4.7 Article

Perturbation analysis of spontaneous action potential initiation by stochastic ion channels

Journal

PHYSICAL REVIEW E
Volume 84, Issue 1, Pages -

Publisher

AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.84.011918

Keywords

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Funding

  1. National Science Foundation [DMS-0718036]
  2. King Abdullah University of Science and Technology (KAUST) [KUK-C1-013-4]
  3. Division Of Mathematical Sciences
  4. Direct For Mathematical & Physical Scien [1122297] Funding Source: National Science Foundation

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A stochastic interpretation of spontaneous action potential initiation is developed for the Morris-Lecar equations. Initiation of a spontaneous action potential can be interpreted as the escape from one of the wells of a double well potential, and we develop an asymptotic approximation of the mean exit time using a recently developed quasistationary perturbation method. Using the fact that the activating ionic channel's random openings and closings are fast relative to other processes, we derive an accurate estimate for the mean time to fire an action potential (MFT), which is valid for a below-threshold applied current. Previous studies have found that for above-threshold applied current, where there is only a single stable fixed point, a diffusion approximation can be used. We also explore why different diffusion approximation techniques fail to estimate the MFT.

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