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

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 t(s) proportional to 1/ρ(T); while for MP-based biosensors with ρ(MP) > ρ(T), t(s) proportional to 1/ρ(MP). The theory (i) explains the performance improvement of MP-sensors by ρ(MP)/ρ(T) (order of 10(3)-10(6)), 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.