  We consider an anisotropically two-dimensional diffusion of a charged
molecule (particle) through a large biological channel under an external
voltage. The channel is modeled as a cylinder of three structure parameters:
radius, length, and surface density of negative charges located at the channel
interior-lining. These charges induce inside the channel a potential that plays
a key role in controlling the particle current through the channel. It was
shown that to facilitate the transmembrane particle movement the channel should
be reasonably self-optimized so that its potential coincides with the resonant
one, resulting in a large particle current across the channel. Observed
facilitation appears to be an intrinsic property of biological channels,
regardless the external voltage or the particle concentration gradient. This
facilitation is very selective in the sense that a channel of definite
structure parameters can facilitate the transmembrane movement of only
particles of proper valence at corresponding temperatures. Calculations also
show that the modeled channel is non-Ohmic with the ion conductance which
exhibits a resonance at the same channel potential as that identified in the
current.
