Fast-slow analysis as a technique for understanding the neuronal response to current ramps.

The standard protocol for studying the spiking properties of single neurons is the application of current steps while monitoring the voltage response. Although this is informative, the jump in applied current is artificial. A more physiological input is where the applied current is ramped up, reflecting chemosensory input. Unsurprisingly, neurons can respond differently to the two protocols, since ion channel activation and inactivation are affected differently. Understanding the effects of current ramps, and changes in their slopes, is facilitated by mathematical models. However, techniques for analyzing current ramps are under-developed. In this article, we demonstrate how current ramps can be analyzed in single neuron models. The primary issue is the presence of gating variables that activate on slow time scales and are therefore far from equilibrium throughout the ramp. The use of an appropriate fast-slow analysis technique allows one to fully understand the neural response to ramps of different slopes. This study is motivated by data from olfactory bulb dopamine neurons, where both fast ramp (tens of milliseconds) and slow ramp (tens of seconds) protocols are used to understand the spiking profiles of the cells. The slow ramps generate experimental bifurcation diagrams with the applied current as a bifurcation parameter, thereby establishing asymptotic spiking activity patterns. The faster ramps elicit purely transient behavior that is of relevance to most physiological inputs, which are short in duration. The two protocols together provide a broader understanding of the neuron's spiking profile and the role that slowly activating ion channels can play.