  Access resistance indicates how well current carriers from a bulk medium can
converge to a pore or opening, and is an important concept in nanofluidic
devices and in cell physiology. In simplified scenarios, when the bulk
dimensions are infinite in all directions, it depends only on the resistivity
and pore radius. These conditions are not valid in all-atom molecular dynamics
(MD) simulations of transport, due to the computational cost of large
simulation cells, and can even break down in micro- and nano-scale systems due
to strong confinement. Here, we examine a scaling theory for the access
resistance that predicts a special simulation cell aspect ratio -- the golden
aspect ratio -- where finite size effects are eliminated. Using both continuum
and all-atom simulations, we demonstrate that this golden aspect ratio exists
and that it takes on a universal value in linear response and moderate
concentrations. Outside of linear response, it gains an apparent dependence on
characteristics of the transport scenario (concentration, voltages, etc.) for
small simulation cells, but this dependence vanishes at larger length scales.
These results will enable the use of all-atom molecular dynamics simulations to
study contextual properties of access resistance -- its dependence on protein
and molecular-scale fluctuations, the presence of charges, and other functional
groups -- and yield the opportunity to quantitatively compare computed and
measured resistances.
