title: Continuation-based numerical detection of after-depolarization and spike-adding thresholds.
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.
authors: jakub.nowacki@tessella.com
authors: Jakub
authors: J
authors: Nowacki
authors: Hinke M
authors: HM
authors: Osinga
authors: Krasimira T
authors: KT
authors: Tsaneva-Atanasova
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D003712:Dendrites / Q000502:physiology; D006624:Hippocampus / Q000502:physiology*; D008959:Models, Neurological; D017966:Pyramidal Cells / Q000502:physiology*