Interpretation of SAXS Data

Dr. Tetsuro FujisawaBiometal Science Laboratory

RIKEN SPring-8 Center

RIKEN Harima Institute/Spring-8

PX/SAXS

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) (0.4×0.8 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

source

s0

s0

s1

s1

r

r.s0

r.s12θ

Ａ

O

Principle of small-angle scattering

211 2 12

12211 2

)2sin()()()( dVrdVrSr

SrrrSiVr Vr∫ ∫ ∆∆= π

πρρ

solvent

particle

ρ∆0.43ρ =

0 0.335ρ =

el. A-3ρ

Contrast of electron density is the source of scattering from protein complex.

∆ρ(r) = ρ(r) - ρ0

In solution

∑∑= =

=N

i

N

j ij

ijji Sr

SrSfSfSi

1 11 2

)2sin()()()(

ππ

In vacuum

λθ /sin2=S

fibermembrane

solution

SAXS

2θ

A reliable instrument on a synchrotron source with a low noise detector is

INDISPENSIBLE

Sample requirements HP and time-resolved measurements

Sample volume50μL

0.1-10 mg/mlfew kDa to hundreds MdaMono-disperse sample

SPring-8/BL-45XU SAXS

λ=0.9Å, 13.8keV 2θ

Sample

II-CCD detector

3600mm

X-ray

S=2sinθ

/λ

I(S)

Identical condition for sample and buffer scattering data collection

Synchrotron source

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

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/Å）

Protein structure and SAXS

？

Why PX users started to use SAXS?

Gauss function

Hydrodynamic values

Rg & I(0)

Shapes

Time

∑∑

∑∑

=

==

nnn

nnnn

obs

nnn

nnnobs

FN

RgFNRg

FNINI

)0(

)0(

)0()0()0(

2

22

2

2

Protein solution dynamics seen by SAXS

Beer’s 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 π

At small S all scattering curves are Gauss function.

Guinier’s law

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

[ ] [ ][ ][ ] [ ][ ] min⇒−

=SCFSCY

[ ] [ ] [ ][ ][ ] [ ][ ][ ] 1

1

ˆ

ˆ−

−

=

=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.

Cytochrome C refolding

Cyt-C

150 µ sec

Akiyama et al. Proc.Natl.Acad.Sci.USA., 99, 1329-1334(2002).

Prof. Satoshi Takahashi’s group (Osaka Univ.)

High resolution protein structures from NMR/PX and SAXS

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

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)

ΩΩ+−==

22)()()()()( SBSESASASI bS δρρ

A(S): atomic scattering in vacuum

E(S): scattering from the excluded volume

B(S): scattering from the hydration shell

HydraχVolShellδρb0.5151.702160673.160.00

Fitting parameters from crysol δρS: contrast from bulk water (0-0.09 e/Å3)

Thickness of hydration shell: 3.16-3.3 Å

Scattering should be taken into account hydration shell especially for small globular proteins.

Crysol (Svergun)

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)

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

σ=(Maximum dimension of ρ+blank)/(Maximum dimension of ρ)

σ>5 phase can be retrieved

Over sampling can retrieve phase information

Barakat, R. & Newsam, G. (1984) J. Math. Phys. 25, 3190–3193.

Reason 3: The fluctuating part also contributes the

SAXS models.

F- Actin

ｔropomyosin

ｔropomodulin

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.

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.

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.

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 …..

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

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) (Å)

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)

GNOM by Svergun et al. (1992)drrS

rSrPSI ∫∞

=0 2

)2sin()(4)(πππ

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

χ = 45.7χ = 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

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

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

CO-Bound CooA(χ = 3.0)

CO-Free CooA(χ = 2.3)

Bent-Conformation !!

CO-Free CooA

CO-Bound CooA

χ = [Σi {Iexp(Si) – Imodel(Si)}2 / σ(Si)2N]-2Best-Fit Structure

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.

High hydrostatic pressure on protein solutions and SAXS

Search for the relation ship between hydrodynamic parameters and thermodynamic parameters

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状態 AM 状態

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(apo⇒holo) 390 ml/mol

Little effect on hydrogen bonding..

Recent HP NMR studies reveals the fraction of high energy conformers

Akasaka, Biochemistry (2003)

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.

0.1ＭＰａ 200ＭＰａ

Green mesh: SAXS model

Red line:

PX structure

The use of SVD method for SAXS HP data revealed intermediate of dissociation.

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: fujisawa@spring8.or.jp