Quasicycles in the stochastic hybrid Morris-Lecar neural model

Intrinsic noise arising from the stochastic opening and closing of voltage-gated ion channels has been shown experimentally and mathematically to have important effects on a neuron's function. Study of classical neuron models with stochastic ion channels is becoming increasingly important, especially in understanding a cell's ability to produce subthreshold oscillations and to respond to weak periodic stimuli. While it is known that stochastic models can produce oscillations (quasicycles) in parameter regimes where the corresponding deterministic model has only a stable fixed point, little analytical work has been done to explore these connections within the context of channel noise. Using a stochastic hybrid Morris-Lecar (ML) model, we combine a system-size expansion in K(+) and a quasi-steady-state (QSS) approximation in persistent Na(+) in order to derive an effective Langevin equation that preserves the low-dimensional (planar) structure of the underlying deterministic ML model. (The QSS analysis exploits the fact that persistent Na(+) channels are fast.) By calculating the corresponding power spectrum, we determine analytically how noise significantly extends the parameter regime in which subthreshold oscillations occur.