Mixtures, assemblies & flexible systems Haydyn Mertens - PowerPoint PPT Presentation

Mixtures, assemblies & flexible systems Haydyn Mertens (EMBL-Hamburg)

DOGMA: No function without structure!

Not true! Flexibility enables more function Hub proteins in networks Interaction specialists Tompa, Peter, et al. “Intrinsically disordered proteins: emerging interaction specialists." Current Opinion in Structural Biology 35 (2015): 49-59.

Basic approaches Ensembles Combinations Chemometric Flexible systems Known components “Model-free” deconvolution - EOM - OLIGOMER - SVD - MES - MIXTURE - MCR-LS - EROS - EFA Basic SAXS/SANS parameters provide initial hints!

D max p ( r )sin( sr ) Standard situation ∫ I ( s ) = 4 π dr sr 0 Monodisperse non-interacting systems Observed scattering proportional to • (averaged over all orientations) Facilitates size, shape internal structure • investigation (at low resolution)

D max p ( r )sin( sr ) ∫ I ( s ) = 4 π dr Polydispersity sr 0 ∑ I ( s ) = v k I k ( s ) Polydisperse and interacting systems k Observed scattering proportional to • (averaged over all orientations) Standard SAS model reconstruction relies on: • • Monodispersity, no-interaction, sample known

D max p ( r )sin( sr ) ∫ I ( s ) = 4 π dr Scattering from a mixture sr 0 • Size polydispersity • Total scattering is a weighted sum I(s) = ∑ k v k I k (s) × v k × v k

D max p ( r )sin( sr ) ∫ I ( s ) = 4 π dr Scattering from a mixture sr 0 • Conformational polydispersity I(s) = ∑ k v k I k (s) × v k × v k

D max p ( r )sin( sr ) ∫ I ( s ) = 4 π dr Scattering from a mixture sr 0 • Both? × v k × v k × v k

Scattering from a mixture • Size/Shape polydispersity (eg. distributions, oligomers) • If component structure unknown requires additional parameters • Conformational polydispersity (eg. IDPs) • Almost infinite range of conformations • Cannot really identify all possible v k and I k (s) • Requires a more indirect approach

Where do you start? Sample characterisation Mixture? Flexible?

Mixture directly from data • Concentration dependence (SAXS parameters change) • Molecular weight not what you expect? Mertens & Svergun, J. Struct. Biol. (2009)

Mixture directly from data • Follow I(0) ( eg . from Guinier plot analysis) • I(0)dimer = 0.058 cm -1 à MM = 80 kDa • I(0)mon = 0.029 cm -1 à MM = 40 kDa -1 -2 10 Protein A (dimer) y = -2.8441 - 284.09 * x Rg = 29.2 Protein A (monomer) -2 10 -4 -1 I(q), cm ln[I(q)] -3 10 y = -5.8408 - 199.89 * x Rg = 24.5 -6 -4 10 -5 -8 10 0.001 0.01 0.1 1 0 0.0005 0.001 0.0015 0.002 -1 2 Å -2 q, Å q

Mixture directly from data • Follow hydrated particle volume, V p • V p (dimer) = 144 nm 3 à (x 0.625) à MM = 90 kDa • V p (mon) = 72 nm 3 à (x 0.625) à MM = 45 kDa V p = 2 π 2 I (0) Q -1 -4 10 10 Protein A (dimer) Protein A (dimer) Protein A (monomer) Protein A (monomer) Via p(r) (reg. curve) -2 -4 10 10 p(r), rel. units -1 I(q), cm -3 -4 ∞ 10 10 q 2 [ I ( q ) − A ] dq ∫ Q = 0 -4 -4 10 10 -5 0 10 0.001 0.01 0.1 1 0 20 40 60 80 100 -1 r, Å q, Å

∑ I ( s ) = v k I k ( s ) MIXTURE k • Describe data with shapes (spheres, cylinders etc.) • Monodisperse/polydisperse ? + I(s) = ∑ k v k I k (s) Konarev et al., J Appl Cryst. 36, 1277-1282.

∑ I ( s ) = v k I k ( s ) OLIGOMER k • Conformational equilibrium • eg. state-0 ßà state-1 ? + I(s) = ∑ k v k I k (s) × v k × v k Konarev et al., J Appl Cryst. 36, 1277-1282.

∑ I ( s ) = v k I k ( s ) Mixture analysis: Rubisco k • OLIGOMER: analysis of equilibrium • GASBORMX: low resolution ab initio model of mon/hex Keown, J, Griffin, M, Mertens H, Pearce, G. J. Biol. Chem. (2013)

An encounter adrenodoxin/cytochrome C complex ∑ I ( s ) = v k I k ( s ) k • Cross-linked complex Ad/CC always heterodimer • Native complex strongly depends on conc. & NaCl Volume fractions 24 mg/ml Mon:Dim: Tri :Tet 12 0 : 0 : 50 : 50 6 0 : 8 : 47 : 45 2.4 5 : 25 : 55 : 15 25 : 25 : 50 : 0 0 : 100 : 0 : 0 Cross-linked SAXS model of hetero-tetrameric native complex at high salt and high solute concentration X. Xu, W. Reinle, F. Hannemann, P. V. Konarev, D. I. Svergun, R. Bernhardt & M. Ubbink (2008) JACS, 130 , 6395-6403

∑ I ( s ) = v k I k ( s ) Flexibility & conformational polydispersity k • 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)

Flexibility directly from data Kratky plot, (Kratky 1982): I*s 2 vs s • Dimensionless Kratky, (Durand, 2010): (I/I0)*(sRg) 2 vs sRg • Unfolded Partially folded Folded (1.73,1.104) Mertens et al., JBC. (2012), 287:41

Flexibility directly from data • “Featureless” curves à flexible • Clear features à “rigid” 20 residue linkers Bernado. Eur. Biophys. J. (2009), 39:769

∑ I ( s ) = v k I k ( s ) EOM k • E nsemble O ptimisation M ethod Pool I k (s) Ensembles Best fitting ensemble Analysis (Bernado et al. JACS, 2007; Tria et al. IUCRJ, 2014)

∑ I ( s ) = v k I k ( s ) EOM k • E nsemble O ptimisation M ethod…. some detail Bernado & Svergun Mol. Biosystems. (2012) 8:151-167

∑ I ( s ) = v k I k ( s ) EOM k LRCMQCKTNGDCRVEECALGQDLCRTTIVRLWEEGEELELVEKS CTCSEKTNRTLSYRTGLKITSLTEVVCGLDLCNQGNSGRAVTYS RSRYLECISCGSSDMSCERGRHQSLQCRSPEEQCLDVVTHWIQE GEEGRPKDDRHLRGCGYLPGCPGSNGFHNNDTFHFLKCCNTTKC NEGPILELENLPQNGRQCYSCKGNSTHGCSSEETFLIDCRGPMN QCLVATGTHEPKNQSYMVRGCATASMCQHAHLGDAFSMCHIDVS CCTKSGCNHPDLDVQYRSG Rigid body 1 (PDB) Rigid body 2 (PDB) Rigid body 3 (PDB)

∑ I ( s ) = v k I k ( s ) EOM k LRCMQCKTNGDCRVEECALGQDLCRTTIVRLWEEGEELELVEKS CTCSEKTNRTLSYRTGLKITSLTEVVCGLDLCNQGNSGRAVTYS RSRYLECISCGSSDMSCERGRHQSLQCRSPEEQCLDVVTHWIQE GEEGRPKDDRHLRGCGYLPGCPGSNGFHNNDTFHFLKCCNTTKC NEGPILELENLPQNGRQCYSCKGNSTHGCSSEETFLIDCRGPMN QCLVATGTHEPKNQSYMVRGCATASMCQHAHLGDAFSMCHIDVS CCTKSGCNHPDLDVQYRSG Rigid body 1 (PDB) Rigid body 2 (PDB) Rigid body 3 (PDB)

∑ I ( s ) = v k I k ( s ) EOM k • Symmetry ❏ Symmetric core ❏ Symmetric linkers/termini ❏ Symmetric core ❏ Asymmetric linkers/termini

∑ I ( s ) = v k I k ( s ) EOM k • Required input Experimental data (*.dat) EOM Sequence (*.txt) Models (*.pdb) χ 2 (fit) R g dist. D max dist. (rigid bodies) Symmetry

Tau protein “structure” ∑ I ( s ) = v k I k ( s ) k • Tau stabilizes microtubles (eg. neurons) • IDP even when bound to microtubles • Tau repeat identified as source of residual secondary structure * * * Pool Sel * * * * * * * * * Mylonas et al. (2008), Biochemistry 47:10345-10353

Flexibility and function: uPAR ∑ I ( s ) = v k I k ( s ) k • Urokinase Plasminogen Activation Receptor • Cell-adhesion, blood clotting, marker for cancer metastasis uPAR WT ❏ uPAR mutant ❏ Mertens et al. , JBC, 2012, 287(41), 34304-34315

Pushing EOM a little further… ∑ I ( s ) = v k I k ( s ) k • Metrics in EOM v2.0 seek to enable more quantitative results H b (S)=-Σ p ( x i )log b [ p ( x i )] R flex = -H b (S) (low uncertainty) (high uncertainty) 0% ← R flex → 100% Rigid Flexible 0 ← R σ → 1 R σ = σ s / σ p Tria, Mertens et al., 2014

Pushing EOM a little further… ∑ I ( s ) = v k I k ( s ) k • Metrics in EOM v2.0 seek to enable more quantitative results H b (S)=-Σ p ( x i )log b [ p ( x i )] Tria, Mertens et al., 2014

SREFLEX ∑ I ( s ) = v k I k ( s ) k • Using an elastic network model and normal modes • Structure deformed to FIT experimental data Panjkovich & Svergun, PCCP , 2016

GASBORMX (mixture) ∑ I ( s ) = v k I k ( s ) k • Ab initio DR modeling • Symmetry operation to build oligomers Cf. Maxim Petoukhov

SASREFMX (mixture) ∑ I ( s ) = v k I k ( s ) k • Rigid body modeling • Symmetry operation to build oligomers Cf. Maxim Petoukhov

Summary ● Polydisperse systems ● Oligomeric and conformational ● Useful approaches ● SAXS profiles (features vs no-features) ● Kratky representations ● Ensemble methods

SAXS workflow with ATSAS Data collection MIXTURE CORMAP DATtools PRIMUS MIXTURE OLIGOMER SVD Ambimeter GNOM MONODISPERSE SHANUM No apriori information Partial hi-res model available Hi-res model available Ab initio modeling Hybrid modeling SREFLEX CRYSOL CRYSON “rigid” system flexible system DAMMIN GASBOR MEMPROT VALIDATE SASREF CORAL EOM 36 SUPALM/DAMAVER/SASRES

Chemometric analysis Chemometrics is the use of mathematical and statistical methods to improve the understanding of chemical information and to correlate quality parameters or physical properties to analytical instrument data .

SVD: Singular value decomposition. Model-free deconvolution approach SVD Factorization of a matrix: Y = USV Matrix = rotate-stretch-rotate