The sedimentation coefficient, as defined by Equation 12.8 (after normalisation to standard conditions), will depend on the size (molecular mass) of a macromolecule. For particles of near-globular shape, s20,w is approximately proportional to M 2/3 . The value of s20,w lies for many macromolecules of biochemical interest typically between 1 and 20, and for larger biological particles such as ribosomes, microsomes and mitochondria between 80 and several thousand. Figure 1 shows the optical records from a sedimentation velocity experiment on a tetanus toxoid protein used in the production of glycoconjugate vaccines against serious disease. The experiment was conducted to determine the sedimentation coefficient of the monomer species and any other com ponents present, to establish the amount of monomer compared to other species. The presence of dimer can clearly be seen for a whole range of different concentrations used.
Fig1. Sedimentation coefficient distribution c ( s ) versus s for tetanus toxoid protein showing ~86% monomer with a sedimentation coefficient of 7.6 S and ~14% of dimer at higher s (11.6 S). A rotor speed of rpm = 45 000 min -1 was used at a temperature of 20.0 °C. Protein solutions were dissolved in a phosphate chloride buffer, pH 6.8, ionic strength 0.1 M. The relative proportions of monomer and dimer do not change with loading concentration, showing the dimerisation process is not reversible. If it was reversible then the proportion of dimer should increase with increasing concentration. Some evidence of a trace amount of a higher-molecular-weight species (with a sedimentation coefficient of approximately 14.5 S) is also seen.
If the molecular mass M is known, the sedimentation coefficient can be used to calculate the frictional coefficient f , which is a measure of the conformation of a macromolecule:
0.9982 g ml–1 is the density of water at 20.0 °C, N A is the Avogadro constant and v- is the partial specific volume (in ml g–1 ) of the protein. For studies attempting accurate characterisation of conformation, another correction of the sedimentation coefficient is usually necessary. Because of the large size of macromolecules compared to the solvent they are dissolved in, they exhibit non-ideality : (i) they get in the way of each other, and (ii) if they are carrying charge, macromolecules can repel each other. The charge effect can be reduced by increasing the ionic strength (concentration of low-molecular-weight salt ions) of the solvent or, in the case of proteins, working near or at the isoelectric pH. Both effects can be reduced by working at low concentrations of macromolecules, or by taking measurements of s20,w at a series of concentrations, c and extrapolating to zero concentration to yield corrected ( s020,w ) values. More accurate extrapolations are generally obtained if the reciprocal 1/ s20,w is plotted versus c. Figure 2 shows such an extrapolation for the tetanus toxoid data of Figure 1.
Fig2. Extrapolation of the reciprocal sedimentation coefficients to zero concentration to correct for non-ideality effects of tetanus toxoid monomers and dimers.
The conformation can be interpreted in terms of ellipsoid models for globular proteins ( Figure 3a) or bead models (Figure 3b) for more complicated structures such as antibodies. It is usually necessary to combine f with other physical data, such as from viscosity or small-angle X-ray scattering measurements.
Fig3. Models for the conformations of proteins from the sedimentation coefficient, molecular mass and other information. (a) Ellipsoid model of axial ratio (ratio of long axis to short axis) of 3:1 for tetanus toxoid protein, and was obtained by combining analytical ultracentrifugation data with intrinsic viscosity data. (b) Bead model for antibody IgE (note the individual beads do not represent atoms or domains). This was the first demonstration of the cusp shape of the IgE molecule and was obtained by combining analytical ultracentrifugation data with the radius of gyration from X-ray scattering, later confirmed by spectroscopic and crystallographic data. (c) Schematic representation showing how the cusp shape of IgE facilitates its binding via its C ε 3 domain to the α-chain of the high affinity membrane IgE receptor known as Fc ε RI, shown with its constituent α, β, and two γ polypeptide chains.
Density Gradients
For very complex systems, the addition of a density gradient material can assist with the resolution of components. Figure 4 illustrates the sedimentation analysis of the dystrophin–glycoprotein complex (DGC) from skeletal muscle fibres. The size of this com plex was estimated to be approximately 18 S by comparing its migration to that of the standards β-galactosidase (16 S) and thyroglobulin (19 S). When the membrane cytoskeletal protein dystrophin was fi rstidentifi ed, it was shown to bind to a lectin matrix, although the protein does not possess any carbohydrate conjugation; this suggested that dystrophin might exist in a complex with surface glycoproteins. Sedimentation velocity analysis confirmed the existence of such a dystrophin–glycoprotein complex and centrifugation following various biochemical modifications of the protein assembly led to a detailed understanding of the composition of this complex. Alkaline extraction, acid treatment or incubation with different types of detergent causes the differential disassembly of the dystrophin–glycoprotein complex. It is now known that dystrophin is tightly associated with at least 10 different surface proteins that are involved in mem brane stabilisation, receptor anchoring and signal transduction processes. The successful characterisation of the dystrophin–glycoprotein complex by sedimentation analysis is an excellent example of how centrifugation methodology can be exploited to quickly gain biochemical knowledge of a newly discovered protein.
Fig4. Sedimentation analysis of a supramolecular protein complex. Shown is the sedimentation of the dystrophin–glycoprotein complex (DGC). Its size was estimated to be approximately 18 S by comparing its migration to that of the standards β-galactosidase (16 S) and thyroglobulin (19 S).
