At present there is no x-ray crystallographic data on the gluten proteins, which means that both the secondary and tertiary structures of the gliadins and the glutenins are unknown. This project is concerned with elucidating the mechanism of interaction between SWP and other proteins. The structures of the other proteins used have been elucidated. It was found necessary, therefore, that studies should be carried out on one of the proteins in SWP to complement the interaction experiments in chapters 5, 6 and 7. Gliadin and deamidated gliadin were selected because gliadin is the least studied protein of the gluten proteins and the information on deamidated gliadin could give an insight into the effect of deamidation on the structure of gliadin and how deamidated gliadin interacts with the other proteins.
Small Angle Neutron Scattering (SANS) Studies
Light scattering and small-angle x-ray scattering are based on electromagnetic radiation, while small-angle neutron scattering is based on particle radiation. The interaction between light and the collective electrical charges of a molecule produces an electric field. Neutron beams, on the other hand, interact with the nuclei of atoms via a strong nuclear force (called nuclear scattering). They also interact with unpaired spins of a molecule, if any, via the magnetic dipole (called magnetic scattering).
There are six types of neutron scattering. The type of neutron scattering depends on the incident wave frequency vo and the scattered wave frequency v. If vo is equal to v, we have coherently scattered radiation; if not, we have incoherently scattered radiation. In coherently scattered radiation, phases of the electric and magnetic fields of incident radiation and those of the scattered radiation are in definite relation to each other.
The scattering events may or may not involve an energy change. If no energy change takes place, the scattering is elastic; if an energy change takes place, the scattering is inelastic. If an energy change is very small and if there is a Doppler shift (that is, a frequency shift), then the scattering is quasielastic. Thus, there are six different types of scatterings: coherently elastic scattering, incoherently elastic scattering, coherently inelastic scattering, incoherently inelastic scattering, coherently quasielastic scattering, and incoherently quasielastic scattering. Coherently elastic scattering of neutrons measures the correlation between scattering centres and is, therefore, useful to the study of the conformation of polymers. This aspect led to the selection of neutron scattering for the present study, in order to obtain information about the structure of gliadin and the effect of deamidation on the conformation of gliadin.
The principle of the wave-particle duality of matter according to de Broglie and Schrödinger (Gamow and Cleveland, 1969; Harvey, 1969; Beiser, 1995) considers neutrons as waves. To a particle of mass m and velocity u, de Broglie assigned a wave of frequency v and wavelength given by
= h / mu, and v = E / h (3.1)
where h = Planck's constant. Since h and m are fixed, control of the wavelength can be exercised by moderating the velocity of the neutrons, and hence the higher the velocity of the neutrons, the shorter the wavelength. For a particle moving along the x-axis of a coordinate system, if its linear momentum is p, then its kinetic energy is p² /2m. If the potential energy of the particle is V(x), which is some function of x, then the total energy of the particle is
E = p²/2m + V(x) (3.2)
The operators which represent momentum and energy are
and i is a complex number (Beiser, 1995).
Partial differentiation is to be performed on both the p and E operators with respect to x and t respectively. In each case, the operand is a function which is given the symbol . Substituting the operators and their operands into equation (3.2) gives
The wave equation (3.5) can be separated into two equations, one of which has t as its only variable, while the other contains only x. The latter equation, is called the time-independent Schrödinger equation, and has the form
Scattering from a single atom can be represented schematically as shown in Figure 3.1. Essentially, a planar wave along the z axis, represented by
is incident upon the particle and is then rescattered by the particle in all directions in the form of a spherical wave, which can be represented by
the wave vector of the neutron, is related to its wavelength by:
The scattering energy is distributed over the surface of a sphere of surface area the minimum value of which is The quantity bo is known as the neutron scattering length and since neutrons are scattered by the nucleus of the atoms bo is of the order of 10-12 cm for all nuclei.
Figure 3.1: The incident plane wave and spherically symmetric scattered wave from a single nucleus (Newport, Rainford and Cywinski, 1988).
In a neutron scattering experiment the quantity to be determined is called the partial differential cross section (the p.d.c.s.), . This function depends on the energy and momentum transferred from the neutron to the sample. In the most general case the p.d.c.s. is a function of four variables since the momentum transfer is a vector quantity with three components. In elastic scattering, where the neutron does not transfer any energy to the sample, the elastic differential cross section is a function of momentum transfer only. From the number of neutrons counted in a detector, the mean values for can be defined (Figure 3.2). is the angle through which the neutron has been scattered, i.e. the angle between the incident and the scattered beam. The paths of the neutrons which are scattered through form a cone so a second (azimuthal) angle, , is also needed to define the detector position. E' is the energy of the scattered neutron.
Figure 3.2: Geometry of scattering problem (Lovesey, 1984)
The detector will in fact count the neutrons arriving within a solid angle of and an energy interval centred on respectively. Together with Eo, the incident energy of the neutron, make up the four variables needed to define the p.d.c.s.
We need to be able to relate the number of neutrons detected to the p.d.c.s.. If it is assumed that we have a steady, monochromatic beam of neutrons with energy Eo, and a target consisting of a single scattering centre and a perfectly efficient detector (one which counts every neutron that hits it) and also that no counts arise from background radiation or electronic noise. Then the p.d.c.s. is given by:
where is the intensity (neutrons/unit time) measured at the detector and is the incident intensity (neutrons/unit area/unit time). As the solid angle is dimensionless the p.d.c.s. has the dimensions of area/energy. The quantities and determine the resolution of the spectrometer. The factors which contribute to and depend on the instrument used. An account of how these quantities are used to calculate the instrumental resolution on a pulse source is given by Windsor (1981).
There are two types of neutron sources - reactors and pulsed sources. In reactors, a nuclear chain reaction produces a continuous flux of neutrons In the latter, sharp bursts of high energy protons or electrons from an accelerator hit a heavy metal target and chip off neutrons, also in sharp bursts. When the neutrons emerge from the nuclei that produce them they have very large energies and are in a very real sense 'too hot to handle'. In a moderator the neutrons are scattered many times within a suitable medium, exchanging energy at each collision until they achieve approximate thermal equilibrium with the moderator material. A proton linear accelerator injects 70 MeV H- ions into the outside of the main 800 MeV proton synchrotron ring. Under the magnetic field in the synchrotron, positive ions bend into the ring direction. At the instant that they are tangent to the ring, they pass through a stripper foil which removes the two electrons to give a bare proton moving with the opposite curvature along the ring path. When the accelerator cycle is complete, a fast kicker magnet extracts the pulse of protons, and sends it down a beam transport line to the target station. The actual target is a set of depleted uranium plates, cooled by heavy water. The short, 0.6mS long, pulse of fast neutrons produced must be moderated to produce neutrons of the energies required for scattering experiments with only the minimum broadening of the pulse. This is achieved by using thin moderators loaded with neutron absorbing poisons which seek to prevent the build up of the equilibrium Maxwellian distribution, which is only obtained at the expense of a broader pulse. Cold moderators are used both to increase the flux of cold neutrons, and also to shift the broad Maxwellian to lower energies and so preserve the sharpest possible pulses. The ISIS facility at the Rutherford Appleton laboratory consists of three major parts. A fast cycling proton synchrotron (design current 200mA at 800 MeV) delivers 0.4 ms proton pulses at 50 Hz to a heavily shielded target station containing a 238U spallation target. The target produces about 25 neutrons per proton with energies in the MeV range. These neutrons are slowed down in four moderators at three different spectral temperatures, and are then delivered to a large experimental hall which is designed to accommodate up to 20 neutron scattering instruments (Fig.3.3).
Experimental method and corrections to data
In an experiment the incident intensity, Io (Eo), will vary with time. This is not a problem since what is required is the ratio I/Io which is proportional to:
No and N are respectively the total number of neutrons hitting the sample and the total number which are scattered into the detector during the course of the experiment. The number of neutrons counted will be less than the number hitting the detector because no detector is perfectly efficient. The detector efficiency, nd(E') is the probability that a neutron hitting the detector is counted and will generally vary with the energy of the neutron. Detector saturation should also be avoided. After the detection of each neutron the detector has a finite dead time during which it is unable to register another count. The dead time is approximatly 10-5 seconds. Provided the detector has not been saturated then,
where N'd is the number of neutrons which are detected after scattering from the sample. The number of neutrons incident on the sample cannot be measured directly. Instead Mo(Eo) is measured, which is the number of neutrons countered by a 'monitor' placed in the incident beam just before the sample.
Figure 3.3: The Experimental Hall at ISIS, Rutherford Appleton Laboratory
The number of neutrons hitting the sample will be proportional to Mo, such that:
will depend on the monitor efficiency, the cross-sectional area of the sample and the intensity profile of the beam. The counts registered by the detector during an experiment originate in many ways and the most important are illustrated in Figure 3.4. They are:
Figure 3.4: Sample independent background
Figure 3.4 also indicates those neutrons absorbed by the sample and those that pass through the detector. Monitor 1 is the incident beam monitor used to normalise the measured counts. Monitor 2 is a similar, low efficiency detector placed in the transmitted beam. A well designed experiment should minimise all processes except neutrons from the incident beam which have been scattered once by the sample.
The study of the sizes and shapes of biological molecules rests on the basic assessment of small-angle scattering by ordinary optical diffraction theory. It was shown (Guinier, 1963) that the scattering by a collection of particles will fall off with the scattering angle according to the expression
I(Q) = I(0)exp(-Q²R²/3) (3.7)where Q is the momentum transfer vector, with a numerical value equal to which approximates to at small angles, and R is the radius of gyration for scattering. By analogy with classical dynamics, R² is defined as the mean value of the square of the distance of each scattering atom from an axis drawn through the centre of gravity and parallel to the scattering vector, assuming that each contribution to the summation is weighted by the atomic scattering amplitude of the atom. It follows from equation (3.7) that
In I(Q) = In I(0) - Q²R²/3 (3.8)
In the case of the scattering by macromolecules in solution the scattering depends on the amount by which the resultant scattering amplitude of the molecule exceeds the scattering of the molecule which it displaces. Accordingly the scattering per unit solid angle, at a particular value of Q is given by
where is the scattering-length density of the solvent. The summation is made over the various atoms in the molecule, of scattering length bi and position vector ri, and the integral is taken over the volume of solvent excluded by the molecule. In aqueous solutions the value of can be controlled by varying the hydrogen / deuterium ratio in the water. It is convenient to define as the scattering-length density at any position r in the molecule and to re-write equation (3.9) in the form
Stuhrmann (1974) has shown that it is advantageous to divide the scattering into two new components dependent respectively on the external shape of the molecule and on its internal fluctuations of scattering-length density. A quantity is defined as the average value of the scattering-length density over the molecule and equation (3.10) is re-written in the equivalent form
This can be written in terms of two form-factors, FMol(Q) and Fshape(Q), defined by
(Higgins and Benoît, 1994; Feigin and Svergun, 1987)
GliadinSigma gliadin samples were prepared at different concentrations as shown in Table 3.1. Ethanol (70%) was required to solubilise gliadin. D2O/H2O ratios from 0 to 30% (v/v) was used to increase contrast (Jacrot, 1976; Stuhrmann and Miller, 1978; Kneale et al., 1977). The samples were then centrifuged at 10,000g for 10 minutes. The supernatant was collected and re-centrifuged again at 10,000g for another 10 minutes. The protein concentration in the supernatant was determined by the method of Lowry et al., (1951).
Amylum SWP was dissolved in distilled water and centrifuged at 10,000g for 10 minutes. The pellet made up of deamidated glutenin was discarded and the supernatant re-centrifuged at 15,000g for another 10 minutes. The supernatant after the second centrifugation, was placed in a dialysis bag (Medicell) with a cut-off MW of 50,000 and dialysed against distilled water overnight in a cold room with continuous stirring. The dialysate was transferred into another dialyses bag with a cut-off MW of 12,000 and covered with polyethylene glycol (aquacide-3) from Calbiochem and left overnight. The concentrated protein (deamidated gliadin rich fraction) was freeze dried for a week. Experimental samples were prepared from the freeze dried protein as shown in Table 3.2. The protein concentration of the deamidated gliadin rich fraction was then measured using the Lowry method (1951).
|deamidated gliadin samples||S1||S2||S3||S4||S5||S6|
The samples were warmed at the ISIS experimental station at 60°C to minimize
aggregation, and then transferred into quartz cuvettes with 2mm path length.
The samples, empty quartz cell, solvent and an empty beam space were run for
both SANS and transmission experiments for 20 minutes each over a period of
24 hours. A beam of neutrons (the incident beam) were allowed to hit the
samples where the neutrons may be scattered or absorbed. The scattered and
transmitted beams were then detected by a 3He-CF4 filled ORDELA "area"
detector. Data from neutron wavelengths of 2.0-9.8Å at 25Hz were combined to
give a useful range of scattering vectors
of 0.006-0.22Å-1 at a sample-detector distance of 4.4 m.
Data Collection and Analysis
Data was collected on a standard ISIS DAE (DAE I). Corrections were carried out and analysed using a COLETTE Program on a DEC VAXstation 3200 with colour monitor at the Rutherford Appleton Laboratory. The corrected data was transmitted through the internet using file transfer protocol (FTP) to a personal computer at home where all the calculations were carried out.