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A small fraction of strongly cooperative sodium channels boosts neuronal encoding of high frequencies.

Huang M, Volgushev M, Wolf F - PLoS ONE (2012)

Bottom Line: Models with a small fraction, [Formula: see text], of strongly cooperative channels generate APs with the most rapid onset dynamics.In this regime APs are triggered by simultaneous opening of the cooperative channel fraction and exhibit a pronounced biphasic waveform often observed in cortical neurons.We conclude that presence of a small fraction of strongly coupled sodium channels can explain characteristic features of cortical APs and has a functional impact of enhancing the spike encoding of rapidly varying signals.

View Article: PubMed Central - PubMed

Affiliation: Max-Planck-Institute for Dynamics and Self-Organization, Bernstein Center for Computational Neuroscience, and Faculty of Physics, Georg August University School of Science, Göttingen, Germany.

ABSTRACT
Generation of action potentials (APs) is a crucial step in neuronal information processing. Existing biophysical models for AP generation almost universally assume that individual voltage-gated sodium channels operate statistically independently, and their avalanche-like opening that underlies AP generation is coordinated only through the transmembrane potential. However, biological ion channels of various types can exhibit strongly cooperative gating when clustered. Cooperative gating of sodium channels has been suggested to explain rapid onset dynamics and large threshold variability of APs in cortical neurons. It remains however unknown whether these characteristic properties of cortical APs can be reproduced if only a fraction of channels express cooperativity, and whether the presence of cooperative channels has an impact on encoding properties of neuronal populations. To address these questions we have constructed a conductance-based neuron model in which we continuously varied the size of a fraction [Formula: see text] of sodium channels expressing cooperativity and the strength of coupling between cooperative channels [Formula: see text]. We show that starting at a critical value of the coupling strength [Formula: see text], the activation curve of sodium channels develops a discontinuity at which opening of all coupled channels becomes an all-or-none event, leading to very rapid AP onsets. Models with a small fraction, [Formula: see text], of strongly cooperative channels generate APs with the most rapid onset dynamics. In this regime APs are triggered by simultaneous opening of the cooperative channel fraction and exhibit a pronounced biphasic waveform often observed in cortical neurons. We further show that presence of a small fraction of cooperative Na+ channels significantly improves the ability of neuronal populations to phase-lock their firing to high frequency input fluctuation. We conclude that presence of a small fraction of strongly coupled sodium channels can explain characteristic features of cortical APs and has a functional impact of enhancing the spike encoding of rapidly varying signals.

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Cooperative channel gating improves the response of a conductance-based model to high-frequency inputs.Frequency response functions for the Wang-Buzsaki model with independent sodium channels and a standard or 10× fold increased density density of sodium channels (WB, triangles); for cooperative WB model with  of cooperative  channels, , measured with 3 different correlation time constants of background noise (cWB, squares).
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pone-0037629-g005: Cooperative channel gating improves the response of a conductance-based model to high-frequency inputs.Frequency response functions for the Wang-Buzsaki model with independent sodium channels and a standard or 10× fold increased density density of sodium channels (WB, triangles); for cooperative WB model with of cooperative channels, , measured with 3 different correlation time constants of background noise (cWB, squares).

Mentions: What are the coding properties of AP generators with cooperative channel gating? We assessed temporal properties of population coding by using the established approaches of measuring frequency response function [12]–[14], [16], [17]. Encoding of signal of a frequency by a neuronal population is characterized by the modulation of the population firing rate by the frequency . Plots of the firing rate modulation against the input signal frequency (Fig. 5) show that modulation by high frequency signals is improved substantially in the models with cooperative channels gating. At input frequencies , the modulation in these models was almost one order of magnitude larger than in the models with uncoupled channels. For high frequency signals, the modulation gain in models with cooperative channels decays roughly exponentially, deviating from power law behaviors reported for conventional conductance based models [12]–[17]. This difference was robust. It remained unaffected by changing time constants of the background noise () from 20 to 60 ms, or by a 10-fold increase of channel density in non-cooperative model that led to a strong increase of the peak of APs (Fig. 5), but did not improve encoding of high frequencies. These results show that the presence of a small fraction of channels with cooperative gating can dramatically improve the encoding of high frequencies by populations of spiking neurons.


A small fraction of strongly cooperative sodium channels boosts neuronal encoding of high frequencies.

Huang M, Volgushev M, Wolf F - PLoS ONE (2012)

Cooperative channel gating improves the response of a conductance-based model to high-frequency inputs.Frequency response functions for the Wang-Buzsaki model with independent sodium channels and a standard or 10× fold increased density density of sodium channels (WB, triangles); for cooperative WB model with  of cooperative  channels, , measured with 3 different correlation time constants of background noise (cWB, squares).
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3362627&req=5

pone-0037629-g005: Cooperative channel gating improves the response of a conductance-based model to high-frequency inputs.Frequency response functions for the Wang-Buzsaki model with independent sodium channels and a standard or 10× fold increased density density of sodium channels (WB, triangles); for cooperative WB model with of cooperative channels, , measured with 3 different correlation time constants of background noise (cWB, squares).
Mentions: What are the coding properties of AP generators with cooperative channel gating? We assessed temporal properties of population coding by using the established approaches of measuring frequency response function [12]–[14], [16], [17]. Encoding of signal of a frequency by a neuronal population is characterized by the modulation of the population firing rate by the frequency . Plots of the firing rate modulation against the input signal frequency (Fig. 5) show that modulation by high frequency signals is improved substantially in the models with cooperative channels gating. At input frequencies , the modulation in these models was almost one order of magnitude larger than in the models with uncoupled channels. For high frequency signals, the modulation gain in models with cooperative channels decays roughly exponentially, deviating from power law behaviors reported for conventional conductance based models [12]–[17]. This difference was robust. It remained unaffected by changing time constants of the background noise () from 20 to 60 ms, or by a 10-fold increase of channel density in non-cooperative model that led to a strong increase of the peak of APs (Fig. 5), but did not improve encoding of high frequencies. These results show that the presence of a small fraction of channels with cooperative gating can dramatically improve the encoding of high frequencies by populations of spiking neurons.

Bottom Line: Models with a small fraction, [Formula: see text], of strongly cooperative channels generate APs with the most rapid onset dynamics.In this regime APs are triggered by simultaneous opening of the cooperative channel fraction and exhibit a pronounced biphasic waveform often observed in cortical neurons.We conclude that presence of a small fraction of strongly coupled sodium channels can explain characteristic features of cortical APs and has a functional impact of enhancing the spike encoding of rapidly varying signals.

View Article: PubMed Central - PubMed

Affiliation: Max-Planck-Institute for Dynamics and Self-Organization, Bernstein Center for Computational Neuroscience, and Faculty of Physics, Georg August University School of Science, Göttingen, Germany.

ABSTRACT
Generation of action potentials (APs) is a crucial step in neuronal information processing. Existing biophysical models for AP generation almost universally assume that individual voltage-gated sodium channels operate statistically independently, and their avalanche-like opening that underlies AP generation is coordinated only through the transmembrane potential. However, biological ion channels of various types can exhibit strongly cooperative gating when clustered. Cooperative gating of sodium channels has been suggested to explain rapid onset dynamics and large threshold variability of APs in cortical neurons. It remains however unknown whether these characteristic properties of cortical APs can be reproduced if only a fraction of channels express cooperativity, and whether the presence of cooperative channels has an impact on encoding properties of neuronal populations. To address these questions we have constructed a conductance-based neuron model in which we continuously varied the size of a fraction [Formula: see text] of sodium channels expressing cooperativity and the strength of coupling between cooperative channels [Formula: see text]. We show that starting at a critical value of the coupling strength [Formula: see text], the activation curve of sodium channels develops a discontinuity at which opening of all coupled channels becomes an all-or-none event, leading to very rapid AP onsets. Models with a small fraction, [Formula: see text], of strongly cooperative channels generate APs with the most rapid onset dynamics. In this regime APs are triggered by simultaneous opening of the cooperative channel fraction and exhibit a pronounced biphasic waveform often observed in cortical neurons. We further show that presence of a small fraction of cooperative Na+ channels significantly improves the ability of neuronal populations to phase-lock their firing to high frequency input fluctuation. We conclude that presence of a small fraction of strongly coupled sodium channels can explain characteristic features of cortical APs and has a functional impact of enhancing the spike encoding of rapidly varying signals.

Show MeSH
Related in: MedlinePlus