theabdus salaminternational centre for theoretical physics

strada costiera, 11 - 34014 trieste italy - tel. +39 040 2240111 fax +39 040 224163 - sci_info@ictp.trieste.it - www.ictp.trieste.it

united nationseducational, scientific

and culturalorganization

international atomicenergy agency

SCHOOL ON SYNCHROTRON RADIATION AND APPLICATIONSIn memory of J.C. Fuggle & L. Fonda

19 April - 21 May 2004

Miramare - Trieste, Italy

1561/32____________________________________________________________

SAXS studies of proteins in solution

A. Craievich

SAXS studies of SAXS studies of proteins in solutionproteins in solution

LNLS SAXS beamline

G. Kellermann, F. Vicentin, E. Tamura, M. Rocha, H. Tolentino, A. Barbosa, A. F. Craievich e I. L. C. Torriani, J. Appl. Cryst. (1997). 30, 880-883

M o n o c r o m a d o r D ip o lo ( F o n te )

D e t e to r ( F o c o )

P o r ta - a m o s t ra s

p = 1 2 .5 m

q = 3 .5 m

B a n c o ó t ic o 2 θ Dipole (White X-ray source)

12.5 m

Monochromator Optical bench 2θ

Sample holder

Detector

3.5 m

εsample

p. s. detectorbeamstopper

( ) ελπε

λπ 22/sin4

≅=q

The shape of the proteins in The shape of the proteins in solution. Foldingsolution. Folding--unfolding process. unfolding process. The envelope functionThe envelope function

Solution of the phase problemSolution of the phase problem

Dilute and monodisperse solutions

Ideality (high dilution) and monodispesity

I(q)= N I1(q)

Small-angle scattering by a macroscopically isotropic material

qrqre rqi sin. =−

rr

drrq

rqrrVIqI e ..sin)(4)(

0

2γπ∫∞

=

dqrq

rqqIqVI

re .

.sin)(48

1)(0

23 ∫

∞= π

πγ

2)().(.)(1)0( rrdrrV V

rrrr ρρργ ∆=∆∆= ∫

QVI e

381)0(

πγ = dqqIqQ )(4

0

2∫∞

= π

Small-angle scattering of a dilute system of isolated nano-objects. General equationsThe reduced correlation function for a single isolated object

∑ ∑= =

⎥⎦

⎤⎢⎣

⎡==

N

i

N

iqI

NNqIqI

1 111 )(1)()( rr )()( 1 qINqI r

=

( )( )[ ]22110 )()( ρργγ −= VVrr( )rVSr 110 41)( −=γ

102 ).(.4 Vdrrr

V=∫ γπ

( ) ∫−=max

00

21

2211 .

.sin)(4)(D

e drrq

rqrrVIqI γπρρ

( ) 21

221)0( VNII e ρρ −=

QIV )0(8 3

1 π=

Asymptotic trend of the scattering intensity at small q. Guinier law Dilute and monodispersed system (identical nano-objects)

( ) ∫−=max

00

21

221

sin)(4)(D

e rdqr

qrrrVNIqI rγπρρ

( ) ( ) ...61sin 22 +−= rqqrqr( ) ∫ −−=max

0

22

02

12

21 )]6

1).((4)(D

e drrqrrVNIqI γπρρ

( ) ( ) ⎥⎦

⎤⎢⎣

⎡−−=

⎥⎥⎦

⎤

⎢⎢⎣

⎡−−= ∫ 2

22

12

210

02

1

22

12

21 61)(41

61)(

max

ge

D

e RqVNIdrrrV

qVNIqI ρργπρρ

∫=max

00

2

1

2 )(41 D

g drrrV

R γπ 22/1

21 rrdrV

RVg =⎥⎦

⎤⎢⎣⎡= ∫

r

( ) 321

221

22

.)(qR

e

g

eVNIqI−

−= ρρ

2/12

).(

.).(

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

=∫∫

V

Vg rdr

rdrrR rr

rr

ρ

ρ

RRg 53= ( ) ( ) 12/8/ 22 HDRg +=

Guinier law

I(q)

Ln I versus q2 (Guinier plot)

[Slope]=α

( ) 321

221

22

.)(qR

e

g

eVNIqI−

−= ρρq 0

Rg=(3.α)1/2

SAXS by an arbitrary two electron density modelThe integral of the scattering intensity in reciprocal spaceAsymptotic behavior of scattering curves at high q. Porod’s law

( ) )()( 02

2121 rr γρρϕϕγ −= ( ) drrq

rqrrVIqI e .

.sin)(4)( 00

222121 γπρρϕϕ ∫

∞−=

( )dq

qrrqqIq

VIr

Vqe

∫−=

.sin)(48

1)( 22

212130 π

ρρϕϕπγ...

41)(

210 +−= rVSr

ϕϕγ

dqqIqQ )(40

2∫∞

= π

( )22121

38 ρρϕϕπ −= eVIQ( )

4

221 .2

)(q

SIqI e ρρπ −

=

For dilute and monodisperse systems

( )2213

.1 8.. ρρπ −= VNIQ e

Porod’ s law (q ∞)

QIq

VS q ∞→=

][4

42

1

1 π

∫∞

=0

22

2

.sin

)(2

)( dqqr

qrqIqrrp

πdr

qrqrrpqI ∫

∞

=0

1sin)(4)( π

dmax

p(r)r

I(q)

Because of the noise of the experiental SAXS curve and the limited q range of SAXS measurements,the mathematical problem for deriving p(r) from I(q)is “ill-defined”. It can be solved using different programs such as GNOM (Svergun)

Structure parameters and function than can be directly derived from SAXS curves of proteins in solution

• Rg radius of gyration

• V1 : volume

• S1 : external surface

• p(r) : distance distribution function

• dmax maximum diameter Detailed shape ???

Practical solution of the phase problem in SAXS studies

1) Guessing an initial shape. From the knowledge of Dmax, an initial spherical shape with R=dmax/2 is proposed.

2) Calculation of the scattering intensity I(q) for the initial (homogeneous) spherical protein.

3) Comparison with the experimental curve. Calculation of the Discrepancy parameter Chi.

4) A number of modifications of the shape leading to the minimum value of Chi.

3D shape function

Experiment

I(q)

I(q)

Proteins in solutionProteins in solution

•• RestaurationRestauration of structural models of structural models abab initioinitio using using only results of smallonly results of small--angle scattering experimentsangle scattering experiments

•• Characterization of proteins in solution using SAXS Characterization of proteins in solution using SAXS and (high resolution) crystallographic data obtained and (high resolution) crystallographic data obtained by single crystal XRDby single crystal XRD

•• Example of application: Example of application: Phosphoenolpyruvate carboxykinase (PEPCK)

Ab initio program DAMMINUsing simulated annealing, finds a compact dummy atoms configuration X that fits the scattering data by minimizing

where χ is the discrepancy between the experimental and calculated curves, P(X) is the penalty to ensure compactness and connectivity, α>0 its weight.

)()],(),([)( exp2 XPXsIsIXf αχ +=

compactcompact

looseloose

disconnecteddisconnected

Local and global search

• Local search always goes to a better point and can thus be trapped in a local minimum

• To avoid local minima, global search must be able go to a worse pointLocal

Global

Some examples of Some examples of

application of SAXS to theapplication of SAXS to thestudy of proteinsstudy of proteins

Low resolution structure obtained from SAXS results by using Dammin

q(Å-1)

0.0 0.1 0.2 0.3 0.4 0.5

Inte

nsity

0.001

0.01

0.1

1

q2 (A-2)

0.0 2.5x10-3 5.0x10-3

ln (I

)

e-1

e0

e1

Solution scattering curves of Pfk-2 without and with ligands. In absence of ligands (black curve), with saturating Fru-6-P (blue curve) and in presence of excess of MgATP (red curve). Inset shows Guinier plot giving values shown in table I.

r(Å )

0 2 5 50 7 5 10 0

p(r)

0

2

4

6

Distance distribution function for Pfk-2 without and with ligands. Curves were calculated using GNOM program from SAXS data of Pfk-2 in absence of ligands (black curve),Pfk-2 in presence of excess Fru-6-P (blue curve) andexcess of MgATP (red curve).

Rotation

Translation

X

α/β dom ain ro ta tion (deg rees)

-15 0 1 5 30

Dis

crep

ancy

χ

1 .0

1 .4

1 .8

2 .2

2 .6

1 .0

1 .4

1 .8

2 .2

2 .6

3 .0

3 23 4

3 63 8

0

1 02 0

3 0

Dis

crep

ancy

χ

C O M d is ta n c e , Å

Dimer rotation, deg

Modelling quarternary packing in tetramer (with Mg-ATP).

(A). Schematic diagram showing X simmetry axis (black arrow) along which, rotations and translations were made.

(B). Chi value of the better adjust of rotation and COM distancewith SAXS data for every degree of a/b domain openness. Curves for tetramer-I (solid line) and tetramer-II (dotted line).

(C). Plot showing Chi value for every combination of rotation and distance modelled for 7 deg domain openness dimer.

References

-“Structural insights into the beta-mannosidase from T-reesei obtained by synchrotron small-angle X-ray solution scattering enhanced by X-ray crystallography”. R. Aparicio, H. Fischer, D.J. Scott, K.H.G. Verschueren, A.A. Kulminskaya, E.V. Eneiskaya, K.N. Neustroev, A.F. Craievich, A.M. Golubev and I. Polikarpov. Biochemistry-US 41 (30): 9370-5 (2002).

-“Crystal structure of the dimeric phosphoenolpyruvate carboxykinase (PEPCK) from trypanosoma cruzi at 2 A resolution”. S. Trapani, J. Linss , S. Goldenberg, H. Fischer, A.F. Craievich and G. Oliva. Journal of Molecular Biology 313, (5) 1059-72 (2001).

-“Domain motions and quaternary packing of phosphofructokinase-2 from Escherichia coli studied by small angle X-ray scattering and homology modeling”. R. Cabrera, H. Fischer, S. Trapani, A.F. Craievich, R.C. Garrat, V. Guixe and J. Babul. Journal of Biological Chemistry. 278, 12913-9 (2003).

--“Low resolution structures of the retinoid X receptor DNA-binding and ligand-binding domains revealed by synchrotron X-ray solution scattering”. H. Fischer, S.M.G. Dias, M.A.M. Santos, A.C. Alves, N. Zanchin, A. F. Craievich, J. W. Apriletti, J. D. Baxter, P. Webb, F.A.R. Neves, R.C.J. Ribeiro, and I. Polikarpov. Journal of Biological Chemistry. 278, 16030-8 (2003).

-“Free human mitochondrial GrpE is a symmetric dimer in solution”. J. C. Borges, H. Fischer, A.F. Craievich, L.D. Hansen, C. H. Ramos. Journal of Biological Chemistry. 278, 35337-44 (2003).

The Brazilian synchrotron light The Brazilian synchrotron light laboratory laboratory -- LNLS) LNLS) -- CampinasCampinas

www.lnls.brwww.lnls.br

LNLSLNLSLaboratório Nacional de Laboratório Nacional de Luz SíncrotronLuz Síncrotron

Brazilian Synchrotron Light Brazilian Synchrotron Light Laboratory Laboratory

1.37 GeV electron storage ring

120 MeV linear accelerator (injector)

(underground)

Beamlines

Construction and commisioning period: 10 anos

June 1987: Starting

December 1989: 50 MeV LINAC operation

Agust 1995: Starting the installationof the beamlines

July 1997: Opening to the externalusers

Electron storage ringElectron storage ringMarch 1996

1.E+09

1.E+10

1.E+11

1.E+12

1.E+13

1.E+14

0.01 0.1 1 10 100

Energy (keV)

Phot

on f

lux

(pho

tons

/s/m

rad/

0.1%

bw)

LNLS 1.37 1.67 160 10

DCI 1.85 1.61 400 200

NSLS VUV 0.80 1.39 800 5

SUPER ACO 0.80 1.57 300 15

CAMD 1.30 1.48 150 8

SRRC 1.50 1.43 240 9

ALS 1.90 1.58 400 3

SUPER ACONSLS VUV

ALSDCI

LNLSSRRC

CAMD

E(GeV) B(T) I(mA) τ (h)

Photon flux

Specified

Jul-97 Dec/98

Energy 1.15 1.37 1.37 GeV

Current 100 75 170 mA

Lifetime (@100 mA) 7 2.2 16 hours

Achieved

Operation parametersOperation parameters

APPLICATIONS:APPLICATIONS:Materials ScienceMaterials Science

ChemistryChemistryBiologyBiology

PhysicsPhysicsMicrofabricationMicrofabrication

......Environmental scienceEnvironmental science

SAXS beamline

Special instrumentation

for the beamlinesWAXS/SAXS WAXS/SAXS chamberchamber

Reactor for Reactor for inin--situ xsitu x--ray ray studiesstudies

Capillary Capillary microfocusingmicrofocusing