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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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The firing rate map and its approximation.(A) The firing rate map derived from the leaky integrate-fire model (1) by simulating the differential equation (1) with fixed  and  on each trial. (B) The approximation of the firing rate map.
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pone-0038402-g003: The firing rate map and its approximation.(A) The firing rate map derived from the leaky integrate-fire model (1) by simulating the differential equation (1) with fixed and on each trial. (B) The approximation of the firing rate map.

Mentions: (8)To find the analytical expression of the firing rate map, we adopt a numerical approach by simulating the leaky integrate-fire model. Simulations of equation (1) for a single cell are conducted by fixing on each trial. Fig. 3A shows the relationship between and corresponding to varied excitatory inputs.


Bifurcations of emergent bursting in a neuronal network.

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

The firing rate map and its approximation.(A) The firing rate map derived from the leaky integrate-fire model (1) by simulating the differential equation (1) with fixed  and  on each trial. (B) The approximation of the firing rate map.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0038402-g003: The firing rate map and its approximation.(A) The firing rate map derived from the leaky integrate-fire model (1) by simulating the differential equation (1) with fixed and on each trial. (B) The approximation of the firing rate map.
Mentions: (8)To find the analytical expression of the firing rate map, we adopt a numerical approach by simulating the leaky integrate-fire model. Simulations of equation (1) for a single cell are conducted by fixing on each trial. Fig. 3A shows the relationship between and corresponding to varied excitatory inputs.

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