Transcript Neutron Scattering: Basics

The Basics of Neutron Scattering
Jill Trewhella, The University of Sydney
EMBO Global Exchange Lecture Course
April 28, 2011
Conceptual diagram of the
small-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 = 2s]
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
Elastic scattering
changes direction
but not the
magnitude of the
wave vector
Inelastic scattering
changes both direction
and magnitude of the
neutron 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
b values for nuclei typically found in bio-molecules
(10-12 cm)
fx-ray for  = 0 in electrons
(and in units of 10-12 cm)a
1.000 (0.28)
Atom
Nucleus
Hydrogen
1H
-0.3742
Deuterium
2H
0.6671
1.000
Carbon
12C
0.6651
6.000 (1.69)
Nitrogen
Oxygen
14N
16O
0.940
0.5804
7.000 (1.97)
8.000 (2.25)
Phosphorous
31P
0.517
15.000 (4.23)
Sulfur
Mostly 32S
0.2847
16.000 (4.5)
(0.28)
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.
Scattering Length Density
average scattering length density  for a
particle is simply the sum of the scattering
lengths (b)/unit volume
 The
The basic scattering equation
For
an ensemble of identical, randomly oriented
particles, the intensity of coherently, elastically
scattered radiation is dependant only upon the
magnitude of q, and can be expressed as:
I (q)  N V  P(q)S (q)
2
N = molecules/unit volume
V = molecular volume
contrast, the scattering density difference
  (r)  s = between
the scattering particle and solvent
P(q) = form factor  particle shape
S(q) = structure factor  inter-particle correlation distances



Inter-particle distance correlations
between charged molecules
D
D
D
D
D
-
D
-
D
D
….. gives a non-unity S(q) term that is concentration dependent
For a single particle in solution (i.e. S(q) = 1):
_
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
P(r) provides a real space interpretation of I(q)

P(r) is calculated
as the inverse
Fourier transform
of I(q) and yields
the probable
frequency of interatomic distances
within the
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
Contrast (or solvent) Matching
 Solvent
matching (i.e. matching
the scattering density of a
molecule with the solvent)
facilitates study of on component
by rendering another “invisible.”
Optical Contrast Matching Example
Using small-angle
X-ray scattering
we showed that
the N-terminal
domains of
cardiac myosin
binding protein C
(C0C2) form an
extended
modular structure
with a defined
disposition of the
modules
Jeffries, Whitten et al. (2008)J. Mol. Biol. 377, 1186-1199
Mixing monodisperse 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 thinfilaments with deuterated the C002
stabilizes F-actin filaments
Solvent 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
I2
I1
I12
For a complex of H- and D-proteins:
I (Q)   I (Q)   I (Q)  H D I HD (Q)
2
H H
_
2
D D
_
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.
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: [email protected] for reprint requests.
Use Rg values for Sturhman analysis
2
obs
R


R 

  2
2
m
RH = 25.40 Å
RD = 25.3 Å
D
= 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 :
Robs


 Rm 

2
 
where Rm is the Rg at infinite contrast,  the second moment
of the internal density fluctuations within the scattering
object,
 V
1

r
2
F
3
(r) r d r
and  is a measure of the displacement of the scattering
length distribution with contrast
  (V
1

r
3
F
(r) r d r)
2
 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
 zero
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:
Rm2  f H RH2  f D RD2  f H f D D2
  ( H   D ) f H f D
R
2
H
  ( H   D ) f f D
2
2
H
2
D
2
 R  ( f  f )D
2
D
2
D
2
H
2

Each experimental scattering profile of a contrast series
can be approximated by:
I (Q)   I (Q)   I (Q)  H D I HD (Q)
2
H H
_
2
D D
_
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.
Solve the resulting
simultaneous equations for
I(q)H, I(q)D, I(q)HD
I2
I1
I12
I (Q)   I (Q)   I (Q)  H D I HD (Q)
2
H H
2
D D
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
Failure to initiate DNA replication
DNA damage
Environmental
signal
Sda
Change in
N2 source
KipA
KipI
KinA
Spo0F
Spo0B
Spo0A
Sporulation
Our molecular actors
KinA
Sda
Based on H853 Thermotoga maritima
to sensor domains
KipI
Pyrococcus horikoshi
CA
Pro410
His405
DHp
Trp
HK853 based KinA model predicts the KinA
KinA2 contracts upon binding 2 Sda molecules
X-ray scattering data
Sda2
Rg = 15.4 Å, dmax = 55 Å
KinA2
Rg = 29.6 Å, dmax = 95 Å
KinA2-Sda2 Rg = 29.1 Å, dmax = 80 Å
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 Å
KinA2
Rg = 29.6 Å, dmax = 80 Å
KinA2-2KipI Rg = 33.4 Å, dmax = 100 Å
Neutron contrast variation: KinA2:2DSda
2
obs
R


R 

  2
2
m
in complex
Rg KinA2 25.40 Å
Rg 2Sda 25.3 Å
I(Q) A-1
uncomplexed
29.6 Å
15.4 Å
Separation of centres of mass = 27.0 Å
MONSA: 3D shape restoration for KinA2:2DSda
Component analysis
I (Q)  12 I1 (Q)  22 I 2 (Q)  12 I12 (Q)
Rigid-body refinement
KinA2-2Sda components
90
Whitten, Jacques, Langely et al., J. Mol.Biol. 368, 407, 2007
I(Q) A-1
KinA2-2KipI
90
Jacques, Langely, Jeffries et al (2008) J. Mol.Biol. 384, 422-435
I(Q) A-1
The KinA helix containing Pro410 sits in the KipIC 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
KipI
Sda and
and
binding
interacts
KipI
KipIdoes
induce
bind
withnot
at
that
the
appear
theregion
same
basetocontraction
of
ofprovide
the
the KinA
DHp
forof
domain
KinA
dimerization
steric
upon
mechanism
thatbinding
includes
phosphotransfer
of(4inhibition
the
Å in
conserved
Rg, 15
(DHp)
Å in
Pro
domain
D410
max)
DHp helical bundle is a critical conduit for signaling
Mean scattering length density (1010 cm2)
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
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
reliable polynucleotide-protein structure interpretation
3CproRNA
3Cpro
3CproRNA complex; Claridge et al. (2009) J. Struct. Biol. 166, 251-262