SAS data reduction and primary analysis. Al Kikhney

Transcription

1 SAS data reduction and primary analysis Al Kikhney

2 Outline SAS experiment setup 3D 2D 1D Background subtraction High vs. low concentration R g, MM Volume Distance distribution function p(r)

3 Small Angle Scattering solution X-rays or neutrons Homogeneous and monodisperse solution solvent 2θ s Detector s = 4π sinθ/λ 1-2 mg purified material concentration from 0.5 mg/ml, exposure times: a few seconds/minutes s scattering vector 2θ scattering angle λ wavelength I(s) intensity

4 Small Angle X-ray Scattering Exposure beamstop Beam X-ray detector X-ray detector

5 Small Angle X-ray Scattering Exposure beamstop X-ray detector

6 Small Angle X-ray Scattering Exposure beamstop Beam lower angle higher angle Beam X-ray detector

7 Small Angle X-ray Scattering Radial averaging Log I(s), a.u. Normalization against: data collection time, transmitted sample intensity s, nm -1

8 Small Angle Scattering Notations and units s = 4π sinθ/λ 2θ scattering angle λ wavelength Log I(s), a.u. s, nm -1

9 Small Angle Scattering Notations and units q = 4π sinθ/λ 2θ scattering angle λ wavelength Log I(q), a.u. q, nm -1

10 Small Angle Scattering Notations and units s = 4π sinθ/λ 2θ scattering angle λ wavelength Log I(s), a.u s, nm -1

11 Small Angle Scattering Notations and units s = 4π sinθ/λ 2θ scattering angle λ wavelength Log I(s), a.u s, Å -1

12 Data quality Radiation damage Log I(s), a.u. sample s, nm -1

13 Data quality Radiation damage Log I(s), a.u. sample same sample again RADIATION DAMAGE! s, nm -1

14 Data quality Log I(s), a.u. sample same sample again average s, nm -1

15 I(s), a.u. Buffer and sample Solvent s, nm -1

16 I(s), a.u. Buffer and sample Solution and Solvent s, nm -1

17 I(s), a.u. Buffer and sample Solution and Solvent Looking for protein signals less than 5% above background level s, nm -1

18 Background subtraction Solution minus Solvent Log I(s), a.u. sample buffer Log I(s), a.u. sample buffer (subtracted) Normalization against: concentration s, nm -1 s, nm -1

19 Data quality Can I use this data for further analysis? Log I(s) lysozyme s, nm -1

20 Data quality Can I use this data for further analysis? Log I(s) Log I(s) lysozyme AGGREGATED! s, nm -1 s, nm -1

21 Aggregation Monodisperse sample

22 Aggregation Aggregated sample

23 Data quality Log I(s) AGGREGATED! s, nm -1

24 Dilution series Low and High Concentration

25 Log I(s) Dilution series Low and High Concentration LytA protein, 60 kda, 1 mg/ml s, nm -1

26 Log I(s) Dilution series Low and High Concentration 1 mg/ml 10 mg/ml s, nm -1

27 Log I(s) Dilution series Low and High Concentration s, nm -1

28 Inter-particle interactions No interactions

29 Inter-particle interactions Attractive interactions Repulsive interactions

30 Log I(s) Dilution series Low and High Concentration s, nm -1

31 Log I(s) Merging data Low and High Concentration s, nm -1

32 Log I(s) Merging data Low and High Concentration s, nm -1

33 Log I(s) Merging data Low and High Concentration s, nm -1

34 Primary data analysis Calculating model-independent parameters

35 Shape lg I(s), relative 0-1 Long rod -2-3 Solid sphere s, s nm -1 Flat disc Hollow sphere Dumbbell

36 Size Log I(s) s, Å -1

37 Shape and size Log I(s) a.u. lysozyme apoferritin s, nm -1

38 SAS data range D min = π/s max Log I(s) Resolution, nm 7 Shape Atomic structure 6 5 Size Fold s, nm -1

39 SAS data range D min = π/s max Log I(s) Resolution, nm 7 Shape Atomic structure 6 5 Size Fold s, nm -1 D max = π/s min

40 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

41 Radius of gyration (R g ) A B 1. R g of A > R g of B 2. R g of A < R g of B 3. Both have same R g

42 Radius of gyration (R g ) A B 1. R g of A > R g of B 2. R g of A < R g of B 3. Both have same R g

43 Radius of gyration (R g ) Guinier plot Ln I(s) Log I(s) Normal Log plot s 2 s

44 Ln I(s) Radius of gyration (R g ) Guinier plot y = ax + b R g = sqrt(-3a) Estimate of the overall size of the particles Guinier approximation: I(s) = I(0)exp(-s 2 R g2 /3) sr g 1.3 s 2 André Guinier

45 Ln I(s) Radius of gyration (R g ) Guinier plot y = ax + b R g = sqrt(-3a) Estimate of the overall size of the particles Quality of the data s 2 Guinier approximation: I(s) = I(0)exp(-s 2 R g2 /3) aggregation sr g 1.3 polydispersity improper background substraction Zero angle intensity I(0) First point to use

46 Radius of gyration (R g ) Log I(s) Bovine serum albumin (BSA) s, 1/nm

47 Radius of gyration (R g ) Guinier plot Ln I(s) s 2

48 Radius of gyration (R g ) Guinier plot Ln I(s) s 2

49 Radius of gyration (R g ) Guinier plot Ln I(s) Ln I(0) y = ax + b R g = sqrt(-3a) s 2

50 Radius of gyration (R g ) Guinier plot Ln I(s) Ln I(0) R g ± stdev Forward scattering I(0) Data quality Data range s 2

51 Log I(s), a.u. Molecular mass Guinier approximation Log I(0) apo Log I(0) lys lysozyme apoferritin s, nm -1

52 I(0) and Molecular Mass MM sample MM BSA = I(0) sample I(0) BSA MM sample = I(0) sample * MM BSA / I(0) BSA BSA R g = 3.1 nm I(0) = 11.7 MM BSA = 66 kda R g = 1.46 nm I(0) = 3.66 MM = 20.6 kda R g = 6.81 nm I(0) = MM = kda

53 Porod law I(s) ~ s -4 Intensity decay is proportional to s -4 at higher angles (for globular particles of uniform density)

54 Porod law I(s)*s 4 s

55 Porod volume Excluded volume of the hydrated particle V P 0 2 [ I( s) 2 I(0) K 4 ] s 2 ds 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

56 Primus Porod volume I(s)*s 4 I(s)*s 4 14 nm 3 ~9 kda 974 nm 3 s ~610 kda s

57 Kratky plot Patterns of globular and flexible proteins

58 Sasplot Kratky plot Patterns of globular and flexible proteins I(s) s 2 Natively unfolded Globular Multidomain with flexible linkers Stratos Mylonas

59 γ(r) Distance distribution function r, nm

60 γ(r) Distance distribution function r, nm

61 γ(r) Distance distribution function r, nm

62 γ(r) Distance distribution function p(r) = r 2 γ(r) r, nm

63 Distance distribution function p(r) p(r) = r 2 γ(r) r, nm

64 p(r) function Distance distribution function

65 p(r) function Distance distribution function D max 2 2 sin( sr) r s I(s) s)sin( sr) II(s) ( 4 p(r) ( dr p(r) ds 2 sr 2 sr 0 0 Indirect Fourier Transform

66 Gnom D max p(r) plot Distance distribution function D max p(r) p(r) r, nm r, nm

67 Data quality D max p(r) I(s) r, nm s min s, 1/nm

68 Data quality D max s min π/d max p(r) I(s) r, nm s min s, 1/nm

69 Yeast bleomycin hydrolase 3GCB Compact dimer 50 kda Monomer Hexamer Extended dimer

70 Yeast bleomycin hydrolase 3GCB 50 kda Monomer Compact dimer Extended dimer Hexamer Yeast bleomycin hydrolase 3GCB

71 p(r) plot 50 kda Monomer Compact dimer Extended dimer Hexamer Bad Good Yeast bleomycin hydrolase 3GCB

72 Summary Exposure 3D 2D Radial averaging 1D Normalization Background subtraction Analysis Log plot Log I(s) s Guinier plot (R g, MM) Ln I(s) s 2 Porod plot I(s)*s 4 Kratky plot (flexibility) I(s)*s 2 s p(r) plot p(r) r s

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75 Thank you!

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