Ion transports through ion channels, biological nanopores, are essential for life: Living cells generate electrical signals by utilizing ion permeation through channels. The measured current-voltage (i-V) relations through most ion channels are sublinear, however, its physical meaning is still elusive. Here we calculated the i-V curves through anion-doped carbon nanotubes, a model of an ion channel, using molecular dynamics simulation. It was found the i-V curve reflects the physical origin of the rate-determining step: the i-V curve is sublinear when the permeation is entropy bottlenecked, while it is superlinear in the case of the energy bottlenecked permeation. Based on this finding, we discuss the relation between the molecular mechanism of ion permeation through the biological K+ channels and the shape of the i-V curves through them. This work also provides a clue for a novel design of nanopores that show current rectification.
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