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FIGURE 5.11. Binding rate curves for 5 mg/ml h-IgG in solution to (a) single adlayer (F') of protein A (single-fractal analysis); (b) double adlayer (F' + F") of protein A (— single-fractal analysis; — double-fractal analysis) adsorbed on a waveguide surface (Nellen and Lukosz, 1991).

Time, min

FIGURE 5.11. Binding rate curves for 5 mg/ml h-IgG in solution to (a) single adlayer (F') of protein A (single-fractal analysis); (b) double adlayer (F' + F") of protein A (— single-fractal analysis; — double-fractal analysis) adsorbed on a waveguide surface (Nellen and Lukosz, 1991).

Zhao and Reichert (1992) analyzed the time-dependent fluorescence intensity of the binding of FITC-avidin in solution to sensor tips doped with biotin lipid at different surface densities. Figure 5.12 shows the curves obtained using Eqs. (5.1) and (5.2) for the binding of FITC-avidin in solution to a biotin lipid surface with densities ranging from 0.28 to 2.70 mol%. Clearly, the dual-fractal analysis provides a better fit than that obtained from a single-fractal analysis at all four biotin lipid concentrations utilized. Note also that an increase in the fractal dimension from Df, to Df2 leads to an increase in the binding rate coefficient from kx to k2. For example, for the binding of FITC-avidin to a sensor tip doped with 0.28 mol% biotin (lowest surface density), an increase in the fractal dimension value by 83.8%—from Df] = 1.38 to Df, = 2.53 leads to an increase in the binding rate coefficient value by a factor of 4.8—from feL = 0.010 to k2 = 0.048. Also, for the binding of FITC-avidin to a sensor doped with 2.70 mol% biotin (highest surface density), an increase in the fractal dimension value by a factor of 2—from Df, = 1.36 to Df2 = 2.72—leads to an increase in the binding rate coefficient by a factor of 4.4—from fe1 = 0.0515 to k2 = 0.234.

Also note that as the biotin lipid surface density increases, the binding rate coefficients, feL and k2, exhibit increases (see Table 5.5). Figure 5.13 shows

FIGURE 5.12 Theoretical curves using Eqs. (5.1) (- - -, single-fractal analysis) and (5.2 —, dual-fractal analysis) for the binding of avidin in solution to different biotin doping densities (in mol%) on a sensor tip (Zhao and Reichert, 1992): (a) 0.28, (b) 0.50, (c) 0.99, (d) 2.70.

20 30 40 Time, min

FIGURE 5.12 Theoretical curves using Eqs. (5.1) (- - -, single-fractal analysis) and (5.2 —, dual-fractal analysis) for the binding of avidin in solution to different biotin doping densities (in mol%) on a sensor tip (Zhao and Reichert, 1992): (a) 0.28, (b) 0.50, (c) 0.99, (d) 2.70.

TABLE 5.5 Influence of Different Parameters on Fractal Dimensions and Binding Rate Coefficients for Different Analyte-Receptor Reactions: Single-and Dual-Fractal Analysis

Analyte in solution/ receptor on surface k Dt k, k2 Df, Df2 Reference a a c

Avidin/0.28 mol%

biotin lipid surface density Avidin/0.50 mol%

biotin lipid surface density Avidin/0.99 mol%

biotin surface density Avidin/2.70 raol0/»

biotin surface density m-Xylene-saturated STE buffer solution/ EDTA-treated cell (transformed E. coli) suspension immobilized on fiber-optic tip with dialysis membrane mXylene/ cell suspension immobilized on fiber-optic tip with polycarbonate membrane m-Xylene/cell suspension immobilized on fiberoptic tip with polycarbonate membrane; lucerfm added after 2 h of luciferase induction; absence of methyl-benzyl alcohol m-Xylene/cell suspension; lucerfin added; presence of methyl-benzyl alcohol

0.018 ±0.005 0.025 ±0.005 0.078 ±0.016 0.074 ±0.025 119.82 ±17.02

1.98 ±0.128 0.010 ±0.002 1.747 ±0.109 0.0181 ±0.003 2.205±0.121 0.051 ±0.008

0.048 ±0.001 0.0648 ±0.003 0.181 ±0.008 0.234 ±0.008 na

na na

Zhao and Reichert, 1992 Zhao and Reichert, 1992 Zhao and Reichert, 1992 Zhao and Reichert, 1992 Ikariyama et al, 1997

Ikariyama ei al, 1997

Ikariyama et al, 1997

1282±7.25 1.210±0.478 0.721±0.06 Ikariyama et al., 1997

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