saxs studies of proteins in solutionindico.ictp.it/event/a0343/session/119/contribution/76/... ·...
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theabdus salaminternational centre for theoretical physics
strada costiera, 11 - 34014 trieste italy - tel. +39 040 2240111 fax +39 040 224163 - [email protected] - 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
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
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
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
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
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
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
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ChemistryChemistryBiologyBiology
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......Environmental scienceEnvironmental science
Special instrumentation
for the beamlinesWAXS/SAXS WAXS/SAXS chamberchamber
Reactor for Reactor for inin--situ xsitu x--ray ray studiesstudies
Capillary Capillary microfocusingmicrofocusing