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    Excitable neurons, firing threshold manifolds and canards

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    © 2013 J. Mitry et al.. This is an Open Access article distributed under the terms of the
Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly
cited.
    Date Issued
    2013-08-14
    Publisher Version
    10.1186/2190-8567-3-12
    Author(s)
    Mitry, John
    McCarthy, Michelle
    Kopell, Nancy
    Wechselberger, Martin
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    Permanent Link
    https://hdl.handle.net/2144/27395
    Citation (published version)
    John Mitry, Michelle McCarthy, Nancy Kopell, Martin Wechselberger. 2013. "Excitable neurons, firing threshold manifolds and canards.." J Math Neurosci, Volume 3, Issue 1:12.
    Abstract
    We investigate firing threshold manifolds in a mathematical model of an excitable neuron. The model analyzed investigates the phenomenon of post-inhibitory rebound spiking due to propofol anesthesia and is adapted from McCarthy et al. (SIAM J. Appl. Dyn. Syst. 11(4):1674-1697, 2012). Propofol modulates the decay time-scale of an inhibitory GABAa synaptic current. Interestingly, this system gives rise to rebound spiking within a specific range of propofol doses. Using techniques from geometric singular perturbation theory, we identify geometric structures, known as canards of folded saddle-type, which form the firing threshold manifolds. We find that the position and orientation of the canard separatrix is propofol dependent. Thus, the speeds of relevant slow synaptic processes are encoded within this geometric structure. We show that this behavior cannot be understood using a static, inhibitory current step protocol, which can provide a single threshold for rebound spiking but cannot explain the observed cessation of spiking for higher propofol doses. We then compare the analyses of dynamic and static synaptic inhibition, showing how the firing threshold manifolds of each relate, and why a current step approach is unable to fully capture the behavior of this model.
    Rights
    © 2013 J. Mitry et al.. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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    • CAS: Mathematics & Statistics: Scholarly Works [332]


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