Protein scattering densities

For typical compact proteins this plot has a positive slope, as the hydrophilic residues on the outside of the dissolved protein have a higher scattering density than the hydrophobic residues on the inside. For casein sub-micelles, the slope is negative (Stothart and Cebula, 1982) (Figure 2). This seems surprising at first sight, but the sub-micelles are so highly hydrated that all the constituent protein... 

Scattering-Density Maps of Chromatium High-Potential Iron Protein, J. Mol. Biol. (1968) 35, 503. 

Fig. 2. Schematic variation of neutron scattering density for an object composed of a central sphere of RNA and a concentric outer shell of protein, i.e. a simple virus. The contrast difference dp is the difference between the scattering density of the solvent pg and the solute py. High positive and negative dp are seen in 0 and 100% H20. The protein shell is matched-out in 43% H20 and the RNA core is matched-out in 72% H20. Note that for reason of solvent H- H exchange, the average protein and RNA densities increase slightly on going from 0 to 100% H20. Solution scattering is observed where the solute and solvent densities are different. Note that the fluctuations in scattering densities pp(r) within each of the protein and RNA components do not disappear at their respective matchpoints. See Section 2.3 for a further explanation of the terms in dp, ps, Py and Pp(r).

Fig. 3. Summary of the scattering densities of biological macromolecules in neutron and X-ray scattering. In neutron scattering, the increase in density for each class as the H20 content increases is the result of exchange. Neutron contrast variation by H20- H20 mixtures is able to match-out each of the five classes shown, while X-ray contrast variation can only be performed in the range between the electron densities of lipids and proteins. From [23].

The term reflects the curvature of the Stuhrmann parabola and is always positive (Fig. 5). Since it is a second-order term and is defined mainly by R% values measured in low Ap (where counting statistics are usually weaker and sample impurity effects are larger), the inherent accuracy of is less than that oi Rc and a. Physically, it corresponds to the displacement of the centre of scattering within the particle as the contrast is varied, i.e. corresponds to the distance between the centres of the shape Py(r) and the fluctuations pp(r). Typical systems where might be measurable include protein-detergent, protein-nucleic acid and proto-nated-deuterated protein complexes (Section 4). If a particle can be divided into two components 1 and 2 with distinctly different scattering densities, the separation between 1 and 2 can be calculated [47] ... 

In the Stuhrmann equation, the centre of gravity of scattering density fluctuations is coincident with that of the shape of the protein to a good approximation, thus the term in can be set as zero. The values of a from Stuhrmann plots... 

Fig. 19. Dependence of 7(0) on the volume fraction of HjO and H20 present in neutron scattering experiments. The vertical scales in (a), (b) and (c) are not to the same scale, (a) The I(O) values for myoglobin in 10 different contrasts are a linear function of the solvent scattering density [44]. This is the usual result of neutron contrast variation and indicates the monodispersity of the sample. The match-point corresponds to the so-called dry unhydrated volume of the protein. Typical Stuhrmann plots for proteins and glycoproteins are exempUfied in Fig. 21. (b) The values tor ferritin in 10 different... 

Fig. 29. Stuhnnann plots of deuterated 70S ribosomes (a) and half-deuterated 70S ribosomes ( ) where the 30S subunits are deuterated and the SOS subunits are protonated [48]. The positive slope a seen for the deuterated 70S ribosomes reflects the higher matchpoint of the deuterated protein over that for the deuterated RNA, where the protein is located on average further from the centre of the particle. In protonated 70S ribosomes, negative a values are observed (Table 14). The strong curvature of 420 X10 nm seen for the half-deuterated 70S ribosomes (Table 16) is a measure of the separation between the 30S and SOS subunits and their relative scattering density differences.

To a first approximation, the sizes of isometric viruses can be estimated by comparing the experimental maxima and minima with the theoretical curves calculated for spheres and hollow spheres [492-494,504]. However, viruses are composed of protein shells and nucleic acid cores (with carbohydrate and lipid in more complex viral structures), so a full analysis requires the explicit consideration of non-uniform scattering densities. In addition, the principle of icosahedral symmetry in the assembly of the protein shell means that, at large Q, deviations from spherical symmetry will influence the scattering curve. The separation of the scattering curve... 

Other anisometric viruses have rod-like helical or cylindrical structures, such as tobacco mosaic virus [495,496,509,533] or alfalfa mosaic virus [551,561,562]. Thus cross-sectional parameters can be determined using / xs Q) Q q->o addition to Rq d I 0) data [537,550]. Stuhrmann plots of the / xs data lead to information on the cross-sectional distribution of protein and RNA. Shell models for the cross-section can likewise be made by analogy with the isometric viruses [550,561,562]. The radial scattering density of the cross-section can be calculated by applying the Hankel transformation to the scattering curve [509]. 

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