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FIGURE 12.11 Binding and dissociation of different concentrations (in fiM) of Fab fragment 48G7l48G7h (analyte) in solution to p-nitrophenyl phosphonate (PNP) transition state analogue (receptor) immobilized on a BIACORE biosensor surface (Patten et ai, 1996). (a) 0.339; (b) 0.169; (c) 0.085 (binding modeled as a dual-fractal analysis); (d) 0.042; (e) 0.021 (binding modeled as a single-fractal analysis); In all cases the dissociation is modeled as a single-fractal analysis.

FIGURE 12.11 Binding and dissociation of different concentrations (in fiM) of Fab fragment 48G7l48G7h (analyte) in solution to p-nitrophenyl phosphonate (PNP) transition state analogue (receptor) immobilized on a BIACORE biosensor surface (Patten et ai, 1996). (a) 0.339; (b) 0.169; (c) 0.085 (binding modeled as a dual-fractal analysis); (d) 0.042; (e) 0.021 (binding modeled as a single-fractal analysis); In all cases the dissociation is modeled as a single-fractal analysis.

fractal analysis is required to adequately describe the binding kinetics [Eq. (12.1b)], and a single-fractal analysis [eq. (12.8a)] is sufficient to describe the dissociation kinetics.

Table 12.4 shows the values of the binding rate coefficient, febind, the dissociation rate coefficient, fcdiss, the fractal dimension for binding, Djhmd, and the fractal dimension for dissociation, %diss. The values of the binding and dissociation rate coefficient(s) and the fractal dimension(s) for association or adsorption (or binding) and dissociation presented in the table were obtained from a regression analysis using Sigmaplot (1993) to model the experimental data using Eq. (12.1b), wherein (analyte -receptor) = fci,bindtp and fe2,bind£p for the binding step(s), and Eq. (12.8a), wherein (analyte • receptor) = — kdisstp for the dissociation step. The binding and dissociation rate coefficient values presented in Table 12.4 are within 95% confidence limits. For example, for the binding of 0.339 /jM 48G7l48G7h in solution to the PNP-immobilized surface, the reported value of fe^bind is 65.8 ± 5.91. The 95% confidence limit indicates that 95% of the k l.bind values will lie between 59.9 and 71.7. This indicates that the values are precise and significant. The curves presented in the figures are theoretical curves.

Figures 12.11b-12.11e show the binding of 0.169, 0.085, 0.042, and 0.021 fxM 48G7L48G7H in solution to a PNP-immobilized surface as well as the dissociation of the 48G7L48G7H-PNP complex from the surface. For the binding of 0.169 and the 0.085 /¿M 48G7L48G7H in solution to the PNP-immobilized surface, a dual-fractal analysis is required to adequately describe the binding kinetics. For the lower concentrations (0.042 and 0.021 /zM 48G7l48G7h in solution to the PNP-immobilized surface), a single-fractal analysis is sufficient. This indicates that there is a change in the binding mechanism as one goes from the lower to the higher 48G7l48G7h concentration in solution. The dissociation kinetics for each of the 48G7l48G7h concentrations utilized may be adequately described by a single-fractal analysis.

The authors (Patten et al, 1996) indicate that nonspecific binding has been eliminated by subtracting out sensorgrams from negative control surfaces. Our analysis here does not include this nonselective adsorption or binding. We do recognize that, in some cases, this may be a significant component of the adsorbed material and that this rate of association, which is of a temporal nature, would depend on surface availability. If we were to accommodate the nonselective adsorption into the model, there would be an increase in the degree of heterogeneity on the surface since by its very nature nonspecific adsorption is more heterogeneous than specific adsorption or binding. 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 12.4 indicates that kl b,nd increases as the 48G7L48G7H concentration in solution increases. Figure 12.12a shows the increase in fei bmd (or fei, to avoid the double subscript nomenclature) with an increase in 48G7L48G7H concentration in solution. In the 48G7L48G7H concentration range (0.021 to u>

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