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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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Flow chart illustrating the model simplification.First, we simplify a network model with a single neuron of 10 variables by discarding the negative feedbacks in the spike threshold and the doublet effects on the impulsive release of oxytocin, and obtain a simplified network model with 4 variables for each neuron. After evaluating the firing rate map, we derive the mean field model, which enables us to perform the bifurcation analysis.
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pone-0038402-g004: Flow chart illustrating the model simplification.First, we simplify a network model with a single neuron of 10 variables by discarding the negative feedbacks in the spike threshold and the doublet effects on the impulsive release of oxytocin, and obtain a simplified network model with 4 variables for each neuron. After evaluating the firing rate map, we derive the mean field model, which enables us to perform the bifurcation analysis.

Mentions: To summarize all procedures above, we include a flow chart (Fig. 4). In the first step, we simplify a network model with a single neuron of 10 variables by discarding the negative feedbacks in the spike threshold and the doublet effects on the impulsive release of oxytocin, and obtain a simplified network model with four variables for each neuron. After evaluating the firing rate map, we derive the reduced deterministic autonomous system (8) (the mean field model) in the second step, which enables us to perform the bifurcation analysis. A similar approach could be employed generally to deal with other complex and stochastic neuronal networks.


Bifurcations of emergent bursting in a neuronal network.

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

Flow chart illustrating the model simplification.First, we simplify a network model with a single neuron of 10 variables by discarding the negative feedbacks in the spike threshold and the doublet effects on the impulsive release of oxytocin, and obtain a simplified network model with 4 variables for each neuron. After evaluating the firing rate map, we derive the mean field model, which enables us to perform the bifurcation analysis.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0038402-g004: Flow chart illustrating the model simplification.First, we simplify a network model with a single neuron of 10 variables by discarding the negative feedbacks in the spike threshold and the doublet effects on the impulsive release of oxytocin, and obtain a simplified network model with 4 variables for each neuron. After evaluating the firing rate map, we derive the mean field model, which enables us to perform the bifurcation analysis.
Mentions: To summarize all procedures above, we include a flow chart (Fig. 4). In the first step, we simplify a network model with a single neuron of 10 variables by discarding the negative feedbacks in the spike threshold and the doublet effects on the impulsive release of oxytocin, and obtain a simplified network model with four variables for each neuron. After evaluating the firing rate map, we derive the reduced deterministic autonomous system (8) (the mean field model) in the second step, which enables us to perform the bifurcation analysis. A similar approach could be employed generally to deal with other complex and stochastic neuronal networks.

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