The effect of hyperpolarizing inputs on the dynamics of a bursting pacemaker neuron model in the pre-Bötzinger complex

The pre-Bötzinger complex (pre-BötC), a subregion of the ventrolateral medulla involved in respiratory rhythm generation, contains intrinsically bursting pacemaker neurons. A previous study proposed Hodgkin–Huxley type minimal models for pacemaker neurons and predicted the effect of a hyperpolarizing input on the dynamics of a model under certain conditions. In this model, bursting is explained by the dynamics of a persistent sodium current. In the present study, the effect of a hyperpolarizing input on the dynamics of a model was investigated under variable conditions. It was observed that immediately after an input of sufficient intensity and duration, an increase in the maximal value of the gating variable h of a persistent sodium current was brought about by a decrease in the timing of the hyperpolarizing input. This corresponds to an observation that immediately after the input, a monotonic increase in the number of spikes in the neuron model was brought about by a decrease in the timing of the hyperpolarizing input. In addition, the dependency of burst duration immediately after the input on the timing of the hyperpolarizing input varied depending on the condition of input. The present study is the first to elucidate that the influence of hyperpolarizing inputs on the number of spikes within a burst in a pacemaker neuron model in the pre-BötC is dependent on the timing of the hyperpolarizing input and to clarify the possible mechanism of this influence, thereby facilitating a detailed understanding of the dynamics of a pacemaker neuron model in the pre-BötC.