Ab initio shape determination - EMBL Hamburg · PDF fileSingle phase dummy atom models A...
Transcript of Ab initio shape determination - EMBL Hamburg · PDF fileSingle phase dummy atom models A...
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Ab initio shape determination
Al Kikhney EMBL Hamburg, Germany
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Outline
• Simple bodies • BODIES
• Single phase dummy atom models • DAMMIN
• DAMMIF
• Multi-phase dummy atom models • MONSA
• Dummy residue models • GASBOR
• Model validity • SUPCOMB
• DAMAVER
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SAXS studies of biological
macromolecules
Rg
MM
Volume
Ab initio shape determination
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Principle of SAS Modeling
3D search model
X ={X} = {X1 …XM} M parameters
Non-linear search
1D scattering data (or multiple data sets)
Trial-and-error
j j
jj
s
scIsI
N
2
exp2
)(
)()(
1
1
Additional information is ALWAYS required to resolve or reduce ambiguity of interpretation at given resolution
discrepancy:
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Simple bodies
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s , n m- 1
0 .0 0 .1 0 .2 0 .3 0 .4 0 .5
lg I ( s ) , r e la t iv e
- 6
- 5
- 4
- 3
- 2
- 1
0
s , n m- 1
0 .0 0 .1 0 .2 0 .3 0 .4 0 .5
lg I ( s ) , r e la t iv e
- 6
- 5
- 4
- 3
- 2
- 1
0
s , n m- 1
0 .0 0 .1 0 .2 0 .3 0 .4 0 .5
lg I ( s ) , r e la t iv e
- 6
- 5
- 4
- 3
- 2
- 1
0
s , n m- 1
0 .0 0 .1 0 .2 0 .3 0 .4 0 .5
lg I ( s ) , r e la t iv e
- 6
- 5
- 4
- 3
- 2
- 1
0
Simple bodies
Sphere
Rod
Disc
Hollow sphere
s
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BODIES
• ellipsoid (semiaxes a, b, c)
• ellipsoid of revolution (semiaxes a, 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)
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Dummy atom models
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Single phase dummy atom models
A sphere of radius Dmax filled by densely packed beads of radius r0<< Dmax
Dmax
2r0
Particle
Solvent Parameterization:
a binary vector,
0 if solvent, 1 if particle
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Dmax
2r0
Parameterization:
a binary vector,
0 if solvent, 1 if particle
Single phase dummy atom models
A sphere of radius Dmax filled by densely packed beads of radius r0<< Dmax
Particle
Solvent
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Single phase dummy atom models
o Scattering computed using
spherical harmonics
o Monte-Carlo type search
o Penalties apply
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Single phase dummy atom models DAMMIN
Disconnected Loose Compact
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P222
symmetry
Tetrameric pyruvate oxidase from yeast, 240 kDal structure
Single phase dummy atom models DAMMIN
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Tetrameric pyruvate oxidase from yeast
Comparison of the ab initio model with the crystal structure
Single phase dummy atom models DAMMIN
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http://www.embl-hamburg.de/biosaxs/atsas-grid/dammin.php
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At the current iteration:
• dark blue particle, might become solvent
• light blue solvent, might become particle
• white solvent, won’t change
DAMMIN DAMMIF
Single phase dummy atom models
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DAMMIF
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http://www.embl-hamburg.de/biosaxs/atsas-grid/dammif.php
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Multi-phase dummy atom models
Single phase shape
determination
Fit one data set
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Multi-phase dummy atom models
Fit data from
several subunits
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http://www.embl-hamburg.de/biosaxs/atsas-online/monsa.php
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Dummy residue models
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Dummy residue models
• Proteins typically consist of folded polypeptide chains composed of amino acid residues
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Dummy residue models
• Proteins typically consist of folded polypeptide chains composed of amino acid residues
• At a resolution of 0.5 nm each amino acid can be represented as one entity (dummy residue)
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Dummy residue models
• Proteins typically consist of folded polypeptide chains composed of amino acid residues
• At a resolution of 0.5 nm each amino acid can be represented as one entity (dummy residue)
• In GASBOR a protein is represented by an ensemble of K dummy residues that are
– Identical
– Have no ordinal number
– For simplicity are centered at the C positions
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Dummy residue models GASBOR
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Dummy residue models GASBOR
• GASBOR finds
coordinates of K dummy
residues within its search
volume (red)
Dmax
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Dummy residue models
= < … >
GASBOR
• GASBOR finds
coordinates of K dummy
residues within its search
volume
• Requires polypeptide
chain-compatible
arrangement of dummy
residues
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Dummy residue models GASBOR
• GASBOR finds
coordinates of K dummy
residues within its search
volume
• Requires polypeptide
chain-compatible
arrangement of dummy
residues
• Scattering is computed
using the Debye (1915)
formula
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http://www.embl-hamburg.de/biosaxs/atsas-grid/gasbor.php
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Model validity
Validate your sample and input data
Check for:
– Monodispersity
– Radiation damage
– Aggregation
– Concentration effects
– Overall parameters
– Signal-to-noise level
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Model validity Original body Typical solution with P5 symmetry
Typical solution with no symmetry
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Model validity Original body Typical solution with P5 symmetry
Typical solution with no symmetry
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Model validity Original body Typical solution with P5 symmetry
Typical solution with no symmetry
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Model validity
Funari et al. (2000) J. Biol. Chem. 275, 31283-31288
Shape determination of 5S RNA: six DAMMIN models yielding identical fits
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Model validity
• Superimpose models by
minimizing the Normalized
Spatial Discrepancy (NSD)
• Steps
• Principle axes alignment
• Gradient minimization
• Local grid search
SUPCOMB
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Model validity SUPCOMB
• NSDi = <NSDij>j
• MIN( NSDi ) => typical (most probable) model
• <NSD> + 2 σ (NSD) => threshold for outliers
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Model validity
Funari et al. (2000) J. Biol. Chem. 275, 31283-31288
5S RNA – Solution spread region
5S RNA – Most Populated Volume
5S RNA – Final Solution
within the Spread Region
DAMAVER
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Resources and references
• ATSAS Manuals – http://www.embl-hamburg.de/biosaxs/software.html
• SAXS Forum – http://www.saxier.org/forum
• BODIES – Konarev et al. (2003) J Appl Cryst, 1277-1282.
• DAMMIN – D. I. Svergun (1999) Biophys J, 2879-2886
• DAMMIF – Franke & Svergun (2009) J. Appl. Cryst, 342-346.
• DAMAVER – Volkov & Svergun (2003) J Appl Cryst, 860-864
• GASBOR – Svergun, Petoukhov, & Koch (2001) Biophys. J, 2946-53
www.saxier.org/forum