Model Vestibular Nuclei Neurons Can Exhibit a Boosting Nonlinearity Due to an Adaptation Current Regulated by Spike-Triggered Calcium and Calcium-Activated Potassium Channels

In vitro studies have previously found a class of vestibular nuclei neurons to exhibit a bidirectional afterhyperpolarization (AHP) in their membrane potential, due to calcium and calcium-activated potassium conductances. More recently in vivo studies of such vestibular neurons were found to exhibit a boosting nonlinearity in their input-output tuning curves. In this paper, a Hodgkin-Huxley (HH) type neuron model, originally developed to reproduce the in vitro AHP, is shown to produce a boosting nonlinearity similar to that seen in vivo for increased the calcium conductance. Indicative of a bifurcation, the HH model is reduced to a generalized integrate-and-fire (IF) model that preserves the bifurcation structure and boosting nonliearity. By then projecting the neuron model's phase space trajectories into 2D, the underlying geometric mechanism relating the AHP and boosting nonlinearity is revealed. Further simplifications and approximations are made to derive analytic expressions for the steady steady state firing rate as a function of bias current, μ, as well as the gain (i.e. its slope) and the position of its peak at μ = μ*. Finally, although the boosting nonlinearity has not yet been experimentally observed in vitro, testable predictions indicate how it might be found.