Mixtures Oligomers and ensembles Polydispersity SAXS modeling - - PowerPoint PPT Presentation

Mixtures

Oligomers and ensembles

Haydyn Mertens, EMBL Hamburg

Polydispersity

SAXS modeling typically assumes: 1.

Polydispersity

SAXS modeling typically assumes:

• 1. Monodispersity

2.

Polydispersity

SAXS modeling typically assumes:

• 1. Monodispersity
• 2. Absence of interparticle interactions (dilute)

3.

Polydispersity

SAXS modeling typically assumes:

• 1. Monodispersity
• 2. Absence of interparticle interactions (dilute)
• 3. Knowledge of sample identity

Polydispersity

SAXS modeling typically assumes:

• 1. Monodispersity
• 2. Absence of interparticle interactions (dilute)
• 3. Knowledge of sample identity

MIXTURES

• 1. Size polydispersity

I(s) =∑kvkIk(s)

Scattering from a mixture

× vk × vk

Scattering from a mixture

• 2. Conformational polydispersity

I(s) =∑kvkIk(s)

× vk × vk

Scattering from a mixture

• 3. Both? I(s) =∑kvkIk(s)

× vk × vk × vk

Scattering from a mixture

❏ Size polydispersity (eg. distributions)

❏ if component structure unknown requires additional parameters

❏ Conformational polydispersity (eg. IDPs)

❏ Almost infinite range of conformations ❏ Cannot really identify all possible vk and Ik(s) ❏ Requires a more indirect approach

OLIGOMER (Konarev et al, 2003)

• eg. monomer - dimer equilibrium

+

× vk × vk I(s) =∑kvkIk(s)

OLIGOMER (Konarev et al, 2003)

Required input I(s) =∑kvkIk(s)

Experimental data (*.dat) Models (*.pdb) Form factors (*.dat) FFMAKER OLIGOMER

Required input

OLIGOMER

I(s) =∑kvkIk(s)

Experimental data (*.dat) Models (*.pdb) Form factors (*.dat) FFMAKER OLIGOMER

Ik(s) vk χ2(goodness of fit)

volume fractions Intensities

OLIGOMER

• eg. monomer - dimer equilibrium

+

× vk × vk I(s) =∑kvkIk(s)

OLIGOMER

• eg. monomer - dimer equilibrium

+

× vk × vk Determine volume fractions! I(s) =∑kvkIk(s)

OLIGOMER

How does OLIGOMER determine the volume fractions? +

× vk × vk ❏ Form factors used to define a set of equations (FFMAKER/CRYSOL) ❏ Experimental data used to drive a non- negative least-squares routine ❏ Determine best set of vk that provides a good fit to the data I(s) =∑kvkIk(s)

Monomer ⇆ extended-dimer + compact-dimer

OLIGOMER example 2 (real case)

Dunne et al., PLoS pathogens, 2014, 10 (7), e1004228

❏ Endolysins ❏ bacteriophage as possible antibacterials ❏

• ligomerisation modulates lytic

activity ❏ Compact-dimer “is active”

inactive active → cell wall lysis

OLIGOMER example 3 (real case)

Netrin + DCC ⇆ DCC-Netrin ⇆ DCC-Netrin-DCC

❏ Netrin acts as an axon guidance cue ❏ 2 DCC binding sites identified ❏ Modulates neural growth toward/away from nerves

Finci, Krueger et al., Neuron, 2014, 83(4), 839-849

❏ Meijers group determined crystal structure of complex ❏ Used components for OLIGOMER analysis of solution behaviour

OLIGOMER example 3 (real case)

Netrin + DCC ⇆ DCC-Netrin ⇆ DCC-Netrin-DCC

❏ Netrin act as an axon guidance cue ❏ 2 DCC binding sites identified ❏ Modulates neural growth toward/away from nerves

Finci, Krueger et al., Neuron, 2014, 83(4), 839-849

❏ SAXS shows DCC preference for Netrin site-1 ❏ Ternary complex formed only with DCC saturation ❏ DCCM933R site-1 mutant leaves site-2 binding unaffected → no cooperativity

OLIGOMER example 3 (real case)

Netrin + DCC ⇆ DCC-Netrin ⇆ DCC-Netrin-DCC

❏ Site-1 DCC + Site-2 DCC → attraction ❏ Site-1 DCC + Site-2 “other” → repulsion

Finci, Krueger et al., Neuron, 2014, 83(4), 839-849

Site-1 Site-2 Site-1 Site-2

OLIGOMER use

1. Generate Form Factor file(s)

$> ffmaker See Usage in the batch mode: ffmaker /help FFmaker calculates formfactor file from pdb models or from scattering curves that can be further used in OLIGOMER. Enter number of components ............. < 0 >: 3 Enter output formfactor filename ....... < .dat >: formfactors. dat Nff= 3 Enter *.pdb or *.dat file name (with extension) Enter file name for component ...........................: protA.pdb Component N= 1 was taken from protA.pdb Enter number of points NS .............. < 201 >: Enter maximum number of harmonics (LmMax) < 15 >: Enter maximum S-vector ................. < 0.5000 >: 0.5 Calculating component 1 from 3 Read atoms and evaluate geometrical center ... Number of atoms read .................................. : 2331 Number of atoms read .................................. : 2331 Geometric Center: 33.253 -57.037 25.951 Percent processed 10 20 30 40 50 60 70 80 90 100 Processing atoms :>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Number of carbons read ................................ : 1499 Number of nitrogens read .............................. : 392 Number of oxigens read ................................ : 431 Number of sulfur atoms read ........................... : 9 Center of the excess electron density: -0.127 -0.099 -0.184 Center of the excess electron density: -0.127 -0.099 -0.184 Processing envelope:>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Enter *.pdb or *.dat file name (with extension)

OLIGOMER use

1. Generate Form Factor file(s) - single line approach (avoid dialog)

$> ffmaker protA.pdb protB.pdb protC.pdb /out formfactors.dat

OLIGOMER use

Command line example 1:

$> oligomer *** POLYDISPERSITY IN TERMS OF OLIGOMERS *** *** Fits a scattering curve by a linear combination *** *** of basic scattering functions (form-factors). The *** *** latter should be precomputed and stored in a *** *** separate file. *** *** Written by A.Sokolova, V.Volkov & D.Svergun *** *** Last revised --- 31.07.2008 20:30 *** Program options : 0 - a set of form-factors and several sets of experimental data 1 - a set of experimental data and several sets of form-factors Enter program option ................... < 0 >:

OLIGOMER use

Enter program option ................... < 0 >: 0 Input file with form-factors ........... < .dat >: formfactor.dat Use constant as additional component [ Y / N ] .................................. < No >: Number of oligomers .................................... : 3 Number of points read .................................. : 201 Form-factor number 1 Calculated MW and Rg ..... < 4376., 19.48 >: Form-factor number 2 Calculated MW and Rg ..... < 2006., 21.47 >: Form-factor number 3 Calculated MW and Rg ..... < 6224., 25.55 >: Experimental data file name ............ < .dat >: protAB_011.dat s range: ................................... : 9.430e-3, 0.5399 Angular units used in experimental data: 4*Pi*SIN(theta)/lambda [1/Angstrom] (1) 4*Pi*SIN(theta)/lambda [1/nm] (2) 2 * SIN(theta)/lambda [1/Angstrom] (3) 2 * SIN(theta)/lambda [1/nm] (4) ....... < 1 >: 1 Combinations = 1 2 3 Operable s range: .......................... : 9.430e-3, 0.5000 Range for evaluation of Scattering < 9.430e-3, 0.5000 >: Use non-negativity condition [ Y / N ] . < Yes >: Output file .......................... < protAB_011.fit >: Plot the result [ Y / N ] .............. < Yes >: n Chi^2 <MW> <Rg> Volume fractions +- errors 0.75 6221 25.54 0.002+-0.001 0.000+-0.000 0.998+-0.001

Conformational polydispersity

Ensemble based approaches

❏ When many structures are required to describe the data ❏ Flexible systems (eg. IDPs) ❏ Chemically denatured proteins ❏ Flexible multi-domain proteins

Mertens & Svergun, JSB, 2010, 172(1), 128-141

EOM (Bernado et al, 2007, Tria et al, 2014)

Ensemble optimisation method

Pool Ik(s) Ensembles Best fitting ensemble Analysis

Required input

EOM (Bernado et al, 2007, Tria et al, 2014)

I(s) =∑kvkIk(s)

Experimental data (*.dat) Models (*.pdb) EOM χ2(fit) Sequence (*.txt) (rigid bodies) Rg dist. Dmax dist.

EOM

Sequence and rigid bodies

LRCMQCKTNGDCRVEECALGQDLCRTTIVRLWEEGEELELVEKSCTCSEKTNRTL SYRTGLKITSLTEVVCGLDLCNQGNSGRAVTYSRSRYLECISCGSSDMSCERGRH QSLQCRSPEEQCLDVVTHWIQEGEEGRPKDDRHLRGCGYLPGCPGSNGFHNNDTF HFLKCCNTTKCNEGPILELENLPQNGRQCYSCKGNSTHGCSSEETFLIDCRGPMN QCLVATGTHEPKNQSYMVRGCATASMCQHAHLGDAFSMCHIDVSCCTKSGCNHPD LDVQYRSG

Rigid body 1 (PDB) Rigid body 2 (PDB) Rigid body 3 (PDB)

EOM

Symmetry

❏ Symmetric core ❏ Symmetric linkers/termini ❏ Symmetric core ❏ Asymmetric linkers/termini

Tria et al., 2014 (submitted)

Flexibility driving function: uPAR

EOM example

❏ uPAR is a receptor involved in cell- adhesion and plasminogen activation ❏ Receptor flexible (SAXS) ❏ Therapeutics based on ligand ❏ Decreased flexibility upon drug binding → and metastasis???

Mertens et al., JBC, 2012, 287(41), 34304-34315

Flexibility driving function: uPAR

EOM example

❏ uPAR is a receptor involved in cell- adhesion and plasminogen activation ❏ Receptor flexible (SAXS) ❏ Therapeutics based on ligand ❏ Decreased flexibility upon drug binding → and metastasis???

Mertens et al., JBC, 2012, 287(41), 34304-34315

Flexibility driving function: uPAR

EOM example

Mertens et al., JBC, 2012, 287(41), 34304-34315

x 2 x 4 x 2 x 10

Flexibility driving function: uPAR

EOM example

❏ uPAR is a receptor involved in cell- adhesion and plasminogen activation ❏ Receptor flexible (SAXS) ❏ Therapeutics based on ligand ❏ Decreased flexibility upon drug binding → and metastasis???

Mertens et al., JBC, 2012, 287(41), 34304-34315

EOM results and metrics

Analysis procedures (EOM v2.0)

Tria et al., 2014 (submitted)

EOM results and metrics

Analysis procedures (EOM v2.0)

Tria et al., 2014 (submitted)

Rflex = -Hb(S) Rσ = σs / σp

0% ← Rflex→ 100% Rigid Flexible 0 ← Rσ→ 1 Rigid Flexible

(high uncertainty)

Hb(S)=-Σp(xi)logb(p(xi))

EOM results and metrics

Analysis procedures (EOM v2.0)

Tria et al., 2014 (submitted)

EOM example

Simple example

Flexible linker?

Summary

❏ Polydisperse systems: ❏ Oligomeric equilibria ❏ Conformational equilibria ❏ Software

❏ OLIGOMER (Konarev et al., 2003) ❏ EOM (Bernado et al., 2007, Tria et al., 2014)

⇄ +

Further approaches

Other useful ATSAS programs: ❏ MIXTURE (Konarev et al., 2003) ❏ SVDplot (Konarev et al., 2003) ❏ PolySAS (Konarev et al., 2014)