Modelling of plasmonic biosensor temporal response influenced by competitive adsorption and analyte depletion

Highly sensitive detection of biological analytes by plasmonic sensors is based on analyte adsorption, which modifies the effective refractive index (RI) at the medium-sensor interface. The main issue with such sensors is the non-ideal sensor selectivity (manifested in multiple analyte adsorption), while sample depletion (significant at low analyte concentrations) also causes a deviation of the sensor response from the expected time dependence. Mathematical modelling of sensor response, presented in this work, simultaneously tackles these two issues that may cause erroneous interpretation of measurement results. Two mathematical models that address the problem of limited selectivity are utilized to analyse the sensor response: the linear (pseudo-first order) model, commonly used for interpretation of measurements, and the nonlinear (second order) model that takes into account analyte depletion in the sensor chamber. While the nonlinear model has a virtue of generality, the advantages of the linear model are its simplicity and a well-established procedure for the analysis of experimental results. However, the linear model can exhibit large errors in the case of significant analyte depletion. Until now, the influence of analyte depletion on the linear model fidelity has not been studied for multianalyte adsorption. In this paper, we quantify the difference between the RI changes predicted by the two models of two-analyte competitive adsorption, and establish the conditions that justify the use of the linear model. The validity of these conditions is confirmed by numerically solving the exact nonlinear model equations. The conditions enable making an objective decision whether it is safe to use the linear model for detection of ultralow analyte concentrations, or the nonlinear model must be used in order to avoid false-positive/false-negative detection results and analyte quantification errors. The results are applicable in adsorption-based chemical/biological sensing in complex samples, as well as for the new generation single-element multianalyte plasmonic sensors