Universal scaling theory of electrochemical immunosensors: An analytical approach to define and compare performance metrics

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Electrochemical immunosensors have emerged as a versatile, sensitive, and selective sensor technology of choice for a variety of applications, including detection of proteins, food pathogens, bacteria, viruses, and cancerous molecules. The combination of highly specific biorecognition elements and electrical readout systems facilitates the detection of antigens down to femtomolar concentrations. However, a lack of quantitative theoretical framework has made the design, optimization, and comparison of sensors difficult, without a clear and definitive understanding of the limits of detection, dynamic range, and sensitivity. In this paper, we integrate reaction-diffusion and effective media theories to derive a generalized scaling model for an arbitrary immunosensor that relates the relative change of redox current to the corresponding change in antigen concentration, through scaling exponents related to the geometry of biomolecules diffusion and the measurement resolution. Experimental data from dozens of immunosensors (for a variety of antigens, material systems, and sensor geometry) validate our sensor-agnostic scaling formula. Our results would allow cross-calibration of the emerging and traditional immunosensors reported across the literature and define a physics-based, standardized methodology to compare performance metrics, such as limits of detection, dynamic range, and sensitivity.