Low-dimensional models of single neurons: a review
Document Type
Article
Publication Date
6-1-2023
Abstract
The classical Hodgkin–Huxley (HH) point-neuron model of action potential generation is four-dimensional. It consists of four ordinary differential equations describing the dynamics of the membrane potential and three gating variables associated to a transient sodium and a delayed-rectifier potassium ionic currents. Conductance-based models of HH type are higher-dimensional extensions of the classical HH model. They include a number of supplementary state variables associated with other ionic current types, and are able to describe additional phenomena such as subthreshold oscillations, mixed-mode oscillations (subthreshold oscillations interspersed with spikes), clustering and bursting. In this manuscript we discuss biophysically plausible and phenomenological reduced models that preserve the biophysical and/or dynamic description of models of HH type and the ability to produce complex phenomena, but the number of effective dimensions (state variables) is lower. We describe several representative models. We also describe systematic and heuristic methods of deriving reduced models from models of HH type.
Identifier
85152554700 (Scopus)
Publication Title
Biological Cybernetics
External Full Text Location
https://doi.org/10.1007/s00422-023-00960-1
e-ISSN
14320770
ISSN
03401200
PubMed ID
37060453
First Page
163
Last Page
183
Issue
3
Volume
117
Grant
2019/10496-0
Fund Ref
Fundação de Amparo à Pesquisa do Estado de São Paulo
Recommended Citation
Chialva, Ulises; González Boscá, Vicente; and Rotstein, Horacio G., "Low-dimensional models of single neurons: a review" (2023). Faculty Publications. 1710.
https://digitalcommons.njit.edu/fac_pubs/1710