Modeling and Theory

This chapter describes the modeling and theory for the binding and dissociation of the different analytes on biosensor surfaces. Classical reaction kinetics is sometimes unsatisfactory when the reactants are spatially constrained at the microscopic level by walls, phase boundaries, or force fields. Such heterogeneous reactions, for example, bioenzymatic reactions that occur at interfaces of different phases, exhibit fractal orders for elementary reactions and rate coefficients with temporal memories. The fractal dimension provides a quantitative measure of the degree of heterogeneity on the biosensor surface. Several approaches have been used to model the binding kinetics on surfaces and for estimating fractal dimension values for analyte-receptor binding and dissociation kinetics observed in biosensor applications, such as Single-Fractal Analysis, Dual-Fractal Analysis, Triple-Fractal Analysis, and Pfeifer's Fractal Binding Rate Theory. The equation for fractal analysis is generic in nature, and the single- and dual-fractal analysis equations can be easily extended to describe the binding (and/or the dissociation) kinetics for a triple fractal analysis. Recently several other approaches have recently appeared in the literature and to help model the binding and the dissociation kinetics of the different analytes (present in the liquid phase) on biosensor surfaces, such as Mautner model (application of the synthetic jet concept to low Reynolds number biosensor microfluidic flows for enhanced mixing), kinetics of analyte capture on nanoscale sensors, and probing the functional heterogeneity of surface binding sites along with the effect of mass transport limitation and its influence on binding and dissociation of analytes on biosensor surfaces.

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