Linear Versus Nonlinear Signal Transmission in Neuron Models With Adaptation Currents or Dynamic Thresholds

Abstract

Spike-frequency adaptation is a prominent aspect of neuronal dynamics that shapes a neuron's signal processing properties on timescales ranging from about 10 ms to >1 s. For integrate-and-fire model neurons spike-frequency adaptation is incorporated either as an adaptation current or as a dynamic firing threshold. Whether a physiologically observed adaptation mechanism should be modeled as an adaptation current or a dynamic threshold, however, is not known. Here we show that a dynamic threshold has a divisive effect on the onset f–I curve (the initial maximal firing rate following a step increase in an input current) measured at increasing mean threshold levels, i.e., adaptation states. In contrast, an adaptation current subtractively shifts this f–I curve to higher inputs without affecting its slope. As a consequence, an adaptation current acts essentially linearly, resulting in a high-pass filter component of the neuron's transfer function for current stimuli. With a dynamic threshold, however, the transfer function strongly depends on the input range because of the multiplicative effect on the f–I curves. Simulations of conductance-based spiking models with adaptation currents, such as afterhyperpolarization (AHP)-type, M-type, and sodium-activated potassium currents, do not show the divisive effects of a dynamic threshold, but agree with the properties of integrate-and-fire neurons with adaptation current. Notably, the effects of slow inactivation of sodium currents cannot be reproduced by either model. Our results suggest that, when lateral shifts of the onset f–I curve are seen in response to adapting inputs, adaptation should be modeled with adaptation currents and not with a dynamic threshold. In contrast, when the slope of onset f–I curves depends on the adaptation state, then adaptation should be modeled with a dynamic threshold. Further, the observation of divisively altered onset f–I curves in adapted neurons with notable variability of their spike threshold could hint to yet known biophysical mechanisms directly affecting the threshold.