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Bifurcations of emergent bursting in a neuronal network.

Wu Y, Lu W, Lin W, Leng G, Feng J - PLoS ONE (2012)

Bottom Line: Here we present a general approach to mathematically tackle a complex neuronal network so that we can fully understand the underlying mechanisms.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.

View Article: PubMed Central - PubMed

Affiliation: Centre for Computational Systems Biology and School of Mathematical Sciences, Fudan University, Shanghai, China.

ABSTRACT
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.

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Phase portraits of the system (8) with  and varied : (A)  Hz; (B)  Hz; (C)  Hz; (D)  Hz; (E)  Hz; (F)  Hz; (G)  Hz; (H)  Hz; (I)  Hz.The -cline and -cline are colored in blue and green respectively. The red circles represent the unstable limit cycles, and the black curves stand for the orbits with the initial point .
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pone-0038402-g005: Phase portraits of the system (8) with and varied : (A) Hz; (B) Hz; (C) Hz; (D) Hz; (E) Hz; (F) Hz; (G) Hz; (H) Hz; (I) Hz.The -cline and -cline are colored in blue and green respectively. The red circles represent the unstable limit cycles, and the black curves stand for the orbits with the initial point .

Mentions: When is small, the unique fixed point equilibrium in the - plane is asymptotically stable. Thus, from the asymptotical convergence of the trajectory if (Fig. 5A) we conclude that there is no bursting activity.


Bifurcations of emergent bursting in a neuronal network.

Wu Y, Lu W, Lin W, Leng G, Feng J - PLoS ONE (2012)

Phase portraits of the system (8) with  and varied : (A)  Hz; (B)  Hz; (C)  Hz; (D)  Hz; (E)  Hz; (F)  Hz; (G)  Hz; (H)  Hz; (I)  Hz.The -cline and -cline are colored in blue and green respectively. The red circles represent the unstable limit cycles, and the black curves stand for the orbits with the initial point .
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3369873&req=5

pone-0038402-g005: Phase portraits of the system (8) with and varied : (A) Hz; (B) Hz; (C) Hz; (D) Hz; (E) Hz; (F) Hz; (G) Hz; (H) Hz; (I) Hz.The -cline and -cline are colored in blue and green respectively. The red circles represent the unstable limit cycles, and the black curves stand for the orbits with the initial point .
Mentions: When is small, the unique fixed point equilibrium in the - plane is asymptotically stable. Thus, from the asymptotical convergence of the trajectory if (Fig. 5A) we conclude that there is no bursting activity.

Bottom Line: Here we present a general approach to mathematically tackle a complex neuronal network so that we can fully understand the underlying mechanisms.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.

View Article: PubMed Central - PubMed

Affiliation: Centre for Computational Systems Biology and School of Mathematical Sciences, Fudan University, Shanghai, China.

ABSTRACT
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.

Show MeSH