A basic biophysical model for bursting neurons

Av-Ron, Evyatar; Parnas, H.; Segel, Lee A.

doi:10.1007/bf00201411

Cited by 69 publications

(53 citation statements)

References 10 publications

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“…The silence, regular spiking, and bursting we observed across connected regions of parameter space have also been reported by others [2,20,52]. In our model, bursting was due to the buildup of Ca 2þ and the activation of I K-Ca , either intrinsically at the soma [2,20,53] or in a weakly coupled dendrite that influenced somatic firing [21]. We expect that both kinds of bursting exist over all three parameter spaces we explored, for appropriate ranges of parameters.…”

Section: Building Upon Previous Approachessupporting

confidence: 81%

Neuronal Firing Sensitivity to Morphologic and Active Membrane Parameters

Weaver¹,

Wearne²

2005

PLoS Comput Biol

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Both the excitability of a neuron's membrane, driven by active ion channels, and dendritic morphology contribute to neuronal firing dynamics, but the relative importance and interactions between these features remain poorly understood. Recent modeling studies have shown that different combinations of active conductances can evoke similar firing patterns, but have neglected how morphology might contribute to homeostasis. Parameterizing the morphology of a cylindrical dendrite, we introduce a novel application of mathematical sensitivity analysis that quantifies how dendritic length, diameter, and surface area influence neuronal firing, and compares these effects directly against those of active parameters. The method was applied to a model of neurons from goldfish Area II. These neurons exhibit, and likely contribute to, persistent activity in eye velocity storage, a simple model of working memory. We introduce sensitivity landscapes, defined by local sensitivity analyses of firing rate and gain to each parameter, performed globally across the parameter space. Principal directions over which sensitivity to all parameters varied most revealed intrinsic currents that most controlled model output. We found domains where different groups of parameters had the highest sensitivities, suggesting that interactions within each group shaped firing behaviors within each specific domain. Application of our method, and its characterization of which models were sensitive to general morphologic features, will lead to advances in understanding how realistic morphology participates in functional homeostasis. Significantly, we can predict which active conductances, and how many of them, will compensate for a given age-or development-related structural change, or will offset a morphologic perturbation resulting from trauma or neurodegenerative disorder, to restore normal function. Our method can be adapted to analyze any computational model. Thus, sensitivity landscapes, and the quantitative predictions they provide, can give new insight into mechanisms of homeostasis in any biological system.

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Section: Building Upon Previous Approachessupporting

confidence: 81%

Neuronal Firing Sensitivity to Morphologic and Active Membrane Parameters

Weaver¹,

Wearne²

2005

PLoS Comput Biol

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“…The numerical simulation used in this study utilized the excitable membrane model of Hodgkin and Huxley (Hodgkin and Huxley 1952) as modified by Av-Ron et al (Av-Ron 1994;Av-Ron et al 1993). Each cell in the simulation is influenced by a set of synaptic inputs as well as ion channel currents, with the membrane potential varying as:…”

Section: Differential Equations and Numerical Integrationmentioning

confidence: 99%

Studies of stimulus parameters for seizure disruption using neural network simulations

et al. 2007

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A large scale neural network simulation with realistic cortical architecture has been undertaken to investigate the effects of external electrical stimulation on the propagation and evolution of ongoing seizure activity. This is an effort to explore the parameter space of stimulation variables to uncover promising avenues of research for this therapeutic modality. The model consists of an approximately 800 μm × 800 μm region of simulated cortex, and includes seven neuron classes organized by cortical layer, inhibitory or excitatory properties, and electrophysiological characteristics. The cell dynamics are governed by a modified version of the Hodgkin-Huxley equations in single compartment format. Axonal connections are patterned after histological data and published models of local cortical wiring. Stimulation induced action potentials take place at the axon initial segments, according to threshold requirements on the applied electric field distribution. Stimulation induced action potentials in horizontal axonal branches are also separately simulated. The calculations are performed on a 16 node distributed 32-bit processor system. Clear differences in seizure evolution are presented for stimulated versus the undisturbed rhythmic activity. Data is provided for frequency dependent stimulation effects demonstrating a plateau effect of stimulation efficacy as the applied frequency is increased from 60 Hz to 200 Hz. Timing of the stimulation with respect to the underlying rhythmic activity demonstrates a phase dependent sensitivity. Electrode height and position effects are also presented. Using a dipole stimulation electrode arrangement, clear orientation effects of the dipole with respect to the model connectivity is also demonstrated. A sensitivity analysis of these results as a function of the stimulation threshold is also provided.

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“…A number of mathematical models of bursting cells have been developed (Av-Ron et al, 1993;Wang, 1993;Sivan et al, 1995;de Vries, 1998;Rinzel and Ermentrout, 1998;Doiron et al, 2002), but they are generally difficult to treat analytically in any detail. Much past analysis of bursting cells has been influenced by the 'slow-fast' separation of timescales in bursting systems (Rinzel and Ermentrout, 1998;Izhikevich, 2000), where it is assumed that fast, spiking variables act on a much shorter time-scale than the slow variable(s) that are responsible for the shifts between spiking and quiescent behavior.…”

Section: Introductionmentioning

confidence: 99%

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

Laing

Longtin

2002

Bulletin of Mathematical Biology

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We present a two-variable delay-differential-equation model of a pyramidal cell from the electrosensory lateral line lobe of a weakly electric fish that is capable of burst discharge. It is a simplification of a six-dimensional ordinary differential equation model for such a cell whose bifurcation structure has been analyzed (Doiron et al., J. Comput. Neurosci., 12, 2002). We have modeled the effects of back-propagating action potentials by a delay, and use an integrate-and-fire mechanism for action potential generation. The simplicity of the model presented here allows one to explicitly derive a two-dimensional map for successive interspike intervals, and to analytically investigate the effects of time-dependent forcing on such a model neuron. Some of the effects discussed include 'burst excitability', the creation of resonance tongues under periodic forcing, and stochastic resonance. We also investigate the effects of changing the parameters of the model.

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A basic biophysical model for bursting neurons

Cited by 69 publications

References 10 publications

Neuronal Firing Sensitivity to Morphologic and Active Membrane Parameters

Neuronal Firing Sensitivity to Morphologic and Active Membrane Parameters

Studies of stimulus parameters for seizure disruption using neural network simulations

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

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