The principles o f coherent neutron scattering are the same as for coherent X-ray
scattering and consequently neutron coherent scattering is also described by the Debye equation (Equation 2.4). However, there are some significant differences between
neutron and X-ray scattering. Neutrons are scattered by the nuclei o f atoms, unlike X-
rays w hich are scattered by electrons. The neutron atomic scattering length b, which
replaces the X-ray scattering length f i n the Debye equation, does not exhibit a simple
relationship to the atomic number. The atoms '^C, '"’N, cind w hich are important
in proteins, have similar b values o f 6.651 fm, 9.400 fm, 5.804 fm and 2.847 fm
respectively. A similar neutron scattering length is observed for the isotope (6.671
fm), how ever the 'H isotope has a large negative b value (-3.742 fm). A negative
to the incident wave. The large difference o f the neutron scattering o f these two
hydrogen isotopes is very im portant in neutron solution scattering experiments. In small
angle X-ray scattering experiments, a second type o f scattering know n as incoherent
scattering is negligible, but incoherent neutron scattering exists for nuclei w ith spin. In
terms o f atoms found in proteins, incoherent scattering is only significant for nuclei
where it becomes very large.
2 3.3.3.
C om parison between X-rays and neutronsX-ray and neutron scattering techniques are com plementary in m any respects.
X-ray scattering has the following characteristics (Perkins, 1994):-
1. M ost biological macromolecules are studied in high positive solute-solvent contrasts.
This contrast corresponds to the situation in w hich the scattering density o f the
m acrom olecule is significantly higher than that o f the solvent. It has been found that this m inim ises the systematic errors in the curve m odelling o f the proteins that result if
internal density fluctuations in the protein are neglected.
2. Good counting statistics are obtained in this contrast despite high background levels
in the buffer curves, unlike neutron scattering in H
2
O where the high incoherentscattering background o f the buffer is a handicap.
3. Errors caused by wavelength polychromicity and beam divergence are not significant
for synchrotron X-ray scattering, so G uinier and wide-angle analyses are not affected by
systematic errors caused by instrument geometry.
4. The hydrated dimensions o f the macromolecule are studied, so the structure is larger
by an additional depth o f 0.36 nm at the surface to correspond to a monolayer o f bound
w ater m olecules. For proteins this is usually about 0.3 g H
20
/g macromolecule.N eutron scattering has the following characteristics (Perkins, 1994):-
1. C ontrast variation in mixtures o f H
2
O and ^H20
perm its the analysis o f hydrophobicand hydrophilic regions w ithin proteins and glycoproteins, and the elucidation o f the
disposition o f detergents or lipids with solubilized membrane proteins, or that o f DNA
or RNA in complexes w ith proteins (Figure 2.7a). D euteration o f components in a
m ulticom ponent system can extend these methods.
synchrotron X-rays. The neutron samples can normally be recovered for other studies.
3. The dry dimensions o f the m acrom olecule are studied and correspond to the
m acrom olecular structure observed by protein crystallography.
4. Absolute m olecular weight calculations are obtained from neutron data in H
2
O, or bythe use o f a deuterated polymer standard, in place o f the relative determ inations by
synchrotron X-ray scattering. The latter are based on a protein o f know n molecular
weight w ith a reliable 280 nm absorption coefficient to determ ine concentrations.
5. Background scattering effects are very low in buffers, even in the presence o f
high salt concentrations, and this permits studies o f m acrom olecules at low
concentrations (0.5 mg/ml). ^H
20
is, however, a prom oter o f macromolecularaggregation if hydrogen bond interactions w ith w ater are im portant for solubility.
6
. Guinier analyses at low scattering angles are not significantly affected by beamdivergence or wavelength polychrom icity (9-10% on D l l at the ILL). However,
intensities at large Q are noticeably affected and this requires consideration in curve
simulations. (See also Table 2.2 for com parison o f SAXS and SANS).
2.3.3.4. The hydration shell
The neutron scattering properties o f ’H atoms necessitate that neutron
experim ents are perform ed in
100
% ^H20
buffers in order to obtain scattering curvesthat are com parable to those m easured in X-ray experiments. However, even under
these conditions, small differences are often observed betw een measurements from
neutron and X-ray experim ents and these are attributed to the hydration shell that
surrounds protein molecules. The hydration shell refers to solvent w ater molecules that
are closely associated with the protein by means o f hydrogen bonds. In X-ray solution
scattering experim ents this hydration shell is detectable around the protein, but it is
invisible in neutron experiments. The model o f scattering by an aqueous protein
solution that is described by Equation 2.5 assumes that the solute and solvent are
discrete entities, but in actuality water molecules hydrogen-bond to the surface o f the
protein. A w ater molecule hydrogen-bonded to the surface o f a protein is electrostricted
and has a sm aller volume (0.0245 nm^) than a w ater m olecule in the bulk solvent
(0.0299 nm^) (Perkins, 1986, 2001). Consequently, the X-ray scattering density o f a
SAXS