Pyramidal cells in the electrosensory lateral line lobe (ELL) of weakly electric fish produce burst discharge. A Hodgkin-Huxley-type model, called ghostburster, consisting of two compartments (soma and dendrite) reproduces ELL pyramidal cell bursting observed in vitro. A previous study analyzed the ghostburster by treating Is and gDr,d as bifurcation parameters (Is: current injected into the somatic compartment and gDr,d: maximal conductance of the delayed rectifying potassium current in the dendritic compartment) and indicated that when both Is and gDr,d are set at particular values, the ghostburster shows a codimension-two bifurcation at which both saddle-node bifurcation of fixed points and saddle-node bifurcation of limit cycles occur simultaneously. In the present study, the ghostburster was investigated to clarify the bursting that occurred at gDr,d values smaller than that at the codimension-two bifurcation. Based on the number of spikes per burst, various burst patterns were observed depending on the (Is, gDr,d) values. Depending on the (Is, gDr,d) values, the burst trajectory in a phase space of the ghostburster showed either a high or a low degree of periodicity. Compared to the previous study, the present findings contribute to a more detailed understanding of ghostburster bursting.
Dopaminergic neurons in the retina show spontaneous tetrodotoxin-sensitive pacemaking, which has been explained by a reduced Hodgkin-Huxley-type computer model. The present study used this model to investigate the effect of variations in transient and persistent sodium conductance values on pacemaking, under variable leakage conductance levels. This study indicated that transient sodium conductance plays an indispensable role in pacemaking, which occurs under conditions in which only a persistent sodium conductance is considerably reduced, thus contributing to a detailed understanding of the relationship between sodium conductance and pacemaking.
The RPa1 neuron identified in the snail, Helix pomatia, produced a variety of electrical activities (e.g. bursting and spiking). A previously developed mathematical model, which described these activities, revealed bistability between bursting and chaotic spiking, where chaotic spiking was transformed into bursting by a short-lasting external stimulus, and vice versa. The present study used this model to detect other types of bistability, i.e. bistability between bursting and period-2 spiking and between bursting and period-4 spiking (period-2 and -4 spiking are generated by period-doubling bifurcation). This contributes to our understanding of the electrophysiological properties of RPa1.
Neocortical pyramidal neurons are capable of intrinsic regenerative firing. A mathematical model introduced by Delord et al.  of these neurons based on the Hodgkin-Huxley formalism, varied the values of two parameters of the model, i.e. the maximal persistent sodium conductance (gNaP) and the leakage one (gl), and revealed the (gNaP, gl) parameter space supporting regenerative firing. The present study focused on another parameter of this model, i.e. the maximal fast sodium conductance (gNa), to investigate the (gNaP, gNa) parameter space involved in regenerative firing. When gNa was completely blocked, regenerative firing was suppressed. In addition, the gNa threshold necessary to induce regenerative firing was almost independent of the gNaP level. Finally, our results were compared with those of other types of neurons.