Ensemble Optimization Method on SAXS EOM 2.0 – tutorial Giancarlo Tria giancarlo.tria@embl-hamburg.de BioSAXS group @ EMBL Hamburg EMBO Practical Course on Solution Scattering from Biological Macromolecular October 21 st , 2012
Kratky Plots to Detect Disorder Unfolded Kratky plot establishes an approximate relationship between I( s ) vs s for folded and unfolded proteins Folded Multi-domains with flexible linkers Ensemble Optimization Method on SAXS – EOM 2.0 2
Indications (not Proofs!!!) of Flexibility ► Smooth Scattering profiles and featureless Kratky Plots ► Large R g and D max ► Absence of correlation peaks in the p(r) function ► Low correlation densities in ab initio reconstructions ► Isolated domains in rigid body modelling ► Prediction of disorder using bioinformatics tools http://www.idpbynmr.eu/home/science/research-tools.html Ensemble Optimization Method on SAXS – EOM 2.0
Detection of Flexibility: A Crucial Issue SAXS curves Analysis of the overall size descriptors (R g , p(r) , Kratky) Rigid Scenario Modelling: ab initio (DAMMIN/DAMMIF) Go for flexibility! and Rigid body (BUNCH/CORAL) Flexible Analysis of the differences Scenario Ensemble Optimization Method on SAXS – EOM 2.0
Flexibility as mixture of different conformations D sin sr ∫ = π I ( s ) 4 p ( r ) dr sr 0 For monodisperse systems the scattering is proportional to that of a single particle averaged over all orientations ∑ = I ( s ) v I ( s ) k k k v k = volume fraction I k (s) = scattering intensity from the k -th component Ensemble Optimization Method on SAXS – EOM 2.0 5
Ensemble methods in SAXS Genetic Algorithm Pool generation ... ... Crysol N 1 ∑ = I ( s ) I n s ( ) N = n 1 ... 2 R g 3 R g R g R g R g 1 4 5 ρ (R g ) The Ensemble Optimization Method (EOM) Bernadó, Mylonas, Petoukhov, Blackledge, and Svergun. Structural characterization of flexible proteins using small-angle X-ray scattering . J Am Chem Soc 2007, 129 :5656-64. Ensemble Optimization Method on SAXS – EOM 2.0 6
Genetic Algorithm (optimized ensemble size) Chromosome Mutation Crossing Elitism Generation 1 Generation 2 N 1 ∑ = I ( s ) I n s ( ) N = n 1 Elitism Crossing Mutation Chromosome Ensemble Optimization Method on SAXS – EOM 2.0 7
C α φ Modelling: Native vs. Random ψ C α Quasi C α -C α Ramachandran plot Bond angles vs. Dihedral angles G. Kleywegt , Validation of protein models from C α coordinates alone , JMB , 1997, 273, 371-376 Theoretical distribution of the bond and dihedral angles for random chains R g R 0 Persistence Length R g = R 0 ·N ν ν Solvent ‘quality’ Several experimental and theoretical studies establish ν ≈ 0.588 as an indication of the ‘random coil’ in chemically denatured (Urea or GuHCl) proteins. Kohn et al. PNAS , 2004, 101, 12491 N Ensemble Optimization Method on SAXS – EOM 2.0 8
Unfolded protein … • TAU protein isoform (124AA) Inputs for using EOM: curve.dat > CYLSRKLMLDARENLKLLDRMNRLSPHSCL QDRKDFGLPQEMVEGDQLQKDQAFPVLYE 9 MLQQSFNLFYTEHSSAAWDTTLLEQLCTGL QQQLDHLDTCRGQVMGEEDSELGNMDPIV sequence.seq TVKKYF Ensemble Optimization Method on SAXS – EOM 2.0
<1min per repetition … Ensemble Optimization Method on SAXS – EOM 2.0 10
… unfolded protein: results 0.07 R g = 45.05 0.06 R g = 32.96 0.05 0.04 pool Series1 0.03 Series2 ensembles 0.02 0.01 0 0 20 40 60 80 R g [Å] 0.08 D max = 140.38 0.07 D max = 101.02 0.06 0.05 pool Series1 0.04 ensembles Series2 0.03 0.02 0.01 0 0 50 100 150 200 250 D max [Å] Ensemble Optimization Method on SAXS – EOM 2.0 11
Missing loops (i.e. flat electron density map) … Nter.pdb Cter.pdb curve.dat Kratky Plot vs. apoferritin MRIGMV……..GGVQSHVLQ…..VLRDAGHEVS…….PHVKLPDYVS seq.seq missing loop 30 AA pool Ensemble Optimization Method on SAXS – EOM 2.0 12
... Missing loops: results 0.09 0.08 R g = 24.46 0.07 R g = 24.28 0.06 0.05 Series1 pool 0.04 Series2 ensembles 0.03 0.02 0.01 0 21 23 25 27 R g [Å] Ensemble Optimization Method on SAXS – EOM 2.0 13
Flexible pentamer in solution … (full length protein measured in two buffers, with low and high ionic strength respectively) high resolution (MX) N-terminal pentamer domain ??missing?? ??missing?? 31 AA 122 AA N-terminal tail inter-domains linker ??missing?? ??missing?? high resolution (MX) C-terminal monomer domain pool Ensemble Optimization Method on SAXS – EOM 2.0 14
… Flexible pentamer in solution: results (full length protein measured in two buffers with low and high ionic strength respectively) 0.08 Pool 0.07 High ionic strength 0.06 Low ionic strength 0.05 0.04 0.03 0.02 0.01 0 20 40 60 80 100 R g , Å pool 0.07 Pool 0.06 High ionic strength Low ionic strength 0.05 0.04 Multi-curves fitting 0.03 0.02 0.01 0 80 130 180 230 280 330 380 D max , Å Ensemble Optimization Method on SAXS – EOM 2.0 15
Case extra: dodecamer (P62, 2 domains) + tRNA 158 AA N-terminal tail high resolution (MX) N-terminal monomer domain (141 AA) max distance in � 9 AA inter-domains linker high resolution (MX) C-terminal monomer domain (270 AA) 30 N single strand tRNA subUnit contact residues range Ensemble Optimization Method on SAXS – EOM 2.0 16
EOM Tests: Size of Pool Number of chains: 10 Number of chains: 100 Number of chains: 1 000 0.30 0.15 0.08 0.25 0.06 0.20 0.10 Density Density Density 0.15 0.04 0.10 0.05 0.02 0.05 0.00 0.00 0.00 10 20 30 40 50 60 10 20 30 40 50 60 10 20 30 40 50 60 Rg Rg Rg Number of chains: 5 000 Number of chains: 10 000 Number of chains: 64 790 0.08 0.08 0.08 0.06 0.06 0.06 Density Density Density 0.04 0.04 0.04 0.02 0.02 0.02 0.00 0.00 0.00 10 20 30 40 50 60 10 20 30 40 50 60 10 20 30 40 50 60 Rg Rg Rg Ensemble Optimization Method on SAXS – EOM 2.0 17
Resolution of Subpopulations by EOM … Generate a pool, select two subpopulations from it and calculate scattering curve for their union Wide subpopulations Narrow subpopulations Rg, Å Rg, Å Rg, Å Ensemble Optimization Method on SAXS – EOM 2.0 18
…resolution of Subpopulations by EOM Genetic Algorithm Scattering curves 0.10 0% < Rg < 5%, 95% < Rg < 100% 100 AA 5% < Rg < 10%, 90% < Rg < 95% 10% < Rg < 15%, 85% < Rg < 90% 15% < Rg < 20%, 80% < Rg < 85% 20% < Rg < 25%, 75% < Rg < 80% 0.08 25% < Rg < 30%, 70% < Rg < 75% 30% < Rg < 35%, 65% < Rg < 70% 15-20% 35% < Rg < 40%, 60% < Rg < 65% 40% < Rg < 45%, 55% < Rg < 60% Undistinguishable 45% < Rg < 50%, 50% < Rg < 55% Pool 0.06 Δ Rg = 11.33 10-15% Density Well distinguishable 0.04 Δ Rg = 13.02 0.02 0.00 Rg, Å 20 30 40 50 Ensemble Optimization Method on SAXS – EOM 2.0 19
Take home messages (EOM 2.0) • EOM allows one to quantitatively characterize the flexibility of a particle (what the conformations that the protein prefers in solution) • Intrinsically unfolded protein (IDP) can be easily modelled with EOM (no Size limitations) • SAXS in solution can be used as complementary technique to model flexible systems, disordered regions, etc.. Ensemble Optimization Method on SAXS – EOM 2.0 20
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