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

Mentions: When stellate cells experience maintained depolarizing currents that drive actionpotential firing at mean frequencies less than 5 Hz, the pattern of firing ischaracterized by clusters of action potentials at a relatively high frequency(8–14 Hz) interspersed with silent periods [14],[18],[24]. We determinedthe conditions for initiation of spikes with mean frequencies less than 5 Hz, atwhich clustered spike patterns might be expected. In the deterministic model thetransition from silence to continuous action potential firing occurs when theamplitude of the injected current is increased above 258.4 pA and 320.5 pA forwild-type and knockout configurations, respectively. For the deterministicmodels this transition corresponds to a sharp transition from silence torepetitive spiking at ∼6 Hz (wild type) and ∼3 Hz (HCN1knockout) and clustered spike patterns were not observed (Figure S5).By contrast, the current threshold for the transition between silent and spikingstates was ∼246 pA and ∼308 pA for the stochastic versions ofthe wild-type and HCN1 knockout models, respectively. In both stochastic models,arbitrarily low firing frequencies could be obtained when the injected currentwas just above this threshold. When the mean frequency of action potentials wasless than approximately 5 Hz, then both stochastic models generated clusteredpatterns of spikes (Figure4). Thus, stochastic ion channel gating enables clustered patterns ofspikes to emerge during firing at low frequencies in response to input currentsthat are of insufficient amplitude to initiate action potentials in thecorresponding 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 longduration simulations (150 s) of the response of the wild-type (WT; left)and knock-out (KO; right) models to DC current injection. In bothexamples the mean firing rate is in the 1–2 Hz range. ISIdistributions were fit with multiple Gaussians (solid blue lines).Insets show individual peak fits for the 0–0.6 s interval ofthe histogram. (B–C) Examples of 10 s duration epochs ofmembrane potential activity from simulations with the wild-type (B) andknockout (C) models. Average firing rate for the trial is stated inblue. (D) Pc is plotted as a function of average firing ratefor the wild-type (closed symbols) and knockout (open symbols) modelsusing the ‘stringent’ clustering definition (leftpanel) and the ‘relaxed’ clustering definition(right panel). Several hundred, 16 s duration simulations of thepartially stochastic model (Figure S6) were used to providedetailed sampling. (E) Number of spikes per cluster is plotted for asubset of the data.
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Related In: Results  -  Collection

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pcbi-1000290-g004: Clustered spiking in the stochastic model.(A) Examples of interspike interval histograms calculated from longduration simulations (150 s) of the response of the wild-type (WT; left)and knock-out (KO; right) models to DC current injection. In bothexamples the mean firing rate is in the 1–2 Hz range. ISIdistributions were fit with multiple Gaussians (solid blue lines).Insets show individual peak fits for the 0–0.6 s interval ofthe histogram. (B–C) Examples of 10 s duration epochs ofmembrane potential activity from simulations with the wild-type (B) andknockout (C) models. Average firing rate for the trial is stated inblue. (D) Pc is plotted as a function of average firing ratefor the wild-type (closed symbols) and knockout (open symbols) modelsusing the ‘stringent’ clustering definition (leftpanel) and the ‘relaxed’ clustering definition(right panel). Several hundred, 16 s duration simulations of thepartially stochastic model (Figure S6) were used to providedetailed sampling. (E) Number of spikes per cluster is plotted for asubset of the data.
Mentions: When stellate cells experience maintained depolarizing currents that drive actionpotential firing at mean frequencies less than 5 Hz, the pattern of firing ischaracterized by clusters of action potentials at a relatively high frequency(8–14 Hz) interspersed with silent periods [14],[18],[24]. We determinedthe conditions for initiation of spikes with mean frequencies less than 5 Hz, atwhich clustered spike patterns might be expected. In the deterministic model thetransition from silence to continuous action potential firing occurs when theamplitude of the injected current is increased above 258.4 pA and 320.5 pA forwild-type and knockout configurations, respectively. For the deterministicmodels this transition corresponds to a sharp transition from silence torepetitive spiking at ∼6 Hz (wild type) and ∼3 Hz (HCN1knockout) and clustered spike patterns were not observed (Figure S5).By contrast, the current threshold for the transition between silent and spikingstates was ∼246 pA and ∼308 pA for the stochastic versions ofthe wild-type and HCN1 knockout models, respectively. In both stochastic models,arbitrarily low firing frequencies could be obtained when the injected currentwas just above this threshold. When the mean frequency of action potentials wasless than approximately 5 Hz, then both stochastic models generated clusteredpatterns of spikes (Figure4). Thus, stochastic ion channel gating enables clustered patterns ofspikes to emerge during firing at low frequencies in response to input currentsthat are of insufficient amplitude to initiate action potentials in thecorresponding 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.

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Related in: MedlinePlus