Nanosensors lost in space. A random walk study of single molecule detection with single-nanopore sensors.

Nanopores by providing single molecule detection and manipulation are lately in the forefront of life science and nanotechnology research. While single nanopore sensors can detect the residence of even one molecule or nanoparticle within the nanopore, the analytical significance of this process is often misunderstood. A fundamental problem of nanosensors is that their sensing zone is generally infinitesimal with respect of the probed sample volume. Consequently, the probability to have in extremely diluted solutions target molecules or nanoparticles encountering the nanosensor is low. Thus, even though the sensor by itself has single molecule detection capability the average time frame in which this occurs is by far not irrelevant for the analysis. In this paper we report on random walk simulations to determine the average time (encounter time) needed by a single molecule to encounter a single nanopore sensor. By assigning the simulation environment with real space and time values a semi-empirical equation for expressing the average encounter time in purely diffusive systems is provided. We also show that random walk simulations can be adapted to evaluate the encounter time in the presence of an external force field acting on the target molecule. As practically relevant application the case of electrophoretically driving DNA strands towards the nanopore sensor is presented and a semi-empirical equation for the encounter time is provided.