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Mechanisms of gain control by voltage-gated channels in intrinsically-firing neurons.

Patel AX, Burdakov D - PLoS ONE (2015)

Bottom Line: Changes in expression (conductance density) of voltage-gated channels increased (Ca2+ channel), reduced (K+ channels), or produced little effect (h-type channel) on gain.We found that the gain-controlling ability of channels increased exponentially with the steepness of their activation within the dynamic voltage window (voltage range associated with firing).This is potentially relevant to understanding input-output scaling in a wide class of neurons found throughout the brain and other nervous systems.

View Article: PubMed Central - PubMed

Affiliation: Brain Mapping Unit, University of Cambridge, Cambridge, UK.

ABSTRACT
Gain modulation is a key feature of neural information processing, but underlying mechanisms remain unclear. In single neurons, gain can be measured as the slope of the current-frequency (input-output) relationship over any given range of inputs. While much work has focused on the control of basal firing rates and spike rate adaptation, gain control has been relatively unstudied. Of the limited studies on gain control, some have examined the roles of synaptic noise and passive somatic currents, but the roles of voltage-gated channels present ubiquitously in neurons have been less explored. Here, we systematically examined the relationship between gain and voltage-gated ion channels in a conductance-based, tonically-active, model neuron. Changes in expression (conductance density) of voltage-gated channels increased (Ca2+ channel), reduced (K+ channels), or produced little effect (h-type channel) on gain. We found that the gain-controlling ability of channels increased exponentially with the steepness of their activation within the dynamic voltage window (voltage range associated with firing). For depolarization-activated channels, this produced a greater channel current per action potential at higher firing rates. This allowed these channels to modulate gain by contributing to firing preferentially at states of higher excitation. A finer analysis of the current-voltage relationship during tonic firing identified narrow voltage windows at which the gain-modulating channels exerted their effects. As a proof of concept, we show that h-type channels can be tuned to modulate gain by changing the steepness of their activation within the dynamic voltage window. These results show how the impact of an ion channel on gain can be predicted from the relationship between channel kinetics and the membrane potential during firing. This is potentially relevant to understanding input-output scaling in a wide class of neurons found throughout the brain and other nervous systems.

No MeSH data available.


Related in: MedlinePlus

Gain modulation and the voltage dependence of channel activation.(A) The firing rate of the model neuron plotted against the average membrane potential, illustrating the ‘dynamic voltage window’ of the neuron (∼ -51 to -50 mV). (B) The voltage dependence of steady-state activation variables (m∞) used in our simulations. The shaded area shows the dynamic voltage window from panel A. The dashed line shows the shifted activation curve of Ih used for simulations in Fig. 10 (half-maximal activation of the shifted curve occurs at -50 mV instead of the baseline value of -75 mV). (C) The correlation between change in m∞ within the dynamic voltage window and the ‘impact on gain’ for each voltage-gated channel (% change in gain per % change in maximal specific conductance from Fig. 3B). Both x and y values are plotted as positive numbers. There is a strong positive correlation (r = 0.92); the fitted line shown is y = 0.134ex/0.004. (D) The effects of different Ca2+-K+ channel coupling strengths (see Methods) on the steady-state activation variable (m∞) of the Ca2+-activated K+ channel. The dynamic voltage window is shaded in grey.
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pone.0115431.g006: Gain modulation and the voltage dependence of channel activation.(A) The firing rate of the model neuron plotted against the average membrane potential, illustrating the ‘dynamic voltage window’ of the neuron (∼ -51 to -50 mV). (B) The voltage dependence of steady-state activation variables (m∞) used in our simulations. The shaded area shows the dynamic voltage window from panel A. The dashed line shows the shifted activation curve of Ih used for simulations in Fig. 10 (half-maximal activation of the shifted curve occurs at -50 mV instead of the baseline value of -75 mV). (C) The correlation between change in m∞ within the dynamic voltage window and the ‘impact on gain’ for each voltage-gated channel (% change in gain per % change in maximal specific conductance from Fig. 3B). Both x and y values are plotted as positive numbers. There is a strong positive correlation (r = 0.92); the fitted line shown is y = 0.134ex/0.004. (D) The effects of different Ca2+-K+ channel coupling strengths (see Methods) on the steady-state activation variable (m∞) of the Ca2+-activated K+ channel. The dynamic voltage window is shaded in grey.

Mentions: Given our observations that voltage-gated channels modulate gain, but non-voltage-gated channels do not, we inferred that the ability of the former to control gain must be a factor of their activation and/or inactivation kinetics. Here, we looked at channel activation. Theoretically, for a channel to effect control over gain, it must exert its effects within the ‘dynamic voltage window’ (the voltage range associated with firing [5], Fig. 6A). Put more simply, as more voltage-gated channels will be active under a greater depolarizing drive (or higher firing rate), channels that activate steeply within the dynamic voltage window will contribute more to the firing rate when the drive is larger. These channels should then preferentially act on the right side of the tuning curve, thus changing gain. Inward currents that activate strongly within this window would be expected to increase gain, and outward currents that activate strongly within this window would be expected to reduce gain. To test this hypothesis, we plotted the steady-state activation variable of each voltage-gated channel as a function of membrane potential (Fig. 6B) and measured the gradient of their activation curves within the dynamic voltage window. We then plotted these gradients (∣Δm∞/ΔV∣, calculated for each channel) against the ability of that channel to impact gain through changes in (Fig. 6C). As predicted, we found that the gain-modulating ability of a channel was proportional (r = 0.92, Pearson correlation) to the steepness of the activation curve of that channel within the dynamic voltage window (Fig. 6C).


Mechanisms of gain control by voltage-gated channels in intrinsically-firing neurons.

Patel AX, Burdakov D - PLoS ONE (2015)

Gain modulation and the voltage dependence of channel activation.(A) The firing rate of the model neuron plotted against the average membrane potential, illustrating the ‘dynamic voltage window’ of the neuron (∼ -51 to -50 mV). (B) The voltage dependence of steady-state activation variables (m∞) used in our simulations. The shaded area shows the dynamic voltage window from panel A. The dashed line shows the shifted activation curve of Ih used for simulations in Fig. 10 (half-maximal activation of the shifted curve occurs at -50 mV instead of the baseline value of -75 mV). (C) The correlation between change in m∞ within the dynamic voltage window and the ‘impact on gain’ for each voltage-gated channel (% change in gain per % change in maximal specific conductance from Fig. 3B). Both x and y values are plotted as positive numbers. There is a strong positive correlation (r = 0.92); the fitted line shown is y = 0.134ex/0.004. (D) The effects of different Ca2+-K+ channel coupling strengths (see Methods) on the steady-state activation variable (m∞) of the Ca2+-activated K+ channel. The dynamic voltage window is shaded in grey.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4376733&req=5

pone.0115431.g006: Gain modulation and the voltage dependence of channel activation.(A) The firing rate of the model neuron plotted against the average membrane potential, illustrating the ‘dynamic voltage window’ of the neuron (∼ -51 to -50 mV). (B) The voltage dependence of steady-state activation variables (m∞) used in our simulations. The shaded area shows the dynamic voltage window from panel A. The dashed line shows the shifted activation curve of Ih used for simulations in Fig. 10 (half-maximal activation of the shifted curve occurs at -50 mV instead of the baseline value of -75 mV). (C) The correlation between change in m∞ within the dynamic voltage window and the ‘impact on gain’ for each voltage-gated channel (% change in gain per % change in maximal specific conductance from Fig. 3B). Both x and y values are plotted as positive numbers. There is a strong positive correlation (r = 0.92); the fitted line shown is y = 0.134ex/0.004. (D) The effects of different Ca2+-K+ channel coupling strengths (see Methods) on the steady-state activation variable (m∞) of the Ca2+-activated K+ channel. The dynamic voltage window is shaded in grey.
Mentions: Given our observations that voltage-gated channels modulate gain, but non-voltage-gated channels do not, we inferred that the ability of the former to control gain must be a factor of their activation and/or inactivation kinetics. Here, we looked at channel activation. Theoretically, for a channel to effect control over gain, it must exert its effects within the ‘dynamic voltage window’ (the voltage range associated with firing [5], Fig. 6A). Put more simply, as more voltage-gated channels will be active under a greater depolarizing drive (or higher firing rate), channels that activate steeply within the dynamic voltage window will contribute more to the firing rate when the drive is larger. These channels should then preferentially act on the right side of the tuning curve, thus changing gain. Inward currents that activate strongly within this window would be expected to increase gain, and outward currents that activate strongly within this window would be expected to reduce gain. To test this hypothesis, we plotted the steady-state activation variable of each voltage-gated channel as a function of membrane potential (Fig. 6B) and measured the gradient of their activation curves within the dynamic voltage window. We then plotted these gradients (∣Δm∞/ΔV∣, calculated for each channel) against the ability of that channel to impact gain through changes in (Fig. 6C). As predicted, we found that the gain-modulating ability of a channel was proportional (r = 0.92, Pearson correlation) to the steepness of the activation curve of that channel within the dynamic voltage window (Fig. 6C).

Bottom Line: Changes in expression (conductance density) of voltage-gated channels increased (Ca2+ channel), reduced (K+ channels), or produced little effect (h-type channel) on gain.We found that the gain-controlling ability of channels increased exponentially with the steepness of their activation within the dynamic voltage window (voltage range associated with firing).This is potentially relevant to understanding input-output scaling in a wide class of neurons found throughout the brain and other nervous systems.

View Article: PubMed Central - PubMed

Affiliation: Brain Mapping Unit, University of Cambridge, Cambridge, UK.

ABSTRACT
Gain modulation is a key feature of neural information processing, but underlying mechanisms remain unclear. In single neurons, gain can be measured as the slope of the current-frequency (input-output) relationship over any given range of inputs. While much work has focused on the control of basal firing rates and spike rate adaptation, gain control has been relatively unstudied. Of the limited studies on gain control, some have examined the roles of synaptic noise and passive somatic currents, but the roles of voltage-gated channels present ubiquitously in neurons have been less explored. Here, we systematically examined the relationship between gain and voltage-gated ion channels in a conductance-based, tonically-active, model neuron. Changes in expression (conductance density) of voltage-gated channels increased (Ca2+ channel), reduced (K+ channels), or produced little effect (h-type channel) on gain. We found that the gain-controlling ability of channels increased exponentially with the steepness of their activation within the dynamic voltage window (voltage range associated with firing). For depolarization-activated channels, this produced a greater channel current per action potential at higher firing rates. This allowed these channels to modulate gain by contributing to firing preferentially at states of higher excitation. A finer analysis of the current-voltage relationship during tonic firing identified narrow voltage windows at which the gain-modulating channels exerted their effects. As a proof of concept, we show that h-type channels can be tuned to modulate gain by changing the steepness of their activation within the dynamic voltage window. These results show how the impact of an ion channel on gain can be predicted from the relationship between channel kinetics and the membrane potential during firing. This is potentially relevant to understanding input-output scaling in a wide class of neurons found throughout the brain and other nervous systems.

No MeSH data available.


Related in: MedlinePlus