Biological ion channels in membranes are selectively permeable to specific ionic species. They maintain the resting membrane potential, generate propagated action potentials, and control a wide variety of cell functions. Here it is demonstrated theoretically that boron nitride nanotubes have the ability to carry out some of the important functions of biological ion channels. Boron nitride nanotubes with radii of 4.83 and 5.52 A embedded in a silicon nitride membrane are selectively permeable to cations and anions, respectively. They broadly mimic some of the permeation characteristics of gramicidin and chloride channels. Using distributional molecular dynamics, which is a combination of molecular and stochastic dynamics simulations, the properties of these engineered nanotubes are characterized, such as the free energy encountered by charged particles, the water-ion structure within the pore, and the current-voltage and current-concentration profiles. These engineered nanotubes have potential applications as sensitive biosensors, antibiotics, or filtration devices.