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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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Oxytocin network and its behavior at multi-time scales.(A) Schematic diagram illustrating the topology of the model network; for each cell, two yellow squares indicate which bundles are occupied by the cell dendrites. (B) A few clusters of cells are found in the network where neurons (circles) interact via both dendrites (lines). Such clusters may occasionally be connected through a common bundle. (C) Ratemeter records of three representative cells showing bursts in response to simulated suckling. A clear spike at the firing rate level is observed. (D) Raster plots of the activity of all 48 cells in the network through the first simulated milk-ejection burst. Note the approximately synchronous activation of all model cells during a burst. (E) Adding excitatory input to the network will paradoxically destroy the bursting activity. (F) Increasing inhibitory input can sometime induce bursting.
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pone-0038402-g001: Oxytocin network and its behavior at multi-time scales.(A) Schematic diagram illustrating the topology of the model network; for each cell, two yellow squares indicate which bundles are occupied by the cell dendrites. (B) A few clusters of cells are found in the network where neurons (circles) interact via both dendrites (lines). Such clusters may occasionally be connected through a common bundle. (C) Ratemeter records of three representative cells showing bursts in response to simulated suckling. A clear spike at the firing rate level is observed. (D) Raster plots of the activity of all 48 cells in the network through the first simulated milk-ejection burst. Note the approximately synchronous activation of all model cells during a burst. (E) Adding excitatory input to the network will paradoxically destroy the bursting activity. (F) Increasing inhibitory input can sometime induce bursting.

Mentions: A simple version of the network model is illustrated in Fig. 1. This model network has 48 cells and 12 bundles, and each cell has two dendrites ended up in different bundles, and two cells can interact if they share a common bundle. Each bundle contains the same number of dendrites, which we refer to as a ‘homogeneous arrangement of the connections’ (Fig. 1A, B). In the model, the dendritic stores of readily-releasable vesicles are continuously incremented by the suckling-related ‘priming’ input. Their level increases relatively steadily between bursts despite activity-dependent depletion, and synchronous bursts tend to occur when the oxytocin level at the store is relatively high (Fig. 1C, D). In addition to the synchronicity, the bursts possess the characteristic that the inter-burst intervals are almost constant. More interestingly, we observed a number of paradoxical behaviors also observed in experimental studies. For example, increased spike activity between bursts enhances depletion of the stores and so can delay or even suppress bursting (Fig. 1E). Conversely, an increase in inhibitory inputs can promote the reflex in a system which fails to express bursting because of insufficient priming. For example, injections of the inhibitory neurotransmitter GABA into the supraoptic nucleus of a suckled, lactating rat can trigger milk-ejection bursts (Fig. 1F).


Bifurcations of emergent bursting in a neuronal network.

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

Oxytocin network and its behavior at multi-time scales.(A) Schematic diagram illustrating the topology of the model network; for each cell, two yellow squares indicate which bundles are occupied by the cell dendrites. (B) A few clusters of cells are found in the network where neurons (circles) interact via both dendrites (lines). Such clusters may occasionally be connected through a common bundle. (C) Ratemeter records of three representative cells showing bursts in response to simulated suckling. A clear spike at the firing rate level is observed. (D) Raster plots of the activity of all 48 cells in the network through the first simulated milk-ejection burst. Note the approximately synchronous activation of all model cells during a burst. (E) Adding excitatory input to the network will paradoxically destroy the bursting activity. (F) Increasing inhibitory input can sometime induce bursting.
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC3369873&req=5

pone-0038402-g001: Oxytocin network and its behavior at multi-time scales.(A) Schematic diagram illustrating the topology of the model network; for each cell, two yellow squares indicate which bundles are occupied by the cell dendrites. (B) A few clusters of cells are found in the network where neurons (circles) interact via both dendrites (lines). Such clusters may occasionally be connected through a common bundle. (C) Ratemeter records of three representative cells showing bursts in response to simulated suckling. A clear spike at the firing rate level is observed. (D) Raster plots of the activity of all 48 cells in the network through the first simulated milk-ejection burst. Note the approximately synchronous activation of all model cells during a burst. (E) Adding excitatory input to the network will paradoxically destroy the bursting activity. (F) Increasing inhibitory input can sometime induce bursting.
Mentions: A simple version of the network model is illustrated in Fig. 1. This model network has 48 cells and 12 bundles, and each cell has two dendrites ended up in different bundles, and two cells can interact if they share a common bundle. Each bundle contains the same number of dendrites, which we refer to as a ‘homogeneous arrangement of the connections’ (Fig. 1A, B). In the model, the dendritic stores of readily-releasable vesicles are continuously incremented by the suckling-related ‘priming’ input. Their level increases relatively steadily between bursts despite activity-dependent depletion, and synchronous bursts tend to occur when the oxytocin level at the store is relatively high (Fig. 1C, D). In addition to the synchronicity, the bursts possess the characteristic that the inter-burst intervals are almost constant. More interestingly, we observed a number of paradoxical behaviors also observed in experimental studies. For example, increased spike activity between bursts enhances depletion of the stores and so can delay or even suppress bursting (Fig. 1E). Conversely, an increase in inhibitory inputs can promote the reflex in a system which fails to express bursting because of insufficient priming. For example, injections of the inhibitory neurotransmitter GABA into the supraoptic nucleus of a suckled, lactating rat can trigger milk-ejection bursts (Fig. 1F).

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