Biosensors Involved in Drug Discovery - Biosensors and Biosensor Kinetics - page 73

Figure 4.2j and Tables 4.1 and 4.2 show theincrease in the affinity, K 2 ( ¼k 2 / k d ), with an
increase in the fractal dimension ratio, D f2 / D fd . For the data shown in Figure 4.2j , the affinity,
K 2 , is given by:

4 : 408 0 : 8925

K 2 ¼ð 1 : 404 0 : 13 Þð D f2 = D fd Þ ð 4 : 4j Þ

The fit is good. Only four data points are available. The availability of more data points
would lead to a more reliable fit. The affinity, K 2 , is sensitive to the ratio of the fractal
dimensions, D f2 / D fd , as noted by the close to four and a half (equal to 4.408) order of depen-
dence exhibited. Once again, this is one way of changing the affinity, K 2 , by changing the
degree of heterogeneity exhibited on the biosensor surface. Here again, one needs to change
the degree of heterogeneity exhibited in the binding and in the dissociation phases differently
so that one may change the ratio, D f2 / D fd , in the required direction.

The data presented in Figures 4.2i and 4.2j are presented together in Figure 4.2k , since only
four data points each were presented in Figures 4.2i and 4.2j , respectively. For the data
shown in Figure 4.2k , the affinities, K 1 or K 2 are given by:

3 : 444 0 : 1818

ð K 1 or K 2 Þ¼ð 1 : 849 0 : 283 Þ½ð D f2 = D fd Þ or ð D f1 = D fd Þ ð 4 : 4k Þ

The fit is very good considering that two different data sets are presented together. The
affinities, K 1 and K 2 , are quite sensitive to the fractal dimension ratios, ( D f1 / D fd )or( D f2 / D fd )
present on the biosensor chip surface as noted by the close to three and a half (equal to 3.444)
order of dependence exhibited.

Figure 4.3a shows the binding of 50 nM ARC-704 in solution to C a (950 RU) immobilized
on a Biacore S51 sensor chip surface ( Viht et al., 2007 ). A dual-fractal analysis is required to
adequately describe the binding and the dissociation kinetics. The values of (a) the binding
rate coefficient, k , and the fractal dimension, D f , for a single-fractal analysis, (b) the binding
rate coefficients, k 1 and k 2 , and the fractal dimensions, D f1 and D f2 , for a dual-fractal analy-
sis, (c) the dissociation rate coefficient, k d , and the fractal dimension, D fd , for a single-fractal
analysis, and (d) the dissociation rate coefficients, k d1 and k d2 , and the fractal dimensions,
D fd1 and D fd2 , for a dual-fractal analysis are given in Tables 4.3 and 4.4 . It is of interest to
note that for a dual-fractal analysis, as the fractal dimension increases by a factor of 1.50
from a value of D f1 equal to 1.9126 to D f2 equal to 2.8771, the binding rate coefficient
increases by a factor of 3.92 from a value of k 1 equal to 4.492 to k 2 equal to 17.6.

Figure 4.3b shows the binding of 25 nM ARC-704 in solution to C a (950 RU) immobilized
on a Biacore S51 sensor chip surface ( Viht et al., 2007 ). A dual-fractal analysis is required to
adequately describe the binding kinetics. A single-fractal analysis is required to adequately
describe the dissociation kinetics. The values of (a) the binding rate coefficient, k , and the
fractal dimension, D f , for a single-fractal analysis, (b) the binding rate coefficients, k 1 and k 2 ,