Ensemble Optimization Method on SAXS
EOM 2.0 – tutorial
Giancarlo Tria
[email protected]
BioSAXS group @ EMBL Hamburg
EMBO Practical Course on Solution Scattering from Biological Macromolecular
October 21st, 2012
Kratky Plots to Detect Disorder
Kratky plot establishes an
approximate relationship
between I(s) vs s for folded and
unfolded proteins
Unfolded
Folded
Multi-domains
with flexible
linkers
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Ensemble Optimization Method on SAXS – EOM 2.0
Indications (not Proofs!!!) of Flexibility
► Smooth Scattering profiles and featureless Kratky Plots
► Large Rg and Dmax
► 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
Rigid
Scenario
Analysis of the overall size descriptors (Rg, p(r), Kratky)
Go for flexibility!
Flexible
Scenario
Modelling: ab initio
(DAMMIN/DAMMIF)
and Rigid body
(BUNCH/CORAL)
Analysis of the differences
Ensemble Optimization Method on SAXS – EOM 2.0
Flexibility as mixture of different conformations
D
sin sr
I ( s ) = 4π ∫ p( r )
dr
sr
0
For monodisperse systems the scattering is
proportional to that of a single particle averaged
over all orientations
I ( s) = ∑ vk I k ( s)
k
vk = volume fraction
Ik(s) = scattering intensity from the k-th component
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Ensemble Optimization Method on SAXS – EOM 2.0
Ensemble methods in SAXS
Genetic Algorithm
Pool generation
...
...
Crysol
I(s) =
1N
∑In(s)
N n=1
...
Rg1 Rg2 Rg3 Rg4 Rg5
ρ (Rg)
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.
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Ensemble Optimization Method on SAXS – EOM 2.0
Genetic Algorithm (optimized ensemble size)
Mutation
Chromosome
Crossing
Elitism
Generation 1
I (s) =
1
N
N
∑I
n =1
Generation 2
n
(s)
Elitism
7
Crossing
Mutation
Ensemble Optimization Method on SAXS – EOM 2.0
Chromosome
Cα
Modelling: Native vs. Random
φ
ψ
Cα
Quasi Cα -Cα Ramachandran plot
Bond angles vs. Dihedral angles
G. Kleywegt , Validation of protein models from Cα
coordinates alone, JMB, 1997, 273, 371-376
Theoretical distribution of the bond and dihedral angles for random chains
Rg
Rg =
N
8
R0·Nν
R0 Persistence Length
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
Ensemble Optimization Method on SAXS – EOM 2.0
Unfolded protein …
• TAU protein isoform (124AA)
Inputs for using EOM:
curve.dat
9
sequence.seq
>
CYLSRKLMLDARENLKLLDRMNRLSPHSCL
QDRKDFGLPQEMVEGDQLQKDQAFPVLYE
MLQQSFNLFYTEHSSAAWDTTLLEQLCTGL
QQQLDHLDTCRGQVMGEEDSELGNMDPIV
TVKKYF
Ensemble Optimization Method on SAXS – EOM 2.0
<1min per repetition
…
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Ensemble Optimization Method on SAXS – EOM 2.0
… unfolded protein: results
0.07
Rg = 45.05
0.06
Rg = 32.96
0.05
0.04
pool
Series1
0.03
ensembles
Series2
0.02
0.01
0
0
20
40
60
0.08
Rg [Å] 80
Dmax = 140.38
0.07
Dmax = 101.02
0.06
0.05
0.04
pool
Series1
0.03
ensembles
Series2
0.02
0.01
0
0
11
50
100
150
Ensemble Optimization Method on SAXS – EOM 2.0
200
250
Dmax [Å]
Missing loops (i.e. flat electron density map) …
Nter.pdb
Cter.pdb
curve.dat
Kratky Plot
vs.
MRIGMV……..GGVQSHVLQ…..VLRDAGHEVS…….PHVKLPDYVS
seq.seq
missing loop
30 AA
pool
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Ensemble Optimization Method on SAXS – EOM 2.0
apoferritin
... Missing loops: results
0.09
0.08
Rg = 24.46
0.07
Rg = 24.28
0.06
0.05
pool
Series1
0.04
ensembles
Series2
0.03
0.02
0.01
0
21
13
23
25
Rg [Å]
Ensemble Optimization Method on SAXS – EOM 2.0
27
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??
31 AA
N-terminal tail
??missing??
??missing??
122 AA
inter-domains linker
??missing??
high resolution (MX)
C-terminal monomer domain
pool
14
Ensemble Optimization Method on SAXS – EOM 2.0
… 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
0.07
100 Rg, Å
pool
Pool
0.06
High ionic strength
Low ionic strength
0.05
0.04
Multi-curves fitting
0.03
0.02
0.01
0
80
15
130
180
230
280
330
380
Dmax, Å
Ensemble Optimization Method on SAXS – EOM 2.0
Case extra: dodecamer (P62, 2 domains) + tRNA
158 AA N-terminal tail
high resolution (MX) N-terminal monomer domain (141 AA)
9 AA inter-domains linker
high resolution (MX) C-terminal monomer domain (270 AA)
30 N single strand tRNA
16
max distance in Հ
subUnit
Ensemble Optimization Method on SAXS – EOM 2.0
contact residues range
EOM Tests: Size of Pool
Number of chains: 100
Number of chains: 1 000
0.08
0.04
0.02
0.05
Density
0.10
Density
0.20
0.15
20
30
40
50
60
10
20
30
Rg
60
10
30
40
Rg
50
60
40
50
60
50
60
0.08
Density
0.06
0.08
0.06
0.02
0.00
0.02
20
30
Number of chains: 64 790
0.00
10
20
Rg
0.04
Density
0.06
0.04
0.00
0.02
Density
50
Number of chains: 10 000
0.08
Number of chains: 5 000
17
40
Rg
0.04
10
0.00
0.00
0.00
0.05
0.10
Density
0.06
0.25
0.30
0.15
Number of chains: 10
10
20
30
40
50
60
10
20
Rg
Ensemble Optimization Method on SAXS – EOM 2.0
30
40
Rg
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
18
Rg, Å
Ensemble Optimization Method on SAXS – EOM 2.0
Rg, Å
…resolution of Subpopulations by EOM
Genetic Algorithm
0.10
Scattering curves
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%
0.08
20% < Rg < 25%, 75% < Rg < 80%
25% < Rg < 30%, 70% < Rg < 75%
30% < Rg < 35%, 65% < Rg < 70%
15-20%
Undistinguishable
ΔRg = 11.33
35% < Rg < 40%, 60% < Rg < 65%
40% < Rg < 45%, 55% < Rg < 60%
45% < Rg < 50%, 50% < Rg < 55%
10-15%
Well distinguishable
ΔRg = 13.02
0.00
0.02
0.04
Density
0.06
Pool
Rg, Å
20
19
30
40
Ensemble Optimization Method on SAXS – EOM 2.0
50
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..
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Ensemble Optimization Method on SAXS – EOM 2.0