A Two-Variable Model of Somatic–Dendritic Interactions in a Bursting Neuron

Laing, Carlo R.; Longtin, André

doi:10.1006/bulm.2002.0303

Cited by 24 publications

(20 citation statements)

References 48 publications

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“…Somatodendritic ping-pong has been previously described in the context of neuronal bursting dynamics [2,9,20,28,39]. Bose and Booth [2] showed that in order for somatodendritic ping-pong bursting activity to occur in two-compartment models, the coupling conductance between the somatic and dendritic compartments and the integration time constant of the dendritic compartment must be tightly tuned so as to allow the dendritic compartment time to be sufficiently depolarized after a somatic spike.…”

Section: Linear Spikementioning

confidence: 99%

Bistability in a Leaky Integrate-and-Fire Neuron with a Passive Dendrite

Schwemmer¹,

Lewis²

2012

SIAM J. Appl. Dyn. Syst.

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Abstract. We examine the influence of dendritic load on the firing dynamics of a spatially extended leaky integrate-and-fire (LIF) neuron that explicitly includes spiking dynamics. We obtain an exact analytical solution for this model and use it to derive a return map that completely captures the dynamics of the system. Using the map, we find that dendritic properties can significantly change the firing dynamics of the system. Under certain conditions, the addition of the dendrite can change the LIF model from type 1 excitability to type 2 excitability and induce bistability between periodic firing and the quiescent state. We identify the mechanism that causes the periodic behavior in the bistable regime as somatodendritic ping-pong. Furthermore, we use the return map to fully explore the model parameter space in order to find regions where this bistable behavior occurs. We then give physical interpretations of the dependence of the bistable behavior on model parameters. Finally, we demonstrate that the simpler two-compartment model displays qualitatively similar dynamics to the more complicated ball-and-stick model. 1. Introduction. Neurons are spatially extensive and heterogeneous. They typically consist of a dendritic tree, a soma (cell body), and an axon. The type of model one uses to represent a neuron depends upon a balance between mathematical tractability and biological realism and on the issue being addressed. A common technique in neuronal modeling is to represent the neuron as a single-compartment object that ignores the spatial anatomy of the cell, e.g., [11,25,26]. Although this simplification allows for greater mathematical tractability and computational efficiency, many neurons are not electrotonically compact. Therefore, singlecompartment models cannot be expected to capture the full spectrum of electrical behavior of neurons. Dendrites can have substantial effects on the dynamics of individual neurons. For example, the architecture and ionic channel density of a dendritic tree can alter the firing pattern and encoding properties of a neuronal oscillator [19,21,24], while the additional electrical load due to the dendrite can alter firing frequency [36,38]. For a full understanding of this behavior, more detailed models are required.

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Section: Linear Spikementioning

confidence: 99%

Bistability in a Leaky Integrate-and-Fire Neuron with a Passive Dendrite

Schwemmer¹,

Lewis²

2012

SIAM J. Appl. Dyn. Syst.

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“…In (9), differentiation is with respect to r . We note that c and s act as parameters in the v d equation, and that s = 0 reduces the Ca equation to a simple equation of exponential decay.…”

Section: Burst Initiationmentioning

confidence: 99%

“…Suppose that a term -I s y n = -g s y n S i n h [ V d -E i n h ] were added to the right side of the u$ equation in ( l ) , (9) or (10). Sinh is a synaptic gating variable which, at the moment of a pre-synaptic spike (or burst), is reset to one and then decays like exp(-Kt) for some decay rate K .…”

Section: Burst Initiationmentioning

confidence: 99%

“…One is to model the neuron using partial differential equations to explicitly capture the spatial dependence [6,15,171. Another is to use ordinary differential equations to model the neuron as a multi-compartment cell where the compartments are coupled via gap junctions [9,14,16,19,211. The third approach is to treat the neuron as a single-compartment, point neuron [13, 201. In choosing one of these approaches, one must balance the need for biological plausibility versus the need for mathematical rigor and understanding of underlying phenomena.…”

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confidence: 99%

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Bursting in 2-Compartment Neurons: A Case Study of the Pinsky-Rinzel Model

Bose

Booth

2005

Bursting

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The two-compartment Pinsky-Rinzel model of a hippocampal CA3 pyramidal neuron consists of electrically coupled soma and dendritic compartments, each with active ionic conductances. This model has been widely used in a variety of contexts, but little analysis has been performed on its bursting solutions. In this chapter, we provide a geometric framework to study the Pinsky-Rinzel model. Using a combination of analysis and simulations, we identify neuronal mechanisms responsible for certain salient features of the model such as burst initiation and somatic-dendritic ping-pong. Some of these mechanisms are then demonstrated in a conceptually simpler, two-compartment Morris-Lecar model. 5.

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“…Recently, computational neuroscientists have begun to use integrate-and-fire methods to model phenomenon such as bursting and calcium oscillations (Coombs et al, 2001;Laing and Longtin, 2002;Liu and Wang, 2001;or van Vreeswijk and Hansel, 2001). Here we consider excitatory networks consisting of RS and IB cortical neurons as described in McCormick et al (1985).…”

Section: Introductionmentioning

confidence: 99%

An integrate-and-fire model for synchronized bursting in a network of cultured cortical neurons

French

Gruenstein

2006

J Comput Neurosci

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It has been suggested that spontaneous synchronous neuronal activity is an essential step in the formation of functional networks in the central nervous system. The key features of this type of activity consist of bursts of action potentials with associated spikes of elevated cytoplasmic calcium. These features are also observed in networks of rat cortical neurons that have been formed in culture. Experimental studies of these cultured networks have led to several hypotheses for the mechanisms underlying the observed synchronized oscillations. In this paper, bursting integrate-and-fire type mathematical models for regular spiking (RS) and intrinsic bursting (IB) neurons are introduced and incorporated through a small-world connection scheme into a two-dimensional excitatory network similar to those in the cultured network. This computer model exhibits spontaneous synchronous activity through mechanisms similar to those hypothesized for the cultured experimental networks. Traces of the membrane potential and cytoplasmic calcium from the model closely match those obtained from experiments. We also consider the impact on network behavior of the IB neurons, the geometry and the small world connection scheme.

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A Two-Variable Model of Somatic–Dendritic Interactions in a Bursting Neuron

Cited by 24 publications

References 48 publications

Bistability in a Leaky Integrate-and-Fire Neuron with a Passive Dendrite

Bistability in a Leaky Integrate-and-Fire Neuron with a Passive Dendrite

Bursting in 2-Compartment Neurons: A Case Study of the Pinsky-Rinzel Model

An integrate-and-fire model for synchronized bursting in a network of cultured cortical neurons

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