The determination of protein structure gives invaluable information of how each protein functions in bioorganisms. X-ray crystallography and nuclear magnetic resonance (NMR) are now widely used techniques for the elucidation of three- dimensional structure of proteins. The protein structures recorded in protein data banks are mostly derived from these two techniques. X-ray crystallography provides the atomic and molecular structure from protein crystals whereas NMR is used to study the structure and dynamics of protein in solution. However, each method has advantages and disadvantages. The limitations of x-ray crystallography are 1) the difficulty in growing protein crystals, 2) the limitation in observing the flexibility of proteins and 3) providing the structure in one conformation due to the crystal constraint. In the case of NMR, the molecular
size of proteins characterised by NMR is limited to less than 70 kDa. Due to these limitations, scientists seek for an alternative way to study the structure and dynamics of proteins. In this present study, we wish to investigate the interaction of a large outer membrane protein (OmpF, 111 kDa) with LPS and the flexible proteins (ColN and TolA). As these complexes are too large for NMR study and difficult to crystallise due to the flexibility, we have used alternative methods to study them.
Due to recent developments of instrumentation and image processing software, cryo-electron microscopy (cryo-EM) of single particles or 2D crystals has become a useful method for the determination of complex molecular structure at atomic scale resolution. Advances in new detector hardware has substantially improved the resolution of cryo-EM (For a recent review see (Milne et al., 2013)). The advantages of cryo-EM over X-ray crystallography are 1) crystals are not required and 2) proteins are in a nearly-native environment. Recently, ordered structures such as viruses or 2D crystals can approach resolutions of 3Å which allows for the definition of secondary structures and the larger side chains. Even with single particles, membrane proteins such as the γ-secretase can be resolved to 4.5 Å (Lu et al., 2014).
Small angle scattering (SAS) is another promising technique exploited for the study of large-scale structure in solutions. It also offers the possibility of analysis of disordered systems. SAS has been introduced to study macromolecules in solution for more than 80 years. In the early days, SAS of biological macromolecules was used to determine a simple structural parameter such as radius of gyration. Due to the development of faster and more sensitive instruments, easy to use software for data analysis and interpretation, and the availability of instrumentation, SAS has now become widely used to study biological molecules in solution. SAS is often used as a complementary technique to other biophysical techniques especially x-ray crystallography. (For recent reviews about SAS see (Jacques and Trewhella, 2010; Mertens and Svergun, 2010)).
24 Basics of small-angle scattering
According to the basic principles of quantum mechanics, x-rays and neutrons show a wave-like character as well as a particle-like behaviour. When x-rays and neutrons pass through a particle, they interact with the atoms of the particle and generate secondary wavelets. These wavelets interfere each other constructively and destructively resulting in the diffraction pattern from the particle. X-rays are an electromagnetic radiation which interacts with the electron clouds of each atom whereas neutrons are neutral particles which are scattered by atomic nuclei. Figure 1.11 shows a typical SAS experiment. A beam of X-rays or neutrons with a narrow band of wavelength is directed at the sample of proteins in solution. X-rays and neutrons interact with proteins and then they are scattered. The scattered radiation is recorded on a detector while the transmitted radiation is absorbed by a beamstop.
Figure 1.11 Schematic illustration of a standard SAS experiment
For simplicity, the scattering pattern is defined as intensity (I) as a function of the momentum transfer, Q.
Where is half the angle between the incident and scattered beams (see Figure 1.11) and is the wavelength of the incident beam. In most SAS experiments,
but not “white beam” time-of-flight small angle neutron scattering (TOF-SANS), is usually constant hence Q depends only on the scattering angle. The scattering profile from SAS is presented as I(Q) versus Q.
Small angle scattering data analysis
The initial analysis of scattering data is to determine the simple structural parameters such as radius of gyration, Rg, and the forward scattering intensity,
I(0). These two parameters are directly related to particle size and shape. Rg
refers to the root-mean-squared distance between all elemental scattering volume and the centre of mass. I(0) is defined as the scattering intensity at zero angle (at the beamstop). I(0) is directly dependent on the molecular mass of particle. The Guinier approximation is used to estimate these values by the equation below.
( ) ( )
Therefore, Rg and I(0) are a slope and the y-intercept from a linear fit of In[I(Q)]
versus Q2 for QRg < 1.3. The linear Guinier plot is also an indicator of high
sample quality which is free of aggregates. The Guinier analysis estimates Rg
and I(0) from the scattering profiles at low angle. To precisely determine Rg and
I(0) from the entire scattering profile, the interatomic distance distribution function P(r) is used to calculate them.
The P(r) function is a real space representation of scattering data. It is computed by the indirect Fourier transformation of the scattering curve using GNOM (Svergun, 1992). This is due to the fact that as the range of scattering data is present from minimum q to maximum q, direct Fourier transformation of the scattering curve from the limited number of data points is not possible. P(r) describes the probable frequency of interatomic distance (r) within the particle. P(r) provides not only the simple structural parameters such as Rg, I(0) and the
maximum linear dimension (Dmax) but also information about the shape,
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shown the effect of particle shape on the scattering profiles and P(r) functions (Figure 1.12) (Mertens and Svergun, 2010). The consistency of Rg estimated
from Guinier approximation and P(r) function indicates an aggregate-free sample and the correct assigned Dmax.
Furthermore, SAS can indicate the folded/unfolded state of proteins. The Kratky plot can be used to represent the compactness of proteins from the scattering profiles by plotting Q2I(Q) versus Q. A folded protein gives a bell-shaped curve while the unfolded protein shows a continuous rise at high Q range. An extended tail of P(r) function is also an indication of unfolded proteins.
Figure 1.12 Theoretical scattering profiles and P(r) functions from simple geometrical shapes. The models used for the calculation are displayed above the plots. Plots taken from (Mertens and Svergun, 2010).
Contrast variation
Even though small angle x-ray scattering (SAXS) is similar to small angle neutron scattering (SANS), one of the key advantages of SANS over SAXS is the use of contrast variation method to study the structure of biomolecules. Due
to the difference between hydrogen and deuterium, in neutron scattering power, it is feasible to have different contrasts for each component of biological complexes if one component is deuterated. The contrast variation allows us to observe the individual component of complexes or the entire complexes. The neutron scattering experiment using this approach is achieved by recording SANS data in solvents with different ratios of H2O:D2O. At certain H2O:D2O, the
scattering contributions of each component in complexes are varied. When the scatter of solvent is equal to that of one component, it is invisible to neutrons. Figure 1.13 shows how the contrast variation approach works.
Figure 1.13 Contrast variation technique used to study the binary complex in small angle neutron scattering. Protein A and B are in different colours as one of them is deuterated. The data are recorded in solutions containing different H2O:D2O ratio. The solutions in each ratio represent in different colour.
The scatter of A is equal to that of D2O but the scatter of B is equal to that of
50% D2O. Therefore, both A and B can be observed in H2O whereas either A or
B is visible to neutrons in 50% D2O or 100% D2O.
Modelling from scattering data
The modelling of biological molecules from SAS data can be achieved in three different ways, ab initio modelling, rigid body modelling, and ensemble optimisation methods. Most modelling software used in this study comes from the ATSAS suite pioneered by the Svergun research group at EMBL Hamburg (Petoukhov et al., 2012). The ab initio method uses dummy atoms to reconstruct a molecular shape based on the scattering data alone. The disadvantage of this method is that several shapes generated from this method are able to fit the data equally well. Therefore, the molecular shape from ab
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contrast to the ab initio method, rigid body modelling exploits the availability of high resolution structures of proteins, for example separate subunits of a complex, from X-ray crystallography. It generates the theoretical scattering data from the high-resolution structure and which is then compared to the experimental data. Additionally, rigid body modelling offers the possibility to model flexible loops or inter domain linkers missing in the crystal structure. The last approach is ensemble optimisation method for flexible systems. A pool of models is randomly generated according to the sequence and structural information of the protein. The program then chooses an ensemble of conformations and fits the averaged theoretical scattering data from an ensemble of conformations to the experimental data.