This article proposes a methodology to extract a low-dimensional integrate-and-fire model from an arbitrarily detailed single-compartment biophysical model. The method aims at relating the modulation of maximal conductance parameters in the biophysical model to the modulation of parameters in the proposed integrate-and-fire model. The approach is illustrated on two well-documented examples of cellular neuromodulation: the transition between type I and type II excitability and the transition between spiking and bursting.

By controlling the state of neuronal populations, neuromodulators ultimately affect behavior. A key neuromodulation mechanism is the alteration of neuronal excitability via the modulation of ion channel expression. This type of neuromodulation is normally studied with conductance-based models, but those models are computationally challenging for large-scale network simulations needed in population studies. This article studies the modulation properties of the multiquadratic integrate-and-fire model, a generalization of the classical quadratic integrate-and-fire model. The model is shown to combine the computational economy of integrate-and-fire modeling and the physiological interpretability of conductance-based modeling. It is therefore a good candidate for affordable computational studies of neuromodulation in large networks.