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Capturing single molecules by nanopores: measured times and thermodynamics
Alexander M Berezhkovskii1, Sergey M Bezrukov2
1Section on Molecular Transport, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, MD 20892, USA and Mathematical and Statistical Computing Laboratory, Office of Intramural Research, Center for Information Technology, National Institutes of Health, Bethesda, MD 20892, USA.
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In numerous nanopore sensing applications transient interruptions in ion current through single nanopores induced by capturing solute molecules are a source of information on how solutes interact with the nanopores. We show that the distribution of time spent by a single captured solute molecule in a nanopore is bimodal with the majority of capture events being too fast to be experimentally resolved. As a result, the exact mean durations of the event and inter-event interval are orders of magnitude shorter than their measured values. Moreover, the exact and measured mean durations have qualitatively different dependences on the molecule diffusivity. This leads to a formal contradiction with the thermodynamics of molecule partitioning between the bulk and the nanopore. Here we resolve this controversy. We also demonstrate that, surprisingly, the probability of finding a molecule in the nanopore, obtained from the ratio of the measured mean durations of the capture event and interevent interval, is essentially identical to the exact equilibrium thermodynamic probability.
