  Experiments measuring currents through single protein channels show unstable
currents, a phenomena called the gating of a single channel. Channels switch
between an 'open' state with a well defined single amplitude of current and
'closed' states with nearly zero current. The existing mean-field theory of ion
channels focuses almost solely on the open state. The physical modeling of the
dynamical features of ion channels is still in its infancy, and does not
describe the transitions between open and closed states, nor the distribution
of the duration times of open states. One hypothesis is that gating corresponds
to noise-induced fast transitions between multiple steady (equilibrium) states
of the underlying system. In this work, we aim to test this hypothesis.
Particularly, our study focuses on the (high order) steric
Poisson-Nernst-Planck-Cahn-Hilliard model since it has been successful in
predicting permeability and selectivity of ionic channels in their open state,
and since it gives rise to multiple steady states. We show that this system
gives rise to a gating-like behavior, but that important features of this
switching behavior are different from the defining features of gating in
biological systems. Furthermore, we show that noise prohibits switching in the
system of study. The above phenomena are expected to occur in other PNP-type
models, strongly suggesting that one has to go beyond over-damped (gradient
flow) Nernst-Planck type dynamics to explain the spontaneous gating of single
channels.
