A fractal analysis of analyte–receptor binding and dissociation kinetics in microcantilever biosensors

A fractal analysis of a confirmative nature only is presented for the binding and dissociation (where ever it is applicable) for (a) CrO42− in solution to a SAM-coated microcantilever surface [8], and (b) for two hybridization reactions occurring on microcantilever surfaces [1,28]. Data taken from these references may be modeled by using a single- or a dual-fractal analysis. Relationships are presented for the binding rate coefficient as a function of the fractal dimension and for the analyte concentration in solution. The binding and the dissociation rate coefficients are very sensitive to the degree of heterogeneity that exists on the microcantilever surface. For the reactions analyzed the binding and dissociation rate coefficients increase with an increase in the degree of heterogeneity on the microcantilever surface. For one of the hybridization reactions analyzed [28] the binding rate coefficient increases with the number of bases (25- and 9-mer) present in the oligomer (analyte) in solution. The analysis should assist in placing the analyte–receptor reactions occurring on microcantilever systems on a kinetic basis.