On scaling laws of biosensors: A stochastic approach

We study the scaling laws of affinity-based biosensors. In particular, we examine the implications of scaling on the response time, signal-to-noise ratio (SNR), and dynamic range (DR) of biosensor systems. Initially, using stochastic differential methods and particularly Fokker-Planck (FP) equation, we formulate the analyte capturing process and derive its uncertainty by computing the probability distribution function of the captured analytes as a function of time. Subsequently, we examine the effects of scaling on the solution to the FP equation and the signal fluctuation, which demonstrates that scaling down significantly reduces the achievable SNR and DR of biosensors. We argue that these results question the advantages of excessive miniaturization of biosensors, especially the fundamental SNR limitation, which transpire in the micro- and nanoregimes.