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58.9 ±5.5

1.76±0.13

Different concentrations of hCG were utilized during the dissociation phase

Different concentrations of hCG were utilized during the dissociation phase more heterogeneous than specific adsorption. This would lead to higher fractal dimension values since the fractal dimension is a direct measure of the degree of heterogeneity that exists on the surface.

Table 7.1 indicates that kd increases as the hCG concentration in solution increases, as expected by Loomans et al. (1997). Figure 7.2a shows an increase in k,j with an increase in hCG concentration in solution. Clearly, fed varies with hCG concentration in solution in a nonlinear fashion. In the hCG concentration range of 0.2 to 4.0 ¿¿M, kd is given by fed = (2.56 + 2.88)[hCG, jUM]L92±0'28. (7.3a)

The fit is not reasonable, especially at the higher hCG concentrations (above 2/uM). A better fit was sought using a four-parameter model. The data was fit in two phases: 0 to 2 fiM, and 2 to 4 fiM hCG concentration. Using this approach, fed is given by fed = (0.916 + 0.127) [hCG]0'671± 0,102 + (1.64±0.53)[hCG]2,68±0,57. (7.3b)

More data points are required to establish this equation more firmly. Nevertheless, Eq. (7.3b) is of value since it provides an indication of the change in fed as the hCG concentration in solution changes. The fractional exponent dependence indicates the fractal nature of the system. The dissociation rate coefficient is quite sensitive to the hCG concentration at the higher hCG concentration in solution, as indicated by the higher-than second-order value of the exponent. These results are consistent with the results obtained by Loomans et al. (1997), who performed a nonfractal analysis. A fractal analysis incorporates the heterogeneity that inherently hCG concentration, micromole Fractal dimension,

FIGURE 7.2 (a) Influence of the hCG concentration in solution on the dissociation rate

Fractal dimension,

FIGURE 7.2 (a) Influence of the hCG concentration in solution on the dissociation rate exists on the biosensor surface, which is an additional advantage of the analysis. This is reflected in the fractal dimension value: A higher value indicates a higher degree of heterogeneity on the surface.

Table 7.1 and Figure 7.2b indicate that fed increases as the fractal dimension for dissociation, Df j, increases. Clearly, fed varies with Df d in a nonlinear fashion. In the hCG concentration range of 0.2 to 4.0 /imol, fed is given by fed = (5.11 ±4.06)[Df,df90±043. (7.3c)

Although the fit is very reasonable, more data points are required to more firmly establish this equation, especially at the higher fractal dimension values. Eq. (7.3c) is of value since it provides an indication of the change in fediss (or fed) as the degree of heterogeneity on the SPR biosensor surface changes. The high exponent dependence indicates that the dissociation rate coefficient is sensitive to the degree of heterogeneity that exists on the SPR

biosensor surface. The value of an expression that relates the dissociation rate coefficient to a fractal dimension is that it provides one with an avenue by which to control the dissociation rate coefficient on the surface by changing the degree of heterogeneity that exists on the surface.

Apparently, the utilization of higher hCG concentrations in solution leads to higher degrees of heterogeneity on the SPR biosensor surface, which eventually leads to higher k,{ values. However, this is just one explanation of the results, and other, perhaps more suitable, explanations are also possible. Finally, since no binding rate coefficients are presented in this analysis, affinity (K = fcd/febmd) values are not given.

Nilsson et al. (1995) utilized the SPR biosensor to monitor DNA manipulations in real time. These authors immobilized DNA fragments on the biosensor surface using the streptavidin-biotin system and monitored DNA hybridization kinetics, DNA strand separation, and enzymatic modifications. Figure 7.3a shows the curves obtained using Eq. (7.2c) for the binding of T7 DNA polymerase in solution to a complementary DNA immobilized on the SPR biosensor surface as well as the dissociation of the analyte from the same surface and its eventual diffusion in solution. A dual-fractal analysis is required to adequately describe the binding kinetics [Eq. (7.2c)], and a single-fractal analysis [Eq. (7.2b)] is sufficient to describe the dissociation kinetics.

Table 7.2 shows the values of the binding rate coefficients, febind, /?]bmd, ^2,bind> the dissociation rate coefficient, kdiss, the fractal dimensions for binding, Dfbind, Df^bind. and Df^md, and the fractal dimension for dissociation, Df diss. Since the dual-fractal analysis is required to adequately describe the binding phase, it will be analyzed further. The affinity, K, is equal to the ratio of the dissociation rate coefficient to the binding rate coefficient. Thus, K] = kdlss/k, has a value of 7.54 and K2 = kdiss/k2 has a value of 0.78 for the T7 DNA polymerase reaction. There is a decrease in the affinity value by a factor of 9.67 on going from the first phase to the second phase in the binding reaction. This is due to the increase in the binding rate coefficient value in the second phase compared to the first phase. The dissociation rate coefficient value remains the same.

In general, typical antigen-antibody affinities are in the nanomolar to picomolar range. In this case, the affinities values reported are quite a few orders of magnitude higher than normally reported. Presumably, the increase in the higher affinity value may be due to a combination of factors. One such factor is that very little or no conformational restriction of the receptor on the surface minimizes the strength of the analyte-receptor reaction (Altschuh et al, 1992). This increases the dissociation rate coefficient. Furthermore, if the binding of the analyte to the receptor involves a conformational adaptation via the induced-fit mechanism, the lower structural flexibility of the analyte may Time, sec 