  In living cells, ion channels passively allow for ions to flow through as the
concentration gradient relaxes to thermal equilibrium. Most ion channels are
selective, only allowing one type of ion to go through while blocking another.
One salient example is KcsA, which allows for larger $\text{K}^+$ ions through
but blocks the smaller $\text{Na}^+$ ions. This counter-intuitive selectivity
has been explained by two distinct theories that both focus on equilibrium
properties: particle-channel affinity and particle-solvent affinity. However,
ion channels operate far from equilibrium. By constructing minimal kinetic
models of channels, we discover a ubiquitous kinetic ratchet effect as a
non-equilibrium mechanism to explain such selectivity. We find that a
multi-site channel kinetically couples the competing flows of two types of
particles, where one particle's flow could suppress or even invert the flow of
another type. At the inversion point (transition between the ratchet and dud
modes), the channel achieves infinite selectivity. We have applied our theory
to obtain general design principles of artificial selective channels.
