Six types of multistability in a neuronal model based on slow calcium current

Background

Multistability of oscillatory and silent regimes is a ubiquitous phenomenon exhibited by excitable systems such as neurons and cardiac cells. Multistability can play functional roles in short-term memory and maintaining posture. It seems to pose an evolutionary advantage for neurons which are part of multifunctional Central Pattern Generators to possess multistability. The mechanisms supporting multistability of bursting regimes are not well understood or classified.

Methodology/Principal Findings

Our study is focused on determining the bio-physical mechanisms underlying different types of co-existence of the oscillatory and silent regimes observed in a neuronal model. We develop a low-dimensional model typifying the dynamics of a single leech heart interneuron. We carry out a bifurcation analysis of the model and show that it possesses six different types of multistability of dynamical regimes. These types are the co-existence of 1) bursting and silence, 2) tonic spiking and silence, 3) tonic spiking and subthreshold oscillations, 4) bursting and subthreshold oscillations, 5) bursting, subthreshold oscillations and silence, and 6) bursting and tonic spiking. These first five types of multistability occur due to the presence of a separating regime that is either a saddle periodic orbit or a saddle equilibrium. We found that the parameter range wherein multistability is observed is limited by the parameter values at which the separating regimes emerge and terminate.

Conclusions

We developed a neuronal model which exhibits a rich variety of different types of multistability. We described a novel mechanism supporting the bistability of bursting and silence. This neuronal model provides a unique opportunity to study the dynamics of networks with neurons possessing different types of multistability.