Limits...
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.

Show MeSH

Related in: MedlinePlus

Different classes of spinal lamina I neurons express differentsubthreshold currents.(A) Traces show responses to 60 pA, 20-ms-long depolarizing pulses(black) and to equivalent hyperpolarizing pulses (gray); the latter areinverted to facilitate comparison with former. In class 1(tonic-spiking) neurons, depolarization was amplified and prolongedrelative to hyperpolarization, consistent with effects of an inwardcurrent activated by perithreshold depolarization. Class 3(single-spiking) neurons exhibited the opposite pattern, consistent witheffects of a subthreshold outward current, which is also evident fromoutward rectification (arrow) in the I–Vcurve. Depolarizing and hyperpolarizing responses were symmetrical inclass 2 (phasic-spiking) neurons, consistent with negligible netsubthreshold current. (B) Membrane current activated by voltage-clampsteps from −70 mV to −60, −50,−40, and −30 mV. For a given command potential,class 3 neurons exhibited the largest persistent outward current andclass 1 neurons exhibited the smallest outward current. Red linehighlights difference in current activated by step to −40 mV.(C) Steady-state I–V curves for voltage clampprotocols in (B). Because recordings were performed in TTX to preventunclamped spiking, the persistent Na+ current(INa,p), which is expressed exclusivelyin tonic-spiking neurons, was blocked; to correct for this,INa,p measured in separate voltage clampramp protocols [26] was added to give a correctedI–V curve (dotted line). Compare withFigure 4. (D)4-AP-sensitive current determined by subtraction of response before andduring application of 5 mM 4-AP to a single-spiking neuron. Protocolincluded prepulse to −100 mV, which revealed a smallpersistent outward current active at −70 mV that wasdeactivated by hyperpolarization to −100 mV (*).Although depolarization also activates a large transient outwardcurrent, we are concerned with the persistent component (arrowhead);effects of the transient outward current are beyond the scope of thisstudy and were minimized by adjusting pre-stimulus membrane potential to−60 mV for all current clamp protocols. Gray line showsbaseline current.
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC2551735&req=5

pcbi-1000198-g005: Different classes of spinal lamina I neurons express differentsubthreshold currents.(A) Traces show responses to 60 pA, 20-ms-long depolarizing pulses(black) and to equivalent hyperpolarizing pulses (gray); the latter areinverted to facilitate comparison with former. In class 1(tonic-spiking) neurons, depolarization was amplified and prolongedrelative to hyperpolarization, consistent with effects of an inwardcurrent activated by perithreshold depolarization. Class 3(single-spiking) neurons exhibited the opposite pattern, consistent witheffects of a subthreshold outward current, which is also evident fromoutward rectification (arrow) in the I–Vcurve. Depolarizing and hyperpolarizing responses were symmetrical inclass 2 (phasic-spiking) neurons, consistent with negligible netsubthreshold current. (B) Membrane current activated by voltage-clampsteps from −70 mV to −60, −50,−40, and −30 mV. For a given command potential,class 3 neurons exhibited the largest persistent outward current andclass 1 neurons exhibited the smallest outward current. Red linehighlights difference in current activated by step to −40 mV.(C) Steady-state I–V curves for voltage clampprotocols in (B). Because recordings were performed in TTX to preventunclamped spiking, the persistent Na+ current(INa,p), which is expressed exclusivelyin tonic-spiking neurons, was blocked; to correct for this,INa,p measured in separate voltage clampramp protocols [26] was added to give a correctedI–V curve (dotted line). Compare withFigure 4. (D)4-AP-sensitive current determined by subtraction of response before andduring application of 5 mM 4-AP to a single-spiking neuron. Protocolincluded prepulse to −100 mV, which revealed a smallpersistent outward current active at −70 mV that wasdeactivated by hyperpolarization to −100 mV (*).Although depolarization also activates a large transient outwardcurrent, we are concerned with the persistent component (arrowhead);effects of the transient outward current are beyond the scope of thisstudy and were minimized by adjusting pre-stimulus membrane potential to−60 mV for all current clamp protocols. Gray line showsbaseline current.

Mentions: Several lines of experimental evidence support this prediction. First, theresponse to brief, subthreshold depolarizing pulses was amplified and prolongedrelative to the equivalent hyperpolarizing response in class 1 neurons,consistent with effects of a subthreshold inward current (Figure 5A, right); the opposite pattern wasobserved in class 3 neurons, consistent with effects of a subthrehsold outwardcurrent (Figure 5A, left).Second, in voltage clamp, stepping command potential from −70 mV toperithreshold potentials elicited the largest outward current in class 3neurons, followed by class 2 and class 1 neurons (Figure 5B). The relative positioning ofI–V curves plotted from those experiments (Figure 5C) bore a strikingresemblance to the relative positioning of I–V curvesin the 2D and 3D models (Figure4); this is especially true if the persistent Na+current that was blocked by TTX in the aforementioned experiments is taken intoaccount; this current is expressed exclusively in tonic-spiking neurons [26].Application of 4-AP confirmed the presence of a persistent, low-thresholdK+ 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 differentsubthreshold currents.(A) Traces show responses to 60 pA, 20-ms-long depolarizing pulses(black) and to equivalent hyperpolarizing pulses (gray); the latter areinverted to facilitate comparison with former. In class 1(tonic-spiking) neurons, depolarization was amplified and prolongedrelative to hyperpolarization, consistent with effects of an inwardcurrent activated by perithreshold depolarization. Class 3(single-spiking) neurons exhibited the opposite pattern, consistent witheffects of a subthreshold outward current, which is also evident fromoutward rectification (arrow) in the I–Vcurve. Depolarizing and hyperpolarizing responses were symmetrical inclass 2 (phasic-spiking) neurons, consistent with negligible netsubthreshold current. (B) Membrane current activated by voltage-clampsteps from −70 mV to −60, −50,−40, and −30 mV. For a given command potential,class 3 neurons exhibited the largest persistent outward current andclass 1 neurons exhibited the smallest outward current. Red linehighlights difference in current activated by step to −40 mV.(C) Steady-state I–V curves for voltage clampprotocols in (B). Because recordings were performed in TTX to preventunclamped spiking, the persistent Na+ current(INa,p), which is expressed exclusivelyin tonic-spiking neurons, was blocked; to correct for this,INa,p measured in separate voltage clampramp protocols [26] was added to give a correctedI–V curve (dotted line). Compare withFigure 4. (D)4-AP-sensitive current determined by subtraction of response before andduring application of 5 mM 4-AP to a single-spiking neuron. Protocolincluded prepulse to −100 mV, which revealed a smallpersistent outward current active at −70 mV that wasdeactivated by hyperpolarization to −100 mV (*).Although depolarization also activates a large transient outwardcurrent, we are concerned with the persistent component (arrowhead);effects of the transient outward current are beyond the scope of thisstudy and were minimized by adjusting pre-stimulus membrane potential to−60 mV for all current clamp protocols. Gray line showsbaseline current.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2551735&req=5

pcbi-1000198-g005: Different classes of spinal lamina I neurons express differentsubthreshold currents.(A) Traces show responses to 60 pA, 20-ms-long depolarizing pulses(black) and to equivalent hyperpolarizing pulses (gray); the latter areinverted to facilitate comparison with former. In class 1(tonic-spiking) neurons, depolarization was amplified and prolongedrelative to hyperpolarization, consistent with effects of an inwardcurrent activated by perithreshold depolarization. Class 3(single-spiking) neurons exhibited the opposite pattern, consistent witheffects of a subthreshold outward current, which is also evident fromoutward rectification (arrow) in the I–Vcurve. Depolarizing and hyperpolarizing responses were symmetrical inclass 2 (phasic-spiking) neurons, consistent with negligible netsubthreshold current. (B) Membrane current activated by voltage-clampsteps from −70 mV to −60, −50,−40, and −30 mV. For a given command potential,class 3 neurons exhibited the largest persistent outward current andclass 1 neurons exhibited the smallest outward current. Red linehighlights difference in current activated by step to −40 mV.(C) Steady-state I–V curves for voltage clampprotocols in (B). Because recordings were performed in TTX to preventunclamped spiking, the persistent Na+ current(INa,p), which is expressed exclusivelyin tonic-spiking neurons, was blocked; to correct for this,INa,p measured in separate voltage clampramp protocols [26] was added to give a correctedI–V curve (dotted line). Compare withFigure 4. (D)4-AP-sensitive current determined by subtraction of response before andduring application of 5 mM 4-AP to a single-spiking neuron. Protocolincluded prepulse to −100 mV, which revealed a smallpersistent outward current active at −70 mV that wasdeactivated by hyperpolarization to −100 mV (*).Although depolarization also activates a large transient outwardcurrent, we are concerned with the persistent component (arrowhead);effects of the transient outward current are beyond the scope of thisstudy and were minimized by adjusting pre-stimulus membrane potential to−60 mV for all current clamp protocols. Gray line showsbaseline current.
Mentions: Several lines of experimental evidence support this prediction. First, theresponse to brief, subthreshold depolarizing pulses was amplified and prolongedrelative to the equivalent hyperpolarizing response in class 1 neurons,consistent with effects of a subthreshold inward current (Figure 5A, right); the opposite pattern wasobserved in class 3 neurons, consistent with effects of a subthrehsold outwardcurrent (Figure 5A, left).Second, in voltage clamp, stepping command potential from −70 mV toperithreshold potentials elicited the largest outward current in class 3neurons, followed by class 2 and class 1 neurons (Figure 5B). The relative positioning ofI–V curves plotted from those experiments (Figure 5C) bore a strikingresemblance to the relative positioning of I–V curvesin the 2D and 3D models (Figure4); this is especially true if the persistent Na+current that was blocked by TTX in the aforementioned experiments is taken intoaccount; this current is expressed exclusively in tonic-spiking neurons [26].Application of 4-AP confirmed the presence of a persistent, low-thresholdK+ 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