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Introduction to biological Introduction to biological small angle scattering small angle scattering
HERCULES Specialized Course 16 (September 15th 2014)
Frank Gabel (IBS/ILL)Frank Gabel (IBS/ILL)
Length-scales and tools in structural biology
crystallography
smallsmall angle angle scatteringscattering in solutionin solution
NMRSAS bridges the gap between atomic
resolution (NMR and crystallography)
and the light microscope
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Objects that can be studied by SAS
SAS cannot determine de novo the positions of individual atoms/residues
in biomacromolecules on the Angstrom scale
Atomic resolution:
NMR and/or
Crystallography
Biological small angle scattering is growing exponentially…
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Scattering basics: Huygens-Fresnel principle
'k
2
' kk
Incoming X-ray/neutron wave
Screen (far away)
r2θ
k
2
)( jrQi
jjebQI
Many scattering centers, FOURIER transform:
sin4
' kkQ
1629-1695
1788-1827
Reciprocal relationship between real spaceand the diffraction pattern
Many scattering centers, Fourier transform:
2
)( jrQi
jjebQI
ji
jij
jii rrQ
rrQbbQI
sin)(
,
Orientational averaging
Debye equation (1915)
Glatter and Kratky (1982)Small Angle X-ray scattering (Academic Press)
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Why “small” angle scattering?
Putnam et al. (2007) Quart. Rev. Biophys. 40(3), 191-285.
SAS sample conditions and information obtained
Global properties:Radius of gyration, molecular weight
structural details
Neutrons, X-rays
solutions ~ mg/mlvolume ~ 10-200 μLmass > 0.1 mg
SAS sensitivity:
-Macromolecules 1 kDa … ~ MDa
-Linear dimension 10 Å … ~ 1000 Å
Information obtained:1) Oligomeric state of macromolecules
2) Shape or conformation (globular, stick etc…)
3) Interaction of different macromolecules
4) Variation of points (1)-(3) as a function of pH, salt, ligands, T, p, ...
5) Contrast variation: visualisation of individual sub-units in situ
+Shape
Interaction
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Concept of scattering densityand contrast
In vacuo:
2
)( jrQi
jjebQI
22
)( dVedVeV
bQI rQi
proteinrQi
j
j j
2
)( dVeNQI rQiprotein
In solution: 2
)( dVeQI rQisolventprotein
constV
bprotein
j
j Continuum approximation: -How are scattering densities calculated?
-Under which conditions is the approximation valid?
Ideal solutions: no inter-particle effects, only form-factors
Model-free parameters
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Guinier approximation and radius of gyration
Feigin and Svergun (1987) Structure analysis by Small-Angle X-ray and Neutron Scattering (Plenum Press)
22
3
1exp)0()( QRIQI g
22
3
1)0(ln)(ln QRIQI g
3.1...1QRg
(from expansion of Debye equation)
i
iig rmM
R 22 1
For a given molecular weight, a spheresphere has the smallest Rg, i.e. it is the most compact object
Radius of gyration:
“See-saw”
Contrast x volume
Calibrating molecular weight (Mr) with water by SANS
2310
)0(
)0(
4
1
rSi
AincSr MVb
tCNI
I
Tf
TM
23
1
410
)0(
)0(rSiAr
S
inc
MVbtNCMT
Tf
I
I
Jacrot, B., and Zaccai, G. (1981) Determination of molecular weight by neutron scattering. Biopolymers 20, 2413-2426.
C: concentration in mg/mlf: correction factor for anisotropicity of incoherent scatteringT: water transmissionTs: sample transmissiont: pathlength in cmI(0): coherent scattering in forward directionIinc(0): incoherent scattering from water
+ or
Often important for the study of oligomeric/association states and flexible systems
Scattering curves look similar!
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Relative measurementof molecular weight (Mr) by SAS
2
)( jrQi
jjebQI
2
)0( j
jbNI
2
)0( j
jbI
rCMI )0(rA MVCNN / 2
2
rj
j Mb
Relative calibration to a known standard (BSA, lysozyme) in same buffer conditions:
standardstandard
protprotstandardprot MC
MCII )0()0(
Concentration in mg/ml
Characteristic anddistance distribution function
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Characteristic anddistance distribution function p(r)
Feigin and Svergun (1987) Structure analysis by Small-Angle X-ray and Neutron Scattering (Plenum Press)
V
rVrr c )(
)0(
)()(0
)()( 2 rrrp
drQr
QrrpQI
D)sin(
)(4)(max
0
21
21
212
,
1
sin)()()(
21
dVdVrrQ
rrQrrQI
VV
Debye equation in integral form
SAS provides information on distanceson different length-scales
Putnam et al. (2007) Quart. Rev. Biophys. 40(3), 191-285.
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Examples of I(Q) and p(r)
Svergun and Koch (2003) Small-angle scattering studies of biologicalmacromolecules in solution. Rep. Prog. Phys. 66, 1735-1782.
2
3)(
)cos()sin(3)(
QR
QRQRQRQI
Putnam et al. (2007) Quart. Rev. Biophys. 40(3), 191-285.
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Putnam et al. (2007) Quart. Rev. Biophys. 40(3), 191-285.
Some words about resolution…
Inter-subunit distancewith a precision of about 1-2 Å!
d
Inter-subunit position/orientationsless well-defined!
Nominal definition:max
2
QR
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Modelling
Sophisticated data analysis and modelling
- Ab initio structure analysis
- Rigid body modellingMatch with
experimental scattering curve
- Validation of structural modelsCompatible with
experimental scattering curve
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Different possibilities of modelling
Monodispersity is paramount (AUC, gels, SEC-MALLS)!
Putnam et al. (2007) Quart. Rev. Biophys. 40(3), 191-285.
( Jacques and Trewhella (2010) Prot. Sci. 19, 642-657 )
Important check: molecular weight!
Flexible systems
Putnam et al. (2007) Quart. Rev. Biophys. 40(3), 191-285.
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Oligomeric equilibria
Again: important check is molecular weight!
Putnam et al. (2007) Quart. Rev. Biophys. 40(3), 191-285.
Neutrons vs. X-rays
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SAXS vs. SANS:scattering processes
Atoms have a form-factor for X-rays but nuclei don’t for neutrons…
λ ~ 5 Å (= 5*10-10 m)
~ 5 fm (= 5*10-15 m)
- X-ray scattering length is proportional to number of electrons
- Neutron scattering length depends irregularly on atom and isotope
Feigin and Svergun (1987) Structure analysis by Small-Angle X-ray and Neutron Scattering (Plenum Press)
Practical calculation of scattering densities
Example glycine in H2O:
ρ = [2*0.67+0.94+0.58+3*(-0.37)]10-12cm/66.4Å3
= 2.68*10-14 cm/Å3 = 2.68*1010 cm-2
Jacrot, B. (1976) The study of biological structures by neutron scattering from solution. Rep. Prog. Phys. 39, 911-953.
j
jprotein V
bb
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SAXS vs. SANS:some practical aspects
high (D2O)low~150µl @ 1-10 mg/mlSANS
weakhigh~15 µl @ 1-10 mg/mlSAXS
contrastfluxsample amount
SAXS, ID02, 1s exposure time SANS, D22, 20min exposure time (H2O) (D2O)
parasitic scattering at low Q
flat background
SANS vs. SAXS instruments
D22 (ILL):SANS Quartz cuvette (SANS)
Exposure times:~ 10-20 minutes (D22)
~ 1-10 seconds (ID02)
~ 10-100 seconds (BM29)
Including sample change:~ 10-20 minutes (D22)
~ 5 minutes (ID02)
~ 2-3 minutes (BM29)
BM29 (ESRF):SAXS
Capillary (SAXS)
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Incoming neutron wave
Understanding contrast : destructive interference in SANS
Detector
Destructive interference!Signal gets weaker!
+ solvent !!!
Natural Contrast in SANS
2
)( dVeQI rQisolventprotein
???
Homogeneous macromolecules can be matched, i.e. made invisible!!!
Not so easy with SAXS…
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Contrast in SAXS
lipoproteins
proteins
RNA
DNA
Feigin and Svergun (1987) Structure analysis by Small-Angle X-ray and Neutron Scattering (Plenum Press)
An analogon in optics: refractive index
water glycerol
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Artificial contrast using deuteration
Careful at high D2O levels in the solvent: favours oligomerisation/aggregation!
42% D2O100% D2O
Protein deuteration not completebut only ~75%!
Talk byMichael Härtlein…
Protein-protein complexes
Jacques and Trewhella (2010) Prot. Sci. 19, 642-657
Petoukhov and Svergun (2006) Eur. Biophys. J. 35, 567-576
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Practical guidelines
Putnam et al. (2007)
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Putnam et al. (2007)
Putnam et al. (2007)
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Putnam et al. (2007)
Combination of SAXS/SANS
and with other techniques:
recent highlights
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Petoukhov and Svergun (2007) Curr. Opin. Struct. Biol. 17(5), 562-571.
F. Gabel (May 6th 2013) EMBO Practical Course
Talks byPau Bernado, Bernd Simon, Christiane Schaffitzel, Olwyn Byron…
Example 1: small protein‐RNA complex
Hennig J, Militti C, Popowicz G, Wang I, Sonntag M, Geerlof A, Gabel F, Gebauer F, and Sattler M (2014). Structural basis for the assembly of the SXL-UNR translation regulatory complex. Nature [in press]
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Translational repression inD. melanogaster dosage compensation
• msl‐2 translation is repressed by binding of UNR
and SXL to the msl‐2 3’ UTR in female flies
• Minimal complex: 18‐mer RNA motif (F‐site) in
msl‐2 mRNA is recognized by UNR cold shock
domain 1 (CSD1) and SXL RRM1‐RRM2
Beckmann et al Cell (2005); Duncan et al Genes Dev (2006); Abaza et al Genes Dev (2006); Patalano et al Development (2009)
3’
Poly(U)
SXL
5’ 43S
ms l - 2
Po
ly(U
)SXL
UNR
Combined NMR/SAXS/SANS structural study
SAXS/SANS‐specific information
SAXS: overall envelope
RNA sandwichedbetween proteins!?
BM29/ESRF (LC: Louiza Zerrad)
SANS:Internal information
Program MONSA:Svergun (1999) Biophys. J. 76, 2879‐2886.
SXL
CSD1RNA
D22/ILL (LC: Anne Martel)
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EXAMPLE 1:A large protein/RNA complex
Lapinaite A, Simon B, Skjaerven L, Rakwalska-Bange M, Gabel F, Carlomagno T. (2013) The structure of the box C/D enzyme reveals regulation of RNA methylation. Nature 502(7472), 519-523
RNA modifications:snoRNPs, snoRNAs and box C/D
snoRNP = “Small nucleolar Ribonucleo‐Protein” Only in archaea and eukaryotes,not in bacteria
snoRNP = sRNP in archaea
“Guide RNA”(> 100 in humans!)
Two different architectures have been proposed:
CrystallographyElectron microscopy
≈ 390 kDa
•Where is the sRNA situated?
•What is mechanism of methylation?
•Why two assymmetric methylation sites?
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Information contained in SANS data: positions of FIB proteins within the complex
dFIB 42% D2O SANS data:FIB positions in the complex!
Important restraints for the atomic models!
Program MONSA:Svergun (1999) Biophys. J. 76, 2879‐2886.
BM29/ESRF (LC: Petra Pernot)
D22/ILL (LC: Anne Martel)
Family of refined structures
FIB
L7
RNA
NOP
Apo(no rRNA substrate)
Holo(with rRNA substrate)
Large conformational change upon substrate binding!
Network of NMR and SAS restraints
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Concluding remarks
A few practical comments…- use SAXS for homogeneous systems composed of a single body
- SAXS is better suited for high-throughput
- SANS good for complex systems (protein-DNA/RNA, membrane proteins…)
- SANS has no radiation damage
- neutrons only possible at large facilities (no “home sources” for the moment!)
- request for beam-time is generally via an electronic proposal system
- deadlines are usually twice a year, beamtime is attributed some months later
- BAG (“Block allocation group”) systems allow more flexible access
- for continuation proposals, reports need to be submitted regularly
- experiments need to be prepared with great careexperiments need to be prepared with great care (i.e. isotopic effect of D2O)!!!!
- “local contacts”, often beamline responsibles, assist during experiments
- access (for non-industrial use) is in general free
- no maintenance, user friendly (software etc…)
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Literature
Basics (scattering, quantum mechanics):- The Feynman lectures on Physics, Volume 3: Quantum mechanics (Addison Wesley, 2006)
- Cohen-Tannoudji et al.: Mécanique Quantique, Vol. 2. Chapter on diffusion. (Hermann, 1997)
Books on small angle (neutron) scattering:- Svergun: Structure Analysis by Small-Angle X-Ray and Neutron Scattering (Plenum, 1987)
- Glatter and Kratky: Small Angle X-ray Scattering (Academic Press, 1982)
- Guinier/Fournet: Small angle scattering of X-rays (John Wiley & Sons, 1955)
- Serdyuk, Zaccai, Zaccai: Methods in molecular biophysics (Cambridge University Press, 2007)
Reviews on SAXS/SANS:- Jacrot, B. (1976) The Study of biological structures by neutron scattering from solution. Rep. Prog. Phys. 39,
911-953.
- Putnam et al. (2007) X-ray solution scattering (SAXS) combined with crystallography and computation:
defining accurate macromolecular structures, conformations and assemblies in solution. Q. Rev. Biophys.
40(3):191-285.