How adaptation currents and synaptic inhibition change threshold, gain and variability of neuronal spiking

We show that a subthreshold adaptation current or synaptic inhibition received from independent neurons (external inhibition) change the neuronal I-O curve subtractively. That is, both mechanisms increase the spike threshold. On the other hand, a spike-triggered adaptation current or inhibitory synaptic feedback (recurrent inhibition) change the I-O curve divisively, i.e., they reduce the neuronal gain, see Figure 1A. Both types of adaptation current naturally increase the mean ISI. Surprisingly, they affect spiking variability in opposite ways. Subthreshold adaptation leads to an increase while spike-triggered adaptation causes a decrease of variability, see Figure 1B. Both types of synaptic inhibition however increase spiking variability. We simplify the model by neglecting the leak conductance which allows to analytically derive expressions describing these effects. For validation purposes, we show that the effective description of subthreshold and spike-triggered adaptation in the aEIF model corresponds well to the biophysical description of a voltage-sensitive muscarinic and a calcium-activated potassium current in a Hodgkin-Huxley type neuron model, respectively. Our results suggest that neuronal adaptation currents differentially contribute to neuronal threshold and gain control as well as ISI-based coding schemes.