dc.contributor.author | Nowacki, J | |
dc.contributor.author | Osinga, HM | |
dc.contributor.author | Tsaneva-Atanasova, KT | |
dc.date.accessioned | 2016-04-21T12:37:06Z | |
dc.date.issued | 2013-03-11 | |
dc.description.abstract | The changes in neuronal firing pattern are signatures of brain function, and it is of interest to understand how such changes evolve as a function of neuronal biophysical properties. We address this important problem by the analysis and numerical investigation of a class of mechanistic mathematical models. We focus on a hippocampal pyramidal neuron model and study the occurrence of bursting related to the after-depolarization (ADP) that follows a brief current injection. This type of burst is a transient phenomenon that is not amenable to the classical bifurcation analysis done, for example, for periodic bursting oscillators. In this letter, we show how to formulate such transient behavior as a two-point boundary value problem (2PBVP), which can be solved using well-known continuation methods. The 2PBVP is formulated such that the transient response is represented by a finite orbit segment for which onsets of ADP and additional spikes in a burst can be detected as bifurcations during a one-parameter continuation. This in turn provides us with a direct method to approximate the boundaries of regions in a two-parameter plane where certain model behavior of interest occurs. More precisely, we use two-parameter continuation of the detected onset points to identify the boundaries between regions with and without ADP and bursts with different numbers of spikes. Our 2PBVP formulation is a novel approach to parameter sensitivity analysis that can be applied to a wide range of problems. | en_GB |
dc.description.sponsorship | The research for this letter was done while J.N. was a Ph.D. student at the
University of Bristol, supported by grant EP/E032249/1 from the Engineering
and Physical Sciences Research Council (EPSRC). The research of K.T-A.
was supported by EPSRC grant EP/I018638/1 and that of H.M.O. by grant
UOA0718 of the Royal Society of NZ Marsden Fund | en_GB |
dc.identifier.citation | Vol. 25, No. 4, pp. 877-900 | en_GB |
dc.identifier.doi | 10.1162/NECO_a_00425 | |
dc.identifier.uri | http://hdl.handle.net/10871/21176 | |
dc.language.iso | en | en_GB |
dc.publisher | Massachusetts Institute of Technology Press (MIT Press) | en_GB |
dc.relation.url | http://www.ncbi.nlm.nih.gov/pubmed/23339609 | en_GB |
dc.rights | This is the final version of the article. Available from Massachusetts Institute of Technology Press (MIT Press) via the DOI in this record. | en_GB |
dc.subject | Action Potentials | en_GB |
dc.subject | Dendrites | en_GB |
dc.subject | Hippocampus | en_GB |
dc.subject | Models, Neurological | en_GB |
dc.subject | Pyramidal Cells | en_GB |
dc.title | Continuation-based numerical detection of after-depolarization and spike-adding thresholds. | en_GB |
dc.type | Article | en_GB |
dc.date.available | 2016-04-21T12:37:06Z | |
dc.identifier.issn | 0899-7667 | |
exeter.place-of-publication | United States | |
dc.description | Published | en_GB |
dc.description | Journal Article | en_GB |
dc.description | Research Support, Non-U.S. Gov't | en_GB |
dc.identifier.eissn | 1530-888X | |
dc.identifier.journal | Neural Computation | en_GB |