Rigid body refinement (basics) D.Svergun, EMBL-Hamburg
Shapes from recent projects at EMBL-HH Complexes and assemblies Complexes and assemblies Domain and quaternary structure Domain and quaternary structure S-layer proteins Toxin B α -synuclein oligomers Dcp1/Dcp2 complex In most cases, high resolution models Giehm et al Albesa-Jové et al She et al, Mol Cell (2008) Fagan et al Mol. JMB (2010) PNAS USA (2011) are drawn inside are drawn inside Microbiol (2009) Microbiol (2009) Flexible/transient systems Structural transitions the shapes Complement factor H Cytochrome/adrenodoxin Src kinase Xu et al Morgan et al Bernado et al JACS (2008) JMB (2008) NSMB (2011)
Using SAXS with MX/NMR: Using SAXS with MX/NMR: ‘hybrid’ modelling ‘hybrid’ modelling h b id h b id d lli d lli Model building where high resolution portions are Model building where high resolution portions are positioned to fit the low resolution SAXS data
The use of high resolution models in SAS The use of high resolution models in SAS Th Theoretical model or complete i l d l l crystal structure available Validation in solution Incomplete structure available Addition of missing loops/domains Structure of subunits available Rigid body model of the complex Structure of domains and Model of the domain multiple curves available structure structure
How to compute SAS from atomic model How to compute SAS from atomic model I solution (s) I solvent (s) I particle (s) ♦ To obtain scattering from the particles, solvent scattering must be subtracted to yield effective density distribution Δρ = < ρ ( r ) - ρ s > , where ρ s is the scattering Δ di t ib ti ( ) h i th tt i density of the solvent ♦ Further, the bound solvent density may differ from Further the bound solvent density may differ from that of the bulk
Scattering from a macromolecule in solution Scattering from a macromolecule in solution 2 2 − ρ δρ I(s) = A( s ) = A ( s ) A ( s ) + A ( s ) a s s b b Ω Ω ♦ A a ( s ) : atomic scattering in vacuum ♦ A s ( s ) : scattering from the excluded volume ♦ A b ( s ) : scattering from the hydration ♦ A b ( s ) : scattering from the hydration shell CRYSOL (X CRYSOL (X-rays): ) Svergun et al. (1995). J. Appl. Cryst. 28 , 768 CRYSON ( neutrons): Svergun et al. (1998) P.N.A.S. USA , 95 , 2267
The use of multipole expansion The use of multipole expansion 2 − ρ δρ 2 s s s s I(s) = A( ) = A ( ) E( ) + B( ) a s b Ω Ω If the intensity of each contribution is represented using spherical harmonics ∞ l ∑ ∑ = π 2 2 I ( s ) 2 A ( s ) lm = = − l 0 m l the average is performed analytically: L L l l ∑ ∑ = π − ρ + δρ 2 2 I ( s ) 2 A ( s ) E ( s ) B ( s ) lm 0 lm lm = = − l 0 m l This approach permits to further use rapid algorithms for rigid body refinement
CRYSOL CRYSOL and and CRYSON CRYSON : : X- -ray and ray and neutron scattering from macromolecules neutron scattering from macromolecules L l ∑ ∑ ∑ ∑ = π π − ρ ρ + + δρ δρ 2 2 I I ( ( s s ) ) 2 2 A A ( ( s s ) ) E E ( ( s s ) ) B B ( ( s s ) ) lm 0 lm lm = = − l 0 m l � The The programs programs: : � either either fit fit the the experimental experimental data data by by varying varying the the density density of of the the hydration hydration layer y layer δρ y δρ (affects ρ ( (affects the the third third term) term) and ) and the the total total excluded excluded volume volume (affects (affects the the second second term) term) � or or predict predict the the scattering scattering from from the the atomic atomic structure structure using using default using using default default parameters default parameters parameters (theoretical parameters (theoretical (theoretical excluded (theoretical excluded excluded volume excluded volume volume volume g/cm 3 ) and and bound bound solvent solvent density density of of 1 1. .1 1 g/cm � provide provide output output files files (scattering (scattering amplitudes) amplitudes) for for rigid rigid b d b d body body refinement refinement routines fi fi t t routines ti ti � compute compute particle particle envelope envelope function function F( F( ω )
Scattering components (lysozyme) Scattering components (lysozyme) Atomic Atomic Atomic Atomic 1) 1) 1) 1) Shape Shape 2) 2) Border Border Border Border 3) 3) 3) 3) Difference Difference 4) 4)
Effect of the hydration shell, X Effect of the hydration shell, X- -rays rays lg I, relative Experimental data Fit with shell Fit without shell 3 3 Lysozyme 2 2 Hexokinase 1 EPT 0 PPase -1 0 1 2 3 4 s, nm -1
Denser shell or floppy chains: X rays versus neutrons X-rays versus neutrons Scattering length density, 10 10 cm -2 ♦ For X-rays: both lead to 12 12 similar effect (particle solvent density appears larger) denser solvent layer 10 ♦ Floppy chains would in ♦ Floppy chains would in floppy side chains oppy s de c a s all cases increase the protein density 8 apparent particle size ♦ Neutrons in H 2 O (shell): ♦ Neutrons in H O (shell): 6 6 particle would appear nearly unchanged 4 ♦ Neutrons in D 2 O (shell): particle would appear 2 smaller than the atomic model model 0 0 SAXS SANS in H2O SANS in D2O -2
X-rays versus neutrons: experiment lg I, relative lg I, relative Neutrons, D 2 O Neutrons, H 2 O 1 X-rays -1 1 0 X-rays -1 Neutrons, H 2 O -2 -2 Neutrons, D 2 O -3 -3 0 1 2 3 s, nm- 1 0 2 4 s, nm- 1 Lysozyme: appears larger for X-rays Thioredoxine reductase : CRYSOL and smaller for neutrons in D 2 O and CRYSON fits with denser shell
Other approaches/programs I Other approaches/programs I method’ (Luzzati Luzzati et et al, al, 1972 1972; ; Fedorov Fedorov and and � The The ‘cube ‘cube method’ Pavlov, Pavlov, 1983 1983; ; M Mü üller ller, , 1983 1983) ) ensures ensures uniform uniform filling filling of of the the excluded excluded volume volume. . Could/should/must Could/should/must be be superior superior over over the effective the effective atomic atomic factors factors method method at at higher higher angles angles. . CRYDAM (still unpublished) (still unpublished) � CRYDAM lg I, relative ♦ Represents hydration shell by dummy water atoms dummy water atoms ♦ Handles proteins, carbohydrates, 2 nucleic acids and their complexes ♦ Is applicable for wide angle ♦ Is applicable for wide angle X-ray data, lysozyme scattering range Fit by CRYSOL Fit by CRYDAM 1 Malfois, M. & Svergun, D.I. (2001), to be submitted o be sub ed CRYSOL 3.0 (is coming) (is coming) � CRYSOL 3.0 0 5 10 s, nm-1
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