1.3 1.4 1.5 1.6 Fractal dimension, Df
FIGURE 5.5 Binding rate curves for five different proteins with different numbers of histidine tags in solution to a Ni + + -NTA surface (Nieba et al, 1997). (a) ■ GroES, A CS-4-His, • CS-2His; (b) • GrpE, ■ MBP. (c) Influence of the fractal dimension, Df, on the binding rate coefficient, k.
Direct optical techniques, such as the surface plasmon resonance (SPR) technique (Sutherland et al, 1984), have been used to analyze biospecific interactions at solid-liquid interfaces. In this technique, there is a resonant coupling of the incident light to plasmons (conducting electrons) at the metal film surface. The oscillations of the plasmons give rise to an evanescent field, which extends into a sample solution. For SPR sensing, the antibody or the antigen (in general, protein) is adsorbed to the metal surface and exposed to the analyte in solution.
Fagerstam et al (1997) used the SPR technique to analyze a dextran-modified sensor chip to which one of the components is attached covalently. These authors analyzed the binding of a fusion protein between the lac repressor and /?-galactosidase, and between the lac operator DNA bound to the matrix of an SPR biosensor. It was found that the lac operator DNA was captured by streptavidin immobilized on the biosensor chip. This DNA is synthetic in nature, has 35 base pairs, and is biotinylated at the 5' end. Figures 5.6a-5.6e show the curves obtained for the binding of fusion protein in the concentration range of 0.4 to 5.0 ¿¿g/ml. Table 5.2 shows the values of the binding rate coefficients and the fractal dimensions obtained from single- and dual-fractal analysis. Once again, the dual-fractal analysis provides a better fit than that obtained from a single-fractal analysis for the binding of the fusion protein in the concentration range of 0.4 to 5.0 Hg/m\.
Note that for the protein fusion concentration range analyzed, an increase in the value of the fractal dimension from Df. to Df2 leads to an increase in the value of the binding rate coefficient from k1 to k2. The magnitude of the changes in the fractal dimension that lead to changes in the binding rate coefficients for a particular fusion protein concentration are significant since they provide one means of controlling or varying the binding rate coefficient on the biosensor surface. Furthermore, these results are consistent with Fagerstam et al. (1997), who inferred from the shape of the binding curves that the binding interaction appears to be heterogeneous on the surface.
Figure 5.7a shows the linear increase in kj and k2 with an increase in the fusion protein concentration in solution. However, the linearity shown is not convincing due to the small number of data points and the scatter in the estimated values for k2 at different fusion protein concentrations. Nevertheless, the trend presented is useful.
Figure 5.7b shows that the fractal dimension, Dft, increases linearly as the fusion protein concentration increases in the concentration range analyzed. Once again, there is scatter in the data, and more data points would more firmly establish the trend presented. Figure 5.6b also shows that Df2 exhibits a slight linearly decreasing trend with an increase in the fusion protein concentration. And again, more data points would more firmly establish the trend presented.
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