4 - Fractal Binding and Dissociation Kinetics of Heart-Related Compounds on Biosensor Surfaces

Abstract

This chapter presents fractal analysis to analyze the binding of various LCAT concentrations in solution to egg-white apoA-I rHDL immobilized on a biosensor chip; native, mildly oxidized, and strongly oxidized LDL in solution to heparin-modified Au-surface of a surface plasmon resonance (SPR) biosensor; TRITC (tetramethylrhodamine-5-(and-6)-isothiocyanate)-labeled HDL in solution to a bare optical fiber; and interactions of other heart-related analytes. The fractal analysis provides a quantitative indication of the state of disorder (fractal dimension) and the binding (and dissociation) rate coefficients on the sensor chip surface. In accordance with the prefactor analysis for fractal aggregates quantitative (predictive) equations are developed for the binding rate coefficients, k1 and k2, as a function of the LCAT concentration in solution; the dissociation rate coefficient, kd2, as a function of the LCAT concentration in solution and as a function of the fractal dimension, Dfd2, or the degree of heterogeneity present in the dissociation phase on the sensor chip surface; the binding rate coefficient, k2, as a function of the degree of heterogeneity or fractal dimension, Df2, present on the sensor chip surface; and the affinity, k2(= k2/kd2), as a function of the ratio of fractal dimensions, Df2/Dfd2. Predictive relations are also developed for the binding rate coefficient, k, as a function of the TRITC-labeled HDL concentration (in μg/ml) in solution, and as a function of the fractal dimension, Df, or the degree of heterogeneity present on abare optical fiber. Predictive relationships are also presented for the affinities, K1 and K2, as a function of the ratio of fractal dimensions, Df1/Dfd and Df2/Dfd, respectively for the anti-CCR5 linear epitope-recognizing antibody, 3A9, in solution to the human chemokine-coupled receptor CCR5.