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Many types of neurons exhibit spike rate adaptation, mediated by intrinsicslow $\mathrm{K}^+$-currents, which effectively inhibit neuronal responses. Howthese adaptation currents change the relationship between in-vivo likefluctuating synaptic input, spike rate output and the spike train statistics,however, is not well understood. In this computational study we show that anadaptation current which primarily depends on the subthreshold membrane voltagechanges the neuronal input-output relationship (I-O curve) subtractively,thereby increasing the response threshold. A spike-dependent adaptation currentalters the I-O curve divisively, thus reducing the response gain. Both types ofadaptation currents naturally increase the mean inter-spike interval (ISI), butthey can affect ISI variability in opposite ways. A subthreshold current alwayscauses an increase of variability while a spike-triggered current decreaseshigh variability caused by fluctuation-dominated inputs and increases lowvariability when the average input is large. The effects on I-O curves matchthose caused by synaptic inhibition in networks with asynchronous irregularactivity, for which we find subtractive and divisive changes caused by externaland recurrent inhibition, respectively. Synaptic inhibition, however, alwaysincreases the ISI variability. We analytically derive expressions for the I-Ocurve and ISI variability, which demonstrate the robustness of our results.Furthermore, we show how the biophysical parameters of slow$\mathrm{K}^+$-conductances contribute to the two different types of adaptationcurrents and find that $\mathrm{Ca}^{2+}$-activated $\mathrm{K}^+$-currents areeffectively captured by a simple spike-dependent description, whilemuscarine-sensitive or $\mathrm{Na}^+$-activated $\mathrm{K}^+$-currents show adominant subthreshold component.

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