Statistical Interpretation of Femto-Molar Detection
Over the last decade, many experiments have demonstrated that nanobiosensors based on Nanotubes and Nanowires are significantly more sensitive compared to their planar counterparts. Yet, there has been persistent gap between reports of analyte detection at ~femto-Molar concentration and theory suggesting the impossibility of sub-pM detection at the corresponding incubation time. This divide has persisted despite the sophistication of the theoretical models. In this paper, we calculate the statistics of diffusion-limited arrival-time distribution by a Monte Carlo method to suggest a statistical resolution of the enduring puzzle: The incubation time in the theory is the mean incubation time, while experiments suggest device stability limited the minimum incubation time. The difference in incubation times - both described by characteristic power-laws - provides an intuitive explanation of different detection limits anticipated by theory and experiments. These power laws broaden the scope of problems amenable to the first-passage process used to quantify the stochastic biological processes.