Langevin approach for stochastic Hodgkin-Huxley dynamics with discretization of channel open fraction

The random opening and closing of ion channels establishes channel noise, which can be approximated and included into stochastic differential equations (Langevin approach). The Langevin approach is often incorporated to model stochastic ion channel dynamics for systems with a large number of channels. Here, we introduce a discretization procedure of a channel-based Langevin approach to simulate the stochastic channel dynamics with small and intermediate numbers of channels. We show that our Langevin approach with discrete channel open fractions can give a good approximation of the original Markov dynamics even for only 10K+ channels. We suggest that the better approximation by the discretized Langevin approach originates from the improved representation of events that trigger action potentials.