The Basics of Neutron Scattering The Basics of Neutron Scattering

Jill Trewhella, The University of SydneyJill Trewhella, The University of SydneyEMBO Global Exchange Lecture CourseEMBO Global Exchange Lecture Course

April 28, 2011April 28, 2011

Conceptual diagram of thesmall-angle scattering experiment

The conceptual experiment and theory is the same for X-rays and neutrons, the differences are the physics of the X-ray (electro-magnetic radiation) versus neutron (neutral particle) interactions with matter. Measurement is of the coherent (in phase) scattering from the sample. Incoherent scattering gives and constant background.[Note: q = 2s]

Fundamentals

Neutrons have zero charge and negligible electric dipole and therefore interact with matter via nuclear forces

Nuclear forces are very short range (a few fermis, where 1 fermi = 10-15 m) and the sizes of nuclei are typically 100,000 smaller than the distances between them.

Neutrons can therefore travel long distances in material without being scattered or absorbed, i.e. they are and highly penetrating (to depths of 0.1-0.01 m).

Example: attenuation of low energy neutrons by Al is ~1%/mm compared to >99%/mm for x-rays

Neutrons are particles that have properties of plane waves

They have amplitude and phase

They can be scattered elastically or inelastically

Inelastic scattering changes both direction and magnitude of the neutron wave vector

Elastic scattering changes direction but not the magnitude of the wave vector

It is the elastic, coherent scattering of neutrons that gives rise to small-angle scattering

Coherent scattering is “in phase” and thus can contribute to small-angle scattering. Incoherent scattering is isotropic and in a small-angle scattering experiment and thus contributes to the background signal and degrades signal to noise.

Coherent scattering essentially describes the scattering of a single neutron from all the nuclei in a sample

Incoherent scattering involves correlations between the position of an atom at time 0 and the same atom at time t

The neutron scattering power of an atom is given as b in units of length

Circular wave scattered by nucleus at the origin is:

(-b/r)eikr

b is the scattering length of the nucleus and measures the strength of the neutron-nucleus interaction.

The scattering cross section

= 4πb2

..as if b were the radius of the nucleus as seen by the neutron.

For some nuclei, b depends upon the energy of the incident neutrons because compound nuclei with energies close to those of excited nuclear states are formed during the scattering process.

This resonance phenomenon gives rise to imaginary components of b. The real part of b gives rise to scattering, the imaginary part to absorption.

b has to be determined experimentally for each nucleus and cannot be calculated reliably from fundamental constants.

Neutron scattering lengths for isotopes of the same element can have very different neutron scattering properties

As nuclei are point scattering centers, neutron scattering lengths show no angular dependence

At very short wavelengths and low q, the X-ray coherent scattering cross-section of an atom with Z electrons is 4π(Zr0)2, where r0 = e2/mec2 = 0.28 x 10-12 cm.

Atom Nucleus (10-12 cm) fx-ray for = 0 in electrons

(and in units of 10-12 cm)a

Hydrogen 1H -0.3742 1.000 (0.28)

Deuterium 2H 0.6671 1.000 (0.28)

Carbon 12C 0.6651 6.000 (1.69)

Nitrogen 14N 0.940 7.000 (1.97)

Oxygen 16O 0.5804 8.000 (2.25)

Phosphorous 31P 0.517 15.000 (4.23)

Sulfur Mostly 32S 0.2847 16.000 (4.5)

b values for nuclei typically found in bio-molecules

Scattering Length DensityScattering Length Density

The average scattering length density The average scattering length density for a for a particle is simply the sum of the scattering particle is simply the sum of the scattering lengths (lengths (bb)/unit volume)/unit volume

The basic scattering equationThe basic scattering equation

For an ensemble of identical, randomly oriented For an ensemble of identical, randomly oriented particles, the intensity of coherently, elastically particles, the intensity of coherently, elastically scattered radiation is dependant only upon the scattered radiation is dependant only upon the magnitude of magnitude of qq, and can be expressed as:, and can be expressed as:

N N = molecules/unit volume= molecules/unit volumeV V = molecular volume= molecular volume = contrast, the scattering density difference = contrast, the scattering density difference

between the scattering particle and solventbetween the scattering particle and solventP(q)P(q) = form factor = form factor particle shape particle shape S(q)S(q) = structure factor = structure factor inter-particle correlation distances inter-particle correlation distances

)()()( 2 qSqPVNqI

s )(r

Inter-particle distance correlations Inter-particle distance correlations between charged moleculesbetween charged molecules

D

D

D

D

D

-

-

--

-

D

-

D

-

D

….. gives a non-unity S(q) term that is concentration dependent

I(q) = | e-i(q•r) dr]|2

where =particle - solvent

Average scattering length density is simply the of the sum of the scattering lengths (b)/unit volume

Because H (1H) and D (2H) have different signs, by manipulating the H/D ratio in a molecule and/or its solvent one can vary the contrast

Zero contrast = no small-angle scattering

_ _ _

_

_

_

For a single particle in solution (i.e. S(q) = 1):

P(r) is calculated P(r) is calculated as the inverse as the inverse Fourier transform Fourier transform of of II((qq) and yields ) and yields the probable the probable frequency of inter-frequency of inter-atomic distances atomic distances within the within the scattering particle.scattering particle.

Svergun, D. I. & Koch, M. H. J. (2003). Small-angle scattering studies of biological macromolecules in solution. Rep. Prog. Phys. 66, 1735-1782

PP((rr) provides a real space interpretation of ) provides a real space interpretation of II((qq))

Contrast (or solvent) MatchingContrast (or solvent) Matching

Solvent matching (i.e. matching Solvent matching (i.e. matching the scattering density of a the scattering density of a molecule with the solvent) molecule with the solvent) facilitates study of on component facilitates study of on component by rendering another “invisible.”by rendering another “invisible.”

Optical Contrast Matching ExampleOptical Contrast Matching Example

Using small-angle Using small-angle X-ray scattering X-ray scattering we showed that we showed that the N-terminal the N-terminal domains of domains of cardiac myosin cardiac myosin binding protein C binding protein C (C0C2) form an (C0C2) form an extended extended modular structure modular structure with a defined with a defined disposition of the disposition of the modulesmodules

Jeffries, Whitten et al. (2008)J. Mol. Biol. 377, 1186-1199

Mixing mono-disperse solutions of C0C2 with G actin results in a dramatic increase in scattering signal due to the formation of a large, rod-shaped assembly

Neutron contrast variation on actin thin-filaments with deuterated the C002 stabilizes F-actin filaments

Solvent matching for the C0C2-actin assemblySolvent matching for the C0C2-actin assembly

Whitten, Jeffries, Harris, Trewhella (2008) Proc Natl Acad Sci USA 105, 18360-18365

Contrast Variation To determine the shapes and dispositions

of labeled and unlabelled components in a complex

For a complex of H- and D-proteins:

H(D) (= H(D)protein - solvent ) is the mean contrast of the H and D components, IDP, IHP their scattering profiles, and Icrs is the cross term that contains information about their relative positions. The contrast terms can be calculated from the chemical composition, so one can solve for ID, IH, and IHD.

)()()()( 22 QIQIQIQI HDDHDDHH _ _

II11II1212

II22

Contrast Variation Experiment

Measure I(q) for a complex of labelled and unlabelled proteins in different concentrations of D2O

References:

Whitten, A. E., Cai, S., and Trewhella, J. “MULCh: ModULes for the Analysis of Small-angle Neutron Contrast Variation Data from Biomolecular Complexes,” J. Appl. Cryst. 41, 222-226, 2008.

Whitten, A. E. and Trewhella, J. “Small-Angle Scattering and Neutron Contrast Variation for Studying Bio-molecular Complexes,” Microfluids, Nanotechnologies, and Physical Chemistry (Science) in Separation, Detection, and Analysis of Biomolecules, Methods in Molecular Biology Series, James W. Lee Ed., Human Press, USA, Volume 544, pp307-23, 2009.

Email: jill.trewhella@sydney.edu.au for reprint requests.

Use Rg values for Sturhman analysis

222

mobs RR

RH = 25.40 ÅRD = 25.3 ÅD = 27.0 Å

Stuhrmann showed that the observed Rg for a scattering object with internal density fluctuations can be expressed as a quadratice function of the contrast :

where Rm is the Rg at infinite contrast, the second moment of the internal density fluctuations within the scattering object,

and is a measure of the displacement of the scattering length distribution with contrast

2

mobs RR

231 ))(( r

rrr dV F

rrrr

321 )( dV F

_

zero implies a homogeneous scattering particle

positive implies the higher scattering density is on average more toward the outside of the particle

negative places the higher scattering density is on average more toward the inside of the particle

For a two component system in which the difference in scattering density between the two components is large enough, the Stuhhmann relationship can provide information on the Rg values for the individual components and their separation using the following relationships:

2222 DffRfRfR DHDDHHm

22222 )()( DffRRff HDDHDHDH

2222)( Dff DHDH

Each experimental scattering profile of a contrast series can be approximated by:

H(D) (= H(D)protein - solvent ) is the mean contrast of the H and D components, IDP, IHP their scattering profiles, and Icrs is the cross term that contains information about their relative positions. The contrast terms can be calculated from the chemical composition, so one can solve for ID, IH, and IHD.

)()()()( 22 QIQIQIQI HDDHDDHH _ _

Solve the resulting Solve the resulting simultaneous equations for simultaneous equations for

I(q)I(q)HH, , I(q)I(q)DD, , I(q)I(q)HDHD

II11II1212

II22

)()()()( 22 QIQIQIQI HDDHDDHH

Use ab initio shape determination or rigid body refinement of the components against the scattering data if you have coordinates

The sensor histidine kinase KinA - response regulator spo0A in Bacillus subtilis

Sda

KinA

Spo0A

KipAKipI

Failure to initiate DNA replicationDNA damage

Change in N2 source

Sporulation

Spo0F

Spo0B

Environmental signal

Our molecular actors

KipIPyrococcus horikoshi

SdaKinABased on H853 Thermotoga maritima

Pro410

His405

Trp

CA

DHp

to sensor domains

Sda2 Rg = 15.4 Å, dmax = 55 ÅKinA2 Rg = 29.6 Å, dmax = 95 ÅKinA2-Sda2 Rg = 29.1 Å, dmax = 80 Å

HK853 based KinA model predicts the KinA X-ray scattering data

KinA2 contracts upon binding 2 Sda molecules

Sda is a trimer in solution!

Jacques, et al “Crystal Structure of the Sporulation Histidine Kinase Inhibitor Sda from Bacillus subtilis – Implications for the Solution State of Sda,” Acta D65, 574-581, 2009.

KipI dimerizes via its N-terminal domains and 2 KipI molecules bind KinA2

KipI2 Rg = 31.3 Å, dmax = 100 ÅKinA2 Rg = 29.6 Å, dmax = 80 ÅKinA2-2KipI Rg = 33.4 Å, dmax = 100 Å

Neutron contrast variation: KinA2:2DSda

222

mobs RR

in complexuncomplexedRg KinA2 25.40 Å 29.6 ÅRg 2Sda 25.3 Å 15.4 Å

Separation of centres of mass = 27.0 ÅI(Q) A-1

MONSA: 3D shape restoration for KinA2:2DSda

)()()()( 12212221

21 QIQIQIQI

Component analysis

Rigid-body refinement KinA2-2Sda components

Whitten, Jacques, Langely et al., Whitten, Jacques, Langely et al., J. Mol.Biol. 368J. Mol.Biol. 368, 407, 2007, 407, 2007

9090

I(Q) A-1

I(Q) A-1

KinA2-2KipI

Jacques, Langely, Jeffries et al (2008) Jacques, Langely, Jeffries et al (2008) J. Mol.Biol. J. Mol.Biol. 384, 422-435384, 422-435

9090

The KinA helix containing Pro410 sits in the KipI-

C domain hydrophobic groove

A possible role for cis-trans isomerization of Pro410 in tightening the helical bundle to transmit the KipI signal to the catalytic domains?

Or is the KipI cyclophilin-like domain simply a

proline binder?

Sda and KipI bind at the base of the KinA dimerization phosphotransfer (DHp) domainSda binding does not appear to provide for steric mechanism of inhibitionKipI interacts with that region of the DHp domain that includes the conserved Pro410

Sda and KipI induce the same contraction of KinA upon binding (4 Å in Rg, 15 Å in Dmax)

DHp helical bundle is a critical conduit for signaling

Contrast variation in biomolecules can take advantage of the fortuitous fact that the major bio-molecular constituents of have mean scattering length densities that are distinct and lie between the values for pure D2O and pure H2O

Mea

n sc

atte

ring

leng

th d

ensi

ty (

1010

cm

2 )

DNA and protein have inherent differences in scattering density that can be used in neutron contrast variation experiments

Under some circumstances, SAXS data can yield Under some circumstances, SAXS data can yield reliable polynucleotide-protein structure interpretationreliable polynucleotide-protein structure interpretation

3CproRNA complex; Claridge et al. (2009) J. Struct. Biol. 166, 251-262

3CproRNA

3Cpro