Low-dimensional models of single neurons: a review

Area of Science:

• Computational neuroscience
• Mathematical biology
• Biophysics

Background:

• The classical Hodgkin-Huxley (HH) model describes neuronal action potential generation using four dimensions.
• Conductance-based HH models are higher-dimensional, capturing complex phenomena like oscillations and bursting.
• These complex models present computational challenges due to their high dimensionality.

Purpose of the Study:

• To present reduced models of Hodgkin-Huxley type that maintain biophysical and dynamic properties.
• To explore models with fewer dimensions for efficient simulation of complex neuronal behaviors.
• To describe systematic and heuristic methods for deriving these reduced models.

Main Methods:

• Review and description of existing biophysically plausible and phenomenological reduced models.
• Analysis of model dimensionality and preservation of key dynamic phenomena.
• Discussion of systematic and heuristic model reduction techniques.

Main Results:

• Reduced models successfully capture essential dynamics of the classical and conductance-based HH models.
• These models exhibit complex phenomena such as oscillations and bursting with fewer state variables.
• Demonstration of methods for deriving simplified yet functionally relevant neuronal models.

Conclusions:

• Reduced Hodgkin-Huxley models offer a computationally efficient approach to studying neuronal dynamics.
• These simplified models are valuable tools for simulating complex behaviors in neuroscience.
• Model reduction techniques provide a systematic way to achieve computational tractability while preserving crucial biological features.