hinder dissociation (Altschuh et al, 1992; Mani et al., 1994). Also, the fractal nature of the surface itself may lead to higher-than-expected affinities. Other reasons for this phenomenon are also possible. In our case, the rebinding phenomenon observed (as in other BIACORE experiments) (Nieba et ah, 1996; Karlsson and Stahlberg, 1995; Wohlhueter et al, 1994; Morton et al, 1995) may be a minimum, due to the fractal nature of the surface. This too leads to an increase in the dissociation rate coefficient.

Figure 7.3b shows the curves obtained using Eq. (7.2c) for the binding of DNA polymerase I (Klenow fragment) 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. Once again, 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, fcbmd, ki.bmd» ^2,bind, the dissociation rate coefficient, /?dlss, the fractal dimension for binding, Dfbmd, Df^ind, and D[2ii3lnc], and the fractal dimension for the dissociation, Df diss. In this case, KL = 0.189 and K2 = 0.018. Once again, the affinity value decreases as one goes from the first phase to the second phase. Note that as one goes from the Klenow fragment case to the T7 DNA polymerase case, the Dfhbind value increases by 20.5%—from 1.46 to 1.76, and the fei bind value increases by a factor of 1.89—from 106.2 to 201.2. Similarly, the Df2)btnd value increases by 13.6%—from 2.42 to 2.75, and the /?2,bmd value increases by a factor of 1.78—from 1088 to 1943. Also, the fractal dimension for dissociation, Df dlss, increases by a factor of 1.76—from 1.55 to 2.73, and the dissociation rate coefficient, fe,:ilss, shows an increase by factor of 75.5. Thus, the dissociation rate coefficient is very sensitive to the degree of heterogeneity on the surface, at least in these two cases.

Figure 7.3c shows the curves obtained using Eq. (7.2a) for the binding of endonuclease Xhol in solution to 69-bp substrate complementary DNA immobilized on the biosensor surface, as well as the dissociation of the analyte from the same surface and its eventual diffusion in solution. In this case, the binding phase as well as the dissociation phase [Eq. (7.2b)] may be adequately described by a single-fractal analysis. The affinity, K( = fediSS/febind). is equal to 0.000014. This is an extremely low value, especially when compared to the values in the two previous cases.

Houshmand et al. (1999) analyzed the binding and dissociation of 80 nM large T-antigen in solution to the monoclonal antibody mAbLTl immobilized on an SPR biosensor surface in the absence and in the presence of a competitor peptide, NH3CPNSLTPADPTMDY-COOH. After a given time interval, the injection of the protein ligand was interrupted, and the subsequent dissociation reaction was monitored. Figure 7.4a shows the

curves obtained using Eq. (7.2a) for the binding of the 80 nM large T-antigen in solution to the mAbLTl immobilized on the SPR surface in the absence of the competitor peptide as well as the dissociation of the analyte from the same surface [using Eq. (7.2b)] and its eventual diffusion into solution. A single-fractal analysis is sufficient to adequately describe both the binding [Eq. (7.2a)] and the dissociation [Eq. (7.2b)] kinetics.

Table 7.3 shows the values of the binding rate coefficient, kbmd. the dissociation rate coefficient, fcdiSS, the fractal dimension for binding, Dfbmd, and the fractal dimension for dissociation, Df diss- When competitor peptide is not used the affinity, K= 1.95. Also, the estimated value for the fractal dimension for dissociation, Dfdiss, is larger (equal to 2.53) than the fractal dimension for binding, Df bind (equal to 1.87). Figures 7.4b-7.4d show the curves obtained using Eq. (7.2c) for the binding of the large T-antigen in the presence of 50-800 /zM peptide to the mAbLTl immobilized on the SPR surface as well as the dissociation [using Eq. (7.2d)] of the analyte from the surface and its eventual diffusion into solution. When the competitor peptide (50-800 /¿M) is used, a dual-fractal analysis is required to adequately describe

TABLE 7.3 Fractal Dimensions and Binding and Dissociation Rate Coefficients Using a Single- and a Dual-Fractal Analysis for the Binding of 80 nM Large Antigen (30 //I) in Solution in the Absence and in the Presence of Competitor Peptide (NH3-CPNSLTPADPTMDY-COOH) to mAbLTl Immobilized on a BIACORE Biosensor Chip Surface (Using Surface Plasmon Resonance) (Houshmand et al., 1999)

TABLE 7.3 Fractal Dimensions and Binding and Dissociation Rate Coefficients Using a Single- and a Dual-Fractal Analysis for the Binding of 80 nM Large Antigen (30 //I) in Solution in the Absence and in the Presence of Competitor Peptide (NH3-CPNSLTPADPTMDY-COOH) to mAbLTl Immobilized on a BIACORE Biosensor Chip Surface (Using Surface Plasmon Resonance) (Houshmand et al., 1999)

Antigen + peptide (/il) in solution/mAbLTl on surface |
kbind |
kl,bind |
bind |
fcdiss |
Df bind |
.bind |
Of, .bind |
I\diSS |

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