A Balance Equation Determines a Switch in Neuronal Excitability

Franci, Alessio; Drion, Guillaume; Seutin, Vincent; Sepulchre, Rodolphe

doi:10.1371/journal.pcbi.1003040

Cited by 51 publications

(110 citation statements)

References 23 publications

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“…The sign, magnitude, and voltage dependence of g f and g s account for the dynamics of a spike. In particular, the sign of the DIC curve determines whether it is restorative or regenerative, that is, whether it tends to provide negative or positive feedback, respectively, via membrane potential variations (8,21,22,28).…”

Section: Resultsmentioning

confidence: 99%

“…7B, Middle and Right), forming an hourglass shape that differs strikingly from the familiar inverted N seen in most planar reductions. The emergence of a lower branch was observed in a previous reduction of the Connor-Stevens model using the method of equivalent potentials (39), although the physiological meaning of this branch remained in question until very recent work (19)(20)(21), which used singularity theory to prove its existence. The lower branch corresponds to the addition of a positive feedback component in the slow timescale, which coexists with the negative feedback in the single recovery variable, w. The existence of a lower V-nullcline branch turns out to be crucial for understanding Type I and Type II* behavior.…”

Section: Ion Channels Have Paradoxical Effects On Excitability In Difmentioning

confidence: 96%

“…Using rigorous but intuitive methods (18) and building on previous technical results (19)(20)(21), we show that introducing I A to a Type II neuron progressively linearizes but then delinearizes the FI curve as I A density increases further. Consequently, I A density must be tuned in a strict range to achieve Type I behavior.…”

mentioning

confidence: 87%

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Ion channel degeneracy enables robust and tunable neuronal firing rates

Drion

O’Leary

Marder

2015

Proc. Natl. Acad. Sci. U.S.A.

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132

165

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Firing rate is an important means of encoding information in the nervous system. To reliably encode a wide range of signals, neurons need to achieve a broad range of firing frequencies and to move smoothly between low and high firing rates. This can be achieved with specific ionic currents, such as A-type potassium currents, which can linearize the frequency-input current curve. By applying recently developed mathematical tools to a number of biophysical neuron models, we show how currents that are classically thought to permit low firing rates can paradoxically cause a jump to a high minimum firing rate when expressed at higher levels. Consequently, achieving and maintaining a low firing rate is surprisingly difficult and fragile in a biological context. This difficulty can be overcome via interactions between multiple currents, implying a need for ion channel degeneracy in the tuning of neuronal properties.FI curve | bifurcation | Type I excitability | Type II excitability | reduced neuron model F iring rates encode the intensities of many signals in the nervous system, whether these are inputs from sensory organs, internal representations of percepts, or muscle contraction commands in motor nerves. For a neuron to represent continuously varying signals in its firing rate, it must be able to fire at low, high, and all intermediate frequencies. Experimentally, this means the frequency-input current (or FI) curve has a specific shape, called Type I, such that firing frequency smoothly approaches zero at current threshold (1-6). By contrast, so-called Type II neurons have a lower bound in their firing frequency and move abruptly from quiescence to fast spiking, with this transition visible as a sharp jump in the FI curve at threshold (1,3,5).Type I behavior is physiologically unlikely with a minimal set of membrane currents such as the voltage-gated sodium and delayed-rectifier potassium currents in the standard squid giant axon Hodgkin-Huxley model, which is Type II. Classic experimental (1, 7) and theoretical studies (3-5, 8, 9) revealed that a Type II membrane (such as a squid giant axon) can be turned into a Type I membrane by adding an inactivating (A-type) potassium conductance, I A . As the density of I A channels increases from zero, the membrane is able to support progressively lower firing frequencies at spiking threshold. The resulting linearization of the FI curve from Type II to Type I has clear consequences for encoding information in firing rate as well as other computational properties such as thresholding and gain scaling, all of which are subjects of intense research (10-17).We now show that this picture is incomplete. Using rigorous but intuitive methods (18) and building on previous technical results (19-21), we show that introducing I A to a Type II neuron progressively linearizes but then delinearizes the FI curve as I A density increases further. Consequently, I A density must be tuned in a strict range to achieve Type I behavior. However, we show that other, unrelated currents including v...

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Section: Resultsmentioning

confidence: 99%

Section: Ion Channels Have Paradoxical Effects On Excitability In Difmentioning

confidence: 96%

See 1 more Smart Citation

Ion channel degeneracy enables robust and tunable neuronal firing rates

Drion

O’Leary

Marder

2015

Proc. Natl. Acad. Sci. U.S.A.

Self Cite

132

165

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“…example, modeling results suggest that changes in the intrinsic currents, e.g. L-type Ca 2+ current, can switch the excitability type of the DA neuron [44,45]. Our model suggests that DA neurons display type II excitability in the presence of the Ih current.…”

Section: Influence Of Intrinsic Currents On the Type Of Excitabilitymentioning

confidence: 67%

“…For example, modeling results suggest that changes in the intrinsic currents, e.g. L-type Ca 2+ current, can switch the excitability type of the DA neuron [44,45]. Here we address the variability in the excitability type under different conditions by studying the contribution of intrinsic and synaptic currents to regulation of the lowfrequency DA neuron firing.…”

Section: Introductionmentioning

confidence: 99%

Dopamine neurons change the type of excitability in response to stimuli

Morozova

Zakharov²,

Gutkin

et al. 2016

Preprint

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The dynamics of neuronal excitability determine the neuron's response to stimuli, its synchronization and resonance properties and, ultimately, the computations it performs in the brain. We investigated the dynamical mechanisms underlying the excitability type of dopamine (DA) neurons, using a conductance-based biophysical model, and its regulation by intrinsic and synaptic currents. Calibrating the model to reproduce low frequency tonic firing results in N-methyl-D-aspartate (NMDA) excitation balanced by γ-Aminobutyric acid (GABA)-mediated inhibition and leads to type I excitable behavior characterized by a continuous decrease in firing frequency in response to hyperpolarizing currents. Furthermore, we analyzed how excitability type of the DA neuron model is influenced by changes in the intrinsic current composition. A subthreshold sodium current is necessary for a continuous frequency decrease during application of a negative current, and the low-frequency "balanced" state during simultaneous activation of NMDA and GABA receptors. Blocking this current switches the neuron to type II characterized by the abrupt onset of repetitive firing. Enhancing the anomalous rectifier Ih current also switches the excitability to type II. Key characteristics of synaptic conductances that may be observed in vivo also change the type of excitability: a depolarized γ-Aminobutyric acid receptor (GABAR) reversal potential or coactivation of α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptors (AMPARs) leads to an abrupt frequency drop to zero, which is typical for type II excitability. Coactivation of N-methyl-D-aspartate receptors (NMDARs) together with AMPARs and GABARs shifts the type I/II boundary toward more hyperpolarized GABAR reversal potentials. To better understand how altering each of the aforementioned currents leads to changes in excitability profile of DA neuron, we provide a thorough dynamical analysis. Collectively, these results imply that type I excitability in dopamine neurons might be important for low firing rates and fine-tuning basal dopamine levels, while switching excitability to type II during NMDAR and AMPAR activation may facilitate a transient increase in dopamine concentration, as type II neurons are more amenable to synchronization by mutual excitation. Author SummaryDopamine neurons play a central role in guiding motivated behaviors. However, complete understanding of computations these neurons perform to encode rewarding and salient stimuli is still forthcoming. Network connectivity influences neural responses to stimuli, but so do intrinsic excitability properties of individual neurons, as such properties define synchronization qualities and neural coding strategy. We investigated the excitability type of the DA neuron and found that, depending on the synaptic and intrinsic current composition, DA neurons can switch from type I to type II excitability. In short, without synaptic inputs or under balanced excitatory and inhibitory inputs DA neurons exhibits type I excitability, w...

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The Bifurcation and Multi-timescale Singularity Analysis of the AII Amacrine Cell Firing Activities in Retina

Zhao,

Song,

et al. 2024

J Nonlinear Sci

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A Balance Equation Determines a Switch in Neuronal Excitability

Cited by 51 publications

References 23 publications

Ion channel degeneracy enables robust and tunable neuronal firing rates

Ion channel degeneracy enables robust and tunable neuronal firing rates

Dopamine neurons change the type of excitability in response to stimuli

The Bifurcation and Multi-timescale Singularity Analysis of the AII Amacrine Cell Firing Activities in Retina

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