  The stochastic opening and closing of voltage-gated ion channels produces
noise in neurons. The effect of this noise on the neuronal performance has been
modelled using either approximate or Langevin model, based on stochastic
differential equations or an exact model, based on a Markov process model of
channel gating. Yet whether the Langevin model accurately reproduces the
channel noise produced by the Markov model remains unclear. Here we present a
comparison between Langevin and Markov models of channel noise in neurons using
single compartment Hodgkin-Huxley models containing either $Na^{+}$ and
$K^{+}$, or only $K^{+}$ voltage-gated ion channels. The performance of the
Langevin and Markov models was quantified over a range of stimulus statistics,
membrane areas and channel numbers. We find that in comparison to the Markov
model, the Langevin model underestimates the noise contributed by voltage-gated
ion channels, overestimating information rates for both spiking and non-spiking
membranes. Even with increasing numbers of channels the difference between the
two models persists. This suggests that the Langevin model may not be suitable
for accurately simulating channel noise in neurons, even in simulations with
large numbers of ion channels.
