Low-dimensional models of single neurons: a review

Ulises Chialva, Vicente González Boscá, Horacio G. Rotstein

Research output: Contribution to journalReview articlepeer-review

1 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)163-183
Number of pages21
JournalBiological Cybernetics
Issue number3
StatePublished - Jun 2023

All Science Journal Classification (ASJC) codes

  • Biotechnology
  • General Computer Science


  • Conductance-based models
  • Linearized and quadratized models
  • Model reduction of dimensions
  • Models of Hodgkin–Huxley type
  • Models of integrate-and-fire type
  • Phenomenological reduced models


Dive into the research topics of 'Low-dimensional models of single neurons: a review'. Together they form a unique fingerprint.

Cite this