Mathematical Modeling of Nanosensor Systems Based on Dynamic Light Scattering

Abstract

A mathematical model describing optical nanosensors, the principle of action of which is based on an increase in the hydrodynamic diameters of functionalized nanoparticles (conjugates) under the influence of an analyte, is constructed. The formation of shells from analyte molecules around conjugates and the aggregation of conjugates to dimers at the expense of “bridges” represented by analyte molecules are considered. Antibodies capable of association with antibody footprints (epitopes) on analyte molecules are considered receptors, which are used for the functionalization of nanoparticles. The input parameters of the model are the sizes and concentrations of conjugates, kinetic constants of association and dissociation of receptors with epitopes, number of receptors per conjugate, and the concentration of the analyte. The model makes it possible to estimate the ranges of defined concentrations, as well as detect the limits during the development of nanosensors for specific analytes and optimizing parameters of these sensors, including the required incubation time for a mixture of conjugates with an analyte.