Small angle scattering Ab initio modelling methods Al Kikhney EMBL Hamburg
Ab initio shape reconstruction Log I(s) Experimental data s
Ab initio shape reconstruction Log I(s) Experimental data Model s
Ab initio shape reconstruction Log I(s) Experimental data Model
Ab initio shape reconstruction Log I(s) Experimental data Model s
Feigin, L.A. and Svergun, D.I. Structure Analysis by Small-Angle X-Ray and Neutron Scattering. Plenum Press 1987
BODIE IES • ellipsoid (semiaxes a, b, c) • ellipsoid of revolution (semiaxes a, c) • cylinder (radius r, height h) • elliptic cylinder (radius semiaxes a, b, height h) • hollow cylinder (outer radius R, inner radius r, height h) • rectangular prism (sides a, b, c) • hollow sphere (outer radius r o , inner radius r i )
Ab initio shape reconstruction log I(s) experimental SAXS pattern experimental SAXS pattern nm -1
Ab initio shape reconstruction: dummy atom modelling log I(s) experimental SAXS pattern experimental SAXS pattern calculated from model nm -1
Ab initio shape reconstruction: dummy atom modelling log I(s) experimental SAXS pattern experimental SAXS pattern calculated from model nm -1
Ab initio shape reconstruction: dummy atom modelling log I(s) R g = 3.4 nm s max = 8/R g experimental SAXS pattern 2.35 nm -1
Ab initio shape reconstruction: dummy atom modelling log I(s) p(r) s max = 8/R g r, nm experimental SAXS pattern fit by p(r) nm -1
Ab initio shape reconstruction: dummy atom modelling log I(s) p(r) r, nm fit by p(r) – target curve nm -1
≈ 2000–10000 “dummy atoms” 2–10 Å log I(s) target curve DAMMIF Franke, D. and Svergun, D.I. (2009) nm -1 J Appl Cryst 42, 342–346.
log I(s) target curve calculated from the model nm -1
log I(s) target curve calculated from the model nm -1
log I(s) target curve calculated from the model nm -1
log I(s) target curve calculated from the model nm -1
DA DAMMIN Svergun, D.I. (1999) Biophys J 76 • Variable number of “dummy atoms” on a fixed grid • Scattering is computed using spherical harmonics • Monte-Carlo type search • Fixed search space (defined by D max ) • Provides volume/molecular mass estimate • Idea first published by P. Chacón et al. (1998) Biophys J 74
DA DAMMIF Franke, D. and Svergun, D.I. (2009) J Appl Cryst 42, 342–346 • Variable number of “dummy atoms” on a fixed grid • Scattering is computed using spherical harmonics • Monte-Carlo type search • Expandable search space • Provides volume/molecular mass estimate • 40 time faster than DAMMI N
DAMMIF Expandable search space Particle
https://www.embl-hamburg.de/biosaxs/atsas-online/dammif.php
Ab initio shape reconstruction: multi-phase dummy atom modelling Single phase shape Fit one data set determination
Ab initio shape reconstruction: multi-phase dummy atom modelling Fit data from several subunits
https://www.embl-hamburg.de/biosaxs/atsas-online/monsa.php
Ab initio reconstruction: dummy residue modelling log I(s) p(r) r, nm experimental SAXS pattern fit by p(r) up to wider angles nm -1
Ab initio reconstruction: dummy residue modelling 3.8 Å D max GASBOR Svergun, D.I., Petoukhov, M.V, Koch, M.H.J. (2001) Biophys J 80, 2946–2953.
Ab initio reconstruction: dummy residue modelling log 10 I(q) q, nm -1
Ab initio reconstruction: dummy residue modelling log 10 I(q) q, nm -1
Ab initio reconstruction: dummy residue modelling log 10 I(q) q, nm -1
GASBOR Svergun, D.I., Petoukhov, M.V, Koch, M.H.J. (2001) Biophys J 80, 2946–2953 • Fixed number of “dummy residues” • Distances to neighbor “residues” like in proteins
GASBOR Svergun, D.I., Petoukhov, M.V, Koch, M.H.J. (2001) Biophys J 80, 2946–2953 • Fixed number of “dummy residues” • Distances to neighbor “residues” like in proteins • Fixed search space • Scattering is computed using Debye formula • Higher angles used (up to 12 nm -1 ) • Only for proteins smaller than 660 kDa
Ambiguity I(s) I(s) s s
Ambiguity First formulated by R. Kirste in 1964 I(s) I(s) s s
Ambiguity From a study by M. Petoukhov, 2015 I(s) I(s) s s
AMBI BIMETE TER Petoukhov, M.V. and Svergun, D.I. (2015) Acta Cryst D71, 1051–1058
AMBI BIMETE TER Petoukhov, M.V. and Svergun, D.I. (2015) Acta Cryst D71, 1051–1058 Curves from all 14 112 possible shapes represented by one to seven interconnected beads
Ab initio model validity First validate your sample and input data! Check for: – monodispersity; – radiation damage; – aggregation; – concentration effects; – overall parameters; – signal-to-noise level. Make sure your model fits the data. Repeat multiple times.
Ab initio model validity Original body Typical solution with P5 symmetry Typical solution with no symmetry
Ab initio model validity Shape determination of 5S RNA: six DAMMIN models yielding identical fits Funari et al. (2000) J. Biol. Chem. 275, 31283-31288
Ab initio model validity SUPCOMB • Superimpose models by minimizing the Normalized Spatial Discrepancy (NSD) • Steps • Principle axes alignment • Gradient minimization • Local grid search SUPALM • Aligns models in Fourier space using spherical harmonics representation • For MDa size particles – about 10 times faster than SUPCOMB
Ab initio model validity DAMAVER • Superimpose and find the “most probable” model and outliers (DAMSEL) • Average all models and make a filtered model (DAMFILT) → may not fit the experimental data! DAMCLUST • Clusters similar models • A single cluster (plus outliers) – less ambiguous reconstruction • More than one cluster – more ambigous
ATSAS online www.embl-hamburg.de/biosaxs/atsas-online/ www.sasbdb.org www.saxier.org/forum
EMBO Global Exchange Lecture Course Structural and biophysical methods for biological macromolecules in solution 14 – 20 October 2019 | Santiago, Chile
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