EMBO Global Exchange Lecture Course 2 May 2011 Beijing China Joint use of SAXS o o with MX and EM Peter Konarev European Molecular Biology Laboratory, Hamburg Outstation BioSAXS group
Information content in SAXS In SAXS, the molecule’s rotationally averaged scattering pattern is measured as a function of spatial frequency, typically t to 1–3-nm resolution 1 3 l ti Because of rotational averaging, the information content of a SAXS spectrum is dramatically reduced compared to a SAXS spectrum is dramatically reduced compared to a diffraction pattern in X-ray crystallography or even a density map from EM. Detector Sample S l Log (Intensity) Monochromatic beam 2 1 2 θ 2 θ 0 X-ray generator -1 Synchrotron Scattering vector 0 1 2 3 s=4 π sin θ / λ s=4 π sin θ/λ, nm- 1 Nevertheless, SAXS can provide important shape information about proteins and assemblies in the wide size range, which are not amenable to cryo- EM and NMR spectroscopy
Structural methods: resolution, accessible size and speed of experiment/analysis size and speed of experiment/analysis Time to answer NMR (high) Months EM Cryo-EM (low) EM, Cryo EM (low) RDC NMR (low) Weeks MX (high) ( g ) Days SAXS/ WAXS SAXS/ WAXS Hours Hours SANS (low) Minutes 10 0 10 1 10 2 10 3 10 4 10 5 10 6 MM, kDa (kDa) (MDa) (GDa)
Information content in SAXS Information content in SAXS ⎡ ⎤ − + ∞ ∑ ∑ sin D ( s s ) sin D ( s s ) = − k k ⎢ ⎢ ⎥ ⎥ I I ( ( s s ) ) s s I I ( ( s s ) ) − + k k k k ⎣ ⎦ D ( s s ) D ( s s ) = k 1 k k A solution scattering curve N s N s 0 0 0 0 2 2 2 2 4 4 4 4 6 6 6 6 8 8 8 8 10 10 10 10 12 12 12 12 s s from a particle with maximum f ti l ith i I(s) I(s) size D can be represented by its values taken at discrete 2 2 10 10 points (Shannon channels) points (Shannon channels) s k = k π / D 1 1 10 10 In a typical SAS experiment, I t i l SAS i t N s ≈ 5-15 0 0 10 10 C. E. Shannon & W. Weaver (1949). ( ) The mathematical theory of 0.00 0.00 0.05 0.05 0.10 0.10 0.15 0.15 0.20 0.20 -1 -1 s, A s, A communication. University of Illinois Press, Urbana .
Information content in SAXS Information content in SAXS SAXS spectrum can be transformed into a radial distribution function which is essentially a histogram of all pairwise function, which is essentially a histogram of all pairwise distances of the atoms in an assembly weighted by their respective atomic numbers. D sin sr ∫ ∫ = π π I I ( ( s s ) ) 4 4 p p ( ( r r ) ) dr dr sr 0 For structure determination, additional information is needed because the radial distribution function alone is relatively y uninformative about the details of molecular structure. The recent renaissance of SAXS is to a large extent the result of The recent renaissance of SAXS is to a large extent the result of efforts on integrating SAXS with other structural information from additional complementary sources (e.g. MX, EM, NMR, bioinformatics etc.).
Integration of SAXS data with other i f information i Similarly to other types of experimental information, SAXS data can be used as a filter for a set of models generated independently by other methods independently by other methods. SAXS data can also be a term in a scoring function that is optimized to obtain a model consistent with the data. ( e.g. ab initio modellig, rigid body modelling, addition of missing fragments) missing fragments) ∑ = χ + α 2 E ({ X }) [( I ( s ), I ( s )] i P exp i i i
Possible use of solution structure in crystallography • Determine a solution scattering structure (Dammin/f, Gasbor) • Place it in unit cell (location & orientation) Place it in unit cell (location & orientation) • Calculate initial phases for phase extension and molecular replacement Possible challenges • Resolution and fidelity of initial structure Resolution and fidelity of initial structure • Same solution and crystal structures? • Limitation of using uniform e- densities (flexible region hydration layer) region, hydration layer)
Possible use of solution structure in EM • Use a solution scattering structure (Dammin/f, Gasbor) as a starting reference for EM reconstruction Hsp90 heat-shock protein Bron, T. et.al. (2008) Biol. Cell 100 , 413 • Superposition of SAXS models and independent EM reconstructions independent EM reconstructions Tumour suppressor p53 and its complex with DNA Tumour suppressor p53 and its complex with DNA Tidow, H et. al. (2007) Proc Natl Acad Sci USA , 104 , 12324
Possible use of SAXS information in EM Solution Structure of the E coli 70S Ribosome Solution Structure of the E. coli 70S Ribosome at 11.5 A° Resolution In the Cryo-EM density map reconstruction In the Cryo-EM density map reconstruction, Fourier amplitudes at higher spatial frequencies are always underrepresented due to charging, instrument instabilities, specimen drift. To compensate for these effects, scattering intensities were obtained using X-ray solution scattering bt i d i X l ti tt i measurements for E.coli ribosomes in the range up to 1/8 Å -1 , and a correction to the Fourier amplitudes up to the 1/11.5 Å -1 was applied. pp I.S. Gabashvili, R.K. Agrawal, C.M.T. Spahn, R.A. Grassucci, D.I. Svergun, J. Frank, P. Penczek (2000) Cell , 100, 537–549
Data analysis SAS experiment Additional information Complementary techniques Radiation sources: X-ray tube ( λ = 0.1 - 0.2 nm) Shape Synchrotron ( λ = 0.05 - 0.5 nm) determination Search volum e EM Thermal neutrons ( λ = 0.1 - 1 nm) Detector Rigid body Crystallography Sample Incident modelling beam Atom ic m odels 2 θ 2 θ NMR NMR Wave Wave vector k , k= 2 π / λ Scattered Missing beam, k 1 fragments Solvent Biochem istry Orientations Resolution, nm: Resolution nm: 3 I, relative 3.1 1.6 1.0 0.8 FRET Oligomeric I nterface 2 2 mixtures mixtures lg m apping Scattering curve I(s) Bioinform atics 1 Flexible Secondary systems structure 0 2 4 6 8 prediction s, nm -1 Scattering vector s= k 1 -k , s= 4 π sin θ / λ
Ab initio modelling (DAMMIN/F) g ( ) Using simulated annealing, finds a compact dummy atoms configuration X that fits the scattering data by minimizing f (X) = χ 2 [I exp (s), I(X,s)] + Σα i P i (X) Discrepancy from the Set of penalties formulating experimental data various restraints where χ is the discrepancy between the experimental and where χ is the discrepancy between the experimental and calculated curves, P(X) is the penalty to ensure compactness and connectivity, α >0 its weight. compact compact compact compact loose loose disconnected disconnected
Bead (dummy atoms) model A sphere of radius D max is filled by densely packed beads of radius r 0 << D max r 0 D max Solvent Particle Vector of model parameters: Vector of model parameters: ⎧ 1 if particle Position ( j ) = x ( j ) = ⎨ ⎩ 0 if solvent ( h (phase assignments) i t ) Chacón, P. et al. (1998) Biophys. J. 74, 2760-2775. 2r 0 2r 0 S Svergun, D.I. (1999) Biophys. J. 76, D I (1999) Bi J 76 h 2879-2886 D max
Validation of Electron Microscopy Models py EM2DAM EM2DAM � Contour level level BEAD MODEL DENSITY MAP (MRC format) from EMDB 13
Validation of Electron Microscopy Models py CRYSOL BEAD MODEL EM2DAM : surface layer + th threshold h ld SAXS EXPERIMENTAL DATA Refinement with DAMMIN 14
Ab initio modelling (GASBOR) g ( ) Using simulated annealing, finds a spatial distribution of K dummy residues within a y sphere with diameter D max to fit the scattering data by minimizing [ ] = χ + α 2 f ({ r }) I ( s ), I ( s , { r }) P ({ r }) i exp DR i i Number of neighbours 6 where χ is the discrepancy between the 5 experimental and calculated curves, P({r i }) experimental and calculated curves, P({r i }) 4 is the penalty to ensure a chain-like 3 2 distribution of neighbors, α >0 its weight. 1 0 0.2 0.4 0.6 0.8 1.0 Shell radius, nm •Has potential for future development ( e.g. phase problem Neighbors in low resolution crystallography) distribution
The use of high resolution models g in SAXS • Validation of theoretically predicted models • Analysis of similarities between macromolecules in solution and in the crystal • Modelling of the quaternary structure of multisubunit particles/complexes by rigid body p / p y g y refinement
Scattering from a Macromolecule in Solution g 2 2 − ρ δρ I(s) = A( s ) = A ( s ) A ( s ) + A ( s ) a s s b b Ω Ω Ω Ω ♦ A a ( s ) : atomic scattering in vacuum The use of multipole expansion If If the the intensity intensity is is represented represented using using spherical spherical harmonics the average is performed analytically: ♦ A s ( s ) : scattering from the excluded ∞ l ∑ ∑ ∑ ∑ = 2 Ω = π π 2 2 I I ( ( s s ) ) A A volume ( ( l ) ) 2 2 A A ( ( s s ) ) s s lm = = − l 0 m l ♦ A b ( s ) : scattering from the hydration This approach permits to further use rapid algorithms for rigid body modelling shell Svergun et al. (1995). J. Appl. Cryst. 28 , 768 Svergun et al (1995) J Appl Cryst 28 768 CRYSOL (X-rays): CRYSOL (X-rays): CRYSON ( neutrons): Svergun et al. (1998) P.N.A.S. USA , 95 , 2267
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