Schematic for a SANS experiment.
Small-angle neutron scattering (SANS) is probably the experimental approach to which neutrons are most often put in biological research. In a typical experiment neutrons are scattered from an aqueous solution of a protein or complex. The scattering occurs in a radially symmetric fashion and is measured on a 2D detector (see diagram below). The scattered intensities measured on the detector are then radially averaged and normalized. The resulting 1-dimensional plot of I(Q) (the intensity of scatter I as a function of the reciprocal space scattering vector Q where Q=(4*pi*sin(theta/2))/lambda, theta is the scattering angle and lambda the neutron wavelength) may be analyzed in a number of ways to provide information at a range of resolutions. However, in a SANS experiment in particular the usefulness of the information obtained is usually critically dependent on the purity and monodispersity of the sample and how thoroughly the theoretical and technical groundwork has been done. Since the data obtained relate to the whole sample and are spherically averaged, the presence of impurities or uncharacterizable interparticle interactions will render them uninterpretable.
Schematic for a SANS experiment.
The Guinier (1942) approximation that at
sufficiently low Q a small-angle scattering curve approximates to a Gaussian
distribution of scattered intensity leads to a number of linear data analyses
from which parameters such as the radius of gyration (Rg) of a
scattering species (or for rod-like structures the cross-sectional
Rg, the Rxs; or for sheet-like structures the thickness
Rg, the Rth) and its mass, may be calculated. An
alternative method of analysis yielding a Patterson-space (spherically-averaged
real-space) distribution of scattering vectors involves Fourier transformation
of the scattering curve, and yields a measure of the particle shape as well as
its maximum length. More information may be gleaned by comparing the
experimental data with those simulated for models, either based on a known
molecular structure expressed in the
form of Debye spheres to facilitate calculation of model data, or
constructed ab initio.
The models used to simulate scattering data are similar in concept to the hydrodynamic models used for calculating hydrodynamic parameters for comparison with experimental data (see for example the work of Jose Garcia de la Torre and colleagues). An excellent introduction (and much of the best software available for analysis and interpretation of small-angle scattering data) is provided by the Hamburg outstation of the EMBL. Software available for download from this site includes GNOM by which the Patterson vector curve alluded to above may be calculated; the packages CRYSOL and CRYSON allowing the calculation of scattering curves for atomic models via spherical-array models for X-ray and neutron scattering data respectively; the program SASHA allowing calculation of a density envelope for the scattering species using spherical harmonics; and the program DAMMIN which uses simulated annealing to reveal the density envelope of the scattering species composed of Debye spheres at up to ~10 Å resolution (seeJ. Appl. Cryst. (2000) 33, 530-534). The interactive program ASSA is used for visualization, manipulation and rigid-body modeling of the results of CRYSOL/N, SASHA and DAMMIN. It is possible to use such models as solvent envelopes in the phasing of X-ray diffraction data and in the correction of the contrast transfer function in electron cryo-microscopy.
The DAMMIN approach represents an attempt to obtain a solution to the inverse-scattering problem, which is that there is no inversion for the Debye equation in the way that a Fourier inversion may be performed on diffraction data. A similar genetic algorithm method has also been described (Chacon et al., Biophys. J. 74, 2760-2775) and, like DAMMIN, is available for download.
Garcia de la Torre and colleagues have sought to provide a bead-based modelling methodology for proteins which permits simulation of a host of parameters and diagnostic functions describing the molecular shape including scattering terms (see for example Eur. Biophys. J. (1999) 28, 119-132 and Biophys. J. (1999) 76, 3044-3057). More recently this approach has been extended in a program (HYDROPROT) for which the only input needed is some atomic model (Biophys. J. (2000) 78, 719-730). Other approaches for constructing models of molecules with beads have been developed by Byron and by Perkins. Modeling software is at present being further developed in Olwyn Byron's group to permit easy use of atomic coordinates in simulating neutron data and interactive representation of the results. A method of calculating scattering curves from atomic models with waters included using the program SASSIM has more recently been described. SASSIM tested well against experimental data and was designed to be particularly appropriate for extensive configurational averaging, such as might arise in relating molecular dynamics simulations to experimental scattering data. Indeed, given the dynamical nature of proteins in solution the use of a series of different potential configurations may allow a more accurate modeling of an experimental scattering curve than a single model provides.
Other methods of modeling use ellipsoidal volumes of scattering elements (beads/spheres), or similar geometrical solid-body respresentations of the scattering species such as those provided in the powerful program FISH by Richard Heenan. This allows for the construction of many kinds of geometrical models (lamellar structures, hollow shells, annulae etc.) and provides for the iterative least-squares refinement of the dimensions of the models to fit the data.
Measuring the structures of biological molecules and their complexes
A number of examples of structural studies using SANS are given, in order to provide an idea of the range of applications possible.
Structure of the hydration layer of proteins.
Changes in the comformation of cAMP receptor protein.
The structure and interactions of calmodulin.
Spin-polarized neutron scattering of ribosomes.
SANS used to characterize molecular interactions: application to the folding problem.
The
ribosome: positions and shapes of protein and RNA components of the 70S
ribosome
Case
study: the structure of the hydration layer around proteins
The interactions and function of proteins in solution will be
strongly affected by the nature of the interface between the solvent and the
protein surface. This has been addressed by Zaccai,
Svergun and colleagues, who used small-angle X-ray and neutron scattering to
demonstrate that a protein-bound hydration layer ~3 Å thick and ~10 %
more densely packed than bulk solvent formed this interface. Their analysis
relied on the use of X-ray scattering, where the hydration layer has long been
known to contribute to the measured signal, compared to neutron scattering,
where controversy surrounded whether surface-bound water was detectable. In
100% 2H2O the proteins appear slightly smaller than
their known structures; while in 100% 1H2O they appear
larger. The reason for the latter observation is that the bound water is
contributing to the neutron scatter at 100% 1H2O as
it does to X-ray scatter. The reason for the former observation is that in 100%
2H2O the protein is observed negatively contrasted against
the high scatter from the background solvent; the fact that the protein seems
smaller than it is known to be results from the strongly negative contrast
imparted by a dense hydration layer. Analysis of the data from this study was
aided by the use of the modeling programs CRYSOL and CRYSON (see
above). Proc. Nat'l
Acad. Sci. USA (1998) 95, 2267-2272.
Case
study: structural changes wrought on the cAMP receptor protein (cAMP-RP) by
cAMP
Krueger and colleagues obtained SANS
data from cAMP-RP before and after addition of cAMP. They analyzed their data in
a thorough and original way, allowing for the scattering contribution from the
hydration layer as one must and demonstrated that binding of cAMP converts
between two known conformations of cAMP-RP determined by X-ray crystallography;
J. Biol. Chem.
(1998) 273, 20001-20006.
Case
study: the structure and interactions of calmodulin
Trewhella and
colleagues have investigated the structure and interactions of calmodulin using
SANS in which different components of a complex between calmodulin and myosin
light-chain kinase (MLCK) with and without AMPPNP and a subtrate mimic for MLCK
had their proton groups replaced by deuterons. This allowed the determination of
the basic scattering functions describing the structures of components within
the complex and the cross-term describing their mutual arrangement. The authors
made use of geometric rigid-body models for the different components; Biochemistry
(1998) 37, 13997-14004. In a further study, Trewhella and colleagues
have again used deuterium labeling to deconvolute scattering data from a
calmodulin complex, this time employing both the spherical harmonics program
SASHA and the atoms-to-beads modelling program CRYSOL to interpret the data in
model terms. In this fine paper they complement these shape data with secondary
structural information derived from Fourier-transform infra-red spectroscopy to
describe the changes occurring when calmodulin binds the smooth-muscle thin
filament protein caldesmon; Biochemistry
(2000) 39, 3979-3987. Trewhella has co-authored a review of this
work, Methods Mol. Biol. (2002) 173, 137-159.
Case study: measurement of protein and lipid structures in model
membranes using SANS
Two recent studies have
applied SANS to proteins inserted into membranes. In the first, by Hunt and
colleagues, scattering was measured from bacteriorhodopsin in a liposome bilayer
membrane, from which its radius of gyration was calculated and its
monodispersity inferred; J.
Mol. Biol. (1997) 273, 1004-1019. In the second, Gilbert and
colleagues studied the structures of liposomes using SANS and interpreted their
data using the program FISH (see above),
allowing the measurement of the thickness of the single bilayer forming the
liposomes; J.
Mol. Biol. (1999) 293, 1145-1160. When the pore-forming toxin
pneumolysin was added to the liposomes in situ, the lipid bilayer became
thinner. This is a result relevant to understanding how the interplay of a
pore-forming toxin and a membrane leads to the latter's perforation. In both
these studies, extensive use of contrast variation was made. Additional
link.
Another model system
for the study of protein interactions with lipids are bicelles, which are
bilayered micelles consisting of a mixture of long- and short-chain
phospholipids. A study by Luchette and colleagues used SANS to demonstrate the
disc morphology of bicelles. Biochim.
Biophys. Acta (2001) 1513, 83-94.
Case
study: spin-polarized neutron scattering of ribosomes
Spin-polarized SANS experiments have been carried out on the ribosome in an
attempt to locate components representing ~1% by mass of the complex. The
spin-polarized experiments are technically very impressive, involving
maintainance of the sample at 0.2 K and the application of magnetic fields in
the region of 3 T. The sample is also doped with paramagnetic centres to aid
spin-polarization of the nuclei. A beam of spin-polarized neutrons is then
applied to the sample. This approach has been used to define the location and
arrangement of two tRNAs before and after translocation (from A and P sites to P
and E sites), demonstrating that their mutual arrangement is maintained during
this process (Nierhaus et al. (1998) Proc. Nat'l Acad. Sci.
USA95,
945-950). These findings were later confirmed by cryo-EM (Nat. Struct.
Biol. (1999) 6, 643-647). In another experiment the movement of the
centre of mass of mRNA in the process of translation was measured, demonstrating
that the mRNA shifts in the tranlocation step by the same amount as the tRNAs
(Biol. Chem. (1998) 379, 807-818). The unexpectedly small
Rg of the mRNA suggested that it adopts a loop-like
conformation.
Measuring the interactions undergone by biological molecules
An alternative strategy permitting the use of SANS
to determine the nature of the interactions between molecules in a sample
involves specifically allowing for the scattering contribution from the
molecular structure. A particularly interesting example of this approach is
provided by ambitious experiments to investigate the interactions undergone by a
hydrophobic amino acid. The aim of this work was to understand better the
interactions occurring during protein folding as a polypeptide collapses to form
a molten globule. Pertsemlidis and colleagues discovered that
N-acetyl-leucine-amide underwent self-interaction both directly and in a manner
mediated by the first hydration layer of the amino acid, having a cage-like
structure (Proc. Nat'l
Acad. Sci. USA (1999) 96, 481-486). This result suggests that
long-range water-mediated interactions may play a role in protein folding within
an expanded (hydrated) molten globule within which greater interaction
plasticity would be achieved compared to a molten globule from which water was
excluded. This in turn would allow for a more creative sampling of interactions
by hydrophobic sidechains, providing more rapid selection of the "correct"
solution. This work and other work by Pertsemlidis and colleagues compares
interestingly with the
neutron crystallographic structure of lysozyme in which cage-like water
structures in the hydration layer around exposed hydrophobic sidechains were
observed.
What is possible with SANS: the mutual arrangement of proteins in the
ribosome
Label triangulation experiments over a number of years permitted
the placing of all the proteins within the 30S ribosomal subunit (Science
(1987) 238, 1403-1406). The placement of 7 proteins of known structure
within the 5.5Å electron density map of the 30S subunit was
subsequently largely based on this neutron map of protein centres-of-mass; only
S15 was incorrectly located in the neutron analysis (Nature (1999)
400, 833-840). A more modest study located 7 proteins in the 50S
ribosomal subunit (EMBO J. (1992) 11, 373-378). Very recently,
Svergun and Nierhaus have sought to define the location and size of protein and
RNA components within the 70S ribosome, deriving a map of the protein-rRNA
distribution in the 70S ribosome (J. Biol. Chem. (2000)
275, 14432-14439). The authors take 42 solution scattering curves
previously derived from hybrid E. coli ribosomes in which the entire
protein and/or RNA moieties belonging to the 30S and/or 50S subunits were
deuterated in all possible combinations. The fitted curves were derived from
isotopic SANS, polarization-dependent SANS and small-angle X-ray scattering. A
variant of the DAMMIN
simulated-annealing-driven algorithm was used to locate proteins and rRNA in the
ribosome, described by a dummy atom (bead, sphere) model based on a cryo-EM
reconstruction from the group of Joachim Frank.
The electron density envelope defined by the 3d reconstruction was divided into
7890 densely packed spheres and simulated annealing employed to assign each
sphere to solvent, protein or rRNA. A view of the cryo-EM reconstruction and
dummy atom model derived from it is shown here:
Deriving a
search model 
(a) Surface representation of an 18 Å resolution reconstruction
of the 70S E. coli ribosome. (b) A similar electron density map obtained
by the group of Joachim Frank was converted to a dummy atom array by Svergun and
Nierhaus. Orange pixels represent the electron density derived directly from the
Frank reconstruction. Purple circles represent dummy atoms belonging to the 30S
subunit and aquamarine circles those belonging to the 50S subunit. Yellow
circles are dummy atoms which may belong to either subunit. The top left
orientation in (b) is the same as in (a). The top right and bottom orientations
in (b) are rotated 45 degrees in the vertical and 90 degrees in the horizontal
respectively into the plane of view. Part (b) kindly provided by Dmitri Svergun
and prepared using the program ASSA.
All the scattering curves were fit simultaneously and the process was repeated ab initio twelve times, demonstrating a high degree of reproducibility to which a probability of 95% is assigned. Examples of the fits are shown in the published paper, which should be consulted.
The fitting process defined 15 protein subvolumes in the 30S subunit and 20 in the 50S. The subvolumes were connected by rRNA and permit the positioning of 17 proteins of known structure in locations agreeing with those defined previously by X-ray crystallographic and cryo-EM data. This work demonstrates the potential of neutron scattering as a method complementary to X-ray crystallography and cryo-EM in the interpretation and modeling of electron density of complex macromolecular assemblies.
Definition of subvolumes
within the 70S ribosome corresponding to the protein components of 30S or 50S
subunits or their rRNA molecules 
The top row displays the same views
of the 70S ribosome as shown in the top row of section b in the previous
figure, with the subvolumes identified by the curve-fitting procedure coloured
distinctly. Green dummy atoms represent protein subvolumes in the 30S subunit;
pink dummy atoms the subvolume occupied by the 16S rRNA molecule. Mauve dummy
atoms represent protein subvolumes in the 50S subunit; ochre dummy atoms the
subvolume occupied by the 23S and 5S rRNA molecules. The next two rows contain
stereoviews of the 30S and 50S subunits respectively, with the same colouring
and viewed in both bases from the subunit interface. Figure kindly provided by
Dmitri Svergun and prepared as above.
The top row shows the same views of the 30S and 50S subunits as
are displayed stereoscopically in the previous figure, with the shoulder (S) and
platform (P) of the 30S subunit and the L1 stalk and L7/L12 stalk of the 50S
subunit labeled. The middle row shows the two subunits rotated 120 degrees in
the vertical into the plane of view. The bottom row shows the 30S and 50S
subunits rotated 240 degrees in the vertical into the plain of view. Figure
kindly provided by Dmitri Svergun and prepared as above.
Location of specific
proteins in the array of protein subvolumes 
(a) Stereoview of dummy atom protein
volumes in the 30S subunit defined by Svergun and Nierhaus. The triangulation
map of protein locations is superimposed. (b) A second stereoview of the 30S
subunit, this time with the structures of proteins which were fitted to the
dummy atom model positioned in their supposed positions concluded on the basis
of the dummy atom model of protein volumes. There is in places a striking
agreement between the triangulation map and the Svergun map (e.g. S4, S8,
S15 and S17). The whole 30S subunit from the cryo-EM reconstruction is shown
inset. (c) A stereoview of dummy atom protein volumes in the 50S subunit with
the known structures of proteins located in it superimposed. In the cases of
discrete proteins in contact only with rRNA the agreement between the dummy atom
model and the fitted coordinates is excellent (e.g. L1, L25). The whole
50S subunit is also shown inset. Figure kindly provided by Dmitri Svergun and
prepared as above.
Another approach:
deconvolution of electron density determined by cryo-electron
microscopy
A recent paper by Frank, Spahn and colleagues has
described the deconvolution of electron density for the 70S E. coli
ribosome by plotting of the density fluctuations within the mass of the
structure. This allowed the analytical separation of the rRNA (which scatters
electrons more intensely) from proteins. This represents a parallel effort to
that described for neutrons above. Structure
Fold. Des. (2000) 8, 937-948.
Other interesting studies:
5S
rRNA
Svergun and colleagues have used small-angle X-ray
scattering to obtain a 13 Å representation of an isolated 5S rRNA molecule in a
particularly interesting example of ab initio structure retrieval from
small-angle scattering data. J.
Biol. Chem. (2000) 275, 31283-31288.
Structure of
melittin pores in situ
Yang and
colleagues have used SANS with a novel sample geometry in which oriented
membrane multilayers with melittin pores were positioned obliquely with respect
to the neutron beam, allowing the measurement of the off-plane scattering (off-specular
diffraction) in a manner analogous to that possible with reflectivity
apparatus. This permitted the authors to conclude that melittin forms a toroidal
pore and not a barrel-stave structure. There are interesting parallels between
this work and that carried out on pneumolysin,
a pore-forming bacterial
protein toxin. Biophys. J.
(2001) 81, 1475-1485.
Small-angle
scattering of lipid mesophases, model biomembranes and proteins at high
pressure
These aspects of neutron research
have been covered in a recent review by Roland Winter (Biochim.
Biophys. Acta (2002) 1595, 160-184). This paper describes in some
detail approaches taken to investigate lipid phase transitions (including
non-lamellar structures) and the behaviour of binary lipid mixtures (studied
with the assistance of neutron
contrast variation). Then the structural effects of the interaction of
proteins with lipids are discussed. The effects of pressure on protein structure
is also covered.
The conformatoin
of the Drosophila motor protein non-claret disjunctional
(ncd)
Svergun and colleagues have used their modeling
procedures to obtain ab initio models for this microtubule-binding
protein. Dimerization of ncd is mediated by a coiled coil which, when omitted
from the construct used, renders the protein monomeric. The C-terminal portion
of the monomeric ncd head domain was missing from its crystal structure; the
model derived directly from scattering data here suggests a clear position for
this C-terminus, which could plausibly be modeled as a beta-hairpin structure.
Scattering from a short dimeric form of ncd with a part of the coiled-coil could
best be fitted by a scattering curve with an unsymmetrical arrangement of ncd
head domains. The full-length dimeric form of ncd indicated positioning for the
remains of the coiled-coil, and a changed position for the beta-hairpin
C-terminal to the head domain. J. Biol. Chem. (2001)
276, 24826-24832.