A kinetic analysis using fractals of cellular analyte-receptor binding and dissociation

A fractal analysis is presented for cellular analyte-receptor binding and dissociation kinetics using a biosensor. Data taken from the literature may be modelled, in the case of binding, using a single-fractal analysis or a dual-fractal analysis. The dual-fractal analysis represents a change in the binding mechanism as the reaction progresses on the surface. The predictive relationship developed for the equilibrium constant, K (affinity which is equal to k(d)/k(1or2)), as a function of the analyte concentration is of particular value since it provides a means by which the affinity may be manipulated. This should be of assistance in cell-surface reactions, drug-candidate optimization and for the design of immunodiagnostic devices. Relationships are also presented for the binding and dissociation rate coefficients as a function of their corresponding fractal dimension, D(f) or the degree of heterogeneity that exists on the surface, and the analyte concentration in solution. When analyte-receptor binding or dissociation is involved, an increase in the heterogeneity on the surface (increase in D(f) or D(fd) as the case may be) leads to an increase in the binding and the dissociation rate coefficients. It is suggested that an increase in the degree of heterogeneity on the surface leads to an increase in the turbulence on the surface owing to the irregularities on the surface. This turbulence promotes mixing, minimizes diffusional limitations and leads subsequently to an increase in the binding and the dissociation rate coefficients. The binding and dissociation rate coefficients are rather sensitive to the degree of heterogeneity, D(f) and D(fd), respectively, that exists on the biosensor surface. The heterogeneity on the surface in general affects the binding and dissociation rate coefficients differently. In general, the analyte concentration in solution has a mild affect on the fractal dimension for binding or the fractal dimension for dissociation. This is indicated by the low values of the exponent in the predictive relationships developed.