Multiple timescale dynamics of conductance-based models of brainstem locomotor neurons

The pedunculopontine nucleus (PPN) is a heterogeneous brainstem locomotor hub implicated in Parkinson's disease and potentially relevant for its treatment. We propose single-compartment, conductance-based models for three classes of PPN neurons, such that each model reproduces relevant experimentally observed stimulus-dependent responses, including post-inhibitory rebound dynamics, transient low-threshold activity, and gamma band oscillations. To understand the mechanisms underlying these transient responses to current stimulation, we leverage the models' intrinsic multi-timescale structure and apply dynamical system methods designed for multiple timescale systems. By separating fast membrane and channel-gating dynamics from slower gating and calcium processes, we identify specific ionic mechanisms underlying hallmark dynamics across cell types. We also generate new predictions about PPN behavior under a post-inhibitory facilitation protocol.