Experiments in micro-patterned model membranes support the narrow escape theory

The narrow escape theory (NET) predicts the escape time distribution of Brownian particles confined to a domain with reflecting borders except for one small window. Applications include molecular activation events in cell biology and biophysics. Specifically, the mean first passage time can be analytically calculated from the size of the domain, the escape window, and the diffusion coefficient of the particles. In this study, we systematically tested the NET in a disc by variation of the escape opening. Our model system consisted of micro-patterned lipid bilayers. For the measurement of , we imaged diffusing fluorescently-labeled lipids using single-molecule fluorescence microscopy. We overcame the lifetime limitation of fluorescent probes by re-scaling the measured time with the fraction of escaped particles. Experiments were complemented by matching stochastic numerical simulations. To conclude, we confirmed the NET prediction in vitro and in silico for the disc geometry in the limit of small escape openings. Significance Statement In the biological context of a cell, a multitude of reactions are facilitated by diffusion. It is astonishing how Brownian motion as a cost-efficient but random process is mediating especially fast reactions. The formalism of the narrow escape theory is a tool to determine the average timescale of such processes to be completed (mean first passage time, MFPT) from the reaction space and diffusion coefficient. We present the systematic proof of this formalism experimentally in a bio-mimetic model system and by random walk simulations. Further, we demonstrate a straightforward solution to determine the MFPT from incomplete experimental traces. This will be beneficial for measurements of the MFPT, reliant on fluorescent probes, that have prior been inaccessible.