Haydyn Mertens, EMBL Hamburg Mixtures Oligomers and ensembles
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 MIXTURES SAXS modeling typically assumes: 1. Monodispersity 2. Absence of interparticle interactions (dilute) 3. Knowledge of sample identity
Scattering from a mixture 1. Size polydispersity I(s) =∑ k v k I k (s) × v k × v k
Scattering from a mixture 2. Conformational polydispersity I(s) =∑ k v k I k (s) × v k × v k
Scattering from a mixture 3. Both? I(s) =∑ k v k I k (s) × v k × v k × v k
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 v k and I k (s) ❏ Requires a more indirect approach
OLIGOMER (Konarev et al , 2003) eg. monomer - dimer equilibrium + I(s) =∑ k v k I k (s) × v k × v k
OLIGOMER (Konarev et al , 2003) Required input I(s) =∑ k v k I k (s) Experimental data (*.dat) OLIGOMER FFMAKER Form factors (*.dat) Models (*.pdb)
OLIGOMER Required input I(s) =∑ k v k I k (s) Experimental data (*.dat) OLIGOMER FFMAKER Form factors (*.dat) I k (s) volume fractions Intensities Models (*.pdb) v k χ 2 (goodness of fit)
OLIGOMER eg. monomer - dimer equilibrium + I(s) =∑ k v k I k (s) × v k × v k
OLIGOMER eg. monomer - dimer equilibrium + Determine volume fractions! I(s) =∑ k v k I k (s) × v k × v k
OLIGOMER How does OLIGOMER determine the volume fractions? + Form factors used to define a set of ❏ equations (FFMAKER/CRYSOL) I(s) =∑ k v k I k (s) Experimental data used to drive a non- ❏ × v k negative least-squares routine Determine best set of v k that provides a ❏ good fit to the data × v k
OLIGOMER example 2 (real case) Monomer ⇆ extended-dimer + compact-dimer inactive active → cell wall lysis Endolysins ❏ bacteriophage as possible ❏ antibacterials oligomerisation modulates lytic ❏ activity Compact-dimer “is active” ❏ Dunne et al. , PLoS pathogens, 2014, 10 (7), e1004228
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 Meijers group determined ❏ crystal structure of complex Used components for ❏ OLIGOMER analysis of solution behaviour Finci, Krueger et al. , Neuron, 2014, 83(4), 839-849
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 SAXS shows DCC preference for ❏ Netrin site-1 Ternary complex formed only with DCC ❏ saturation DCC M933R site-1 mutant leaves site-2 ❏ binding unaffected → no cooperativity Finci, Krueger et al. , Neuron, 2014, 83(4), 839-849
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 ❏ Site-2 Site-2 Site-1 Site-1 Finci, Krueger et al. , Neuron, 2014, 83(4), 839-849
OLIGOMER use Enter maximum S-vector ................. < 0.5000 >: 0.5 1. Generate Form Factor file(s) Calculating component 1 from 3 $> ffmaker Read atoms and evaluate geometrical center ... See Usage in the batch mode: ffmaker /help Number of atoms read .................................. : 2331 Number of atoms read .................................. : 2331 FFmaker calculates formfactor file Geometric Center: 33.253 -57.037 25.951 from pdb models or from scattering curves Percent processed 10 20 30 40 50 60 70 80 90 100 that can be further used in OLIGOMER. Processing atoms :>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Enter number of components ............. < 0 >: 3 Number of carbons read ................................ : 1499 Enter output formfactor filename ....... < .dat >: formfactors. Number of nitrogens read .............................. : 392 dat Number of oxigens read ................................ : 431 Nff= 3 Number of sulfur atoms read ........................... : 9 Enter *.pdb or *.dat file name (with extension) Center of the excess electron density: -0.127 -0.099 -0.184 Enter file name for component ...........................: protA.pdb Center of the excess electron density: -0.127 -0.099 -0.184 Component N= 1 was taken from protA.pdb Processing envelope:>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Enter number of points NS .............. < 201 >: Enter *.pdb or *.dat file name (with extension) Enter maximum number of harmonics (LmMax) < 15 >:
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 Angular units used in experimental data: Input file with form-factors ........... < .dat >: formfactor.dat 4*Pi*SIN(theta)/lambda [1/Angstrom] (1) Use constant as additional component [ Y 4*Pi*SIN(theta)/lambda [1/nm] (2) / N ] .................................. < No >: 2 * SIN(theta)/lambda [1/Angstrom] (3) Number of oligomers .................................... : 3 2 * SIN(theta)/lambda [1/nm] (4) ....... < 1 >: 1 Number of points read .................................. : 201 Combinations = 1 2 3 Form-factor number 1 Operable s range: .......................... : 9.430e-3, 0.5000 Calculated MW and Rg ..... < 4376., 19.48 >: Range for evaluation of Scattering < 9.430e-3, 0.5000 >: Form-factor number 2 Use non-negativity condition [ Y / N ] . < Yes >: Calculated MW and Rg ..... < 2006., 21.47 >: Output file .......................... < protAB_011.fit >: Form-factor number 3 Plot the result [ Y / N ] .............. < Yes >: n Calculated MW and Rg ..... < 6224., 25.55 >: Chi^2 <MW> <Rg> Volume fractions +- errors Experimental data file name ............ < .dat >: protAB_011.dat 0.75 6221 25.54 0.002+-0.001 0.000+-0.000 0.998+-0.001 s range: ................................... : 9.430e-3, 0.5399
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 I k (s) Ensembles Best fitting ensemble Analysis
EOM (Bernado et al , 2007, Tria et al , 2014) Required input I(s) =∑ k v k I k (s) Experimental data (*.dat) EOM Sequence (*.txt) Models (*.pdb) χ 2 (fit) R g dist. D max dist. (rigid bodies)
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 Tria et al., 2014 (submitted) Symmetric core Symmetric core ❏ ❏ Symmetric linkers/termini Asymmetric linkers/termini ❏ ❏
EOM example Flexibility driving function: uPAR 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
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