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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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Transition between spiking and bursting in the ONN with Hz (left column) and in the SNN with  Hz (right column).Both networks are composed of 48 neurons and 12 bundles. (A,B) Ratemeter records of 5 representative cells with time span of 600 s. (C,D) Records of the oxytocin store level of cell 1. (E,F) Voltage trace(blue) and spiking threshold(red) of cell 1. Note that bursting events are essentially attributed to the drop of the spiking threshold and store level.
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pone-0038402-g002: Transition between spiking and bursting in the ONN with Hz (left column) and in the SNN with Hz (right column).Both networks are composed of 48 neurons and 12 bundles. (A,B) Ratemeter records of 5 representative cells with time span of 600 s. (C,D) Records of the oxytocin store level of cell 1. (E,F) Voltage trace(blue) and spiking threshold(red) of cell 1. Note that bursting events are essentially attributed to the drop of the spiking threshold and store level.

Mentions: The ONN in [23] displays the transition between spiking and bursting (Fig. 2). The spiking rate is recorded on a network of 48 neurons and 12 bundles in Fig. 2A, and the voltage trace and store level of oxytocin are shown in Fig. 2C and E. The bursting events are essentially attributed to the drop of the spike threshold (red line) and store level. Our simplification of the ONN does not destroy such basic behaviors of the network in the sense that the SNN displays similar network activity in Fig. 2B, 2D and 2F as the ONN in Fig. 2A, 2C and 2E. As expected, the SNN fires faster than the ONN even though the input rate in the SNN (50 Hz) is smaller than in the ONN (80 Hz), because we have discarded all bursting terminating mechanisms related to the negative feedback effects of the HAP and AHP on the spike threshold, the doublet effects in the impulsive release of oxytocin and the feedback inhibition by endocannabinoids.


Bifurcations of emergent bursting in a neuronal network.

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

Transition between spiking and bursting in the ONN with Hz (left column) and in the SNN with  Hz (right column).Both networks are composed of 48 neurons and 12 bundles. (A,B) Ratemeter records of 5 representative cells with time span of 600 s. (C,D) Records of the oxytocin store level of cell 1. (E,F) Voltage trace(blue) and spiking threshold(red) of cell 1. Note that bursting events are essentially attributed to the drop of the spiking threshold and store level.
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC3369873&req=5

pone-0038402-g002: Transition between spiking and bursting in the ONN with Hz (left column) and in the SNN with Hz (right column).Both networks are composed of 48 neurons and 12 bundles. (A,B) Ratemeter records of 5 representative cells with time span of 600 s. (C,D) Records of the oxytocin store level of cell 1. (E,F) Voltage trace(blue) and spiking threshold(red) of cell 1. Note that bursting events are essentially attributed to the drop of the spiking threshold and store level.
Mentions: The ONN in [23] displays the transition between spiking and bursting (Fig. 2). The spiking rate is recorded on a network of 48 neurons and 12 bundles in Fig. 2A, and the voltage trace and store level of oxytocin are shown in Fig. 2C and E. The bursting events are essentially attributed to the drop of the spike threshold (red line) and store level. Our simplification of the ONN does not destroy such basic behaviors of the network in the sense that the SNN displays similar network activity in Fig. 2B, 2D and 2F as the ONN in Fig. 2A, 2C and 2E. As expected, the SNN fires faster than the ONN even though the input rate in the SNN (50 Hz) is smaller than in the ONN (80 Hz), because we have discarded all bursting terminating mechanisms related to the negative feedback effects of the HAP and AHP on the spike threshold, the doublet effects in the impulsive release of oxytocin and the feedback inhibition by endocannabinoids.

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