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Small-Angle Scattering Atomic Structure Based Modeling Alejandro Panjkovich EMBL Hamburg 07.12.2017 A. Panjkovich (EMBL) BioSAS atomic modeling 07.12.2017 1 / 49 From the forest to the particle accelerator A. Panjkovich (EMBL) BioSAS

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Small-Angle Scattering Atomic Structure Based Modeling

Alejandro Panjkovich

EMBL Hamburg

07.12.2017

  • A. Panjkovich (EMBL)

BioSAS atomic modeling 07.12.2017 1 / 49

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From the forest to the particle accelerator

  • A. Panjkovich (EMBL)

BioSAS atomic modeling 07.12.2017 2 / 49

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Outline - Combining SAS data and atomic models

Introduction Comparison of atomic models to scattering data (CRYSOL/CRYSON) Graphical interface to modeling (SASpy) Rigid-body modeling (SASREF) Missing fragments (BUNCH & CORAL) Flexible refinement (SREFLEX)

  • A. Panjkovich (EMBL)

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Structural biology techniques

Macromolecular crystallography (up to atomic resolution) Nuclear magnetic resonance (up to atomic resolution) Electron microscopy (resolution revolution, already beyond 3 ˚ A) Small angle X-ray scattering (nominal resolution 10 ˚ A)

High brilliance EMBL beamline P12 at DESY synchrotron, Hamburg

  • A. Panjkovich (EMBL)

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Small angle X-ray scattering (SAXS)

homogeneous and monodisperse solution (no crystal) sample can be at room temperature ‘no limitation’ in terms of size or oligomeric state requisites: 1.0 mg purified material, concentration > 0.5 mg/ml

  • A. Panjkovich (EMBL)

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Shape

  • A. Panjkovich (EMBL)

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Size

  • A. Panjkovich (EMBL)

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SAXS applications in structural biology

ab-initio shape determination atomistic (hybrid) modeling

◮ validation ◮ rigid-body ◮ missing fragments ◮ refinement ◮ conformational transitions

mixtures ensemble approach

  • A. Panjkovich (EMBL)

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ATSAS software package http://www.embl-hamburg.de/biosaxs/

Large collection of programs for SAS data analysis. Online and standalone versions (Windows, Mac & Linux). Multiple algorithms and modeling approaches:

◮ ab-initio (simulated annealing) ◮ Rigid-body (Monte Carlo) ◮ Ensemble approach (genetic algorithm) ◮ Reference-less superposition ◮ kd-trees search, PCA, etc.

  • A. Panjkovich (EMBL)

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Computing SAS from atomic model

Scattering from the particles can be obtained by subtracting solvent scattering, yielding effective density distribution: ∆ρ = ρ(r) − ρs (1) where ρs is the scattering density of the solvent. Bound solvent density may differ from that of the bulk.

  • A. Panjkovich (EMBL)

BioSAS atomic modeling 07.12.2017 10 / 49

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Scattering from a macromolecule in solution

I(s) =

  • |A(s)|2

Ω =

  • |Aa(s) − ρsAs + δρbAb(s)|2

Ω

(2) Aa(s): atomic scattering in vacuum As(s): scattering from the excluded volume Ab(s): scattering from the hydration shell Programs: CRYSOL (X-rays): Svergun et al. (1995) J. Appl. Cryst. 28, 768 CRYSON (neutrons): Svergun et al. (1998) P.N.A.S USA 95, 2267

  • A. Panjkovich (EMBL)

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Multipole expansion

I(s) =

  • |A(s)|2

Ω =

  • |Aa(s) − ρsE(s) + δρbB(s)|2

Ω

(3) If the intensity of each contribution is represented using spherical harmonics I(s) = 2π2

inf

  • l=0

l

  • m=−l

|Alm(s)|2 (4) the average is performed analytically: I(s) = 2π2

L

  • l=0

l

  • m=−l

|Alm(s) − ρ0Elm(s) + δρBlm(s)|2 (5) This approach permits to further use rapid algorithms for rigid body refinement.

  • A. Panjkovich (EMBL)

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CRYSOL (X-ray) and CRYSON (neutron) scattering from macromolecules

I(s) = 2π2

L

  • l=0

l

  • m=−l

|Alm(s) − ρ0Elm(s) + δρBlm(s)|2 (6) The programs: either fit the experimental data by varying the density of the hydration layer δρ (affects the third term) and the total excluded volume (affects the second term)

  • r predict the scattering from the atomic structure using default

parameters (theoretical excluded volumen and bound solvent density

  • f 1.1 g/cm3)

provide output files (scattering amplitudes) for rigid body refinement routines compute particle envelope function F(ω)

  • A. Panjkovich (EMBL)

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CRYSOL: SAXS data and atomic models

How does the atomic model fit the solution scattering profile? χ2 = 1 N

Np

  • i=1

Ie(si) − cI(si) σ(si) 2 (7)

  • A. Panjkovich (EMBL)

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CRYSOL: how to run CRYSOL (+ other ATSAS programs)

command line, batch mode command line, interactive mode ATSAS-Online GUI, through Primus GUI, through SASpy

  • A. Panjkovich (EMBL)

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SASpy: integrating ATSAS and PyMOL

SASpy combines ATSAS and PyMOL ATSAS SAS analysis software package

◮ Freely available for academics ◮ Compiled for Win, Mac and Linux ◮ From initial data reduction to advanced

modeling

PyMOL Molecular visualization software

◮ Visualize and edit 3D molecular models ◮ Ray-rendering for publication quality figures ◮ Extensible through ‘plugins’

  • A. Panjkovich (EMBL)

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SASpy - ATSAS PyMOL plugin

Panjkovich A & Svergun DI (2016) Bioinformatics 32, 2062-64

  • A. Panjkovich (EMBL)

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SUPALM, superposition of high- and low-resolution models

Konarev PV, Svergun DI. IUCrJ. 2015 Apr 21;2(Pt 3):352-60

  • A. Panjkovich (EMBL)

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SAS modeling principle

  • A. Panjkovich (EMBL)

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The idea of rigid body modeling

The structures of two subunits in reference positions are known. Arbitrary complex can be constructed by moving and rotating the second subunit. This operation depends on three Euler rotation angles and three Cartesian shifts.

  • A. Panjkovich (EMBL)

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The idea of rigid body modeling

The structures of two subunits in reference positions are known. Arbitrary complex can be constructed by moving and rotating the second subunit. This operation depends on three Euler rotation angles and three Cartesian shifts.

  • A. Panjkovich (EMBL)

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Equation for rigid body modeling

Using spherical harmonics, the amplitude(s) of arbitrarily rotated and displaced subunit(s) are analytically expressed via the initial amplitude and the six positional parameters: Clm(s) = Clm(Blmα, β, γ, x, y, z). The scattering from the complex is then rapidly calculated as: I(s) = IA(s) + IB(s) + 4π2

∞

  • l
  • −l

Re[Alm(s)C ∗

lm(s)]

(8)

Svergun, D.I. (1991). J. Appl. Cryst. 24, 485-492

  • A. Panjkovich (EMBL)

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Constraints for rigid body modeling

interconnectivity absence of steric clashes symmetry intersubunit contacts (from chemical shifts by NMR or mutagenesis) Distances between residues (e.g. FRET) Relative orientations of subunits (RDC by NMR) Scattering data from subcomplexes

Petoukhov & Svergun (2005). Biophys J. 89, 1237; Petoukhov & Svergun (2006). Biophys J. 35, 567

  • A. Panjkovich (EMBL)

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Global rigid body modeling (SASREF)

Fits (multiple X-ray and neutron) scattering curve(s) from partial constructs or contrast variation using simulated annealing Requires models of subunits, builds interconnected models without steric clashes. Uses constrains: symmetry, distance, relative orientation if applicable.

Petoukhov & Svergun (2005). Biophys J. 89, 1237; Petoukhov & Svergun (2006). Biophys J. 35, 567

  • A. Panjkovich (EMBL)

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Addition of missing fragments (BUNCH)

BUNCH combines rigid body and ab-initio modelling to find the positions and orientations of rigid domains and probable conformations of flexible linkers represented as dummy residues chains Multiple experimental scattering data sets from partial constructs (e.g. deletion mutants) can be fitted simultaneously with the data of the full-length protein. accounts for symmetry, allows one to fix some domains and to restrain the model by contacts between specific residues

  • A. Panjkovich (EMBL)

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Addition of missing fragments (CORAL)

A combination of SASREF and BUNCH to account for missing loops in multi-subunit biological macromolecules. Loops are modeled based on known high-resolution structures.

  • A. Panjkovich (EMBL)

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User example: hybrid rigid-body modeling of a protein complex

  • A. Panjkovich (EMBL)

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Rigid-body modeling - SAXS model (SASREF)

0.0 0.1 0.2 0.3 0.4 s, A ° -1 log I(s), relative sasref

χ2 = 1.0

  • A. Panjkovich (EMBL)

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Crystallographic complex 1

0.0 0.1 0.2 0.3 0.4 s, A ° -1 log I(s), relative MX1

χ2 = 6.7

  • A. Panjkovich (EMBL)

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Crystallographic complex 2

0.0 0.1 0.2 0.3 0.4 s, A ° -1 log I(s), relative MX2

χ2 = 3.0

  • A. Panjkovich (EMBL)

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SAXS-model vs. crystallographic model 2

  • A. Panjkovich (EMBL)

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Flexible refinement

  • A. Panjkovich (EMBL)

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Mismatch between homology model and SAXS data (and ab-initio model)

0.0 0.1 0.2 0.3 0.4 s, A ° -1 log I(s), relative homologyModel

  • A. Panjkovich (EMBL)

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SREFLEX fits SAS data by exploring conformational changes

0.0 0.1 0.2 0.3 0.4 s, A ° -1 log I(s), relative homologyModel sreflex

  • A. Panjkovich (EMBL)

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Conformational change and ligand binding

  • A. Panjkovich (EMBL)

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SAXS and conformational change

Crystalline and solution conformation may differ SAXS can provide insight into conformational transition

  • A. Panjkovich (EMBL)

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SREFLEX: SAS REFinement through FLEXibility

  • A. Panjkovich (EMBL)

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Estimating protein flexibility: normal mode analysis (NMA)

Delarue M, Sanejouand YH (2002) Simplified normal mode analysis of conformational transitions in dna-dependent polymerases: the elastic network model. J Mol Biol 320: 1011-1024.

  • A. Panjkovich (EMBL)

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SREFLEX: SAS REFinement through FLEXibility

Input: SAXS data PDB coordinates Program stages:

1 Structure partition 2 Domain level refinement 3 Residue level refinement

  • A. Panjkovich (EMBL)

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Automatic domain assignment based on dynamics

  • A. Panjkovich (EMBL)

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SREFLEX web interface (ATSAS online)

www.embl-hamburg.de/biosaxs/atsas-online/sreflex.php Also available in Primus/qt, SASpy and through the command line

  • A. Panjkovich (EMBL)

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SREFLEX advanced usage

Exploit options and parameters (more details in the manual)

◮ Provide domain definitions a priori ◮ Use CONCOORD refinement (protein only) ◮ Skip one of the refinement stages

Current limitations:

◮ Long linkers (better use BUNCH or CORAL) ◮ Bead models ◮ Future developments: ⋆ Very large assemblies ⋆ Symmetric complexes ⋆ Membrane proteins

  • A. Panjkovich (EMBL)

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Model quality depends of SAXS data quality

monodispersity radiation damage aggregation concentration effects

  • verall parameters

signal-to-noise level (SHANUM) ambiguity (AMBIMETER)

  • A. Panjkovich (EMBL)

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Ambimeter - ambiguity measurement

Petoukhov MV, Svergun DI Acta Crystallogr D Biol Crystallogr. 2015 May;71(Pt 5):1051-8.

  • A. Panjkovich (EMBL)

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Ambimeter - different shapes, same scattering profile

  • A. Panjkovich (EMBL)

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DARA: structural neighbours, dara.embl-hamburg.de

searches stuctural space available at PDB (∼150000 structures) fast query thanks to PCA and k-d trees. nearest neighbours suggest shape, Rg, MW, etc.

Kikhney AG, Panjkovich A, Sokolova AV, Svergun DI. Bioinformatics. 2016 Feb 15;32(4):616-8.

  • A. Panjkovich (EMBL)

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Resources and references

ATSAS manuals: www.embl-hamburg.de/biosaxs/manuals/ ATSAS online: www.embl-hamburg.de/biosaxs/atsas-online/ SAXS forum: www.saxier.org/forum/ email: atsas@embl-hamburg.de, apanjkovich@embl-hamburg.de

  • A. Panjkovich (EMBL)

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Summary on combining SAS data with high-res models

Comparison of atomic models to scattering data (CRYSOL/CRYSON) Graphical interface to modeling (SASpy) Rigid-body modeling (SASREF) Missing fragments (BUNCH & CORAL) Flexible refinement (SREFLEX)

  • A. Panjkovich (EMBL)

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Acknowledgements

Dmitri Svergun and the whole BioSAXS team at EMBL Hamburg.

◮ BioStruct-X 283570 and iNext. ◮ Marie Curie Actions and EMBL for postdoc fellowship (EIPOD).

  • A. Panjkovich (EMBL)

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