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0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 Fractal dimension, Df

FIGURE 11.4 Influence of the fractal dimension, Df, on the binding rate coefficient, k. mutant form (E1037A), the binding rate coefficient is given by

This equation predicts the k values presented in Table 11.1c reasonably well. There is some deviation in the data, which is reflected in the error estimate for the coefficient as well as in the exponent. The availability of more data points would more firmly establish this equation. Note the very high value of the exponent. This, once again, underscores that the binding rate coefficient is very sensitive to the degree of heterogeneity that exists on the surface. Once again, and as indicated previously in this text, the data in Fig. 11.6 could very easily be reasonably represented by a linear function. The Sigmaplot (1993) program provides the nonlinear function. The lack of data points (only three data points are available) once again prevents a clearer model discrimination between a nonlinear and a linear representation.

Figures 11.7a-f show the binding of different concentrations (100 to 500 nM) of wild-type fragment in solution to salivary agglutinin immobilized on a sensor chip. In each case, starting from 100 nM with increasing increments of 100 nM to 500 nM, the binding curve may be described by a single-fractal analysis. The values of k and Dj for each case are given in Table 11. Id. The 400 nM wild-type fragment run was repeated once.

Time, sec

FIGURE 11.5 (a) Binding of 500 nM of the mutant form of the E1037 fragment in solution to salivary agglutinin immobilized on a sensor chip; (b) and (c) 500 nM wild-type fragment in solution to salivary agglutinin immobilized on a sensor chip (Kelly et al, 1999).

FIGURE 11.6 Influence of the fractal dimension, Dj, on the binding rate coefficient, k.

Fractal dimension, Df

FIGURE 11.6 Influence of the fractal dimension, Dj, on the binding rate coefficient, k.

Table 11.Id and Fig. 11.8a indicate that an increase in the wild-type fragment concentration in solution leads to an increase in the binding rate coefficient, k. For the 100 to 500 nM wild-type fragment concentration in solution, the binding rate coefficient is given by k = (0.097±0.016)[wild-type fragment]0'86±0'12. (11.6a)

This equation predicts the k values presented in Table 11.Id reasonably well. This is a nonlinear representation, although the exponent dependence is close to 1 (0.86). There is some scatter in the data, reflected in the error estimate for the coefficient as well as in the exponent. The availability of more data points would more firmly establish this equation. A better fit could presumably be obtained from an equation such as k = a[wild-type fragment]1" + c[wild type fragment]''. (11.6b)

However, this would only involve more parameters. Here a, b, c, and d are parameters that need to be determined by regression. In this case, more data points would definitely be required.

Table 11.Id and Fig. 11.8b indicate that an increase in the wild-type fragment concentration in solution leads to an increase in the fractal

FIGURE 11.7 Binding of different concentrations (in nM) of wild-type fragment in solution to salivary agglutinin immobilized on a sensor chip (Kelly et al., 1999). (a) 100; (b) 200; (c) 300; (d) 400; (e) 400; (0 500.

dimension, Dj. For the 100 to 500 nM wild-type concentration in solution utilized, the fractal dimension is given by

Df = (1.28+ 0.03) [wild-type fragment]0075 ± 0019. (11.6c)

This equation predicts the Devalues given in Table 11.Id reasonably well. The representation is nonlinear, even though the exponent dependence on the

100 200 300 400 500

wild-type fragment concentration, nM

100 200 300 400

wild-type concentration, nM

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