Control of firing patterns by two transient potassium currents: Leading spike, latency, bistability

Transient potassium currents distinctively affect firing properties, particularly in regulating the latency before repetitive firing. Pyramidal cells of the dorsal cochlear nucleus (DCN) have two transient potassium currents, I _Kif and I _Kis, fast and slowly inactivating, respectively, and they exhibit firing patterns with dramatically variable latencies. They show immediate repetitive firing, or only after a long latency with or without a leading spike, the so-called pauser and buildup patterns. We consider a conductance-based, ten-variable, single-compartment model for the DCN pyramidal cells (Kanold and Manis 2001). We develop and analyze a reduced three-variable integrate-and-fire model (KM-LIF) which captures the qualitative firing features. We apply dynamical systems methods to explain the underlying biophysical and mathematical mechanisms for the firing behaviors, including the characteristic firing patterns, the latency phase, the onset of repetitive firing, and some discontinuities in the timing of latency duration (e.i. first spike latency and first inter spike interval). Moreover, we obtain new insights associated with the leading spike by phase plane analysis. We further demonstrate the effects of possible heterogeneity of I _Kis. The latency before repetitive firing can be controlled to cover a large range by tuning of the relative amounts of I _Kif and I _Kis. Finally, we find for the full system robust bistability when enough I _Kis is present.