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Stochastically gating ion channels enable patterned spike firing through activity-dependent modulation of spike probability.

Dudman JT, Nolan MF - PLoS Comput. Biol. (2009)

Bottom Line: Unlike deterministic mechanisms that generate spike patterns through slow changes in the state of model parameters, this general stochastic mechanism does not require retention of information beyond the duration of a single spike and its associated afterhyperpolarization.Instead, clustered patterns of spikes emerge in the stochastic model of stellate neurons as a result of a transient increase in firing probability driven by activation of HCN channels during recovery from the spike afterhyperpolarization.Using this model, we infer conditions in which stochastic ion channel gating may influence firing patterns in vivo and predict consequences of modifications of HCN channel function for in vivo firing patterns.

View Article: PubMed Central - PubMed

Affiliation: Janelia Farm Research Campus, Howard Hughes Medical Institute, Ashburn, Virginia, United States of America. dudmanj@janelia.hhmi.org

ABSTRACT
The transformation of synaptic input into patterns of spike output is a fundamental operation that is determined by the particular complement of ion channels that a neuron expresses. Although it is well established that individual ion channel proteins make stochastic transitions between conducting and non-conducting states, most models of synaptic integration are deterministic, and relatively little is known about the functional consequences of interactions between stochastically gating ion channels. Here, we show that a model of stellate neurons from layer II of the medial entorhinal cortex implemented with either stochastic or deterministically gating ion channels can reproduce the resting membrane properties of stellate neurons, but only the stochastic version of the model can fully account for perithreshold membrane potential fluctuations and clustered patterns of spike output that are recorded from stellate neurons during depolarized states. We demonstrate that the stochastic model implements an example of a general mechanism for patterning of neuronal output through activity-dependent changes in the probability of spike firing. Unlike deterministic mechanisms that generate spike patterns through slow changes in the state of model parameters, this general stochastic mechanism does not require retention of information beyond the duration of a single spike and its associated afterhyperpolarization. Instead, clustered patterns of spikes emerge in the stochastic model of stellate neurons as a result of a transient increase in firing probability driven by activation of HCN channels during recovery from the spike afterhyperpolarization. Using this model, we infer conditions in which stochastic ion channel gating may influence firing patterns in vivo and predict consequences of modifications of HCN channel function for in vivo firing patterns.

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Clustered spiking in the stochastic model.(A) Examples of interspike interval histograms calculated from long                            duration simulations (150 s) of the response of the wild-type (WT; left)                            and knock-out (KO; right) models to DC current injection. In both                            examples the mean firing rate is in the 1–2 Hz range. ISI                            distributions were fit with multiple Gaussians (solid blue lines).                            Insets show individual peak fits for the 0–0.6 s interval of                            the histogram. (B–C) Examples of 10 s duration epochs of                            membrane potential activity from simulations with the wild-type (B) and                            knockout (C) models. Average firing rate for the trial is stated in                            blue. (D) Pc is plotted as a function of average firing rate                            for the wild-type (closed symbols) and knockout (open symbols) models                            using the ‘stringent’ clustering definition (left                            panel) and the ‘relaxed’ clustering definition                            (right panel). Several hundred, 16 s duration simulations of the                            partially stochastic model (Figure S6) were used to provide                            detailed sampling. (E) Number of spikes per cluster is plotted for a                            subset of the data.
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pcbi-1000290-g004: Clustered spiking in the stochastic model.(A) Examples of interspike interval histograms calculated from long duration simulations (150 s) of the response of the wild-type (WT; left) and knock-out (KO; right) models to DC current injection. In both examples the mean firing rate is in the 1–2 Hz range. ISI distributions were fit with multiple Gaussians (solid blue lines). Insets show individual peak fits for the 0–0.6 s interval of the histogram. (B–C) Examples of 10 s duration epochs of membrane potential activity from simulations with the wild-type (B) and knockout (C) models. Average firing rate for the trial is stated in blue. (D) Pc is plotted as a function of average firing rate for the wild-type (closed symbols) and knockout (open symbols) models using the ‘stringent’ clustering definition (left panel) and the ‘relaxed’ clustering definition (right panel). Several hundred, 16 s duration simulations of the partially stochastic model (Figure S6) were used to provide detailed sampling. (E) Number of spikes per cluster is plotted for a subset of the data.

Mentions: When stellate cells experience maintained depolarizing currents that drive action potential firing at mean frequencies less than 5 Hz, the pattern of firing is characterized by clusters of action potentials at a relatively high frequency (8–14 Hz) interspersed with silent periods [14],[18],[24]. We determined the conditions for initiation of spikes with mean frequencies less than 5 Hz, at which clustered spike patterns might be expected. In the deterministic model the transition from silence to continuous action potential firing occurs when the amplitude of the injected current is increased above 258.4 pA and 320.5 pA for wild-type and knockout configurations, respectively. For the deterministic models this transition corresponds to a sharp transition from silence to repetitive spiking at ∼6 Hz (wild type) and ∼3 Hz (HCN1 knockout) and clustered spike patterns were not observed (Figure S5). By contrast, the current threshold for the transition between silent and spiking states was ∼246 pA and ∼308 pA for the stochastic versions of the wild-type and HCN1 knockout models, respectively. In both stochastic models, arbitrarily low firing frequencies could be obtained when the injected current was just above this threshold. When the mean frequency of action potentials was less than approximately 5 Hz, then both stochastic models generated clustered patterns of spikes (Figure 4). Thus, stochastic ion channel gating enables clustered patterns of spikes to emerge during firing at low frequencies in response to input currents that are of insufficient amplitude to initiate action potentials in the corresponding deterministic model.


Stochastically gating ion channels enable patterned spike firing through activity-dependent modulation of spike probability.

Dudman JT, Nolan MF - PLoS Comput. Biol. (2009)

Clustered spiking in the stochastic model.(A) Examples of interspike interval histograms calculated from long                            duration simulations (150 s) of the response of the wild-type (WT; left)                            and knock-out (KO; right) models to DC current injection. In both                            examples the mean firing rate is in the 1–2 Hz range. ISI                            distributions were fit with multiple Gaussians (solid blue lines).                            Insets show individual peak fits for the 0–0.6 s interval of                            the histogram. (B–C) Examples of 10 s duration epochs of                            membrane potential activity from simulations with the wild-type (B) and                            knockout (C) models. Average firing rate for the trial is stated in                            blue. (D) Pc is plotted as a function of average firing rate                            for the wild-type (closed symbols) and knockout (open symbols) models                            using the ‘stringent’ clustering definition (left                            panel) and the ‘relaxed’ clustering definition                            (right panel). Several hundred, 16 s duration simulations of the                            partially stochastic model (Figure S6) were used to provide                            detailed sampling. (E) Number of spikes per cluster is plotted for a                            subset of the data.
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pcbi-1000290-g004: Clustered spiking in the stochastic model.(A) Examples of interspike interval histograms calculated from long duration simulations (150 s) of the response of the wild-type (WT; left) and knock-out (KO; right) models to DC current injection. In both examples the mean firing rate is in the 1–2 Hz range. ISI distributions were fit with multiple Gaussians (solid blue lines). Insets show individual peak fits for the 0–0.6 s interval of the histogram. (B–C) Examples of 10 s duration epochs of membrane potential activity from simulations with the wild-type (B) and knockout (C) models. Average firing rate for the trial is stated in blue. (D) Pc is plotted as a function of average firing rate for the wild-type (closed symbols) and knockout (open symbols) models using the ‘stringent’ clustering definition (left panel) and the ‘relaxed’ clustering definition (right panel). Several hundred, 16 s duration simulations of the partially stochastic model (Figure S6) were used to provide detailed sampling. (E) Number of spikes per cluster is plotted for a subset of the data.
Mentions: When stellate cells experience maintained depolarizing currents that drive action potential firing at mean frequencies less than 5 Hz, the pattern of firing is characterized by clusters of action potentials at a relatively high frequency (8–14 Hz) interspersed with silent periods [14],[18],[24]. We determined the conditions for initiation of spikes with mean frequencies less than 5 Hz, at which clustered spike patterns might be expected. In the deterministic model the transition from silence to continuous action potential firing occurs when the amplitude of the injected current is increased above 258.4 pA and 320.5 pA for wild-type and knockout configurations, respectively. For the deterministic models this transition corresponds to a sharp transition from silence to repetitive spiking at ∼6 Hz (wild type) and ∼3 Hz (HCN1 knockout) and clustered spike patterns were not observed (Figure S5). By contrast, the current threshold for the transition between silent and spiking states was ∼246 pA and ∼308 pA for the stochastic versions of the wild-type and HCN1 knockout models, respectively. In both stochastic models, arbitrarily low firing frequencies could be obtained when the injected current was just above this threshold. When the mean frequency of action potentials was less than approximately 5 Hz, then both stochastic models generated clustered patterns of spikes (Figure 4). Thus, stochastic ion channel gating enables clustered patterns of spikes to emerge during firing at low frequencies in response to input currents that are of insufficient amplitude to initiate action potentials in the corresponding deterministic model.

Bottom Line: Unlike deterministic mechanisms that generate spike patterns through slow changes in the state of model parameters, this general stochastic mechanism does not require retention of information beyond the duration of a single spike and its associated afterhyperpolarization.Instead, clustered patterns of spikes emerge in the stochastic model of stellate neurons as a result of a transient increase in firing probability driven by activation of HCN channels during recovery from the spike afterhyperpolarization.Using this model, we infer conditions in which stochastic ion channel gating may influence firing patterns in vivo and predict consequences of modifications of HCN channel function for in vivo firing patterns.

View Article: PubMed Central - PubMed

Affiliation: Janelia Farm Research Campus, Howard Hughes Medical Institute, Ashburn, Virginia, United States of America. dudmanj@janelia.hhmi.org

ABSTRACT
The transformation of synaptic input into patterns of spike output is a fundamental operation that is determined by the particular complement of ion channels that a neuron expresses. Although it is well established that individual ion channel proteins make stochastic transitions between conducting and non-conducting states, most models of synaptic integration are deterministic, and relatively little is known about the functional consequences of interactions between stochastically gating ion channels. Here, we show that a model of stellate neurons from layer II of the medial entorhinal cortex implemented with either stochastic or deterministically gating ion channels can reproduce the resting membrane properties of stellate neurons, but only the stochastic version of the model can fully account for perithreshold membrane potential fluctuations and clustered patterns of spike output that are recorded from stellate neurons during depolarized states. We demonstrate that the stochastic model implements an example of a general mechanism for patterning of neuronal output through activity-dependent changes in the probability of spike firing. Unlike deterministic mechanisms that generate spike patterns through slow changes in the state of model parameters, this general stochastic mechanism does not require retention of information beyond the duration of a single spike and its associated afterhyperpolarization. Instead, clustered patterns of spikes emerge in the stochastic model of stellate neurons as a result of a transient increase in firing probability driven by activation of HCN channels during recovery from the spike afterhyperpolarization. Using this model, we infer conditions in which stochastic ion channel gating may influence firing patterns in vivo and predict consequences of modifications of HCN channel function for in vivo firing patterns.

Show MeSH
Related in: MedlinePlus