Scattering of X-rays (basics) - embl-hamburg.de · J.J. Thomson. 1856-1940. Cambridge, UK. EMBO Practical Course on Solution Scatteringfrom Biological Macromolecules Hamburg, November

EMBO Practical Course on Solution Scattering from Biological MacromoleculesHamburg, November 19th -26th 2018

Scattering of X-raysP. Vachette

I2BC (CNRS-Université Paris-Sud-CEA), Orsay, France


SAXS measuring cellSample

SAXS measurement


SAXS measurement

Scattering experiment

Detector

?

1

10

100

1000

0 0.1 0.2 0.3 0.4 0.5

I(q)

q = 4π(sinθ)/λ Å-1

SAXS pattern

?X-ray beam


1

10

100

1000

0 0.1 0.2 0.3 0.4 0.5

I(q)


SAXS pattern

? Structural parameters:

MM, Rg, Dmax, V

SAXS measurement


Solution X-ray Scattering from Biological Macromolecules J. Pérez, Hercules Course, April 2016

Structural information about macromolecules in solution

DAMMINDAMMIFDENFERT

CRYSOLFOXS

SASREFBUNCHCORAL

DADIMODO

EOM

MES

Existence of flexible regionsSelection within an Ensemble

of Random Conformations

Nothing known (except the curve)

Shape determination

Known or hypothetical all-atom models

Model validation / elimination

Rigid body modeling of the complex

Structures of subunits available


General Outline

X-ray scattering by particles in solution Contrast Spherical averaging, Monodispersity, ideality

Data analysis Guinier Analysis Porod law and Kratky plot Real-space : Distance distribution function P(r)

Reminder of elementary tools and notions X-ray Scattering by an electron X-ray Scattering by assemblies of electrons Fourier transform Convolution Product


REMINDER OF ELEMENTARY TOOLS AND NOTIONS


2θ : scattering angle,cos2θ close to 1 at small-angles

I0 intensity (energy/unit area /s) of the incident beam.

Elastic scattering by a single electron

212

0 2 0.282 10 cmermc

−= =r0 classical radius of the electron.

O 2θr

-elastic : interaction without exchange of energy. The scattered photon has the same energy (or wavelength) than the incident photon.

22

0 02

1 cos (2 ) 1(2 )2

I r Ir

θθ +=

The elastically scattered intensity by an electron placed at the origin isgiven by the Thomson formula below:

J.J. Thomson

1856-1940Cambridge, UK


22 2 26 20 0

1 cos (2 )/ 7.9510 cm2d d r rθσ −+Ω= ≈ =

differential scattering cross-section of the electron

the scattering length of the electron be

2 /eb d dσ= Ω


The scattering factor f of an object is defined as the ratio between the amplitude of the scattering of the object and that of one electron in identical conditions.

The scattering factor of a single electron fe ≡ 1. We therefore eliminate dσ/dΩ from all expressions.

Scattering factor


Scattering by an electron at a position r

Path difference = r.u1-r.u0 = r.(u1 - u0) corresponding to a phase difference φ = 2πr.(u1 - u0)/λ for X-rays of wavelength λ.

O

source

u0

u0

u1

u1

r

r.u0

r.u1

2θ

M


0 12πλ

= =k k

4 sinq π ϑλ

= =q

k1

k0

M

q

length 2π/λ

length 2π/λ

2θ

scattered

1 0 = −q k k

q is the momentum transfer

The scattered amplitude by the electron at r iswhere A(q) is the scattered amplitude by an electron at the originPhase difference φ=q.r

.( ) iA q e r q

momentum transferwavevector k


Scattering vector

2sins ϑλ

=

! 4 sins π ϑλ

= D. Svergun and coll.

Phase difference φ = 2πr.s


scattering by assemblies of electrons the distance ∆ between scatterers is fixed, e.g. atoms in a molecule :

coherent scattering one adds up amplitudes

N

ii=1F( ) = Σ f iie r qq

∆ is not fixed, e.g. two atoms in two distant molecules in solution :incoherent scattering one adds up intensities.

Use of a continuous electron density ρ(r):

F( ) ( ) iV

e dVρ= ∫r

rqrq r I( ) F( ).F ( )∗=q q qand


Fourier Transform

ρ(r) F. T.

F(q) is the Fourier transform of the electron density ρ(r) describing the scattering object.

Properties of the Fourier Transform

- 1 – linearityFT (λ1ρ1 + λ2ρ2) = λ1 FT(ρ1) + λ2 FT(ρ2)

F(0) ( )V

dVρ= ∫r

rr- 2 – value at the origin

F( ) ( ) iV

e dVρ= ∫r

rqrq r


Convolution product

A( ) B( ) A( )B( )V

dV∗ = −∫u

ur r u r u

A convolution is an integral that expresses the amount of overlap of one function B as it is shifted over another function A.

r r

B(r)

A(r)

A(r)*B(r)

rArB

1


r

A(r)*B(r)

rA + rB-(rA + rB)

Convolution product

u

B(r-u)

A(u)

rArB-(rA + rB)


r

A(r)*B(r)

rA + rB-(rA + rB)

Convolution product

u

B(r-u)

A(u)

rArB


r

A(r)*B(r)

rA + rB-(rA + rB)

Convolution product

u

B(r-u)

A(u)

rArB


r

A(r)*B(r)

rA + rB-(rA + rB)

- (rA - rB)

Convolution product

u

B(r-u)

A(u)

rArB


r

A(r)*B(r)

rA + rB-(rA + rB)

- (rA - rB)

Convolution product

u

B(r-u)

A(u)

rArB


Convolution product

r

A(r)*B(r)

rA + rB

rA - rB

-(rA + rB)

- (rA - rB)

r

B(r)

A(r)

rArB


The convolution operation

24

f(x) g(x) g(-x) f(x)

EMBO Practical Course on Solution Scattering from Biological MacromoleculesHamburg, November 19th -26th 2018Courtesy of P. DUMAS, IGBMC (Strasbourg, France)

25

f(u) g(x-u)h(x) = [f∗ g](x)

25EMBO Practical Course on Solution Scattering from Biological Macromolecules

Hamburg, November 19th -26th 2018Courtesy of P. DUMAS, IGBMC (Strasbourg, France)

The convolution operation

Fourier transformof a convolution product

FT(A B) FT(A) FT(B)∗ = ⋅

FT(A B) FT(A) FT(B)⋅ = ∗


Autocorrelation function( ) ( ) ( ) ( ) ( )

VdVγ ρ ρ ρ ρ= ∗ − = +∫

uur r r r u u

ρ(r)=ρ (uniform density)


ghostr

particle

=> γ(r)= ρ2Vov(r) and γ(0)= ρ2V

particle ∩ ghost


spherical average ( ) ( )rγ γ= r

0 ( ) ( ) (0)r rγ γ γ=characteristic function

γ0(r) : probability of finding a point withinthe particle at a distance r from a givenpoint

r

γ0(r)

1

Dmax

Autocorrelation function

Distance (pair) distribution function

2 2 20( ) ( ) ( )p r r Vr r rρ γ γ= =

- γ0(r) : probability of finding within the particle a point j at a distance r from a given point i- number of el. vol. i ∝ V - number of el. vol. j ∝ r2

number of pairs (i,j) separated by the distance r ∝ r2Vγ0(r)

p(r) is the distribution of distances between all pairs of points within the particle weighted by the respective electron densities

r ji

r

p(r)

Dmax


PARTICLES IN SOLUTION


In solution, what matters is the contrast of electron density between the particle and the solvent ∆ρ(r) = ρp (r) - ρ0 that may be small for biological samples.

A particle is described by the associated electron density distribution ρp (r). Particles in solution

ρ∆0.43ρ =

00.335ρ =

el. Å-3

ρ

particle

solvent


X-ray scattering power of a protein solution

A 1 mg/ml solution of a globular protein 15kDa molecular mass

such as lysozyme or myoglobin will scatter in the order of

from H.B. StuhrmannSynchrotron Radiation ResearchH. Winick, S. Doniach Eds. (1980)

1 photon in 106 incident photons


Solution X-ray scattering: a pair of measurements

To obtain scattering from the particles, buffer scattering must be subtracted, which also permits to eliminate contribution from parasitic background (slits, sample holder, etc) which should be reduced to a minimum.

Isample(q) Ibuffer (q) Iparticle(q)


particle in solution

Particle in solution => thermal motion => during the measurement, the particleadopts all orientations / X-ray beam. Therefore, only the spherical average of the scattered intensity is experimentally accessible.

1F ( ) ( ) iV

e dVρ= ∆∫r

rqrq r

scattering amplitude and intensity

and

1 1 1 1( ) ( ) F ( ).F ( )i q i ∗= =q q qtime

particles I( ) I( ) F( ).F ( )q ∗= =q q q

𝐈𝐈𝟏𝟏 𝐪𝐪 = 𝐅𝐅1 q .𝐅𝐅𝟏𝟏 *(q)


The sample is isotropic and the vectorial (3D) scattering intensity

distribution i(q) reduces to a scalar (1D) intensity distribution i(q).

This entails a loss of information which constitutes the most severe

limitation of the method.

particle in solution

1

10

100

1000

0 0.1 0.2 0.3 0.4 0.5

I(q)


continuous, 1-dimensional SAXS profile


1( ) [ ( )]. [ ( )] [ ( ) * ( )]i q FT FT FTρ ρ ρ ρ= ∆ ∆ − = ∆ ∆ −r r r r

1( ) [ ( )] ( ) di

Vi q FT e Vγ γ= = ∫

r

rqrr r

Let us use the properties of the Fourier transformand of the convolution product

1 1 1 1( ) ( ) F ( ).F ( )i q i ∗= =q q q


1( ) [ ( )] ( ) i

Vi q FT e dVγ γ= = ∫

r

rqrr r

1 0

sin( )( ) 4 ( )

qri q p r dr

qrπ

∞

= ∫

sin(qr)< exp(i ) > =

qrqrspherical average:

2d = r d d dV sin rθ θ ϕr

p(r)= 𝑟𝑟2𝛾𝛾 𝑟𝑟 = 𝑟𝑟2

2𝜋𝜋2 ∫0∞ 𝑞𝑞2𝐼𝐼(𝑞𝑞) 𝑠𝑠𝑠𝑠𝑠𝑠(𝑞𝑞𝑟𝑟)

𝑞𝑞𝑟𝑟𝑑𝑑𝑞𝑞

and



Solution of particles

Yes: identical particlesNo: size and shape polydispersity

- 1 – monodispersity

- 2 - ideality

Yes: no intermolecular interactions no correlations between particle positions.No: existence of interactions between particles

correlations between particle positions.


Ideal and monodispersed solution

Ideality I( ) i ( )j jj

q n q= ∑

Monodispersity j∀1i ( ) i ( )j q q=

measured contains structural information

Ideality and monodispersity Iexp(q) = N i1 (q)


Ideality

Monodispersity

experimental

One must check that bothassumptions are valid for the

sample under study.

Iexp(q)

molecule

i1 (q)

!

Ideality : reached by working in buffers with screened interactions or at high dilution In practice : measurements at decreasing concentrations and checks whether

the scattering pattern is independent of concentration.

Checking the validity of both assumptions for the sampleunder study is crucial for correct data interpretation

Size Monodispersity must be checked independently Purification protocol ; SEC, DLS, AUC, MALS, etc.


Non ideality: interactions

0

500

1000

1500

2000

2500

3000

3500

4000

0 0.02 0.04 0.06 0.08 0.1 0.12

92.5 mg/ml31.5 mg/ml13.3 mg/ml 6.6 mg/ml 3.3 mg/ml

I(q,c

) / c

q = 4π (sinθ)/λ A-1

0

1 104

2 104

3 104

4 104

5 104

0 0.02 0.04 0.06 0.08 0.1 0.12

10°C15°C20°C 25°C30°C

I(q)

q = 4π (sinθ)/λ A-1


repulsion attraction

SE-HPLC on line with the SAXS instrument.


G. David & J. Pérez, J. Appl. Cryst. (2009). 42, 892–900

A major step towards the obtention of a monodispersed

and ideal solution

SE-HPLC on line with the SAXS instrument.

Basic law of reciprocity in scattering

- large dimensions r small scattering angles q

-small dimensions r large scattering angles q

argument qr (phase)


Rotavirus VLP : diameter = 700 Å, 44 MDa MW

Lysozyme Dmax=45 Å

14.4 kDa MW

101

102

103

104

105

106

107

108

0 0.125 0.25 0.375

lysozyme

rotavirus VLP

I(q)/

c

-1q=4πsinθ/λ (Å )


DATA ANALYSIS


• Guinier Analysis

• Porod law and Kratky plot

• Real-space : Distance distribution function P(r)

Data Analysis





Data Analysis


Guinier law

idealmonodispersed

A. Guinier

The scattering intensity of a particle can be described by a Gaussian curve in the vicinity of the origin.The validity domain actually depends on the shape of the particle and isaround q < 1.2 / Rg for a globular shape.

Radius of gyrationExtrapolated intensity at origin

1911-2000Orsay, France

I(q) = I(0) exp(− q2Rg2

3 ).

ln[I(s)] vs q2 : linear variation.Linear regression on experimental data yields slope and y-intercept.

Guinier law, in log form :

ln I(q) = ln I(0) − q2Rg2

3


Radius of gyration

Radius of gyration :2

2( )

( )V

g

V

r dVR

dV

ρ

ρ

∆=

∆

∫∫

r

r

r

r

r

r

Rg2 is the mean square distance to the center of mass weighted

by the contrast of electron density.

35gR R=Rg is an index of non sphericity.

For a given volume the smallest Rg is that of a sphere.

If ∆ρ(r) ≈ constant then Rg is a geometrical quantity.

idealmonodispersed


0.3

0.4

0.5

0.6

0.7

0.8

0 0.001 0.002 0.003 0.004I(q

)

q2 (Å-2)

Validity range :

0 < Rgq<1 for a solid sphere0 < Rgq<1.2 rule of thumb for a

globular protein

Swing – SAXS Instrument, resp. J. PérezSOLEIL (Saclay, France)

[ ] [ ]3

≅ −2g 2R

ln I(q) ln I(0) q

Guinier analysisRg (shape) I(0) mol mass /

oligomerisation state)

Data analysis: Guinier plot

idealmonodispersed


Validity range :

0 < Rgq<1 for a solid sphere0 < Rgq<1.2 rule of thumb for a

globular protein

0.3

0.4

0.5

0.6

0.7

0.8

0 0.001 0.002 0.003 0.004I(q

)

q2 (Å-2)

qRg=1.2

Swing – SAXS Instrument, resp. J. PérezSOLEIL (Saclay, France)

idealmonodispersed

[ ] [ ]3

≅ −2g 2R

ln I(q) ln I(0) q

Guinier analysisRg (shape) I(0) mol mass /

oligomerisation state)

Data analysis: Guinier plot


Intensity at the origin

If : the concentration c (w/v),the partial specific volume , the intensity on an absolute scale,i.e. the number of incident photons are known,

Then the molecular mass of the particle can be determinedfrom the value of the intensity at the origin.

In actual fact one only gets an estimate of the MM.Its determination is a useful check of ideality and monodispersity.

(0)∝

I Mc

idealmonodispersed


νp

idealmonodispersed

Guinier lawThe scattering intensity of a particle i1(q) can be described by a Gaussian curve in the vicinity of the origin.

measured contains structural information

Iexp(q) = N i1 (q)


Irreversible aggregation

0.01

0.1

1

10

100

0 0.001 0.002 0.003 0.004

1.6 mg/ml3.4 mg/ml7 mg/ml

I(q)

q2 (Å-2)

Useless data: the whole curve is affected

I(0): > 150 fold the expected value for the given MM

Evaluation of the solution properties

0.001

0.01

0.1

1

10

100

0 0.05 0.1 0.15 0.2 0.25 0.3

I(q)

q (Å-1)

Approx. expected curve


weak association → possible improvementattraction centrifugation, buffer change

Nanostar –PR65 protein

50

60

708090

100

200

0 0.0005 0.001 0.0015 0.002

I(q)

q2 (Å-2)

50

60

708090

100

200

0 0.0005 0.001 0.0015 0.002

I(q)

q2 (Å-2)

qRg=1.2qRg=1.2

Rg ~ 36 Å


Rg ~ 38 Å – too high!!!EMBO Practical Course on Solution Scattering from Biological Macromolecules

Hamburg, November 19th -26th 2018

Guinier plot

No aggregation, no interactions.

Swing, SOLEIL

0.01

0.1

0 0.001 0.002 0.003 0.004

I(q)

q2 (Å-2)

qRg=1.3

same Rg at all threeconcentrations

N. Leulliot et al., JBC (2009), 284, 11992-99.


idealmonodispersed


Guinier plot

c4Rg = 49.3 Å


RNA moleculeL. Ponchon, C. Mérigoux et al.


Guinier plot

c3Rg = 56.6 Åc4Rg = 49.3 Å




Guinier plot

c2Rg = 59.9 Å

c3Rg = 56.6 Åc4Rg = 49.3 Å




Guinier plot

c1Rg = 60.8 Åc2Rg = 59.9 Å

c3Rg = 56.6 Åc4Rg = 49.3 Å




Guinier plot

A linear Guinier plot is a requirement, but it is NOT a sufficient condition ensuring ideality (nor monodispersity) of the sample.






Data Analysis



The asymptotic regime : Porod law

Hypothesis : the particule has a uniform electron density and a sharp interface withthe solvent.

Porod law has limited applications for proteins :- short distance density fluctuations- uncertainties of I(q) at large q (weak signal)

S is the area of the solute / solvent interface

- introduction of a corrective constant factor B.

(+B)

!

idealmonodispersed

𝐢𝐢𝟏𝟏 *(q)=𝐢𝐢𝟏𝟏 (q)-B

ρp

ρ0

Porod showed that the asymptotic behaviour of the scattering intensity is given by :

Porod invariant

2 2

0(0) ( ) dV Vγ ρ ρ

∞= ∆ = ∆∫ rrBy definition :

p(r)= 𝑟𝑟2𝛾𝛾 𝑟𝑟 = 𝑟𝑟2

2𝜋𝜋2 ∫0∞ 𝑞𝑞2𝐼𝐼(𝑞𝑞) 𝑠𝑠𝑠𝑠𝑠𝑠(𝑞𝑞𝑟𝑟)

𝑞𝑞𝑟𝑟𝑑𝑑𝑞𝑞

For r=0 : 𝛾𝛾 0 = 12𝜋𝜋2 ∫0

∞ 𝑞𝑞2𝐼𝐼 𝑞𝑞 𝑑𝑑𝑞𝑞 = 12𝜋𝜋2

Q

Q is called the Porod invariant Q = 2𝜋𝜋2∆𝜌𝜌2V = ∫0∞𝑞𝑞2𝐼𝐼 𝑞𝑞 𝑑𝑑𝑞𝑞


Q depends on the mean square electron density contrast.


Porod invariant and volume

volume of a particle of uniform density.

Crude estimate of MM independant of the concentration M = V/1.5

*

*

Then, and since

Special case: the particule has a uniform electron density!


Molecular mass of the particleAnother procedure, also based on Q, has been developed to derive an estimate of V and M independant of the concentration

H Fischer, M de Oliveira Neto, HB Politano, AF Craievich, I Polikarpov, J. Appl. Cryst (2010), 43, 101-109

http://www.if.sc.usp.br/~saxs/

Empirical approach: estimate the truncation(+ fluctuations) error using 1148 calculatedSAXS patterns and V= Aqmax

V’qmax+Bqmax

Set of 21 experimental curves: averageerror of 5.3% on MM , all < 10%


Molecular mass of the particle Another procedure, also based on empirical observation of correlations

between integral quantities derived from the SAXS curve and the MM has been proposed by R. Rambo and J. Tainer; Vc QR

R. Rambo & J. Tainer, Nature (2013), 496, 477-82.

D. Franke et al., Biophys. J.(2018), 114, 2485-92.

A last procedure has also been put forward by D. Franke and coll.

N. Hajizadeh et al., Sc. Reports (2018), 8: 7204.

At that point, it was tempting to combine all those approaches in a statistically rigorous way : Recent work from the group of D. Svergun. Details hopefully provided in other talks.

Take home message: Compare the estimate from I(0)/C and those above independent from concentration.

Control with complementary technique such as SEC-MALS always welcome.


Folded particle : bell-shaped curve (asymptotic behaviour I(q)~q-4

Kratky Plot

Random polymer chain : plateau at large q-values (asymptotic behaviour in I(q)~ q-2 )

Extended polymer chain : increase at large q-values (asymptotic behaviour in I(q)~ q-1.x )

O. Kratky

q2 I(q) versus q

1902-1995Graz, Austria

0.1

1

10

100

0 0.05 0.1 0.15 0.2 0.25 0.3

I(q)

q A-1

0.01

0.1

1

0 0.05 0.1 0.15 0.2 0.25 0.3

q2 *I(q

)

q (A-1)

Folded

Partially folded

Unfolded


0

0.0005

0.001

0.0015

0.002

0.0025

0 0.1 0.2 0.3 0.4 0.5

G-ActinASNPASDGCDA2BCDA3

q2 I(

q)

q (Å-1)

Kratky Plots of folded proteins

Folded proteins display a bell shape. Can we go further?


0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 2 4 6 8 10

G-ActinRg=23.2 Angs, Mass=41.7 kDaASNPRg=26.0 Angs, Mass=71.4 kDaASDGRg=35.6 Angs, Mass=146.6 kDaCDA2Rg=39.1 Angs, Mass=98.9 kDaBCDA3Rg=51.7 Angs, Mass=144.4 kDa

(qR g)2

I(q)

/ I(0

)

qRg

1.75

1.1

For globular structures, DLKPs fold into the same maximum

The position of the maximum on the dimensionless bell shape tells whether the protein is globular.

Dimensionless Kratky Plots of folded proteinsIntroduced for biology in Durand et al. (2010), J. Struct. Biol. 169, 45-53.


Dimensionless Kratky Plots of (partially) unfolded proteinsReceveur-Bréchot V. and Durand D (2012), Curr. Protein Pept. Sci., 13:55-75.

The bell shape vanishes as folded domains disappear and flexibility increases.

The curve increases at large q as the structure extends.

globular

unfolded

0

0.5

1

1.5

2

2.5

3

3.5

0 2 4 6 8 10

PolXp47p67XPCIB5

(qR g)2 I(

q)/I(

0)

qRg

1.1

1.75




Data Analysis


p(r) is obtained by histogramming the distances between anypair of scattering elements within the particle.

Distance distribution function

idealmonodispersed

r ji

r

p(r)

Dmax


22

2 0

sin( )( ) I( )2r qrp r q q dq

qrπ∞

= ∫

In theory, the calculation of p(r) from I(q) is simple.Problem : I(q) - is only known over [qmin, qmax] : truncation

- is affected by experimental errors

⇒ Calculation of the Fourier transform of incomplete and noisy data,requires (hazardous) extrapolation to lower and higher angles.

idealmonodispersed



Calculation of p(r) Solution : Indirect Fourier Transform. First proposed by O. Glatter in 1977.Basic hypothesis : The particle has a finite size

p(r) is parameterized on [0, DMax] by a linearcombination of orthogonal basis functions:

1

( ) ( )ϕ=

= ∑M

n nn

p r c r

The equation above holds true for all experimental q-values.

The coefficients cn are found by least-squares methods.Ill-posed problem solved using regularization methods.

Minimize the functional Φα= χ2 + α.f(constraints)

0

sin( )I( ) 4 ( )MaxD qrq p r drqr

π= ∫Graz, Austria

𝐼𝐼𝑒𝑒𝑒𝑒𝑒𝑒(q) = 4π0

𝐷𝐷𝑀𝑀𝑀𝑀𝑀𝑀𝑠𝑠=1

𝑀𝑀

𝑐𝑐𝑠𝑠ϕ𝑠𝑠(𝑟𝑟)sin(𝑞𝑞𝑟𝑟)𝑞𝑞𝑟𝑟

𝑑𝑑𝑟𝑟


Calculation of p(r)

D. Svergun (1988, 1992) : program "GNOM""perceptual criteria" : smoothness, stability,absence of systematic deviations, goodness-of-fit D. Svergun


The radius of gyration and the intensity at the origin can be derived from p(r)using the following expressions :

and

This alternative estimate of Rg makes use of the whole scattering curve, andis much less sensitive to interactions or to the presence of a small fractionof oligomers.Comparison of both estimates : useful cross-check

max

max

22 0

0

( )

2 ( )

D

g D

r p r drR

p r dr= ∫

∫

max

0(0) 4 ( )

DI p r drπ= ∫



0

0.0005

0.001

0.0015

0.002

0 20 40 60 80 100 120 140

p(r)

/I(0

)

r (Å)

DMax

Elongated particle p47 : component of NADPH oxidase from neutrophile, a 46kDa protein

D. Durand et al., Biochemistry (2006), 45, 7185-93.



Bimodal distribution

Topoisomerase VI

70 Å

0

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

0.0007

0.0008

0 50 100 150 200 250P(

r) /

I(0)

r (Å)

M. Graille et al., Structure (2008), 16, 360-370.



Empty spherePhage T5 capsid


0 200 400 600 800

r (Å)P(

r)

Preux et al., J. Mol. Biol. (2013) 425, 1999–2014


Books on SAS- " The origins" (no recent edition) : Small Angle Scattering of X-rays

A. Guinier and A. Fournet, (1955), in English, ed. Wiley, NY

- Small-Angle X-ray Scattering:O. Glatter and O. Kratky (1982), Academic Press. pdf available on the Internet at

http://physchem.kfunigraz.ac.at/sm/Software.htm

- Structure Analysis by Small Angle X-ray and Neutron ScatteringL.A. Feigin and D.I. Svergun (1987), Plenum Press. pdf available on the Internet at

http://www.embl-hamburg.de/ExternalInfo/Research/Sax/reprints/feigin_svergun_1987.pdf

- Neutrons, X-Rays and Light, Scattering methods applied to soft condensed matter. P. Lindner and T. Zemb Eds, (2002) Elsevier, North-Holland.

-The Proceedings of the SAS Conferences held every three years are usually published in the Journal of Applied Crystallography. -The latest proceedings are in the J. Appl. Cryst., 49, (2016).


selected reviews

Small angle scattering: a view on the properties, structures and structural changes of biological macromolecules in solution.Michel H. J. Koch, Patrice Vachette and Dmitri I. SvergunQuarterly Review of Biophysics (2003), 36, 147-227.

X-ray solution scattering (SAXS) combined with crystallography and computation: defining accurate macromolecular structures, conformations and assemblies in solutionChristopher Putnam, Michal Hammel, Greg Hura and John TainerQuarterly Review of Biophysics (2007), 40, 191-285.

Structural characterization of proteins and complexes using small-angleX-ray solution scatteringHaydin D.T. Mertens and Dmitri I. SvergunJournal of Structural Biology (2010), 172, 128-141.


Robust, high-throughput solution structural analyses by small angle X-ray scattering (SAXS).Hura, G.L., Menon, A.L., Hammel, M., Rambo, R.P., Poole, F.L., 2nd, Tsutakawa, S.E., Jenney, F.E., Jr., Classen, S., Frankel, K.A., Hopkins, R.C., Yang, S.J., Scott, J.W., Dillard, B.D., Adams, M.W., and Tainer, J.A. Nat Methods (2009), 6, 606-612.

Small-angle scattering and neutron contrast variation for studying bio-molecular complexes. Whitten, A.E., and Trewhella, J. Methods Mol Biol (2009), 544, 307-323.

Bridging the solution divide: comprehensive structural analyses of dynamic RNA, DNA, and protein assemblies by small-angle X-ray scattering. Rambo, R.P., and Tainer, J.A. Curr Opin Struct Biol (2010), 20, 128-137.

Small-angle scattering for structural biology--expanding the frontier while avoiding the pitfalls. Jacques, D.A., and Trewhella, J. Protein Sci (2010), 19, 642-657.


Small and Wide Angle X-ray Scattering from Biological Macromoleculesand their Complexes in Solution.Doniach, S. & Lipfert, J., Comprehensive Biophysics, Vol 1. (2012).

Preparing monodisperse macromolecular samples for successful biological small-angle X-ray and neutron-scattering experiments.Jeffries, C. M., Graewert, M. A., Blanchet, C. E., Langley, D. B., Whitten, A. E. &Svergun, D. I. Nat. Protoc. (2016), 11, 2122-53.

Guidelines

2017 publication guidelines for structural modelling of small-angle scattering data from biomolecules in solution: an update. Trewhella J, Duff AP, Durand D, Gabel F, Guss JM, Hendrickson WA, Hura GL, Jacques DA, Kirby NM, Kwan AH, Pérez J, Pollack L, Ryan TM, Sali A, Schneidman-Duhovny D, SchwedeT, Svergun DI, Sugiyama M, Tainer JA, Vachette P, Westbrook J, Whitten AE.Acta D Struct Biol. (2017), 710-728.


Book on SAS

Dmitri Svergun

Michel Koch

Peter Timmins

Roland May


A survival kit for the travel you are embarking on

Guinier plot

0.3

0.4

0.5

0.6

0.7

0.8

0 0.001 0.002 0.003 0.004

I(q)

q2 (Å-2)

p(r)

0

0.0005

0.001

0.0015

0 20 40 60 80 100 120 140

p(r)

/I(0)

r (Å)

Kratky plot

0

0.5

1

1.5

2

2.5

3

3.5

0 2 4 6 8 10

PolXp47p67XPCIB5

(qR

g)2

I(q

)/I(

0)

qRg

1.1

1.75

monodispersity

ideality Iexp(q) = N i1 (q)


Remember

The method is simple but deceptively so:

analysis and modelling require a monodispersed and ideal solution.

it is critical to check the validity of these assumptions. Otherwise …

SAXSIN OUT


1

10

100

1000

0 0.1 0.2 0.3 0.4 0.5

I(q)


with good quality, validated data

you can apply to your system any of the modelingapproaches that you willdiscover during the course:


Solution X-ray Scattering from Biological Macromolecules J. Pérez, Hercules Course, April 2016

Structural information about macromolecules in solution

DAMMINDAMMIFDENFERT

CRYSOLFOXS

SASREFBUNCHCORAL

DADIMODO

EOM

MES

Existence of flexible regionsSelection within an Ensemble

of Random Conformations

Nothing known (except the curve)

Shape determination

Known or hypothetical all-atom models

Model validation / elimination

Rigid body modeling of the complex

Structures of subunits available



Documents

Scattering of X-rays (basics) - embl-hamburg.de · J.J. Thomson. 1856-1940. Cambridge, UK. EMBO Practical Course on Solution Scatteringfrom Biological Macromolecules Hamburg, November