Low-dimensional models of single neurons: A review

TL;DR

This review discusses reduced low-dimensional models of single neurons, especially Hodgkin-Huxley type, that simplify complex biophysical models while preserving key dynamic behaviors like oscillations and bursting.

Contribution

It provides an overview of biophysically plausible and phenomenological reduced neuron models and systematic methods for deriving them from higher-dimensional models.

Findings

Reduced models can replicate complex neuronal phenomena.

Systematic methods help derive simplified models from detailed Hodgkin-Huxley models.

Reduced models facilitate understanding of neuronal dynamics.

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 sub-threshold 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.