Power consumption has been recognized as a grand challenge for nanoelectronics. With continuous scaling, wires (much more than devices) are going to be determining (almost entirely) the dynamic power: (i) their numbers are increasing exponentially, as each device needs a few wires; and (ii) they do not scale well, as their parasitic capacitances and RC-delays are not scaling in synch with device scaling. That is why innovations on both evolutionary (i.e., based-on-wires) as well as revolutionary (i.e., without-wire, or beyond-wire) solutions are called upon to tackle this challenge. Trying to find inspiration from neurons, we focus on axons which are able to communicate at quite large distances on an amazingly limited power budget. In particular, the paper analyzes axon-inspired communications as dense locally-connected arrays of voltage-gated (non-linear) ion channels. Our theoretical results suggest that hexagonal arrays should minimize power consumption. Emulating the logical functioning of voltage-gated ion channels by single-electron technology/transistor gates can lead to practical power/energy lower bounds for nanoelectronics.