Interactive GIF neuron model

Considering its simplicity, the leaky integrate-and-fire (LIF) neuron model does a surprisingly good job of describing the electrical properties of neurons. According to this model, neurons leakily accumulate excitatory input until a voltage threshold is reached, at which point they fire an action potential (also called a “spike”) and reset to a lower voltage, letting the cycle begin again.

Real neurons are, of course, more complicated. One particularly important and common feature of real neurons missing from the LIF model is spike frequency adaptation. Around a century ago, Lord Edward Douglas Adrian noticed that in the presence of a constant stimulus, many sensory neurons would initially respond by firing at a high rate before gradually adapting to the stimulus and ultimately firing more slowly.

The generalized integrate-and-fire (GIF) model of Mensi, Naud, et al. captures adaptation by adding two ingredients to the LIF model: an adaptation current and an adapting spike threshold. Whenever the voltage of the GIF model reaches the spike threshold, a transient inhibitory current is activated that pushes down the voltage. At the same time, the spike threshold temporarily increases. Both of these features cause the model to fire more and more slowly over time, providing a simple way to mimic the sensory neurons recorded by Lord Adrian.

To build an intuition for how the adaptation current and threshold movement affect the behaviour of the GIF neuron model, try playing with the parameters in the widget below.

If you’re interested in learning more about the GIF model and how it can be applied to neuroscience experiments, check out my User’s Guide.