Primary data reduction and analysis Al Kikhney, EMBL Hamburg - - PowerPoint PPT Presentation

Primary data reduction and analysis

Al Kikhney, EMBL 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-ray detector 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 time

X-ray detector solution

X-ray →

2θ

s

Notations and units

solution

X-ray →

2θ

s

I(s), a.u. s, nm-1

Notations and units

|s| = 4π sinθ/λ

2θ λ s I(s) – scattering angle – wavelength – scattering vector – intensity

I(s), cm-1 s, nm-1

Notations and units

|s| = 4π sinθ/λ

2θ λ s I(s) – scattering angle – wavelength – scattering vector – intensity

I(q), a.u. q, nm-1 |q| = 4π sinθ/λ

2θ – scattering angle λ – wavelength

Notations and units

I(s), a.u. s, nm-1 |s| = 4π sinθ/λ

2θ – scattering angle λ – wavelength 1 2 3

Notations and units

I(s), a.u. s, Å-1 |s| = 4π sinθ/λ

2θ – scattering angle λ – wavelength 0.1 0.2 0.3

Notations and units

I(s), a.u. s, nm-1 |s| = 4π sinθ/λ

2θ – scattering angle λ – wavelength

Notations and units

0.05 second 0.2 second 0.8 second

Exposure time

I(s) s, nm-1

Exposure time

0.05 second 0.2 second 0.8 second 1.6 second I(s) s, nm-1 RADIATION DAMAGE!

frame 1 I(s) s, nm-1

Multiple exposures

I(s) s, nm-1 frame 1 frame 2

Multiple exposures

I(s) s, nm-1 average

Multiple exposures

I(s) s, nm-1 frame 1 frame 10 – discard

Multiple exposures

3.2 mg/ml lysozyme + buffer + cell

Sample and buffer

I(s) s, nm-1

3.2 mg/ml lysozyme

Sample and buffer

I(s) s, nm-1

Background subtraction

Solution minus Solvent

I(s) s, nm-1

Background subtraction

Solution minus Solvent

I(s) s, nm-1

Normalization against:

• Concentration

Log I(s) s, nm-1

Logarithmic plot

Dilution series

2 mg/ml

Log I(s) s, nm-1

Dilution series

8 mg/ml

Log I(s) s, nm-1

Dilution series

32 mg/ml

Log I(s) s, nm-1

Dilution series

2 mg/ml 32 mg/ml

Log I(s) s, nm-1

Inter-particle interactions

No interactions

Inter-particle interactions

Attractive interactions Repulsive interactions

Merging data

Log I(s) s, nm-1

Merging data

Log I(s) s, nm-1

Merging data

Log I(s) s, nm-1

Data analysis

Log I(s) s

Shape

100 nm3

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

6 nm 100 nm3 3.6 nm 6.4 nm 3.4 nm 4.8 nm 2.2 nm Radius of gyration (Rg)

Radius of gyration (Rg)

André Guinier 1911-2000 Guinier approximation:

I(s) ≈ I(0) exp(s2Rg

2/-3)

s ≲ 1/Rg

Ln I(s)

s2

Guinier plot

Radius of gyration (Rg)

Ln I(s)

s2

Guinier plot

Radius of gyration (Rg)

Ln I(s)

s2

Guinier plot

Radius of gyration (Rg)

y = ax + b Rg = √-3a Ln I(0)

sRg < 1.0~1.3

Ln I(s)

s2

Guinier plot

Radius of gyration (Rg)

Rg ± stdev Forward scattering I(0) Data quality Data range

Log I(s) s, 1/nm

Sample quality

Aggregation

Monodisperse sample

Aggregated sample

Aggregation

Log I(s) s, 1/nm

Logarithmic plot

Guinier plot

Ln I(s)

s2

Guinier plot

Ln I(s)

s2 0.26 nm-1 0.63 nm-1 Rg = 2.0 nm sminRg = 0.52 smaxRg = 1.26 < 1.3

Guinier plot

Ln I(s)

s2 0.44 nm-1 0.63 nm-1 Rg = 2.3 nm sminRg = 1.01 smaxRg = 1.45 > 1.3

lysozyme apoferritin

Log I(s), a.u.

s, nm-1

Guinier approximation

Molecular mass

Log I(0)lys Log I(0)apo

I(0) and Molecular Mass

MMsample MMBSA I(0)sample I(0)BSA =

Rg = 1.46 nm I(0) = 2.68 a.u. MM = 15.1 kDa

MMsample = I(0) sample ∙ MMBSA / I(0)BSA

Rg = 6.81 nm I(0) = 79.45 a.u. MM = 450 kDa Rg = 3.1 nm I(0) = 11.7 a.u. MMBSA = 66 kDa

BSA

Porod volume

Excluded volume of the hydrated particle

∫

∞

− =

2 4 2

] ) ( [ ) ( 2 ds s K s I I VP π

∫

∞ 2

) ( ds s s I

Porod volume

Excluded volume of the hydrated particle

∫

∞

− =

2 4 2

] ) ( [ ) ( 2 ds s K s I I VP π

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

974 nm3 21 nm3

Excluded volume of the hydrated particle

~13 kDa ~610 kDa (?!)

Porod law

Distance distribution function

Distance distribution function

r, nm γ(r) 1

Distance distribution function

r, nm γ(r) 1

Distance distribution function

r, nm γ(r) 1

p(r) = r2γ(r)

Distance distribution function

r, nm p(r)

p(r) = r2γ(r)

6 nm 100 nm3 r, nm p(r) Dmax= 6 nm

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

Distance distribution function

r, nm p(r) Log I(s) s, nm-1

dr sr sr r p s I

D

∫

=

max

) sin( ) ( 4 ) ( π

ds sr sr s I s r r p

∫

∞

=

2 2 2

) sin( ) ( 2 ) ( π

p(r) plot

Distance distribution function

r, nm r, nm p(r) p(r)

Dmax Dmax

r, nm p(r)

Dmax

Data quality

smin ≤ π/Dmax

I(s) s, 1/nm

smin

Data range

Atomic structure

Fold Shape

5 10 15

Log I(s)

5 6 7 8 “Resolution”, nm 2.00 1.00 0.67 0.50 0.33

Size s, nm-1

smin < π/Dmax

Beamline P12

Data range can be adjusted by changing the wavelength λ or the sample-detector distance

Beamline P12

Detector closer to the sample – collect wider angles (for smaller particles)

Beamline P12

Detector further from the sample – collect smaller angles (for larger particles)

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 3s

X

p(r) p(r)

Thank you!

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