Quasicycles in the stochastic hybrid Morris-Lecar neural model

Heather A. Brooks, Paul C. Bressloff
2015 Physical Review E  
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
more » ... ameter 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 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.
doi:10.1103/physreve.92.012704 pmid:26274200 fatcat:eicg2cl2s5de7gnkzwnblq76te