Theoretical detection limits of magnetic biobarcode sensors and the phase space of nanobiosensing

Abstract

A scaling theory of the sub atto-molar (aM) detection limits of magnetic particle (MP) based biosensors (e.g., bio-barcode assays) is developed and discussed. Despite the dramatic differences of sensing protocols and detection limits, the MP-based sensors can be interpreted within the same theoretical framework as any other classical biosensor (e.g., nanowire sensors), except that these sensors are differentiated by the geometry of diffusion and the probe (ρ_MP)/target (ρ_T) density ratio. Our model predicts two regimes for biomolecule detection: For classical biosensors with ρ_MP ≤ ρ_T, the response time ; while for MP-based biosensors with . The theory (i) explains the performance improvement of MP-sensors by (order of 10³–10⁶), broadly validating the sub-aM detection limits reported in literature, (ii) offers intuitive interpretation for the counter-intuitive ρ_T-independence of detection time in MP-sensors, (iii) shows that statistical fluctuations should reduce with ρ_T for MP sensors, and (iv) offers obvious routes to sensitivity improvement of classical sensors.