  Transport of colloid particles through narrow channels is ubiquitous in cell
biology as well as becoming increasingly important for microfluidic
applications or targeted drug delivery. Membrane channels in cells are useful
models for artificial designs because of their high efficiency, selectivity and
robustness to external fluctuations. Here we model the passive channels that
let cargo simply diffuse through them, affected by a potential profile along
the way. Passive transporters achieve high levels of efficiency and specificity
from binding interactions with the cargo inside the channel. This however leads
to a paradox: why should channels which are so narrow that they are blocked by
their cargo evolve to have binding regions for their cargo if that will
effectively block them? Using Brownian dynamics simulations, we show that
different potentials, notably symmetric, increase the flux through narrow
passive channels -- and investigate how shape and depth of potentials influence
the flux. We find that there exist optimal depths for certain potential shapes
and that it is most efficient to apply a small force over an extended region of
the channel. On the other hand, having several spatially discrete binding
pockets will not alter the flux significantly. We also explore the role of
many-particle effects arising from pairwise particle interactions with their
neighbours and demonstrate that the relative changes in flux can be accounted
for by the kinetics of the absorption reaction at the end of the channel.
