Ab initio shape determination Al Kikhney EMBL Hamburg, Germany - - PowerPoint PPT Presentation

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 j j

s s cI s I N

2 exp 2

) ( ) ( ) ( 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 tiv e

• 6
• 5
• 4
• 3
• 2
• 1

s , n m

• 1

0 .0 0 .1 0 .2 0 .3 0 .4 0 .5

lg I( s ) , r e la tiv e

• 6
• 5
• 4
• 3
• 2
• 1

s , n m

• 1

0 .0 0 .1 0 .2 0 .3 0 .4 0 .5

lg I( s ) , r e la tiv e

• 6
• 5
• 4
• 3
• 2
• 1

s , n m

• 1

0 .0 0 .1 0 .2 0 .3 0 .4 0 .5

lg I( s ) , r e la tiv e

• 6
• 5
• 4
• 3
• 2
• 1

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

• Scattering computed using

spherical harmonics

• Monte-Carlo type search
• 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