Introduction to biological small angle scattering

Transcription

1 Introduction to biological small angle scattering Frank Gabel (IBS/ILL) EMBO Practical Course (May 6th 013) F. Gabel (May 6th 013) EMBO Practical Course Length-scales and tools in structural biology small angle scattering in solution SAS bridges the gap between atomic resolution (NMR and crystallography) and the light microscope crystallography NMR

2 Obects that can be studied by SAS Atomic resolution: NMR and/or Crystallography SAS cannot determine de novo the positions of individual atoms/residues in biomacromolecules on the Angstrom scale Biological small angle scattering is growing exponentially

3 Scattering basics: Huygens-Fresnel principle Incoming X-ray/neutron wave r r r k ' = k = π λ k r θ k r ' Many scattering centers, FOURIER transform: I ( Q ) = b e r r iq Screen (far away) r r 4π Q = k ' k = sin θ λ Reciprocal relationship between real space and the diffraction pattern Many scattering centers, Fourier transform: r r iq I( Q) = b e Orientational averaging Glatter and Kratky (198) Small Angle X-ray scattering (Academic Press) I( Q) = bib sin Q r i, Q( ri r ) ( r ) i Debye equation (1915)

4 Why small angle scattering? Putnam et al. (007) Quart. Rev. Biophys. 40(3), SAS sample conditions and information obtained Neutrons, X-rays solutions ~ mg/ml volume ~ µl mass > 0.1 mg Global properties: Radius of gyration, molecular weight SAS sensitivity: -Macromolecules 1 kda ~ MDa -Linear dimension 10 Å ~ 1000 Å structural details Information obtained: 1) Oligomeric state of macromolecules ) Shape or conformation (globular, stick etc ) Shape 3) Interaction of different macromolecules 4) Variation of points (1)-(3) as a function of ph, salt, ligands, T, p,... 5) Contrast variation: visualisation of individual sub-units in situ Interaction +

5 Concept of scattering density and contrast In vacuo: I ( Q ) = b e r r iq r b r r iq r iq I( Q) = e dv proteine dv V ρ iq r I( Q) = N ρ e dv protein r r In solution: I Q) ( ρ ρ ) r r iq r ( = protein solvent e dv Continuum approximation: b V ρ protein = const -How are scattering densities calculated? -Under which conditions is the approximation valid? Ideal solutions: no inter-particle effects, only form-factors Model-free parameters

6 Guinier approximation and radius of gyration 1 I( Q) I(0) exp RgQ 3 (from expansion of Debye equation) R g Q ln 1 3 [ I( Q) ] ln[ I(0) ] R Q g Radius of gyration: R = M 1 g i m r i i Contrast x volume Feigin and Svergun (1987) Structure analysis by Small-Angle X-ray and Neutron Scattering (Plenum Press) See-saw For a given molecular weight, a sphere has the smallest R g, i.e. it is the most compact obect Calibrating molecular weight (M r ) with water by SANS Often important for the study of oligomeric/association states and flexible systems + or Scattering curves look similar! I(0) I (0) inc 4πT 1 T 3 S = 10 f CM r N At i [( b ρ V ) M ] S r C: concentration in mg/ml f: correction factor for anisotropicity of incoherent scattering T: water transmission T s : sample transmission t: pathlength in cm I(0): coherent scattering in forward direction I inc (0): incoherent scattering from water M r [( b ρ V ) M ] T I = r 3 1 (0) 10 i S f 4πTS I inc (0) CN At Jacrot, B., and Zaccai, G. (1981) Determination of molecular weight by neutron scattering. Biopolymers 0,

7 Relative measurement of molecular weight (M r ) by SAS I ( Q ) b e r r iq I( 0) b I( 0) N b N = CN V / A M r b M r Concentration in mg/ml I(0) CM r Relative calibration to a known standard (BSA, lysozyme) in same buffer conditions: I prot ( 0) = I standard (0) C C prot standard M M prot standard Characteristic and distance distribution function

8 Characteristic and distance distribution function p(r) I ( Q) Debye equation in integral form = ρ V1, V ρ( r ) 1 sin ( r ) Q Q( r1 r ) dv1dv ( r r ) 1 I( Q) = 4π Dmax 0 sin( Qr) p( r) dr Qr γ ( r) γ ( r) = γ (0) 0 = V ( r c ) V p( r) = r γ ( r) Feigin and Svergun (1987) Structure analysis by Small-Angle X-ray and Neutron Scattering (Plenum Press) SAS provides information on distances on different length-scales Putnam et al. (007) Quart. Rev. Biophys. 40(3),

9 Examples of I(Q) and p(r) sin( QR) QR cos( QR) I( Q) = 3 3 ( ) QR Svergun and Koch (003) Small-angle scattering studies of biological macromolecules in solution. Rep. Prog. Phys. 66, Putnam et al. (007) Quart. Rev. Biophys. 40(3),

10 Putnam et al. (007) Quart. Rev. Biophys. 40(3), Some words about resolution Nominal definition: π R = Q max Inter-subunit distance with a precision of about 1- Å! d Inter-subunit position/orientations less well-defined!

11 Modelling Sophisticated data analysis and modelling - Ab initio structure analysis - Rigid body modelling Match with experimental scattering curve - Validation of structural models Compatible with experimental scattering curve

12 Different possibilities of modelling Putnam et al. (007) Quart. Rev. Biophys. 40(3), Monodispersity is paramount (AUC, gels, SEC-MALLS)! ( Jacques and Trewhella (010) Prot. Sci. 19, ), Talks by Marc Jamin, Olwyn Byron Flexible systems Putnam et al. (007) Quart. Rev. Biophys. 40(3), Important check: molecular weight!

13 Oligomeric equilibria Putnam et al. (007) Quart. Rev. Biophys. 40(3), Again: important check is molecular weight! Neutrons vs. X-rays

14 SAXS vs. SANS: scattering processes Feigin and Svergun (1987) Structure analysis by Small-Angle X-ray and Neutron Scattering (Plenum Press) - X-ray scattering length is proportional to number of electrons - Neutron scattering length depends irregularly on atom and isotope Atoms have a form-factor for X-rays but nuclei don t for neutrons ~ 5 fm (= 5*10-15 m) λ ~ 5 Å (= 5*10-10 m) Practical calculation of scattering densities b = ρ protein = b V Example glycine in H O: ρ = [* *(-0.37)]10-1 cm/66.4å 3 =.68*10-14 cm/å 3 =.68*10 10 cm - Jacrot, B. (1976) The study of biological structures by neutron scattering from solution. Rep. Prog. Phys. 39,

15 SAXS vs. SANS: some practical aspects sample amount flux contrast SAXS ~ mg/ml high weak SANS 1-10 mg/ml low high (D O) parasitic scattering at low Q flat background SAXS, ID0, 1s exposure time SANS, D, 0min exposure time (H O) (D O) SANS vs. SAXS instruments D (ILL): SANS Quartz cuvette (SANS) Capillary (SAXS) Exposure times: ~ 10-0 minutes (D) ~ 1-10 seconds (ID0) ~ seconds (BM9) BM9 (ESRF): SAXS Including sample change: ~ 10-0 minutes (D) ~ 5 minutes (ID0) ~ -3 minutes (BM9)

16 Understanding contrast : destructive interference in SANS Incoming neutron wave Destructive interference! Signal gets weaker! + solvent!!! Detector Natural Contrast in SANS ( ρ ρ ) r r iq r I( Q) = protein solvent e dv??? Homogeneous macromolecules can be matched, i.e. made invisible!!! Not so easy with SAXS

17 Contrast in SAXS Feigin and Svergun (1987) Structure analysis by Small-Angle X-ray and Neutron Scattering (Plenum Press) DNA RNA proteins lipoproteins An analogon in optics: refractive index water glycerol

18 SANS contrast variation: relative arrangement of DNA and protein Pardon et al. (1975) Nucl. Acids Res. (11) Relative topology of DNA and protein at low resolution before availability of high-resolution models! Triangulation in the ribosome Capel et al. (1987) Science 38, Internal arrangement of proteins before availability of high-resolution models! Nierhaus et al. (1983) Proc. Natl. Acad. Sci. USA 80,

19 Protein-protein complexes Jacques and Trewhella (010) Prot. Sci. 19, Petoukhov and Svergun (006) Eur. Biophys. J. 35, Negative radii of gyration!? ln R? 1 3 [ I( Q) ] ln[ I(0) ] R Q 1 1 g = miri M i = M i g ρ V r i i i + - h-prot d-rna I( Q) = b e r r iq ~ 70% D O Scattering in forward direction, I(0), can be weak (or zero) Scattering can get stronger going to higher angles Result: apparent negative radius of gyration

20 Can proteins be considered as homogeneous particles? Ribosome Transcription factor Jacrot, B. (1976) Rep. Prog. Phys. 39, ??? Membrane proteins and lipids/detergents Talks by Joe Zaccai, Lise Arleth

21 Artificial contrast using deuteration Protein deuteration not complete but only ~75%! 4% D O 100% D O Talk by Michael Härtlein Careful at high D O levels in the solvent: favours oligomerisation/aggregation! Practical guidelines

22 Putnam et al. (007) F. Gabel (May 6 th 013) EMBO Practical Course Putnam et al. (007)

23 F. Gabel (May 6 th 013) EMBO Practical Course Putnam et al. (007) F. Gabel (May 6 th 013) EMBO Practical Course Putnam et al. (007)

24 Combination of SAXS/SANS with other techniques SANS allows to go beyond the global shape and study internal structure! Often problematic to position/orient subunits in a larger complex using SAXS alone Internal structure: contrast variation and SANS!

25 Talks by Pau Bernado, Bernd Simon, Christiane Schaffitzel, Olwyn Byron Petoukhov and Svergun (007) Curr. Opin. Struct. Biol. 17(5), Strategy for low-resolution refinement of protein-rna/dna complexes NMR: Binding-site mapping + orientation SAXS: Global envelope SAXS/SANS: Envelopes of components

26 Protein-RNA complex in the spliceosome Madl, T., Gabel, F. and Sattler, M. (011) J. Struct. Biol. 173, Concluding remarks

27 A few practical comments - use SAXS for homogeneous systems composed of a single body - SAXS is better suited for high-throughput - SANS good for complex systems (protein-dna/rna, membrane proteins ) - SANS has no radiation damage - neutrons only possible at large facilities (no home sources for the moment!) - request for beam-time is generally via an electronic proposal system - deadlines are usually twice a year, beamtime is attributed some months later - BAG ( Block allocation group ) systems allow more flexible access - for continuation proposals, reports need to be submitted regularly - experiments need to be prepared with great care (i.e. isotopic effect of D O)!! - local contacts, often beamline responsibles, assist during experiments - access (for non-industrial use) is in general free - no maintenance, user friendly (software etc ) Literature Basics (scattering, quantum mechanics): - The Feynman lectures on Physics, Volume 3: Quantum mechanics (Addison Wesley, 006) - Cohen-Tannoudi et al.: Mécanique Quantique, Vol.. Chapter on diffusion. (Hermann, 1997) Books on small angle (neutron) scattering: - Svergun: Structure Analysis by Small-Angle X-Ray and Neutron Scattering (Plenum, 1987) - Glatter and Kratky: Small Angle X-ray Scattering (Academic Press, 198) - Guinier/Fournet: Small angle scattering of X-rays (John Wiley & Sons, 1955) - Serdyuk, Zaccai, Zaccai: Methods in molecular biophysics (Cambridge University Press, 007) Reviews on SAXS/SANS: - Jacrot, B. (1976) The Study of biological structures by neutron scattering from solution. Rep. Prog. Phys. 39, Putnam et al. (007) X-ray solution scattering (SAXS) combined with crystallography and computation: defining accurate macromolecular structures, conformations and assemblies in solution. Q. Rev. Biophys. 40(3):

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