Bifurcations of emergent bursting in a neuronal network.
Complex neuronal networks are an important tool to help explain paradoxical phenomena observed in biological recordings. Here we present a general approach to mathematically tackle a complex neuronal network so that we can fully understand the underlying mechanisms. Using a previously developed network model of the milk-ejection reflex in oxytocin cells, we show how we can reduce a complex model with many variables and complex network topologies to a tractable model with two variables, while retaining all key qualitative features of the original model. The approach enables us to uncover how emergent synchronous bursting can arise from a neuronal network which embodies known biological features. Surprisingly, the bursting mechanisms are similar to those found in other systems reported in the literature, and illustrate a generic way to exhibit emergent and multiple time scale oscillations at the membrane potential level and the firing rate level.
Centre for Computational Systems Biology and School of Mathematical Sciences, Fudan University, Shanghai, China.
Yu
Y
Wu
Wenlian
W
Lu
Wei
W
Lin
Gareth
G
Leng
Jianfeng
J
Feng
D000200:Action Potentials / Q000502:physiology; D000465:Algorithms; D000818:Animals; D003712:Dendrites / Q000502:physiology; D005260:Female; D006801:Humans; D008564:Membrane Potentials / Q000502:physiology; D008893:Milk Ejection / Q000502:physiology*; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology*; D009474:Neurons / Q000166:cytology / Q000378:metabolism / Q000502:physiology; D010121:Oxytocin / Q000378:metabolism; D012018:Reflex / Q000502:physiology; D009435:Synaptic Transmission / Q000502:physiology
D010121:Oxytocin