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dc.contributor.authorMitry, Johnen_US
dc.contributor.authorMcCarthy, Michelleen_US
dc.contributor.authorKopell, Nancyen_US
dc.contributor.authorWechselberger, Martinen_US
dc.coverage.spatialGermanyen_US
dc.date2013-03-20
dc.date.accessioned2018-03-07T15:40:13Z
dc.date.available2018-03-07T15:40:13Z
dc.date.issued2013-08-14
dc.identifierhttps://www.ncbi.nlm.nih.gov/pubmed/23945278
dc.identifier.citationJohn Mitry, Michelle McCarthy, Nancy Kopell, Martin Wechselberger. 2013. "Excitable neurons, firing threshold manifolds and canards.." J Math Neurosci, Volume 3, Issue 1:12.
dc.identifier.issn2190-8567
dc.identifier.urihttps://hdl.handle.net/2144/27395
dc.description.abstractWe 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.en_US
dc.format.extent12en_US
dc.languageeng
dc.relation.ispartofJ Math Neurosci
dc.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.en_US
dc.rights.urihttp://creativecommons.org/licenses/by/2.0
dc.titleExcitable neurons, firing threshold manifolds and canardsen_US
dc.typeArticleen_US
dc.identifier.doi10.1186/2190-8567-3-12
pubs.elements-sourcepubmeden_US
pubs.notesEmbargo: Not knownen_US
pubs.organisational-groupBoston Universityen_US
pubs.organisational-groupBoston University, College of Arts & Sciencesen_US
pubs.organisational-groupBoston University, College of Arts & Sciences, Department of Mathematics & Statisticsen_US
pubs.publication-statusPublished onlineen_US
dc.identifier.orcid0000-0002-8568-8750 (Kopell, Nancy)


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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.
Except where otherwise noted, this item's license is described as © 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.