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 R g MM Volume Ab initio shape determination

Principle of SAS Modeling 1D scattering data 3D search model (or multiple data sets) X ={X} = { X 1 … X M } M parameters Trial-and-error Non-linear search 2 I ( s ) cI ( s ) 1 discrepancy: exp j j 2 N 1 ( s ) j j Additional information is ALWAYS required to resolve or reduce ambiguity of interpretation at given resolution

Simple bodies

Simple bodies lg I( s ) , r e la tiv e lg I( s ) , r e la tiv e lg I( s ) , r e la tiv e lg I( s ) , r e la tiv e 0 0 0 0 Rod - 1 - 1 - 1 - 1 - 2 - 2 - 2 - 2 - 3 - 3 - 3 - 3 Sphere - 4 - 4 - 4 - 4 - 5 - 5 - 5 - 5 Disc - 6 - 6 - 6 - 6 0 .0 0 .0 0 .0 0 .0 0 .1 0 .1 0 .1 0 .1 0 .2 0 .2 0 .2 0 .2 0 .3 0 .3 0 .3 0 .3 0 .4 0 .4 0 .4 0 .4 0 .5 0 .5 0 .5 0 .5 s - 1 - 1 - 1 - 1 s , n m s , n m s , n m s , n m Hollow sphere

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 D max filled by densely packed beads of radius r 0 << D max Parameterization: Solvent a binary vector, Particle 0 if solvent, 1 if particle 2r 0 D max

Single phase dummy atom models A sphere of radius D max filled by densely packed beads of radius r 0 << D max Parameterization: Solvent a binary vector, Particle 0 if solvent, 1 if particle 2r 0 D max

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

Single phase dummy atom models DAMMIN 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

http://www.embl-hamburg.de/biosaxs/atsas-grid/dammin.php

Single phase dummy atom models DAMMIN DAMMIF At the current iteration: • dark blue particle, might become solvent • light blue solvent, might become particle • white solvent, won’t change

DAMMIF

http://www.embl-hamburg.de/biosaxs/atsas-grid/dammif.php

Multi-phase dummy atom models Single phase shape Fit one data set determination

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) D max

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 Shape determination of 5S RNA: six DAMMIN models yielding identical fits Funari et al. (2000) J. Biol. Chem. 275, 31283-31288

Model validity SUPCOMB • Superimpose models by minimizing the Normalized Spatial Discrepancy (NSD) • Steps • Principle axes alignment • Gradient minimization • Local grid search

Model validity SUPCOMB • NSD i = <NSD ij > j • MIN( NSD i ) => typical (most probable) model • <NSD> + 2 σ (NSD) => threshold for outliers

DAMAVER Model validity 5S RNA – Solution spread region 5S RNA – Final Solution within the Spread Region 5S RNA – Most Populated Volume Funari et al. (2000) J. Biol. Chem. 275, 31283-31288

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