Ion channels can either be modelled at a macroscopic level, using a deterministic representation such as the Hodgkin-Huxley formalism, or at a more detailed single-channel level, where their stochastic nature is taken into account by using a Markov formalism. The Hodgkin-Huxley model describes the combined collective effect of the channel population on the membrane potential, but it does not provide a comprehensive kinetic diagram. As a result, various aspects of the behaviour and consequently the functional role of individual channels can be overlooked. On the other hand, a more accurate alternative channel formalism is the Markov model. In Markov models, a single channel is represented by a kinetic scheme comprising a finite set of discrete intermediate states with probabilistic transitions from one state to another. Channel noise, introduced by the stochastic gating of the ion channels, can affect the generation and timing of action potentials and therefore potentially also single neuron computations.
In the present study, the voltage-gated channels of a morphologically realistic conductance based cerebellar nucleus (CN) neuron model were expressed as Markov formalisms and their behaviour was compared with their deterministic Hodgkin-Huxley type counterparts. Our results show that the majority of the deterministic CN channel models could easily be replaced by stochastic versions, without affecting neuronal behaviour. However, this was not the case for the fast sodium channel, where the parameter changes that had to be introduced in order to match the activity of the stochastic and deterministic models depended on the level of activation of the neuron, even for very small single channel conductances in the stochastic model.