The Allen Cell Types Database contains two types of neuronal models: perisomatic biophysical models and generalized leaky integrate-and-fire (GLIF) models. These models attempt to mathematically reproduce a cell's recorded response to a current injection. The perisomatic biophysical models take into account dendritic morphological structure, whereas GLIF models rely strictly on the cell's stimulus and response. are simple point neuron models which represent the neuron as a single compartment.
There are five types levels of GLIF models with varying increasing levels of complexity. The most basic model is a simple leaky integrate-and-fire equation. More advanced GLIFs attempt to model variable spike threshold, afterspike currents, and threshold adaptation.
Models with active conductances at the soma and morphology based on full 3D reconstruction.
1 Leaky Integrate and Fire (LIF)
Membrane potential evolves as a function of neuron properties and external current and is reset to a fixed value if it surpasses a fixed threshold Standard circuit representation of a resistor and capacitor in parallel with a leaky membrane.
2 LIF + Reset Rules (LIF-R)
LIF with biologically-defined afterspike derived threshold and voltage reset rules in addition to a biologically derived threshold decay rules.
3 LIF + Afterspike Currents (LIF-ASC)
LIF with spike-induced currents to model long-term effects of fast voltage-activated ion channels.
4 LIF-R + Afterspike Currents (LIF-R-ASC)
LIF with additional Reset Rules and Afterspike Currents.
5 LIF-R-ASC + Threshold Adaptation (LIF-R-ASC-A)
All of the above, with an additional voltage-dependent component of threshold.
Models with active conductances at the soma and passive dendritic morphology based on full 3D reconstruction.
See the perisomatic biophysical and GLIF technical whitepapers for more details on how these models were created.