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Interpretation of SAXS Data
Dr. Tetsuro FujisawaBiometal Science Laboratory
RIKEN SPring-8 Center
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RIKEN Harima Institute/Spring-8
PX/SAXS
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RIKEN Structural Biology Beamline BL45XU
Ideal optics at the expense of flux High-resolution data collection with minimum smearing Low parasitic scattering
Relatively small beam size at the fixed energy (13.7 keV) (0.40.8 mm) Time-resolved experiments with continuous flow apparatus High-pressure small-angle X-ray scattering
Moderate flux (ca. mid 1011 photons) Diluted protein concentration Time-resolved experiments with stopped flow experiment
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source
s0
s0
s1
s1
r
r.s0
r.s12
O
Principle of small-angle scattering
211 2 12
12211 2
)2sin()()()( dVrdVrSr
SrrrSiVr Vr =
solvent
particle
0.43 =
0 0.335 =
el. A-3
Contrast of electron density is the source of scattering from protein complex.
(r) = (r) - 0
In solution
= =
=N
i
N
j ij
ijji Sr
SrSfSfSi
1 11 2
)2sin()()()(
In vacuum
/sin2=S
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fibermembrane
solution
SAXS
2
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A reliable instrument on a synchrotron source with a low noise detector is
INDISPENSIBLE
Sample requirements HP and time-resolved measurements
Sample volume50L
0.1-10 mg/mlfew kDa to hundreds MdaMono-disperse sample
SPring-8/BL-45XU SAXS
=0.9, 13.8keV 2
Sample
II-CCD detector
3600mm
X-ray
S=2sin
/
I(S)
Identical condition for sample and buffer scattering data collection
Synchrotron source
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Development of fast mixing flow cell in sub-milli time region
In order to satisfy the identical condition for buffer subtraction, we uses remote bulb switch with continuous liquid flow.
Drs. Takahashi & Akiyama
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0.000 0.100 0.200 0.300 0.400 0.500
5
6
7
8
9
L=4
L=1
log(I(Q))
Q (1/
Protein structure and SAXS
Why PX users started to use SAXS?
Gauss function
Hydrodynamic values
Rg & I(0)
Shapes
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Time
=
==
nnn
nnnn
obs
nnn
nnnobs
FN
RgFNRg
FNINI
)0(
)0(
)0()0()0(
2
22
2
2
Protein solution dynamics seen by SAXS
Beers law: In case of dilute solutions, scattering from the mixture of protein conformers are sum of scattering from each.
Obs
Real
S2
ln(I
(S))
Iobs(0)Rgobs
22
2
34exp)0()( SRgISI
At small S all scattering curves are Gauss function.
Guiniers law
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Singular Value Decomposition (SVD) analyses
ndata
mframe
mframendata
M
[ ] [ ] [ ] [ ][ ][ ]TVWUCSF ==
ndata
mframe mframe
mfram
e0
0==
'cyd.krt' 0.0039 0.00331 0.00271 0.00212 0.00152
0.010.02
0.030.04
0.05 510
1520
2530
3540
0.00050.001
0.00150.002
0.00250.003
0.00350.004
0.0045
S
Time *0.02429sec
I(S)*S*S
[F]Data matrix
Sigular value decomposition shows the number of components incorporated in data matrix
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[ ] [ ][ ][ ] [ ][ ] min
=SCFSCY
[ ] [ ] [ ][ ][ ] [ ][ ][ ] 1
1
=
=TT
TT
SSSFC
FCCCS
[ ] [ ]
[ ] [ ] { }
[ ] [ ] ( )
=
=
=
)exp()exp(11
)exp()exp(
)exp(
121212
0
2112
01
10
21
tkktkkkk
AC
tktkkk
AkB
tkAACBA kk
Determination of each scattering curves by global fittingTime resolved experiments can resolve each scattering curves because the change of fraction can be easily calculated.
When matrix [C] is known, the [S] can be determined.
The number of parameter to be determined is 3 from mframe*3 parameters.
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Cytochrome C refolding
Cyt-C
150 sec
Akiyama et al. Proc.Natl.Acad.Sci.USA., 99, 1329-1334(2002).
Prof. Satoshi Takahashis group (Osaka Univ.)
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High resolution protein structures from NMR/PX and SAXS
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s
log
( I )
Reason 1: Simulation from PDB has been greatly improved.
Freely available software packages (ATSAS, HASY Lab, EMBL)
Rigid body modeling of symmetric oligomers and subunits
GLOBSYM,MASHA (ATSAS package, Svergun, Petoukhov, Konarev)
Add Missing Loops and Domains to High and Low Resolution Models of Proteins
CREDO(Petoukhov, Svergun)
Ab initio Reconstruction of a Protein Structure by a Chain-Like Ensemble of Dummy Residues
GASBOR (Petoukhov, Svergun,Koch)
http://www.embl-hamburg.de/ExternalInfo/Research/Sax/software.html
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Small-angle scattering comprises bound water
0.000 0.010 0.020 0.030 0.040 0.0500.1
1
10
100
Exp data Rg=13.54 (0.03) A Hydrated Theoretical curve Rg=13.51 A
calculated by crysol No hydration Rg=12.81 A
I(S) (a.u.)
S (A -1)
+==
22)()()()()( SBSESASASI bS
A(S): atomic scattering in vacuum
E(S): scattering from the excluded volume
B(S): scattering from the hydration shell
HydraVolShellb0.5151.702160673.160.00
Fitting parameters from crysol S: contrast from bulk water (0-0.09 e/3)
Thickness of hydration shell: 3.16-3.3
Scattering should be taken into account hydration shell especially for small globular proteins.
Crysol (Svergun)
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Reason 2: Low resolution shape determination is robust
Takahashi, Y., Nishikawa, Y., Fujisawa, T. Evaluation of three algorithms for ab initio determination of three-dimensional shape from one-dimensional solution scattering profiles, (2003) J Appl Cryst, 36, 549-552.
Independent of algorithms bead model converged to the average structure.
Ab initio Shape Determination using a Single Phase Dummy Atom Model
by Simulated Annealing (DAMMIN,Svergun)
by Genetic Algorithm (DALAI_GA, Chacon)
by Monte Calro style give 'n' take algorithm (SAXS3D, Walther)
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Ab initio determination from 2 dimensional data to 3 dimensional shape with constraints of non-negativity
N
2N
N2N
FFT-1 2 dimensional diffraction image
3 dimensional structure
Zero constraints
J.Miao et al. (2001) PNAS, 98, 6641
=(Maximum dimension of +blank)/(Maximum dimension of )
>5 phase can be retrieved
Over sampling can retrieve phase information
Barakat, R. & Newsam, G. (1984) J. Math. Phys. 25, 31903193.
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Reason 3: The fluctuating part also contributes the
SAXS models.
F- Actin
ropomyosin
ropomodulin
Low resolution model andcrystal structure of Tropo-modulin C- terminus
Model for the interaction between Tropomodulin and Thin Filament
0.00 0.01 0.02 0.03 0.04
1
10
100
Tmod(N39)
log(I(S
))
S
experimentalmodel Fit ting
Profile of solution scattering
Low resolutionstructure analysis
T.Fujisawa, A.Kostyukova, Y.Maeda, "The shapes and sizes of two domains of tropomodulin,the P-end-capping protein of actin-tropomyosin", FEBS Lett. 498, 67-71 (2001).
I.Krieger, A.Kostyukova, A.Yamashita, Y.Nitanai, Y.Maeda Crystal structure of the C-terminal half oftropomodulin and structural basis of actin filament pointed-end capping.Biophys J. 83,2716-25 (2002).
T. Uchida, T. Yamasaki, S. Eto, H. Sugawara , G. Kurisu,A. Nakagawa, M.Kusunoki, and T. Hatakeyama, Crystal Structure of the Hemolytic Lectin CEL-III Isolated from the Marine Invertebrate Cucumaria echinata JBC in press (2004)
T.Fujisawa, H.Kuwahara, Y.Hiromasa, T.Niidome, H.Aoyagi, T.Hatakeyama, Small-angle X-ray Scattering study on CEL-III, a hemolytic lectin from Holothuroidea Cucumaria echinata, and its oligomerinduced by the binding of specific carbohydrate, FEBS Lett., 414, 79-83 (1997)
CEL-III
SAXS successfully determined protein shape prior to protein crystallography.
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High resolution protein structures from NMR/PX and SAXS
Example of rigid body refinement
CooA Akiyama, S. et al. (2004) J. Mol. Biol., 341, 651-668.
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CO + H2O CO2 + H2CooS, CooH, CooF
CooACO
CRP
CooACOCOCO
CooACO
CooACooA
CO
CRP CRPCRP
cAMPcAMP
DNA
RNAP RNAPCooACO
CooACO
CooACooA
CO
RNAPCRPCRPCRP
cAMP
DNA
RNAP
Transcription ofCO-Oxidizing Proteins
Transcription
Effector-Induced Conformational Changes
Specific Binding to Target DNA
He et al. (1999, 2000)
R. rubrum synthesizes an enzyme system to generate energy from CO oxidation.
CooA, A Transcriptional Activator Belonging to CAP FamilyAkiyama, S. et al. (2004) J. Mol. Biol., 341, 651-668.
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CooA
- CO
- cAMP + cAMP + cAMP & DNA
+ CO + CO & DNA
?
? ?
A B
C
A: McKay et al. (1981) C : Lanzilotta et al. (2000)B : Schultz et al. (1981)
CRP
Known Crystal Structures of CAP Family
Exact activation mechanisms remained unknown ..
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Effector-Free (Linear) + Effectors & DNA
Lanzilotta et al. (2000), Chan et al. (2000)
Global Repositioning of the DNA-Binding Domains
Dramatic Switching from the Linear- to Bent-Conformations
Effector-Bound (Bent)
Linear-Bent Hypothesis
CO-Dependent Hinge-Bending
Proposed Regulation Mechanisms of CooA
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cAMcI
Kc
w22
1),0(
+=
CO-Bound CooACO-Free CooA
- 5.48 0.1357.6 0.23051 4525.8 0.6- 0.39 0.2556.0 0.5 3009 4225.3 0.5
A2 (10-4 ml mol g-2)MW (kDa)I(0,0) (a.u.)Rg (0) ()
CO-Bound CooA
CO-Free CooA
CO-Bound CooA
CO-Free CooA
Negative Values in A2 Attractive Interparticle Interactions
Drastic Changes in A2 CO-Dependent Conformational Change
Interference-Free SAXS Parameters (at Infinite Dilution)
Concentration Dependence of Rg and I(0)
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GNOM by Svergun et al. (1992)drrS
rSrPSI
=0 2
)2sin()(4)(
CO-Bound CooACO-Free CooA
Experimental P(r)s Simulated P(r)s
The CO-dependent conformational change of CooA is not so drastic as suggested in Linear-Bent Hypothesis.
Examinations of Linear-Bent Hypothesis
Similarity of Molecular Shapes between CO-Free and CO-Bound CooA
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= 45.7 = 34.1
Neither the crystal structure nor homodimer model was consistent
with the experimental SAXS profile of CO-free CooA.
Two Linear Subunits (Model)Original Crystal Structure
ExperimentSimulation
ExperimentSimulation
CO-free CooA does not adopt the linear-conformation in solutions.
Simulation of the Scattering from CO-Free CooA
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Exploring Conformational Space by Sampling the Dihedral Angles
of the Hinge-Region (Phe132, His133 and Asp134)
The heterogeneous positioning of the DNA-binding domains
suggests a structural flexibility of the hinge-region.
Heme Domain > DNA-Binding Domain
Amino Acid Sequence of the Hinge-Region
Building Solution Structures of CooA
The problem of backbone connectivity after refinementLacking some sequence in high-resolution structure
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MOLMOL
CRYSOL
CRYMOL
Svergun et al. (1995)
Koradi et al. (1996)
Ramachandran Plot(CO-free CooA)
Modeling
Results
Calculation of Scattering Curves
Visualization
743 of conformations were evaluated under the assumption of two-fold symmetry.
3 Dihedral Anglesto be Sampled
Evaluation
Rigid-Body Refinements of CooA Structure
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CO-Bound CooA( = 3.0)
CO-Free CooA( = 2.3)
Bent-Conformation !!
CO-Free CooA
CO-Bound CooA
= [i {Iexp(Si) Imodel(Si)}2 / (Si)2N]-2Best-Fit Structure
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Effector-Free (Linear)
Lanzilotta et al. (2000), Chan et al. (2000)
Effector-Bound (Bent)
Linear-Bent Hypothesis
Global Repositioning of the DNA-Binding Domains
X
Z
Y
+ CO
X
Y
Z
+ CO~ 8 deg.
CO-Free CooACO-Bound CooA
Positional Changes in DNA-binding Sites (Arg177, Gln178 and Ser181)
The C-terminus of the DNA-binding domains is rich in Asp content and retains an extensive acidic nature.
Significant Decrease in A2 value
Recognition of Target DNA or RNAP ?
Recognition of Target DNA ?
Our Proposal for the Regulation Mechanism of CooA
Akiyama et al. J Mol Biol. (2004) 341, 651-68.
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High hydrostatic pressure on protein solutions and SAXS
Search for the relation ship between hydrodynamic parameters and thermodynamic parameters
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High pressure axis as a tool for studying enzymes
Shift of Keq Shift of k Fluctuation
m yosin S1F-actin F-actin
AM -AD P Pi AM
m yosin S1
Force generation
=volume change
Reaction could be controlled by hydrostatic pressure
Developing SAXS system in order to correlate shape change with macroscopic physico-chemical values.
Applying pressure induces Ion-pair formation
H2O H+ + OH- 21.3 ml/molHydrophobic hydration
(CH4)hexane (CH4)water 22.7 ml/molProtein dissociation
LDH (M4 4M) 500 ml/molApo to holo transition (LDH)
LDH(apoholo) 390 ml/mol
Little effect on hydrogen bonding..
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Recent HP NMR studies reveals the fraction of high energy conformers
Akasaka, Biochemistry (2003)
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Example of preliminary high-pressure SAXS measurementLactate dehydrogenase desocciation (Fujisawa,Kato,Inoko,Biochemistry,1999)
Fluorescence study suggested monomer at 200MPa while SAXS determined dimer configuration.
Dissociation by high pressure did not follow volume minimum pathway.
0.1 200
Green mesh: SAXS model
Red line:
PX structure
The use of SVD method for SAXS HP data revealed intermediate of dissociation.
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Concluding remarks SAXS sees time and spatial averaged shape of protein
complex, which inevitably comprises bound waters. The shift of equilibrium by rapid mixing experiments or
pressure perturbations is effective for detecting minor conformers.
Rigid body refinement of multi-domain protein by SAXS can play more and more important roles: SAXS selected the structure model proposed by PX.
In the SAXS workshop SAXS in the 21 st century Dr. MHJ Koch pointed that
Small-angle scatteringoffers a bridge between low resolution methods including hydrodynamic and thermodynamic methods and high resolution or theoretical models.
If you want to collaborate with us, please mail me first.
E-mail: [email protected]