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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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Effects of stochastic channel gating alter the response to stellatecells to naturalistic stimuli.(A,B) Plot of mean spike frequency (A) and coefficient of variation ofthe ISI distribution (B) as a function of the mean and standarddeviation of band limited white noise inputs obtained from 5 s durationsimulations (N = 384). (C) CV plottedas a function of mean firing frequency for the same data shown in A andB. The frequency and CV of several recordings (see [49]) fromneurons in the superifical layers of the medial entorhinal cortexin vivo are plotted for comparison (red dots).These values from in vivo data were used to define aregion of stimulus space selected for further analysis (red box). (D) Amasked plot of stimulus space shows the simulations that resulted invalues within the red box defined in C. Longer simulations (150 s) wererun for the points indicated in red using both the deterministic andstochastic models. (E) The mean ISI probability density for experimentalrecordings plotted in C. Gray shaded region indictates the range of ISIsfor spike clusters (see text). (F, G) ISI histograms obtainedfrom simulations with the deterministic (“D”) andstochastic (“S”) versions of the model using inputstatistics at the extrema of the plot in D (indicated by“F” and “G”). (H) The differencein spike counts between the D and S simulations for the data plotted inF (blue) and G (red). The stochastic model shows a selectiveredistribution in the probability of spiking that produces an increasein the clustering interval (shaded region) and a decrease at longer ISIintervals. (I) ISI histograms obtained from simulations withdeterministic (blue) and stochastic (black) versions of the model usinginput statistics that fluctuate randomly between the two statesindicated by the double-headed arrow in D. (J) The difference in spikecounts between the D and S simulations for the data plotted in I. (K)ISI histogram for response of the knockout model to the unscaled(“us”; blue) and the scaled(“s”; red) poisson stimuli (see text). Gray shaded region is the data from I replotted. (L) Thedifference in count between the “us” and“s” simulations for the data plotted in K. Allhistograms use exponentially spaced bins.
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pcbi-1000290-g009: Effects of stochastic channel gating alter the response to stellatecells to naturalistic stimuli.(A,B) Plot of mean spike frequency (A) and coefficient of variation ofthe ISI distribution (B) as a function of the mean and standarddeviation of band limited white noise inputs obtained from 5 s durationsimulations (N = 384). (C) CV plottedas a function of mean firing frequency for the same data shown in A andB. The frequency and CV of several recordings (see [49]) fromneurons in the superifical layers of the medial entorhinal cortexin vivo are plotted for comparison (red dots).These values from in vivo data were used to define aregion of stimulus space selected for further analysis (red box). (D) Amasked plot of stimulus space shows the simulations that resulted invalues within the red box defined in C. Longer simulations (150 s) wererun for the points indicated in red using both the deterministic andstochastic models. (E) The mean ISI probability density for experimentalrecordings plotted in C. Gray shaded region indictates the range of ISIsfor spike clusters (see text). (F, G) ISI histograms obtainedfrom simulations with the deterministic (“D”) andstochastic (“S”) versions of the model using inputstatistics at the extrema of the plot in D (indicated by“F” and “G”). (H) The differencein spike counts between the D and S simulations for the data plotted inF (blue) and G (red). The stochastic model shows a selectiveredistribution in the probability of spiking that produces an increasein the clustering interval (shaded region) and a decrease at longer ISIintervals. (I) ISI histograms obtained from simulations withdeterministic (blue) and stochastic (black) versions of the model usinginput statistics that fluctuate randomly between the two statesindicated by the double-headed arrow in D. (J) The difference in spikecounts between the D and S simulations for the data plotted in I. (K)ISI histogram for response of the knockout model to the unscaled(“us”; blue) and the scaled(“s”; red) poisson stimuli (see text). Gray shaded region is the data from I replotted. (L) Thedifference in count between the “us” and“s” simulations for the data plotted in K. Allhistograms use exponentially spaced bins.

Mentions: Could the stochastic model that we outline here also explain aspects of thefiring patterns of neurons in behaving animals? Consistent with thispossibility, spike times obtained from in vivo single unitrecordings [49] show elevations (made clear by exponentialbin spacing [50]) in their ISI distribution at around 100 ms(Figure 9E). This ISIresembles the peak of P(st/st0) in simulations of ourstochastic model, but unlike the responses of our model to constant currentinput, the in vivo spike trains contain a much broader overalldistribution of ISIs. To provide a more realistic comparison between the modeland in vivo data, we therefore carried out stimulations of theresponse of the model neuron to simulated synaptic drive.


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

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

Effects of stochastic channel gating alter the response to stellatecells to naturalistic stimuli.(A,B) Plot of mean spike frequency (A) and coefficient of variation ofthe ISI distribution (B) as a function of the mean and standarddeviation of band limited white noise inputs obtained from 5 s durationsimulations (N = 384). (C) CV plottedas a function of mean firing frequency for the same data shown in A andB. The frequency and CV of several recordings (see [49]) fromneurons in the superifical layers of the medial entorhinal cortexin vivo are plotted for comparison (red dots).These values from in vivo data were used to define aregion of stimulus space selected for further analysis (red box). (D) Amasked plot of stimulus space shows the simulations that resulted invalues within the red box defined in C. Longer simulations (150 s) wererun for the points indicated in red using both the deterministic andstochastic models. (E) The mean ISI probability density for experimentalrecordings plotted in C. Gray shaded region indictates the range of ISIsfor spike clusters (see text). (F, G) ISI histograms obtainedfrom simulations with the deterministic (“D”) andstochastic (“S”) versions of the model using inputstatistics at the extrema of the plot in D (indicated by“F” and “G”). (H) The differencein spike counts between the D and S simulations for the data plotted inF (blue) and G (red). The stochastic model shows a selectiveredistribution in the probability of spiking that produces an increasein the clustering interval (shaded region) and a decrease at longer ISIintervals. (I) ISI histograms obtained from simulations withdeterministic (blue) and stochastic (black) versions of the model usinginput statistics that fluctuate randomly between the two statesindicated by the double-headed arrow in D. (J) The difference in spikecounts between the D and S simulations for the data plotted in I. (K)ISI histogram for response of the knockout model to the unscaled(“us”; blue) and the scaled(“s”; red) poisson stimuli (see text). Gray shaded region is the data from I replotted. (L) Thedifference in count between the “us” and“s” simulations for the data plotted in K. Allhistograms use exponentially spaced bins.
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pcbi-1000290-g009: Effects of stochastic channel gating alter the response to stellatecells to naturalistic stimuli.(A,B) Plot of mean spike frequency (A) and coefficient of variation ofthe ISI distribution (B) as a function of the mean and standarddeviation of band limited white noise inputs obtained from 5 s durationsimulations (N = 384). (C) CV plottedas a function of mean firing frequency for the same data shown in A andB. The frequency and CV of several recordings (see [49]) fromneurons in the superifical layers of the medial entorhinal cortexin vivo are plotted for comparison (red dots).These values from in vivo data were used to define aregion of stimulus space selected for further analysis (red box). (D) Amasked plot of stimulus space shows the simulations that resulted invalues within the red box defined in C. Longer simulations (150 s) wererun for the points indicated in red using both the deterministic andstochastic models. (E) The mean ISI probability density for experimentalrecordings plotted in C. Gray shaded region indictates the range of ISIsfor spike clusters (see text). (F, G) ISI histograms obtainedfrom simulations with the deterministic (“D”) andstochastic (“S”) versions of the model using inputstatistics at the extrema of the plot in D (indicated by“F” and “G”). (H) The differencein spike counts between the D and S simulations for the data plotted inF (blue) and G (red). The stochastic model shows a selectiveredistribution in the probability of spiking that produces an increasein the clustering interval (shaded region) and a decrease at longer ISIintervals. (I) ISI histograms obtained from simulations withdeterministic (blue) and stochastic (black) versions of the model usinginput statistics that fluctuate randomly between the two statesindicated by the double-headed arrow in D. (J) The difference in spikecounts between the D and S simulations for the data plotted in I. (K)ISI histogram for response of the knockout model to the unscaled(“us”; blue) and the scaled(“s”; red) poisson stimuli (see text). Gray shaded region is the data from I replotted. (L) Thedifference in count between the “us” and“s” simulations for the data plotted in K. Allhistograms use exponentially spaced bins.
Mentions: Could the stochastic model that we outline here also explain aspects of thefiring patterns of neurons in behaving animals? Consistent with thispossibility, spike times obtained from in vivo single unitrecordings [49] show elevations (made clear by exponentialbin spacing [50]) in their ISI distribution at around 100 ms(Figure 9E). This ISIresembles the peak of P(st/st0) in simulations of ourstochastic model, but unlike the responses of our model to constant currentinput, the in vivo spike trains contain a much broader overalldistribution of ISIs. To provide a more realistic comparison between the modeland in vivo data, we therefore carried out stimulations of theresponse of the model neuron to simulated synaptic drive.

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