0 50 100 150 200 250 300 Time, sec

0 50 100 150 200 250 300 Time, sec

FIGURE 6.19 Binding of 0.03 mg/ml IgG-FITC in solution (a) in the presence of 0.01 mg/ml BSA (—, single-fractal analysis; —, dual-fractal analysis) and (b) in the absence of BSA to the biotinylated ITO surface (Asanov et al, 1998).

Time, sec

FIGURE 6.19 Binding of 0.03 mg/ml IgG-FITC in solution (a) in the presence of 0.01 mg/ml BSA (—, single-fractal analysis; —, dual-fractal analysis) and (b) in the absence of BSA to the biotinylated ITO surface (Asanov et al, 1998).

TABLE 6.7 Influence of Different Parameters on Fractal Dimensions and Binding Rate Coefficients for Analyte-Receptor Reaction Kinetics (Kyono et al, 1998)

Analyte concentration in solution/receptor on surface k Df ki k2 Df, Df2

20 ng per well 3.6058 1.5936 1.5671 18.710 0.8782 2.4402

helicase/ ±1.344 ±0.271 ±0.197 ±2.001 ±0.1736 ±0.173

nonstructural protein 3 (NS3) of hepatitis virus (HCV) [HCV NS3 protein] using a scintillation proximity assay (SPA) system

An evanescent fiber-optic biosensor has been developed to detect lipopolysaccharide (LPS) found in the outer cell membrane of gram-negative bacteria by James et al. (1996). These authors analyzed the kinetics and stability of the binding of 25 to 200 ng/ml TRITC-LPS (also known as endotoxin) in solution to polymyxin B immobilized on the fiber-optic biosensor. Figure 6.20 shows the curves obtained using Eqs. (6.2a) and (6.2b) for the binding of LPS in solution to the polymyxin immobilized on the

TABLE 6.8 Influence of Nonspecific and Specific Adsorption on the Fractal Dimensions for the Binding of Anti-biotin Antibody in Solution to Biotin Immobilized on a Transparent Indium-Tin Oxide (ITO) Electrode (Asanov et al., 1998)

Analyte concentration in solution/ receptor on surface k Df hi k2 Dtl D(2

0.03 mg/ml IgG-FITC 0.00657 ± 0.0012 1.7812 ± 0.1132 0.00251 ± 0.00023 0.03962 ±0.0011 1.2766±0.1463 2.4570±0.061

adsorption in the presence of 0.01 mg/ml B S A/bi o tiny la ted ITO surface

0.03 mg/ml IgG-FlTC in the 0.00844 ± 0.0004 1.3688 ± 0.00048 na na na na absence of BSA/biotinylated ITO surface

TABLE 6.9 Influence of Different Parameters on Fractal Dimensions and Binding Rate Coefficients for Analyte-Receptor Reaction Kinetics (James et al., 1996)

Analyte concentration in solution/ receptor on surface

10 ng/ml LPS/ polymyxin B 25 ng/ml LPS/ polymyxin B 50 ng/ml LPS/ polymyxin B 100 ng/ml LPS/

polymyxin B 200 ng/ml LPS/ polymyxin B

10.451 ± 1.836 13.900 ±2.207 18.433 ±3.148 28.34 ±3.443 47.289 ±3.665

2.7190 ±0.1064 2.6218 ±0.0968 2.6528 ±0.1036 2.6792 ±0.0754 2.7102 ±0.0484

13.731 ±4.612 17.019 ±6.169 23.571 ±7.710 33.939 ±9.434 56.082 ±5.447

12.094 ±0.469 15.384 ±0.700 21.519 ±0.604 31.136 ±0.825 51.391 ±1.711

3.00-0.050 2.6218 ±0.0968 2.9508 ±0.0364 2.8633 ±0.0344 2.7102 ±0.0484

biosensor. Table 6.9 shows the values of the binding rate coefficients and the fractal dimensions obtained using a single- and a dual-fractal analysis. Figure 6.20 shows that for each of the 25 to 200 ng/ml TRITC-LPS concentrations used, a dual-fractal analysis provides a better fit. Therefore, only the dual-fractal analysis is analyzed further.

Table 6.9 indicates that for a dual-fractal analysis an increase in the TRITC-LPS concentration in solution leads to an increase in the binding rate coefficients, feL and k2. Figure 6.21 also shows this increase. In the 25 to 200 ng/ml TRITC-LPS concentration, ki is given by h = (4.120 + 0.573) [TRITC-LPS]04696 ± 00556 (6.na)

and k2 is given by k2 = (3.5515 + 0.4574) [TRITC-LPS]0'4827 ±0'0518. (6.11b)

These predictive equations fit the values of the fei and k2 presented in Table 6.9 reasonably well. The exponent dependence of the binding rate coefficients

TRITC-LPS concentration, ng/ml

FIGURE 6.21 Influence of the TRITC-LPS concentration in solution on the binding rate coefficients, (a) hi, (b) k2.

TRITC-LPS concentration, ng/ml

FIGURE 6.21 Influence of the TRITC-LPS concentration in solution on the binding rate coefficients, (a) hi, (b) k2.

on the TRITC-LPS concentration in solution lends support to the fractal nature of the system.

Figure 6.22a shows the influence of the TRITC-LPS concentration on the fractal dimension, Dfx. An increase in the TRITC-LPS concentration in solution leads to an increase in Dfl. In the 25 to 200 ng/ml TRITC-LPS concentration, Df, is given by

Dfl = (1.7882 ± 0.0778) [TRITC-LPS]0'04501 ±0'0182. (6.11c)

The fit of this predictive equation is reasonable. Since there is some scatter in the data, more data points are required to more firmly establish the equation. The fractal dimension, Dfl, is not very sensitive to the TRITC-LPS concentration in solution, as noted by the very low exponent dependence of Dfj on TRITC-LPS concentration.

Figure 6.22b shows the influence of the TRITC-LPS concentration in solution on the fractal dimension Df2. In the 25 to 200 ng/ml TRITC-LPS

TRITC-LPS concentration, ng/ml

FIGURE 6.22 Influence of the TRITC-LPS concentration in solution on the fractal dimensions, (a) Dfl; (b) Df2.

TRITC-LPS concentration, ng/ml

FIGURE 6.22 Influence of the TRITC-LPS concentration in solution on the fractal dimensions, (a) Dfl; (b) Df2.

concentration, Df2 is given by

D{2 = (3.0445 ± 0.0746) [TRITC-LPS] ~001294 - 00103 (6.lld)

Note that an increase in the TRITC-LPS concentration in solution leads to a decrease in Df2. There is scatter in the data at the lower TRITC-LPS concentrations used. This scatter is also indicated by the "error" in estimating the exponent dependence in Eq. (6.lid). Once again, the fractal dimension, Df2 is rather insensitive to the TRITC-LPS concentrations in solution, as noted by the low exponent dependence on [TRITC-LPS] in Eq. (6.lid). More data points are required, especially at the lower TRITC-LPS concentrations, to more firmly establish the predictive equation.

Figure 6.23a shows that the binding rate coefficient, fei, increases as the fractal dimension, Dft, increases. For the data presented in Table 6.9, is given by fei = (0.0793 ±0.0292)D7'6335± 24367. (6. lie)

The fit of the above predictive equation is reasonable. The binding rate

coefficient, ki, is very sensitive to the fractal dimension, Df], as noted by the high exponent dependence of k} on Dfl. Once again, this underscores that the binding rate coefficient, klt is very sensitive to the surface roughness or heterogeneity that exists on the biosensor surface.

Figure 6.23b shows that the binding rate coefficient, k2, decreases as the fractal dimension, Df2, increases. For the data presented in Table 6.9, k2 is given by k2 = (4.9640 + 3.7788) D^ 1155±la9525_ (6.nf)

There is scatter in the data, especially at the lower values of Df2 presented. This is reflected in the both of the coefficients shown in Eq. (6.1 If). More data is required at the lower Df2 values to more firmly establish the predictive equation. However, the k2 presented is still very sensitive to Df2 or the heterogeneity that exists on the biosensor surface. Once again, the data analysis in itself does not provide any evidence for surface roughness or heterogeneity, and the assumed existence of surface roughness or heterogeneity may not be correct.

Mauro et al. (1996) used fluorometric sensing to detect polymerase chain-reaction-amplified DNA using a DNA capture protein immobilized on a fiberoptic biosensor. These authors utilized amplified DNA labeled with the fluorophore tetramethylrhodamine and the AP-1 consensus nucleotide sequence recognized by GCN4. This DNA was noncovalently bound to IgG-modified fibers. Wanting to see if they could reuse the fiber, the authors performed regeneration studies. They focused their attention on conditions that would permit the release of the bound DNA while leaving the IgG-PG/GCN4 assembly in a functional state. Figure 6.24 shows the curves obtained using Eqs. (6.2a) (single-fractal analysis) and (6.2b) (dual-fractal analysis) for ten consecutive runs. The points are the experimental results obtained by Mauro et al. A dual-fractal analysis was required since the single-fractal analysis did not provide an adequate fit for the binding curves.

Table 6.10 shows the values of k and Df obtained using Sigmaplot (1993) to fit the data. The values of the parameters presented are within 95% confidence limits. For example, the value of k reported for run 2 (single-fractal analysis) is 40.248 ± 36.3232. The 95% confidence limit indicates that 95% of the k values will lie between 3.925 and 76.571. Since a dual-fractal analysis was needed to adequately model the binding curves, the results obtained from the single-fractal analysis will not be analyzed further. The Df, values reported for each of the ten runs were all equal to zero. This is due to the sigmoidal shape or concave nature of the curve (toward the origin) at very low values of time, t.

Figures 6.25a and 6.25b show the fluctuations in the binding rate coefficient, k2, and in the fractal dimension, Df2, respectively, as the run

FIGURE 6.24 Influence of the run number (regeneration study) on the binding of polymerase chain-reaction-amplified DNA in solution using a DNA capture protein immobilized on a fiberoptic biosensor (Mauro et al., 1996) (---, single-fractal analysis; —, dual-fractal analysis).

Run number |
h |
Df |
fei |

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