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Biophysical basis for three distinct dynamical mechanisms of action potential initiation.

Prescott SA, De Koninck Y, Sejnowski TJ - PLoS Comput. Biol. (2008)

Bottom Line: Hodgkin identified three classes of neurons with qualitatively different analog-to-digital transduction properties.From this, we conclude that the spike-initiating dynamics associated with each of Hodgkin's classes represent different outcomes in a nonlinear competition between oppositely directed, kinetically mismatched currents.Through detailed analysis of the spike-initiating process, we have explained a fundamental link between biophysical properties and qualitative differences in how neurons encode sensory input.

View Article: PubMed Central - PubMed

Affiliation: Computational Neurobiology Laboratory, Salk Institute, La Jolla, California, United States of America. prescott@neurobio.pitt.edu

ABSTRACT
Transduction of graded synaptic input into trains of all-or-none action potentials (spikes) is a crucial step in neural coding. Hodgkin identified three classes of neurons with qualitatively different analog-to-digital transduction properties. Despite widespread use of this classification scheme, a generalizable explanation of its biophysical basis has not been described. We recorded from spinal sensory neurons representing each class and reproduced their transduction properties in a minimal model. With phase plane and bifurcation analysis, each class of excitability was shown to derive from distinct spike initiating dynamics. Excitability could be converted between all three classes by varying single parameters; moreover, several parameters, when varied one at a time, had functionally equivalent effects on excitability. From this, we conclude that the spike-initiating dynamics associated with each of Hodgkin's classes represent different outcomes in a nonlinear competition between oppositely directed, kinetically mismatched currents. Class 1 excitability occurs through a saddle node on invariant circle bifurcation when net current at perithreshold potentials is inward (depolarizing) at steady state. Class 2 excitability occurs through a Hopf bifurcation when, despite net current being outward (hyperpolarizing) at steady state, spike initiation occurs because inward current activates faster than outward current. Class 3 excitability occurs through a quasi-separatrix crossing when fast-activating inward current overpowers slow-activating outward current during a stimulus transient, although slow-activating outward current dominates during constant stimulation. Experiments confirmed that different classes of spinal lamina I neurons express the subthreshold currents predicted by our simulations and, further, that those currents are necessary for the excitability in each cell class. Thus, our results demonstrate that all three classes of excitability arise from a continuum in the direction and magnitude of subthreshold currents. Through detailed analysis of the spike-initiating process, we have explained a fundamental link between biophysical properties and qualitative differences in how neurons encode sensory input.

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Different classes of spinal lamina I neurons express different                            subthreshold currents.(A) Traces show responses to 60 pA, 20-ms-long depolarizing pulses                            (black) and to equivalent hyperpolarizing pulses (gray); the latter are                            inverted to facilitate comparison with former. In class 1                            (tonic-spiking) neurons, depolarization was amplified and prolonged                            relative to hyperpolarization, consistent with effects of an inward                            current activated by perithreshold depolarization. Class 3                            (single-spiking) neurons exhibited the opposite pattern, consistent with                            effects of a subthreshold outward current, which is also evident from                            outward rectification (arrow) in the I–V                            curve. Depolarizing and hyperpolarizing responses were symmetrical in                            class 2 (phasic-spiking) neurons, consistent with negligible net                            subthreshold current. (B) Membrane current activated by voltage-clamp                            steps from −70 mV to −60, −50,                            −40, and −30 mV. For a given command potential,                            class 3 neurons exhibited the largest persistent outward current and                            class 1 neurons exhibited the smallest outward current. Red line                            highlights difference in current activated by step to −40 mV.                            (C) Steady-state I–V curves for voltage clamp                            protocols in (B). Because recordings were performed in TTX to prevent                            unclamped spiking, the persistent Na+ current                                (INa,p), which is expressed exclusively                            in tonic-spiking neurons, was blocked; to correct for this,                                INa,p measured in separate voltage clamp                            ramp protocols [26] was added to give a corrected                                I–V curve (dotted line). Compare with                                Figure 4. (D)                            4-AP-sensitive current determined by subtraction of response before and                            during application of 5 mM 4-AP to a single-spiking neuron. Protocol                            included prepulse to −100 mV, which revealed a small                            persistent outward current active at −70 mV that was                            deactivated by hyperpolarization to −100 mV (*).                            Although depolarization also activates a large transient outward                            current, we are concerned with the persistent component (arrowhead);                            effects of the transient outward current are beyond the scope of this                            study and were minimized by adjusting pre-stimulus membrane potential to                            −60 mV for all current clamp protocols. Gray line shows                            baseline current.
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pcbi-1000198-g005: Different classes of spinal lamina I neurons express different subthreshold currents.(A) Traces show responses to 60 pA, 20-ms-long depolarizing pulses (black) and to equivalent hyperpolarizing pulses (gray); the latter are inverted to facilitate comparison with former. In class 1 (tonic-spiking) neurons, depolarization was amplified and prolonged relative to hyperpolarization, consistent with effects of an inward current activated by perithreshold depolarization. Class 3 (single-spiking) neurons exhibited the opposite pattern, consistent with effects of a subthreshold outward current, which is also evident from outward rectification (arrow) in the I–V curve. Depolarizing and hyperpolarizing responses were symmetrical in class 2 (phasic-spiking) neurons, consistent with negligible net subthreshold current. (B) Membrane current activated by voltage-clamp steps from −70 mV to −60, −50, −40, and −30 mV. For a given command potential, class 3 neurons exhibited the largest persistent outward current and class 1 neurons exhibited the smallest outward current. Red line highlights difference in current activated by step to −40 mV. (C) Steady-state I–V curves for voltage clamp protocols in (B). Because recordings were performed in TTX to prevent unclamped spiking, the persistent Na+ current (INa,p), which is expressed exclusively in tonic-spiking neurons, was blocked; to correct for this, INa,p measured in separate voltage clamp ramp protocols [26] was added to give a corrected I–V curve (dotted line). Compare with Figure 4. (D) 4-AP-sensitive current determined by subtraction of response before and during application of 5 mM 4-AP to a single-spiking neuron. Protocol included prepulse to −100 mV, which revealed a small persistent outward current active at −70 mV that was deactivated by hyperpolarization to −100 mV (*). Although depolarization also activates a large transient outward current, we are concerned with the persistent component (arrowhead); effects of the transient outward current are beyond the scope of this study and were minimized by adjusting pre-stimulus membrane potential to −60 mV for all current clamp protocols. Gray line shows baseline current.

Mentions: Several lines of experimental evidence support this prediction. First, the response to brief, subthreshold depolarizing pulses was amplified and prolonged relative to the equivalent hyperpolarizing response in class 1 neurons, consistent with effects of a subthreshold inward current (Figure 5A, right); the opposite pattern was observed in class 3 neurons, consistent with effects of a subthrehsold outward current (Figure 5A, left). Second, in voltage clamp, stepping command potential from −70 mV to perithreshold potentials elicited the largest outward current in class 3 neurons, followed by class 2 and class 1 neurons (Figure 5B). The relative positioning of I–V curves plotted from those experiments (Figure 5C) bore a striking resemblance to the relative positioning of I–V curves in the 2D and 3D models (Figure 4); this is especially true if the persistent Na+ current that was blocked by TTX in the aforementioned experiments is taken into account; this current is expressed exclusively in tonic-spiking neurons [26]. Application of 4-AP confirmed the presence of a persistent, low-threshold K+ current in single-spiking lamina I neurons (Figure 5D).


Biophysical basis for three distinct dynamical mechanisms of action potential initiation.

Prescott SA, De Koninck Y, Sejnowski TJ - PLoS Comput. Biol. (2008)

Different classes of spinal lamina I neurons express different                            subthreshold currents.(A) Traces show responses to 60 pA, 20-ms-long depolarizing pulses                            (black) and to equivalent hyperpolarizing pulses (gray); the latter are                            inverted to facilitate comparison with former. In class 1                            (tonic-spiking) neurons, depolarization was amplified and prolonged                            relative to hyperpolarization, consistent with effects of an inward                            current activated by perithreshold depolarization. Class 3                            (single-spiking) neurons exhibited the opposite pattern, consistent with                            effects of a subthreshold outward current, which is also evident from                            outward rectification (arrow) in the I–V                            curve. Depolarizing and hyperpolarizing responses were symmetrical in                            class 2 (phasic-spiking) neurons, consistent with negligible net                            subthreshold current. (B) Membrane current activated by voltage-clamp                            steps from −70 mV to −60, −50,                            −40, and −30 mV. For a given command potential,                            class 3 neurons exhibited the largest persistent outward current and                            class 1 neurons exhibited the smallest outward current. Red line                            highlights difference in current activated by step to −40 mV.                            (C) Steady-state I–V curves for voltage clamp                            protocols in (B). Because recordings were performed in TTX to prevent                            unclamped spiking, the persistent Na+ current                                (INa,p), which is expressed exclusively                            in tonic-spiking neurons, was blocked; to correct for this,                                INa,p measured in separate voltage clamp                            ramp protocols [26] was added to give a corrected                                I–V curve (dotted line). Compare with                                Figure 4. (D)                            4-AP-sensitive current determined by subtraction of response before and                            during application of 5 mM 4-AP to a single-spiking neuron. Protocol                            included prepulse to −100 mV, which revealed a small                            persistent outward current active at −70 mV that was                            deactivated by hyperpolarization to −100 mV (*).                            Although depolarization also activates a large transient outward                            current, we are concerned with the persistent component (arrowhead);                            effects of the transient outward current are beyond the scope of this                            study and were minimized by adjusting pre-stimulus membrane potential to                            −60 mV for all current clamp protocols. Gray line shows                            baseline current.
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC2551735&req=5

pcbi-1000198-g005: Different classes of spinal lamina I neurons express different subthreshold currents.(A) Traces show responses to 60 pA, 20-ms-long depolarizing pulses (black) and to equivalent hyperpolarizing pulses (gray); the latter are inverted to facilitate comparison with former. In class 1 (tonic-spiking) neurons, depolarization was amplified and prolonged relative to hyperpolarization, consistent with effects of an inward current activated by perithreshold depolarization. Class 3 (single-spiking) neurons exhibited the opposite pattern, consistent with effects of a subthreshold outward current, which is also evident from outward rectification (arrow) in the I–V curve. Depolarizing and hyperpolarizing responses were symmetrical in class 2 (phasic-spiking) neurons, consistent with negligible net subthreshold current. (B) Membrane current activated by voltage-clamp steps from −70 mV to −60, −50, −40, and −30 mV. For a given command potential, class 3 neurons exhibited the largest persistent outward current and class 1 neurons exhibited the smallest outward current. Red line highlights difference in current activated by step to −40 mV. (C) Steady-state I–V curves for voltage clamp protocols in (B). Because recordings were performed in TTX to prevent unclamped spiking, the persistent Na+ current (INa,p), which is expressed exclusively in tonic-spiking neurons, was blocked; to correct for this, INa,p measured in separate voltage clamp ramp protocols [26] was added to give a corrected I–V curve (dotted line). Compare with Figure 4. (D) 4-AP-sensitive current determined by subtraction of response before and during application of 5 mM 4-AP to a single-spiking neuron. Protocol included prepulse to −100 mV, which revealed a small persistent outward current active at −70 mV that was deactivated by hyperpolarization to −100 mV (*). Although depolarization also activates a large transient outward current, we are concerned with the persistent component (arrowhead); effects of the transient outward current are beyond the scope of this study and were minimized by adjusting pre-stimulus membrane potential to −60 mV for all current clamp protocols. Gray line shows baseline current.
Mentions: Several lines of experimental evidence support this prediction. First, the response to brief, subthreshold depolarizing pulses was amplified and prolonged relative to the equivalent hyperpolarizing response in class 1 neurons, consistent with effects of a subthreshold inward current (Figure 5A, right); the opposite pattern was observed in class 3 neurons, consistent with effects of a subthrehsold outward current (Figure 5A, left). Second, in voltage clamp, stepping command potential from −70 mV to perithreshold potentials elicited the largest outward current in class 3 neurons, followed by class 2 and class 1 neurons (Figure 5B). The relative positioning of I–V curves plotted from those experiments (Figure 5C) bore a striking resemblance to the relative positioning of I–V curves in the 2D and 3D models (Figure 4); this is especially true if the persistent Na+ current that was blocked by TTX in the aforementioned experiments is taken into account; this current is expressed exclusively in tonic-spiking neurons [26]. Application of 4-AP confirmed the presence of a persistent, low-threshold K+ current in single-spiking lamina I neurons (Figure 5D).

Bottom Line: Hodgkin identified three classes of neurons with qualitatively different analog-to-digital transduction properties.From this, we conclude that the spike-initiating dynamics associated with each of Hodgkin's classes represent different outcomes in a nonlinear competition between oppositely directed, kinetically mismatched currents.Through detailed analysis of the spike-initiating process, we have explained a fundamental link between biophysical properties and qualitative differences in how neurons encode sensory input.

View Article: PubMed Central - PubMed

Affiliation: Computational Neurobiology Laboratory, Salk Institute, La Jolla, California, United States of America. prescott@neurobio.pitt.edu

ABSTRACT
Transduction of graded synaptic input into trains of all-or-none action potentials (spikes) is a crucial step in neural coding. Hodgkin identified three classes of neurons with qualitatively different analog-to-digital transduction properties. Despite widespread use of this classification scheme, a generalizable explanation of its biophysical basis has not been described. We recorded from spinal sensory neurons representing each class and reproduced their transduction properties in a minimal model. With phase plane and bifurcation analysis, each class of excitability was shown to derive from distinct spike initiating dynamics. Excitability could be converted between all three classes by varying single parameters; moreover, several parameters, when varied one at a time, had functionally equivalent effects on excitability. From this, we conclude that the spike-initiating dynamics associated with each of Hodgkin's classes represent different outcomes in a nonlinear competition between oppositely directed, kinetically mismatched currents. Class 1 excitability occurs through a saddle node on invariant circle bifurcation when net current at perithreshold potentials is inward (depolarizing) at steady state. Class 2 excitability occurs through a Hopf bifurcation when, despite net current being outward (hyperpolarizing) at steady state, spike initiation occurs because inward current activates faster than outward current. Class 3 excitability occurs through a quasi-separatrix crossing when fast-activating inward current overpowers slow-activating outward current during a stimulus transient, although slow-activating outward current dominates during constant stimulation. Experiments confirmed that different classes of spinal lamina I neurons express the subthreshold currents predicted by our simulations and, further, that those currents are necessary for the excitability in each cell class. Thus, our results demonstrate that all three classes of excitability arise from a continuum in the direction and magnitude of subthreshold currents. Through detailed analysis of the spike-initiating process, we have explained a fundamental link between biophysical properties and qualitative differences in how neurons encode sensory input.

Show MeSH
Related in: MedlinePlus