Biosensors Involved in Drug Discovery - Biosensors and Biosensor Kinetics - page 61

methylcoumarin (MET-AMC) in solution in the competitive scintillation proximity
aminoacyl-tRNA synthetase charging assay (cSPA) ( Forbes et al., 2007 ). These authors
report that protein kinases play a significant role in the regulation of protein function in living
cells, and the above interactions help identify inhibitors for protein kinases. These authors
point out that protein phosphatases are involved in the control of the phosphorylation state
of many proteins. Furthermore, these authors add that the measurement of the phosphate
ion, P i is an important target for the understanding of cellular activities involving such
proteins. They report that this is a good and high-throughput screening (HTS) compatible
method for measuring the concentration of most naturally occurring amino acids. They fur-
ther assert that the quantitative detection of amino acids is important in the areas of patient
care and drug discovery.

The fractal analysis is just one method of providing values for the binding and the dissocia-
tion (if applicable) rate coefficient values. Other methods for obtaining values for the binding
and the dissociation rate coefficient values on biosensor surfaces are also available. Needless
to say each method of analysis has different assumptions involved. The present fractal anal-
ysis method also provides values for the fractal dimension that exists on the biosensor sur-
face, or in other words, the degree of heterogeneity that exists on the biosensor surface.

4.2 Theory

4.2.1 Single-Fractal Analysis

Binding Rate Coefficient

Havlin ( 1989 ) reports that the diffusion of a particle (analyte [Ag]) from a homogeneous
solution to a solid surface (e.g., receptor [Ab]-coated surface) on which it reacts to form a
product (analyte-receptor complex; (Ab Ag)) is given by:

t ð 3 D f , bind Þ= 2 t p ,

¼ t < t c

ð Ab Ag Þ ð 4 : 1 Þ

t 1 = 2 , t > t c

Here D f,bind or D f is the fractal dimension of the surface during the binding step. t c is the
cross-over value. Havlin (1989) reports that the cross-over value may be determined by
r c t c . Above the characteristic length, r c , the self-similarity of the surface is lost and the
surface may be considered homogeneous. Above time, t c , the surface may be considered
homogeneous, because the self-similarity property disappears, and “regular” diffusion is
now present. For a homogeneous surface where D f is equal to 2, and when only diffusional
limitations are present, p ½ case

(where D f,bind is equal to 2) is that the analyte in solution views the fractal object, in our case,
the receptor-coated biosensor surface, from a “large distance.” In essence, in the association
process, the diffusion of the analyte from the solution to the receptor surface creates a

¼ ½ as it should be. Another way of looking at the p ¼