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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