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Breakdown of FastSlow Analysis in an Excitable System with Channel Noise
week ending
PRL 111, 128101 (2013) P H Y S I C A L R E V I E W L E T T E R S 20 SEPTEMBER 2013
Breakdown of Fast-Slow Analysis in an Excitable System with Channel Noise
Jay M. Newby,1,* Paul C. Bressloff,2 and James P. Keener2
1
Mathematical Bioscience Institute, Ohio State University, 1735 Neil Avenue, Columbus, Ohio 43210, USA
2Department of Mathematics, University of Utah, 155 South 1400 East, Salt Lake City, Utah 84112, USA
(Received 25 April 2013; published 20 September 2013)
We consider a stochastic version of an excitable system based on the Morris-Lecar model of a neuron,
in which the noise originates from stochastic sodium and potassium ion channels opening and closing.
One can analyze neural excitability in the deterministic model by using a separation of time scales
involving a fast voltage variable and a slow recovery variable, which represents the fraction of open
potassium channels. In the stochastic setting, spontaneous excitation is initiated by ion channel noise.
If the recovery variable is constant during initiation, the spontaneous activity rate can be calculated using
Kramer’s rate theory. The validity of this assumption in the stochastic model is examined using a
systematic perturbation analysis. We find that, in most physically relevant cases, this assumption breaks
down, requiring an alternative to Kramer’s theory for excitable systems with one deterministic fixed point.
We also show that an exit time problem can be formulated in an excitable system by considering
maximum likelihood trajecto
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