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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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Ih enhances perithreshold stability.Example membrane potential responses (top) of the wild-type (A) and HCN1                            knockout (B) model to injections of a suprathreshold ramp current                            (bottom). The region indicated by the box is shown to the right on an                            expanded scale. Dashed blue line is at −50 mV. Scale bars: 5                            mV, 0.1 s. (C) Overlaid membrane potential response to ramp current                            injection for several trials (n = 20)                            for the wild-type (black) and knockout (red) models. (D) For each trial                            the membrane potential was aligned to the time of the first spike. The                            mean response for the wild-type (black) and HCN1 knock-out models (red)                            is plotted for both the deterministic (dashed lines) and stochastic                            models (solid lines). Shaded areas indicate the standard error of the                            mean. (E) The mean (left) and standard deviation (right) of the                            spike-triggered membrane potential from −0.5 to −0.1                            s prior to the action potential.
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pcbi-1000290-g003: Ih enhances perithreshold stability.Example membrane potential responses (top) of the wild-type (A) and HCN1 knockout (B) model to injections of a suprathreshold ramp current (bottom). The region indicated by the box is shown to the right on an expanded scale. Dashed blue line is at −50 mV. Scale bars: 5 mV, 0.1 s. (C) Overlaid membrane potential response to ramp current injection for several trials (n = 20) for the wild-type (black) and knockout (red) models. (D) For each trial the membrane potential was aligned to the time of the first spike. The mean response for the wild-type (black) and HCN1 knock-out models (red) is plotted for both the deterministic (dashed lines) and stochastic models (solid lines). Shaded areas indicate the standard error of the mean. (E) The mean (left) and standard deviation (right) of the spike-triggered membrane potential from −0.5 to −0.1 s prior to the action potential.

Mentions: The most depolarized average membrane potential that can be maintained without initiation of an action potential appears to determine the maximal observable amplitude of membrane potential fluctuations and is altered both in the HCN1 knockout model (Figure 2) and in experimental recordings of stellate cells from HCN1 knockout mice [18]. To further assess the stability of the membrane potential prior to action potential initiation we injected slow, ramp-like currents that crossed spike threshold for both the wild-type (Figure 3A) and knockout (Figure 3B) versions of the model. We averaged the membrane potential from several sweeps in a time window 0.1–0.5 s before the initial action potential for each trial (Figure 3E). The spike-triggered averages (Figure 3D) revealed that removal of the HCN1-like current from the model causes spikes to initiate from a more hyperpolarized membrane potential (wild-type: −51.15+/−0.12 mV; knockout: −52.72+/−0.12 mV; P = 4×10−11; N = 20 total trials; Figure 3E). This difference between the wild-type and knockout models is independent of stochastic channel gating (Figure 3D), but is to be expected from the increased rate of depolarization resulting from the reduced membrane conductance following removal of HCN1 channels. However, for both of the deterministic models the membrane potential follows a more depolarized trajectory than in the corresponding stochastic models (Figure 3D). This is consistent with spontaneous membrane potential fluctuations in the stochastic models triggering action potentials relatively early during the ramp current. Consistent with the difference in responses to DC current injection (Figure 2), during the time-window preceding the spike, the more depolarized potentials in the wild-type model are associated with an increased standard deviation of the membrane potential due to stochastic channel gating (wild-type: 0.90+/−0.06 mV; knockout: 0.69+/−0.04 mV; P = 0.005; Figure 3E). The shift in membrane potential stability was accompanied by a small increase in the standard deviation of the time of the first action potential in the stochastic HCN1 knockout model (wild-type: 0.119±0.008 s; knockout: 0.152±0.015 s; Figure 3C; P<0.05, N = 60 simulations), suggesting that HCN1 channels may increase the reliability of spike timing as well as the stability of the sub-threshold membrane potential.


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

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

Ih enhances perithreshold stability.Example membrane potential responses (top) of the wild-type (A) and HCN1                            knockout (B) model to injections of a suprathreshold ramp current                            (bottom). The region indicated by the box is shown to the right on an                            expanded scale. Dashed blue line is at −50 mV. Scale bars: 5                            mV, 0.1 s. (C) Overlaid membrane potential response to ramp current                            injection for several trials (n = 20)                            for the wild-type (black) and knockout (red) models. (D) For each trial                            the membrane potential was aligned to the time of the first spike. The                            mean response for the wild-type (black) and HCN1 knock-out models (red)                            is plotted for both the deterministic (dashed lines) and stochastic                            models (solid lines). Shaded areas indicate the standard error of the                            mean. (E) The mean (left) and standard deviation (right) of the                            spike-triggered membrane potential from −0.5 to −0.1                            s prior to the action potential.
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC2631146&req=5

pcbi-1000290-g003: Ih enhances perithreshold stability.Example membrane potential responses (top) of the wild-type (A) and HCN1 knockout (B) model to injections of a suprathreshold ramp current (bottom). The region indicated by the box is shown to the right on an expanded scale. Dashed blue line is at −50 mV. Scale bars: 5 mV, 0.1 s. (C) Overlaid membrane potential response to ramp current injection for several trials (n = 20) for the wild-type (black) and knockout (red) models. (D) For each trial the membrane potential was aligned to the time of the first spike. The mean response for the wild-type (black) and HCN1 knock-out models (red) is plotted for both the deterministic (dashed lines) and stochastic models (solid lines). Shaded areas indicate the standard error of the mean. (E) The mean (left) and standard deviation (right) of the spike-triggered membrane potential from −0.5 to −0.1 s prior to the action potential.
Mentions: The most depolarized average membrane potential that can be maintained without initiation of an action potential appears to determine the maximal observable amplitude of membrane potential fluctuations and is altered both in the HCN1 knockout model (Figure 2) and in experimental recordings of stellate cells from HCN1 knockout mice [18]. To further assess the stability of the membrane potential prior to action potential initiation we injected slow, ramp-like currents that crossed spike threshold for both the wild-type (Figure 3A) and knockout (Figure 3B) versions of the model. We averaged the membrane potential from several sweeps in a time window 0.1–0.5 s before the initial action potential for each trial (Figure 3E). The spike-triggered averages (Figure 3D) revealed that removal of the HCN1-like current from the model causes spikes to initiate from a more hyperpolarized membrane potential (wild-type: −51.15+/−0.12 mV; knockout: −52.72+/−0.12 mV; P = 4×10−11; N = 20 total trials; Figure 3E). This difference between the wild-type and knockout models is independent of stochastic channel gating (Figure 3D), but is to be expected from the increased rate of depolarization resulting from the reduced membrane conductance following removal of HCN1 channels. However, for both of the deterministic models the membrane potential follows a more depolarized trajectory than in the corresponding stochastic models (Figure 3D). This is consistent with spontaneous membrane potential fluctuations in the stochastic models triggering action potentials relatively early during the ramp current. Consistent with the difference in responses to DC current injection (Figure 2), during the time-window preceding the spike, the more depolarized potentials in the wild-type model are associated with an increased standard deviation of the membrane potential due to stochastic channel gating (wild-type: 0.90+/−0.06 mV; knockout: 0.69+/−0.04 mV; P = 0.005; Figure 3E). The shift in membrane potential stability was accompanied by a small increase in the standard deviation of the time of the first action potential in the stochastic HCN1 knockout model (wild-type: 0.119±0.008 s; knockout: 0.152±0.015 s; Figure 3C; P<0.05, N = 60 simulations), suggesting that HCN1 channels may increase the reliability of spike timing as well as the stability of the sub-threshold membrane potential.

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