Abstract
The generalized integrate-and-fire (GIF) neuron model accounts for some of the most fundamental behaviours of neurons within a compact and extensible mathematical framework. Here, we introduce the main concepts behind the design of the GIF model in terms that will be familiar to electrophysiologists, and show why its simple design makes this model particularly well suited to mimicking behaviours observed in experimental data. Along the way, we will build an intuition for how specific neuronal behaviours, such as spike-frequency adaptation, or electrical properties, such as ionic currents, can be formulated mathematically and used to extend integrate-and-fire models to overcome their limitations. This chapter will provide readers with no previous exposure to modelling a clear understanding of the strengths and limitations of GIF models, along with the mathematical intuitions required to digest more detailed and technical treatments of this topic.
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Notes
- 1.
In this case, the points at the tops of hills are higher than all points within a small neighbourhood, but not necessarily all points in the landscape. After all, there might be taller hills elsewhere. Points that are only optimal within a small neighbourhood are called locally optimal, and the point at the top of the tallest hill is called globally optimal.
- 2.
Although the measures of similarity and dissimilarity used by the GIF model will be presented briefly in Sect. 3.3.3, the reasons that these measures are associated with landscapes that have a particular structure are beyond the scope of this chapter. For a thorough introduction, see (Gerstner et al., 2014; Paninski et al., 2004).
- 3.
The gating functions in Hodgkin–Huxley current models are usually expressed in terms of an equilibrium gating function, which is a sigmoidal function of voltage, and one or more gating time constants, which may themselves depend on voltage. Readers with a background in whole-cell electrophysiology will likely already be familiar with techniques for measuring these quantities. For a comprehensive treatment, see Hille (2001).
- 4.
For an example of a similar approach used to estimate the parameters of ionic currents in a more detailed model, see Huys et al. (2006).
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Harkin, E.F., Béïque, JC., Naud, R. (2022). A User’s Guide to Generalized Integrate-and-Fire Models. In: Giugliano, M., Negrello, M., Linaro, D. (eds) Computational Modelling of the Brain. Advances in Experimental Medicine and Biology(), vol 1359. Springer, Cham. https://doi.org/10.1007/978-3-030-89439-9_3
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