ab initio shape determination - embl hamburg · pdf filesingle phase dummy atom models a...
TRANSCRIPT
Ab initio shape determination
Al Kikhney EMBL Hamburg, Germany
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
SAXS studies of biological
macromolecules
Rg
MM
Volume
Ab initio shape determination
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:
Simple bodies
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
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)
Dummy atom models
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
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
Single phase dummy atom models
o Scattering computed using
spherical harmonics
o Monte-Carlo type search
o Penalties apply
Single phase dummy atom models DAMMIN
Disconnected Loose Compact
P222
symmetry
Tetrameric pyruvate oxidase from yeast, 240 kDal structure
Single phase dummy atom models DAMMIN
Tetrameric pyruvate oxidase from yeast
Comparison of the ab initio model with the crystal structure
Single phase dummy atom models DAMMIN
http://www.embl-hamburg.de/biosaxs/atsas-grid/dammin.php
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
DAMMIF
http://www.embl-hamburg.de/biosaxs/atsas-grid/dammif.php
Multi-phase dummy atom models
Single phase shape
determination
Fit one data set
Multi-phase dummy atom models
Fit data from
several subunits
http://www.embl-hamburg.de/biosaxs/atsas-online/monsa.php
Dummy residue models
Dummy residue models
• Proteins typically consist of folded polypeptide chains composed of amino acid residues
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)
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
Dummy residue models GASBOR
Dummy residue models GASBOR
• GASBOR finds
coordinates of K dummy
residues within its search
volume (red)
Dmax
Dummy residue models
= < … >
GASBOR
• GASBOR finds
coordinates of K dummy
residues within its search
volume
• Requires polypeptide
chain-compatible
arrangement of dummy
residues
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
http://www.embl-hamburg.de/biosaxs/atsas-grid/gasbor.php
Model validity
Validate your sample and input data
Check for:
– Monodispersity
– Radiation damage
– Aggregation
– Concentration effects
– Overall parameters
– Signal-to-noise level
Model validity Original body Typical solution with P5 symmetry
Typical solution with no symmetry
Model validity Original body Typical solution with P5 symmetry
Typical solution with no symmetry
Model validity Original body Typical solution with P5 symmetry
Typical solution with no symmetry
Model validity
Funari et al. (2000) J. Biol. Chem. 275, 31283-31288
Shape determination of 5S RNA: six DAMMIN models yielding identical fits
Model validity
• Superimpose models by
minimizing the Normalized
Spatial Discrepancy (NSD)
• Steps
• Principle axes alignment
• Gradient minimization
• Local grid search
SUPCOMB
Model validity SUPCOMB
• NSDi = <NSDij>j
• MIN( NSDi ) => typical (most probable) model
• <NSD> + 2 σ (NSD) => threshold for outliers
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
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