When an experimentalist injects a strong step current into the soma of a neuron, the response consists of a series of spikes separated by long or short intervals. The stereotypical arrangement of short, long or very long interspike intervals defines the neuronal firing pattern. In Chapter 2 we have already encountered firing patterns such as tonic, adapting, or delayed spike firing. In addition to these, several variants of burst firing have also been observed in real neurons (see Figure 6.1). This diversity of firing patterns can be explained, to a large extent, by adaptation mechanisms which in turn depend on the zoo of available ion channels (Chapter 2) and neuronal anatomy (Chapter 3).

In order to describe firing patterns, and in particular adaptation, in a transparent mathematical framework, we start in this chapter with the simplified model of spike initiation from Chapter 5 and include a phenomenological equation for subthreshold and spike-triggered adaptation. The resulting model is called the Adaptive Exponential Integrate-and-Fire (AdEx; Section 6.1). We then use this simple model to explain the main firing patterns (Section 6.2). In Section 6.3, we describe how the parameters of the subthreshold and spike-triggered adaptation reflect the contribution of various ion channels and of dendritic morphology. Finally, we introduce the Spike Response Model (SRM; Section 6.4) as a transparent framework to describe neuronal dynamics. The Spike Response Model will serve as a starting point for the Generalized Linear Models which we will discuss later in Chapter 9.

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