Co-existent activity patterns in inhibitory neuronal networks with short-term synaptic depression

Bose, Amitabha; Booth, Victoria

doi:10.1016/j.jtbi.2010.12.001

Cited by 9 publications

(38 citation statements)

References 41 publications

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“…For numerical simulations we consider a pair of identical Morris-Lecar neurons (Morris and Lecar, 1981), with parameters adopted from Bose and Booth (2011). The Morris-Lecar model is a set of two first-order differential equations that describe the membrane dynamics of a spiking neuron.…”

Section: Modelmentioning

confidence: 99%

“…see Ermentrout and Terman, 2010). Thus, when a constant inhibitory conductance is applied, g * acts as a release conductance : a cell is prevented from tonic spiking when and it will fire spikes when (Bose and Booth, 2011).…”

Section: Modelmentioning

confidence: 99%

“…At low firing frequency, in contrast, it allows sufficient time for the synapse to recover from depression between spikes, leading to a stronger postsynaptic response. In reciprocal networks, synaptic depression has been shown to act as a “switch”, giving rise to a wide range of network dynamics such as synchronous and multi-stable rhythms, as well as fine tuning the frequency of network oscillations (Nadim and Manor, 2000; Nadim et al, 1999; Bose and Booth, 2011).…”

Section: Introductionmentioning

confidence: 99%

“…Our model reduction is based on the approach previously taken by Bose and Booth (2011), where the dynamics of a similar two-cell reciprocal inhibitory network with depression has been analysed. Bose and Booth (2011) relied on the methods from geometric singular perturbation theory to separate the timescales of the fast membrane, and the slow synaptic dynamics of the network to derive one-dimensional conditions for the existence of stable anti-phase burst solutions. While these conditions justify the existence of bursting, they do not explain how such solutions are created nor what shapes their parameter space.…”

Section: Introductionmentioning

confidence: 99%

“…While these conditions justify the existence of bursting, they do not explain how such solutions are created nor what shapes their parameter space. Here, we extend the analysis by Bose and Booth (2011) by constructing a scalar Poincareè map which tracks the evolution of depression from one burst to the next, and whose fixed points correspond to stable burst solutions of the two-cell network. Our map construction is motivated by the burst length map of a T-type calcium current, utilised in Matveev et al (2007), which approximates the anti-phase bursting dynamics of a network of two coupled Morris-Lecar (Morris and Lecar, 1981) neurons.…”

Section: Introductionmentioning

confidence: 99%

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A scalar Poincaré map for struggling in Xenopus tadpoles

Olenik

Houghton

2019

Preprint

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Synaptic plasticity is widely found in many areas of the central nervous system. In particular, it is believed that synaptic depression can act as a mechanism to allow simple networks to generate a range of different firing patterns. The simplicity of the locomotor circuit in hatchling Xenopus tadpoles provides an excellent place to understand such basic neuronal mechanisms. Depending on the nature of the external stimulus, tadpoles can generate two types of behaviours: swimming when touched and slower, stronger struggling movements when held. Struggling is associated with rhythmic bends of the body and is accompanied by anti-phase bursts in neurons on each side of the spinal cord. Bursting in struggling is thought to be governed by a short-term synaptic depression of inhibition. To better understand burst generation in struggling, we study a minimal network of two neurons coupled through depressing inhibitory synapses. Depending on the strength of the synaptic conductance between the two neurons, such a network can produce symmetric n−n anti-phase bursts, where neurons fire n spikes in alternation, with the period of such solutions increasing with the strength of the synaptic conductance. Using a fast/slow analysis, we reduce the multidimensional network equations to a scalar Poincaé burst map. This map tracks the state of synaptic depression from one burst to the next, and captures the complex bursting dynamics of the network. Fixed points of this map are associated with stable burst solutions of the full network model, and are created through fold bifurcations of maps. We prove that the map has an infinite number of stable fixed points for a finite coupling strength interval, suggesting that the full two-cell network also can produce n−n bursts for arbitrarily large n. Our findings further support the hypothesis that synaptic depression can enrich the variety of activity patterns a neuronal network generates.

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Section: Modelmentioning

confidence: 99%