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

Chemometric

“Model-free” deconvolution

• SVD
• MCR-LS
• EFA

Ensembles

Flexible systems

• EOM
• MES
• EROS

Combinations

Known components

• OLIGOMER
• MIXTURE

Basic SAXS/SANS parameters provide initial hints!

Standard situation

Monodisperse non-interacting systems

I(s) = 4π p(r)sin(sr) sr

Dmax

∫

dr

• Observed scattering proportional to

(averaged over all orientations)

• Facilitates size, shape internal structure

investigation (at low resolution)

Polydispersity

Polydisperse and interacting systems

I(s) = 4π p(r)sin(sr) sr

Dmax

∫

dr

• Observed scattering proportional to

(averaged over all orientations)

• Standard SAS model reconstruction relies on:
• Monodispersity, no-interaction, sample known

I(s) = vkIk(s)

k

∑

• Size polydispersity
• Total scattering is a weighted sum

× vk

Scattering from a mixture

I(s) = 4π p(r)sin(sr) sr

Dmax

∫

dr

× vk

I(s) =∑kvkIk(s)

• Conformational polydispersity

× vk

Scattering from a mixture

I(s) = 4π p(r)sin(sr) sr

Dmax

∫

dr

× vk

I(s) =∑kvkIk(s)

Scattering from a mixture

I(s) = 4π p(r)sin(sr) sr

Dmax

∫

dr

• Both?

× vk × vk × vk

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 vk and Ik(s)
• Requires a more indirect approach

Where do you start?

Sample characterisation

Mixture? Flexible?

• Concentration dependence (SAXS parameters change)
• Molecular weight not what you expect?

Mixture directly from data

Mertens & Svergun, J. Struct. Biol. (2009)

• Follow I(0) (eg. from Guinier plot analysis)

Mixture directly from data

0.0005 0.001 0.0015 0.002 q

• 2
• 8
• 6
• 4
• 2

ln[I(q)] y = -2.8441 - 284.09 * x y = -5.8408 - 199.89 * x Rg = 29.2 Rg = 24.5 0.001 0.01 0.1 1 q, Å

• 1

10

• 5

10

• 4

10

• 3

10

• 2

10

• 1

I(q), cm

• 1

Protein A (dimer) Protein A (monomer)

• I(0)dimer = 0.058 cm-1 à MM = 80 kDa
• I(0)mon = 0.029 cm-1 à MM = 40 kDa

• Follow hydrated particle volume, Vp

Mixture directly from data

0.001 0.01 0.1 1 q, Å

• 1

10

• 5

10

• 4

10

• 3

10

• 2

10

• 1

I(q), cm

• 1

Protein A (dimer) Protein A (monomer) 20 40 60 80 100 r, Å 10

• 4

10

• 4

10

• 4

10

• 4

p(r), rel. units Protein A (dimer) Protein A (monomer)

Vp = 2π 2 I(0) Q

Q = q2[I(q)− A]dq

∞

∫

Via p(r) (reg. curve)

• Vp (dimer) = 144 nm3 à (x 0.625) à MM = 90 kDa
• Vp (mon) = 72 nm3 à (x 0.625) à MM = 45 kDa

MIXTURE

• Describe data with shapes (spheres, cylinders etc.)
• Monodisperse/polydisperse

I(s) = vkIk(s)

k

∑

+

I(s) =∑kvkIk(s)

?

Konarev et al., J Appl Cryst. 36, 1277-1282.

OLIGOMER

• Conformational equilibrium
• eg. state-0 ßà state-1

I(s) = vkIk(s)

k

∑

+

× vk × vk

I(s) =∑kvkIk(s)

?

Konarev et al., J Appl Cryst. 36, 1277-1282.

Mixture analysis: Rubisco

• 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)

I(s) = vkIk(s)

k

∑

An encounter adrenodoxin/cytochrome C complex

• Cross-linked complex Ad/CC always heterodimer
• Native complex strongly depends on conc. & NaCl

I(s) = vkIk(s)

k

∑

• X. Xu, W. Reinle, F. Hannemann, P. V. Konarev, D. I. Svergun, R. Bernhardt & M. Ubbink (2008) JACS, 130, 6395-6403

Volume fractions Mon:Dim:Tri:Tet 0 : 0 : 50 : 50 0 : 8 : 47 : 45 5 : 25 : 55 : 15 25 : 25 : 50 : 0 0 : 100 : 0 : 0

SAXS model

• f

hetero-tetrameric native complex at high salt and high solute concentration

24 mg/ml 12 6 2.4 Cross-linked

• Ensemble based approaches
• When many structures are required to

describe the data

• Flexible systems (eg. IDPs)
• Chemically denatured proteins
• Flexible multi-domain proteins

Flexibility & conformational polydispersity

I(s) = vkIk(s)

k

∑

Mertens & Svergun,JSB, 2010, 172(1)

• Kratky plot, (Kratky 1982): I*s2 vs s
• Dimensionless Kratky, (Durand, 2010): (I/I0)*(sRg)2 vs sRg

Mertens et al., JBC. (2012), 287:41

Unfolded Partially folded Folded (1.73,1.104)

Flexibility directly from data

• “Featureless” curves à flexible
• Clear features à “rigid”

Flexibility directly from data

20 residue linkers

• Bernado. Eur. Biophys. J. (2009), 39:769

• Ensemble Optimisation Method

EOM

I(s) = vkIk(s)

k

∑

Pool Ik(s) Ensembles Best fitting ensemble Analysis

(Bernado et al. JACS, 2007; Tria et al. IUCRJ, 2014)

• Ensemble Optimisation Method…. some detail

EOM

I(s) = vkIk(s)

k

∑

Bernado & Svergun Mol. Biosystems. (2012) 8:151-167

EOM

I(s) = vkIk(s)

k

∑

LRCMQCKTNGDCRVEECALGQDLCRTTIVRLWEEGEELELVEKS CTCSEKTNRTLSYRTGLKITSLTEVVCGLDLCNQGNSGRAVTYS RSRYLECISCGSSDMSCERGRHQSLQCRSPEEQCLDVVTHWIQE GEEGRPKDDRHLRGCGYLPGCPGSNGFHNNDTFHFLKCCNTTKC NEGPILELENLPQNGRQCYSCKGNSTHGCSSEETFLIDCRGPMN QCLVATGTHEPKNQSYMVRGCATASMCQHAHLGDAFSMCHIDVS CCTKSGCNHPDLDVQYRSG Rigid body 1 (PDB) Rigid body 2 (PDB) Rigid body 3 (PDB)

EOM

I(s) = vkIk(s)

k

∑

Rigid body 1 (PDB) Rigid body 2 (PDB) Rigid body 3 (PDB) LRCMQCKTNGDCRVEECALGQDLCRTTIVRLWEEGEELELVEKS CTCSEKTNRTLSYRTGLKITSLTEVVCGLDLCNQGNSGRAVTYS RSRYLECISCGSSDMSCERGRHQSLQCRSPEEQCLDVVTHWIQE GEEGRPKDDRHLRGCGYLPGCPGSNGFHNNDTFHFLKCCNTTKC NEGPILELENLPQNGRQCYSCKGNSTHGCSSEETFLIDCRGPMN QCLVATGTHEPKNQSYMVRGCATASMCQHAHLGDAFSMCHIDVS CCTKSGCNHPDLDVQYRSG

EOM

I(s) = vkIk(s)

k

∑

• Symmetry

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

• Required input

EOM

I(s) = vkIk(s)

k

∑

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

Tau protein “structure”

• Tau stabilizes microtubles (eg. neurons)
• IDP even when bound to microtubles
• Tau repeat identified as source of residual secondary structure

I(s) = vkIk(s)

k

∑

Mylonas et al. (2008), Biochemistry 47:10345-10353

* * * * * * * * * * * *

Pool Sel

Flexibility and function: uPAR

• Urokinase Plasminogen Activation Receptor
• Cell-adhesion, blood clotting, marker for cancer metastasis

I(s) = vkIk(s)

k

∑

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

❏ uPAR WT ❏ uPAR mutant

Pushing EOM a little further…

• Metrics in EOM v2.0 seek to enable more quantitative results

I(s) = vkIk(s)

k

∑

Hb(S)=-Σp(xi)logb[p(xi)] Rflex = -Hb(S)

(high uncertainty) (low uncertainty)

Rσ = σs / σp 0% ← Rflex→ 100% Rigid Flexible 0 ← Rσ→ 1

Tria, Mertens et al., 2014

Pushing EOM a little further…

• Metrics in EOM v2.0 seek to enable more quantitative results

I(s) = vkIk(s)

k

∑

Hb(S)=-Σp(xi)logb[p(xi)]

Tria, Mertens et al., 2014

SREFLEX

• Using an elastic network model and normal modes
• Structure deformed to FIT experimental data

I(s) = vkIk(s)

k

∑

Panjkovich & Svergun, PCCP, 2016

GASBORMX (mixture)

• Ab initio DR modeling
• Symmetry operation to build oligomers

I(s) = vkIk(s)

k

∑

• Cf. Maxim Petoukhov

SASREFMX (mixture)

• Rigid body modeling
• Symmetry operation to build oligomers

I(s) = vkIk(s)

k

∑

• Cf. Maxim Petoukhov

Summary

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

36

PRIMUS GNOM DATtools SHANUM

Data collection No apriori information Hi-res model available Partial hi-res model available

CRYSOL CRYSON DAMMIN GASBOR Ab initio modeling Ambimeter Hybrid modeling SREFLEX EOM SASREF CORAL

flexible system “rigid” system

CORMAP

MONODISPERSE MIXTURE

MIXTURE OLIGOMER SVD

VALIDATE

SUPALM/DAMAVER/SASRES

SAXS workflow with ATSAS

MEMPROT

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

SVD

Singular value decomposition of data matrix Y (I(s) vs s): Y (S x W) = USV U (S x N) formed by significant eigenvectors of YYt V (N x W) formed by significant eigenvectors of YtY Columns of U and rows of V orthogonal: UtU = VVt = I (identity matrix) S (N x N) diagonal matrix, elements are positive square roots of the significant eigenvalues of YYt or YtY in descending order

SVDplot

Y= CA = USV

Right singular vectors Left singular vectors SAXS profiles

• Conc. profiles

(elution peaks)

Rotation (A=VR) Rotation (C=UR)

EFA: Evolving Factor Analysis.

SVD using order from eg. SEC-SAXS

SVD with direction

EFA

• 1. Find the number of components (number of factors in Y)
• 2. EFA plots of eigenvalues VS time
• 3. Determine regions of existence (concentration window) for each

component

• 4. Time evolution of the rank of Y in forward and reverse direction
• 5. Reconstruct concentration profiles and SAXS curves
• 6. Simple linear regression or via calculation of a rotation matrix

Follow change/evolution of rank of Y

Model Concentration Profile EFA Plot 4 components

• Appearance of each new component at

detector associated with increase of rank by 1

• EFA Plot: log (eigenvalue) vs time
• Inflection points indicate change in

rank

• Can also perform EFA backwards to

find point of disappearance

Concentration Window of each component

❏ Concentration of a component is zero outside its “window” ❏ EFA forward/backward defines limits

❏ Component i appears where rank Y rises to i (in forward direction) ❏ Disappears when rank rises to N + 1 - i (in backward direction)

Cheers!

Mixtures

Be aware! Be careful!

Fibrillation of α-synuclein (αSN)

• Aggregation of αSN leads to Parkinson decease
• Fibril formation process characterized by SAXS
• Intermediate oligomer formed by several partially unfolded αSN molecules
• Mature fibril is formed by association of these oligomers (similar to mechanism found for insulin

fibrillation)

I(s) = vkIk(s)

k

∑

Giehm, L., Svergun, D.I., Otzen, D.E. & Vestergaard, B. (2011) PNAS USA, 108, 3246

The oligomer is shown to disrupt liposomes, i.e. it is potentially cytotoxic