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.