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: R g , I(0), molecular mass • Volume • p(r), D max
SAXS experiment solution X-ray → X-ray detector solvent • Few kDa to GDa • Monodisperse and homogeneous • Concentration: 0.5– 10 mg/ml • Amount: 10 – 100 μ l
2D → 1D Log I(s) a.u. 10 5 10 4 10 3 10 2 10 1 s, nm - 1
Log I(s) a.u. 10 5 10 4 Normalization • Transmitted beam 10 3 • Exposure time 10 2 10 1 s, nm - 1
Notations and units solution X-ray → 2θ s X-ray detector
Notations and units solution X-ray → 2θ s I(s), a.u. |s| = 4π sinθ / λ 2θ – scattering angle – wavelength λ s – scattering vector – intensity I(s) s, nm - 1
Notations and units I(s), cm -1 |s| = 4π sinθ / λ 2θ – scattering angle – wavelength λ s – scattering vector – intensity I(s) s, nm - 1
Notations and units I(q), a.u. |q| = 4π sinθ / λ 2θ – scattering angle λ – wavelength q, nm - 1
Notations and units I(s), a.u. |s| = 4π sinθ / λ 2θ – scattering angle λ – wavelength 1 2 3 s, nm - 1
Notations and units I(s), a.u. |s| = 4π sinθ / λ 2θ – scattering angle λ – wavelength 0.1 0.2 0.3 s, Å - 1
Notations and units I(s), a.u. |s| = 4π sinθ / λ 2θ – scattering angle λ – wavelength s, nm - 1
I(s) Exposure time 0.05 second 0.2 second 0.8 second s, nm - 1
I(s) Exposure time 0.05 second 0.2 second RADIATION 0.8 second DAMAGE! 1.6 second s, nm - 1
I(s) Multiple exposures frame 1 s, nm - 1
I(s) Multiple exposures frame 1 frame 2 s, nm - 1
I(s) Multiple exposures average s, nm - 1
I(s) Multiple exposures frame 1 frame 10 – discard s, nm - 1
Sample and buffer I(s) 3.2 mg/ml lysozyme + buffer + cell s, nm - 1
Sample and buffer I(s) 3.2 mg/ml lysozyme s, nm - 1
Background subtraction Solution minus Solvent I(s) s, nm - 1
Background subtraction Solution minus Solvent I(s) Normalization against: • Concentration s, nm - 1
Logarithmic plot Log I(s) s, nm - 1
Log I(s) Dilution series 2 mg/ml s, nm - 1
Log I(s) Dilution series 8 mg/ml s, nm - 1
Log I(s) Dilution series 32 mg/ml s, nm - 1
Log I(s) Dilution series 2 mg/ml 32 mg/ml s, nm - 1
Inter-particle interactions No interactions
Inter-particle interactions Attractive interactions Repulsive interactions
Log I(s) Merging data s, nm - 1
Log I(s) Merging data s, nm - 1
Log I(s) Merging data s, nm - 1
Data analysis
Shape Log I(s) 100 nm 3 s
Size 200 nm 3 Log I(s) 100 nm 3 50 nm 3 25 nm 3
Radius of gyration (R g ) 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
2.2 nm Radius of gyration (R g ) 3.6 nm 6 nm 100 nm 3 6.4 nm 3.4 nm 4.8 nm
Radius of gyration (R g ) Guinier approximation: I(s) ≈ I(0) exp( s 2 R g 2 / -3) s ≲ 1/ R g André Guinier 1911 - 2000
Radius of gyration (R g ) Guinier plot Ln I(s) s 2
Radius of gyration (R g ) Guinier plot Ln I(s) s 2
Radius of gyration (R g ) Guinier plot Ln I(s) Ln I(0) y = ax + b R g = √ -3a sR g < 1.0~1.3 s 2
Radius of gyration (R g ) Guinier plot Ln I(s) R g ± stdev Forward scattering I(0) Data quality Data range s 2
Sample quality Log I(s) s, 1/nm
Aggregation Monodisperse sample
Aggregation Aggregated sample
Logarithmic plot Log I(s) s, 1/nm
Guinier plot Ln I(s) s 2
Guinier plot Ln I(s) R g = 2.0 nm s min R g = 0.52 s max R g = 1.26 < 1.3 s 2 0.63 nm - 1 0.26 nm - 1
Guinier plot Ln I(s) R g = 2.3 nm s min R g = 1.01 s max R g = 1.45 > 1.3 s 2 0.63 nm - 1 0.44 nm - 1
Molecular mass Log I(s), a.u. Guinier approximation Log I(0) apo Log I(0) lys lysozyme apoferritin s, nm - 1
I(0) and Molecular Mass MM sample I(0) sample = MM BSA I(0) BSA MM sample = I(0) sample ∙ MM BSA / I(0) BSA R g = 3.1 nm BSA I(0) = 11.7 a.u. MM BSA = 66 kDa R g = 1.46 nm R g = 6.81 nm I(0) = 2.68 a.u. I(0) = 79.45 a.u. MM = 15.1 kDa MM = 450 kDa
Porod volume Excluded volume of the hydrated particle π 2 2 I ( 0 ) = V P ∞ ∞ ∫ ∫ − 2 2 [ I ( s ) I ( s ) K s ] ds s ds 4 0 0
Porod volume Excluded volume of the hydrated particle π 2 2 I ( 0 ) = V P ∞ ∫ − 2 [ I ( s ) K ] s ds 4 0 K 4 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 law Excluded volume of the hydrated particle 21 nm 3 974 nm 3 ~13 kDa ~610 kDa (?!)
Distance distribution function
Distance distribution function γ (r) 1 0 r, nm
Distance distribution function γ (r) 1 0 r, nm
Distance distribution function γ (r) 1 p(r) = r 2 γ (r) 0 r, nm
Distance distribution function p(r) p(r) = r 2 γ (r) 0 r, nm
Distance distribution function p(r) 100 nm 3 r, nm 6 nm D max = 6 nm
Distance distribution function p(r) r, nm
Distance distribution function p(r) r, nm
Distance distribution function Log I(s) p(r) s, nm - 1 r, nm
Log I(s) p(r) D ∞ sin( sr ) max 2 2 r s I ( s ) sin( sr ) ∫ ∫ = π = I ( s ) 4 p ( r ) dr p ( r ) ds π 2 sr sr 2 0 0 s, nm - 1 r, nm
p(r) plot Distance distribution function D max D max p(r) p(r) r, nm r, nm
Data quality D max s min ≤ π /D max I(s) p(r) r, nm s, 1/nm s min
Data range “Resolution”, nm 2.00 1.00 0.67 0.50 0.33 Log I(s) 8 Atomic 7 structure Shape 6 Fold Size 5 0 5 10 15 s, nm - 1 s min < π /D max
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 Normalization Radiation damage check X 1s 2 s 3s Background subtraction Merge multiple concentrations 0.5 1.0 2.0 R g , molecular weight D max , p ( r ) p(r) Porod volume Ab initio shape determination p(r) …
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