Our central aim is to understand conduction and selectivity in biological ion channels and artificial nanopores, taking advantage of the insights afforded by the recently discovered phenomenon of ionic Coulomb blockade (ICB), combined with the discreteness of the ions and their hydration shells. The ICB is a fundamental electrostatic phenomenon based on charge discreteness, electrostatic exclusion principle, and single-file stochastic ion motion through the channel. The theoretical and numerical results, obtained from the Brownian dynamics simulations, are tested against earlier observations and new experimental measurements on mutation transformations in bacterial sodium ion channels.