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
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…
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)
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
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
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!
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
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.
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.
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
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
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.
Oligomeric equilibria
Again: important check is molecular weight!
Putnam et al. (2007) Quart. Rev. Biophys. 40(3), 191-285.
Neutrons vs. X-rays
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
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)
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…
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
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
Practical guidelines
Putnam et al. (2007)
Putnam et al. (2007)
Putnam et al. (2007)
Putnam et al. (2007)
Combination of SAXS/SANS
and with other techniques:
recent highlights
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]
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)
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?
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
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…)
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.
