Temporal response of biochemical and biological sensors with bimodal surface adsorption from a finite sample

The importance of adsorption-based biochemical/biological sensors in biochemistry and biophysics is paramount. Their temporal response gives information about the presence of a biochemical/biological analyte, its concentration and its interactions with the adsorption sites (which may be an integral part of the surface itself or immobilized functionalizing molecules). Mathematical models of the temporal response taking into account as many relevant effects as possible are essential for obtaining reliable information. We present a novel model taking into account the bimodal affinity of a sensing surface (adsorption occurs on two distinct site types), and the adsorption-caused depletion of the analyte from the sample. We perform qualitative and quantitative analysis of the analyte depletion influence on the bimodal adsorption, and of the influence of the sensing surface inhomogeneity on the sensor temporal response, for different analyte concentrations and different fractions of two types of adsorption sites. Since the presented mathematical model deals with the realistic cases of the sensing surface non-uniformity and the finite amount of analyte present in the sensor reaction chamber, it enables improved accuracy in interpreting the measurement data. Our results are general, i.e. valid for any adsorption sensor (microcantilevers, plasmonics) and for arbitrary sensor dimensions.