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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 HCN1knockout (B) model to injections of a suprathreshold ramp current(bottom). The region indicated by the box is shown to the right on anexpanded scale. Dashed blue line is at −50 mV. Scale bars: 5mV, 0.1 s. (C) Overlaid membrane potential response to ramp currentinjection for several trials (n = 20)for the wild-type (black) and knockout (red) models. (D) For each trialthe membrane potential was aligned to the time of the first spike. Themean response for the wild-type (black) and HCN1 knock-out models (red)is plotted for both the deterministic (dashed lines) and stochasticmodels (solid lines). Shaded areas indicate the standard error of themean. (E) The mean (left) and standard deviation (right) of thespike-triggered membrane potential from −0.5 to −0.1s 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 HCN1knockout (B) model to injections of a suprathreshold ramp current(bottom). The region indicated by the box is shown to the right on anexpanded scale. Dashed blue line is at −50 mV. Scale bars: 5mV, 0.1 s. (C) Overlaid membrane potential response to ramp currentinjection for several trials (n = 20)for the wild-type (black) and knockout (red) models. (D) For each trialthe membrane potential was aligned to the time of the first spike. Themean response for the wild-type (black) and HCN1 knock-out models (red)is plotted for both the deterministic (dashed lines) and stochasticmodels (solid lines). Shaded areas indicate the standard error of themean. (E) The mean (left) and standard deviation (right) of thespike-triggered membrane potential from −0.5 to −0.1s prior to the action potential.

Mentions: The most depolarized average membrane potential that can be maintained withoutinitiation of an action potential appears to determine the maximal observableamplitude of membrane potential fluctuations and is altered both in the HCN1knockout model (Figure 2)and in experimental recordings of stellate cells from HCN1 knockout mice [18]. Tofurther assess the stability of the membrane potential prior to action potentialinitiation we injected slow, ramp-like currents that crossed spike threshold forboth the wild-type (Figure3A) and knockout (Figure3B) versions of the model. We averaged the membrane potential fromseveral sweeps in a time window 0.1–0.5 s before the initial actionpotential for each trial (Figure3E). The spike-triggered averages (Figure 3D) revealed that removal of theHCN1-like current from the model causes spikes to initiate from a morehyperpolarized 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 thewild-type and knockout models is independent of stochastic channel gating (Figure 3D), but is to beexpected from the increased rate of depolarization resulting from the reducedmembrane conductance following removal of HCN1 channels. However, for both ofthe deterministic models the membrane potential follows a more depolarizedtrajectory than in the corresponding stochastic models (Figure 3D). This is consistent withspontaneous membrane potential fluctuations in the stochastic models triggeringaction potentials relatively early during the ramp current. Consistent with thedifference in responses to DC current injection (Figure 2), during the time-window precedingthe spike, the more depolarized potentials in the wild-type model are associatedwith an increased standard deviation of the membrane potential due to stochasticchannel gating (wild-type: 0.90+/−0.06 mV; knockout:0.69+/−0.04 mV; P = 0.005;Figure 3E). The shift inmembrane potential stability was accompanied by a small increase in the standarddeviation of the time of the first action potential in the stochastic HCN1knockout model (wild-type: 0.119±0.008 s; knockout:0.152±0.015 s; Figure3C; P<0.05, N = 60 simulations),suggesting that HCN1 channels may increase the reliability of spike timing aswell 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 HCN1knockout (B) model to injections of a suprathreshold ramp current(bottom). The region indicated by the box is shown to the right on anexpanded scale. Dashed blue line is at −50 mV. Scale bars: 5mV, 0.1 s. (C) Overlaid membrane potential response to ramp currentinjection for several trials (n = 20)for the wild-type (black) and knockout (red) models. (D) For each trialthe membrane potential was aligned to the time of the first spike. Themean response for the wild-type (black) and HCN1 knock-out models (red)is plotted for both the deterministic (dashed lines) and stochasticmodels (solid lines). Shaded areas indicate the standard error of themean. (E) The mean (left) and standard deviation (right) of thespike-triggered membrane potential from −0.5 to −0.1s prior to the action potential.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2631146&req=5

pcbi-1000290-g003: Ih enhances perithreshold stability.Example membrane potential responses (top) of the wild-type (A) and HCN1knockout (B) model to injections of a suprathreshold ramp current(bottom). The region indicated by the box is shown to the right on anexpanded scale. Dashed blue line is at −50 mV. Scale bars: 5mV, 0.1 s. (C) Overlaid membrane potential response to ramp currentinjection for several trials (n = 20)for the wild-type (black) and knockout (red) models. (D) For each trialthe membrane potential was aligned to the time of the first spike. Themean response for the wild-type (black) and HCN1 knock-out models (red)is plotted for both the deterministic (dashed lines) and stochasticmodels (solid lines). Shaded areas indicate the standard error of themean. (E) The mean (left) and standard deviation (right) of thespike-triggered membrane potential from −0.5 to −0.1s prior to the action potential.
Mentions: The most depolarized average membrane potential that can be maintained withoutinitiation of an action potential appears to determine the maximal observableamplitude of membrane potential fluctuations and is altered both in the HCN1knockout model (Figure 2)and in experimental recordings of stellate cells from HCN1 knockout mice [18]. Tofurther assess the stability of the membrane potential prior to action potentialinitiation we injected slow, ramp-like currents that crossed spike threshold forboth the wild-type (Figure3A) and knockout (Figure3B) versions of the model. We averaged the membrane potential fromseveral sweeps in a time window 0.1–0.5 s before the initial actionpotential for each trial (Figure3E). The spike-triggered averages (Figure 3D) revealed that removal of theHCN1-like current from the model causes spikes to initiate from a morehyperpolarized 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 thewild-type and knockout models is independent of stochastic channel gating (Figure 3D), but is to beexpected from the increased rate of depolarization resulting from the reducedmembrane conductance following removal of HCN1 channels. However, for both ofthe deterministic models the membrane potential follows a more depolarizedtrajectory than in the corresponding stochastic models (Figure 3D). This is consistent withspontaneous membrane potential fluctuations in the stochastic models triggeringaction potentials relatively early during the ramp current. Consistent with thedifference in responses to DC current injection (Figure 2), during the time-window precedingthe spike, the more depolarized potentials in the wild-type model are associatedwith an increased standard deviation of the membrane potential due to stochasticchannel gating (wild-type: 0.90+/−0.06 mV; knockout:0.69+/−0.04 mV; P = 0.005;Figure 3E). The shift inmembrane potential stability was accompanied by a small increase in the standarddeviation of the time of the first action potential in the stochastic HCN1knockout model (wild-type: 0.119±0.008 s; knockout:0.152±0.015 s; Figure3C; P<0.05, N = 60 simulations),suggesting that HCN1 channels may increase the reliability of spike timing aswell 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