Dynamic mechanism of multiple bursting patterns in a whole-cell multiscale model with calcium oscillations

Abstract

The dynamic mechanism of a whole-cell model containing electrical signalling and two-compartment Ca $ ^{2+} $ signalling in gonadotrophs is investigated. The transition from spiking to bursting by Hopf bifurcation of the fast subsystem about the slow variable is detected via the suitable parameters. When the timescale of K $ ^+ $ gating variable is changed, the relaxation oscillation with locally small fluctuation, chaotic bursting and mixed-mode bursting (MMB) are revealed through chaos. In addition, the bifurcation of $ [{\rm Ca}^{2+}]_i $ with regard to $ [\rm IP_3] $ is analysed, showing periodic solutions, torus, period doubling solutions and chaos. Finally, hyperpolarizations and torus canard-like behaviours of the full system under a set of specific parameters are elucidated.

Keywords

• chaotic bursting
• mixed-mode bursting
• torus canard-like
• hyperpolarization
• bifurcation
• torus