rg and I(0) change in a linear way with concentration, extrapolate

to infinite dilution (remove structure factor) Low-s region often contains significant structure factor

Option 1: Merging data sets

19/06/12

Rg changes linearly (or close enough) with concentration

Option 1: Merging data sets

19/06/12

• Select low-s region of low concentration data

Reduce influence of interparticle interference

Merge with data

Option 1: Merging data sets

19/06/12

• Select overlapping region with high concentration data set

(should be no influence of structure factor at these “atomic distances”)

Reduce influence of interparticle interference

Merge data

• Merged and scaled to lowest concentration data set

Option 1: Merging data sets

19/06/12

Reduce influence of inter-particle interference

New 1D SAXS profile

Option 2: extrapolation to infinite dilution

19/06/12

• Find linear relationship between Rg and/or I(0) and

concentration

• Simple extrapolation to zero concentration à ideal SAXS

Reduce influence of interparticle interference

• Works well for repulsive

interference

• Extrapolate:
• I(q) – (a) and (b)
• I(0) or Rg (c) directly
• Automated method available
• ALMERGE (ATSAS)

Glatter, O., and O. Kratky. 1982. Small Angle X-ray Scattering. Vol. 102. Academic Press London.

Option 2: extrapolation to infinite dilution

19/06/12

Extrapolation procedure in PRIMUS

Extrapolate data

The importance of buffer matching!

Sample preparation

• Buffer matching!
• Must be almost (if not actually) PERFECT
• If not you will over/under subtract the data and not have anything

meaningful to work with

Haydyn Mertens, EMBO 2017 (Singapore)

• 4. December 2017

sample unmatched buffer matched buffer

• versubtracted

subtracted

Data flow

19/06/12

Obtain 1D profiles of frames (sample & buffer) Average frames

(in PRIMUS)

Subtract background/buffer scattering

(in PRIMUS)

Guinier analysis Concentration dependent behaviour? average Merge/extrapolate No Yes IFT (eg. GNOM) Modeling Fitting (eg. CRYSOL)

Haydyn Mertens, EMBO 2017 (Singapore)

• 4. December 2017

① SAMPLE OPTIMISATION ② DATA COLLECTION ③ DATA REDUCTION ④ PRIMARY ANLAYSIS ⑤ MODELING ⑥ VALIDATION

Overall Parameters

Size and Shape

Rg, Dmax I0, Vp

• Scattering at low angles (range limited)
• Convenient plot to extract parameters

Guinier approximation

Description by Guinier & Fournet (1950s) to describe:

I q

( ) ≅ I 0 ( )exp −1

3q2Rg

2

# $ % & ' (

ln[I(q)]= ln[I(0)]+ −q2Rg

2

3 " # $ % & '

Guinier approximation

• 4. December 2017

The Guinier plot

ln[I(q)]= ln[I(0)]+ −q2Rg

2

3 " # $ % & '

y = c + mx (x = q2) (m = - Rg

2 / 3)

ln[(q)] q2,Å-2 Rg = 10 Å Rg = 100 Å I(0) = 10 I(0) = 100 Extract Rg and I(0) from the linear region of the plot

Haydyn Mertens, EMBO 2017 (Singapore)

Guinier approximation

• 7. December 2017

The Guinier plot

ln[I(q)]= ln[I(0)]+ −q2Rg

2

3 " # $ % & '

y = c + mx (x = q2) (m = - Rg

2 / 3)

ln[(q)] Extract Rg and I(0) from the linear region of the plot

Haydyn Mertens, EMBO 2017 (Singapore)

Radius of gyration, Rg

Haydyn Mertens, EMBO 2017 (Singapore)

• 4. December 2017
• A SAXS parameter for “size”
• Distribution of components around an axis (or center of mass)
• “the root-mean-square distance of all elemental scattering volumes

from their center of mass weighted by their scattering densities”

Rg solid sphere < Rg hollow sphere

Radius of gyration, Rg

Haydyn Mertens, EMBO 2017 (Singapore)

• 4. December 2017
• Proteins of different Rg
• Distribution of components around an axis (or center of mass)

Rg 2.8 nm Rg 3.9 nm

BSA monomer BSA dimer

I(0) à MM

Haydyn Mertens, EMBO 2017 (Singapore)

• 4. December 2017
• Forward scattering intensity, I(0)
• Relates to the “volume of electrons/scattering centers” in the particle(s)

I(q) = ξ dσ (q) dΩ = ξ nΔρ2V 2P(q)S(q)

I(0) = nΔ⍴ 2V2

I(0) à MM

Haydyn Mertens, EMBO 2017 (Singapore)

• 4. December 2017
• Molecular mass calculation
• From standard (eg. BSA, glucose isomerase, lysozyme)
• Absolute calibration using water ( I_water = 0.0163 cm-1)

I(0) = nΔ⍴ 2V2

6.02E23 mol-1 Concentration (g.cm-3) Contrast (cm-2) Partial specific volume of protein (eg. 0.7425 cm3.g-1) (cm-1)

I(0) à MM

Haydyn Mertens, EMBO 2017 (Singapore)

• 7. December 2017
• Molecular mass calculation
• From standard (eg. BSA, glucose isomerase, lysozyme)
• Absolute calibration using water ( I_water = 0.0163 cm-1)

I(0) = nΔ⍴ 2V2

MMsample = [(I0/c)sample / (I0/c)standard] X MMstandard

Real space distance distribution, P(r)

Haydyn Mertens, EMBO 2017 (Singapore)

• 7. December 2017

Shapes

I 0

( ) = 4π

p(r).dr

∫

Rg

2 r

∫ I(q) = 4π p(r)sin(qr) qr .dr

Dmax

∫

p(r) = r2 2π 2 q2I(q)sin(qr) qr .dq

∞

∫ FT-1 FT Proteins

Relation to “real-space”

19/06/12

• Solution is Indirect Fourier Transformation (IFT), (Glatter, 1977)
• Fit a function to the SAXS data and transform à p(r)
• Regularisation parameter (α) helps balance between the fit and the FT.

Indirect Fourier Transformation (IFT) of SAXS data

p(r) = ckφk(si)

k=1 K

∑

Φ = χ 2 +αP(p) χ 2 = 1 N −1 Iexp(sj)−cIcalc(sj) σ (sj) " # $ $ % & ' '

j=1 N

∑

2

P(p) = p'

[ ]

Dmax

∫

2

dr

Relation to “real-space”

19/06/12

• Dmax estimate (3.5 nm) poor solution – too small

So, what is a good p(r)? How do I know a good solution?

OK fit Truncated

Relation to “real-space”

19/06/12

• Dmax estimate (4.0 nm) poor solution – still too small

So, what is a good p(r)? How do I know a good solution?

OK fit Truncated

Relation to “real-space”

19/06/12

• Dmax estimate (4.5 nm) - good solution

So, what is a good p(r)? How do I know a good solution?

Good fit Smooth

Relation to “real-space”

19/06/12

• Dmax estimate (5.0 nm) poor solution – too long
• And exceeding confidence limits of method (Dmax*qmin > π)

So, what is a good p(r)? How do I know a good solution?

Good fit Smooth but “tailing”

Relation to “real-space”

19/06/12

• Dmax estimate (5.5 nm) poor solution – definitely too long
• And exceeding confidence limits of method (Dmax*qmin > π)

So, what is a good p(r)? How do I know a good solution?

Good fit Oscillating

Relation to “real-space”

19/06/12

• Balance between fit and p(r) smoothness

Playing with alpha (regularisation parameter)

α = 212 α = 0.1

Relation to “real-space”

19/06/12

• Balance between fit and p(r) smoothness

Playing with alpha (regularisation parameter)

α = 212 α = 212,000

19/06/12

Particle volume

• “Porod” volume – excluded volume of hydrated particle
• Can be related (empirically) to particle mass
• Force decay of scattering intensity by s-4 (Constant K)
• Follows Porod law for homogenous particles

Vol = 23 nm3 (MM = 14 kDa) MM ~ Vp/1.6

19/06/12

Particle volume

• “Porod” volume – excluded volume of hydrated particle
• Can be related (empirically) to particle mass

Vp = 23 nm3 MM ~ 23 / 1.6 = 15 kDa

Summary

Data obtained from 2D images à 1D profiles Buffer (and background) subtraction Profiles tell you a lot about the sample Parameters (Rg, I0, Dmax, Vp) extracted

Data reduction steps

Parameters

SAXS invariants

• Rg
• I0 (MM)
• Vp

Acquisition

SAXS instrumentation

• Sample
• Buffer
• Background

Reduction

2D images to 1D profile

• Integration
• Normalisation
• Averaging/Subtract

Important

Steps!

• cf. Al Kikhney (EMBL-Hamburg)