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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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Comparison of spikes initiated through different dynamicalmechanisms.(A) Spikes initiated through a QSC or SNIC bifurcation exhibit differentspike amplitude variability. Data are from 2D models stimulated withnoisy Istim(σnoise = 10µA/cm2). V-clines areshown for rest (red) and for one stimulus intensity (blue) althoughIstim varies continuously duringstimulation. Spikes initiated through a QSC exhibit variable amplitudes(yellow shading) because variations in Istimaffect the V-w trajectory: trajectories starting closeto the quasi-separatrix (produced by Istimfluctuations just exceeding rheobase) produce smaller spikes thantrajectories starting further from the quasi-separatrix (produced bylarger Istim fluctuations). Spikes initiatedthrough an SNIC bifurcation exhibit little variability (pink shading)because all trajectories follow the invariant circle once theheteroclinic trajectories (green curves) fuse at the moment of the SNICbifurcation to form a single homoclinic orbit. Histogram showsdistribution of voltage maxima; maxima above cutoff (*) areconsidered spikes. Distributions differed significantly between cellclasses after normalizing by maximum or by average spike amplitude(p<0.005 andp<0.001, respectively; Kolmogorov-Smirnov test).(B) As predicted, class 3 (single-spiking) neurons showed significantlygreater variability in spike amplitude than class 1 (tonic-spiking)neurons (p<0.001 regardless of normalization bypeak or average; Kolmogorov-Smirnov test).σnoise = 10 pA.
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pcbi-1000198-g003: Comparison of spikes initiated through different dynamicalmechanisms.(A) Spikes initiated through a QSC or SNIC bifurcation exhibit differentspike amplitude variability. Data are from 2D models stimulated withnoisy Istim(σnoise = 10µA/cm2). V-clines areshown for rest (red) and for one stimulus intensity (blue) althoughIstim varies continuously duringstimulation. Spikes initiated through a QSC exhibit variable amplitudes(yellow shading) because variations in Istimaffect the V-w trajectory: trajectories starting closeto the quasi-separatrix (produced by Istimfluctuations just exceeding rheobase) produce smaller spikes thantrajectories starting further from the quasi-separatrix (produced bylarger Istim fluctuations). Spikes initiatedthrough an SNIC bifurcation exhibit little variability (pink shading)because all trajectories follow the invariant circle once theheteroclinic trajectories (green curves) fuse at the moment of the SNICbifurcation to form a single homoclinic orbit. Histogram showsdistribution of voltage maxima; maxima above cutoff (*) areconsidered spikes. Distributions differed significantly between cellclasses after normalizing by maximum or by average spike amplitude(p<0.005 andp<0.001, respectively; Kolmogorov-Smirnov test).(B) As predicted, class 3 (single-spiking) neurons showed significantlygreater variability in spike amplitude than class 1 (tonic-spiking)neurons (p<0.001 regardless of normalization bypeak or average; Kolmogorov-Smirnov test).σnoise = 10 pA.

Mentions: Since model parameters were chosen to produce one or another spiking pattern,simply reproducing a given pattern is not necessarily informative—thisconstitutes an inverse problem akin to circular reasoning. To ensure that themodel does not simply mimic spiking pattern, it must predict behaviors separatefrom those used to choose parameters. The model makes such a prediction: spikesinitiated through different dynamical mechanisms are predicted to exhibitdifferent variability in their amplitudes. Specifically, spikes initiatedthrough an SNIC bifurcation should have uniform amplitudes because allsuprathreshold trajectories follow the invariant circle formed when the stablemanifolds (green curves on Figure3A) fuse at the moment of the bifurcation. In contrast, spikesinitiated through a QSC are predicted to have variable amplitudes that aresensitive to stimulus intensity because each trajectory (including how far itextends on the abscissa) depends on where that trajectory starts relative to thequasi-separatrix.


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

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

Comparison of spikes initiated through different dynamicalmechanisms.(A) Spikes initiated through a QSC or SNIC bifurcation exhibit differentspike amplitude variability. Data are from 2D models stimulated withnoisy Istim(σnoise = 10µA/cm2). V-clines areshown for rest (red) and for one stimulus intensity (blue) althoughIstim varies continuously duringstimulation. Spikes initiated through a QSC exhibit variable amplitudes(yellow shading) because variations in Istimaffect the V-w trajectory: trajectories starting closeto the quasi-separatrix (produced by Istimfluctuations just exceeding rheobase) produce smaller spikes thantrajectories starting further from the quasi-separatrix (produced bylarger Istim fluctuations). Spikes initiatedthrough an SNIC bifurcation exhibit little variability (pink shading)because all trajectories follow the invariant circle once theheteroclinic trajectories (green curves) fuse at the moment of the SNICbifurcation to form a single homoclinic orbit. Histogram showsdistribution of voltage maxima; maxima above cutoff (*) areconsidered spikes. Distributions differed significantly between cellclasses after normalizing by maximum or by average spike amplitude(p<0.005 andp<0.001, respectively; Kolmogorov-Smirnov test).(B) As predicted, class 3 (single-spiking) neurons showed significantlygreater variability in spike amplitude than class 1 (tonic-spiking)neurons (p<0.001 regardless of normalization bypeak or average; Kolmogorov-Smirnov test).σnoise = 10 pA.
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Related In: Results  -  Collection

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

pcbi-1000198-g003: Comparison of spikes initiated through different dynamicalmechanisms.(A) Spikes initiated through a QSC or SNIC bifurcation exhibit differentspike amplitude variability. Data are from 2D models stimulated withnoisy Istim(σnoise = 10µA/cm2). V-clines areshown for rest (red) and for one stimulus intensity (blue) althoughIstim varies continuously duringstimulation. Spikes initiated through a QSC exhibit variable amplitudes(yellow shading) because variations in Istimaffect the V-w trajectory: trajectories starting closeto the quasi-separatrix (produced by Istimfluctuations just exceeding rheobase) produce smaller spikes thantrajectories starting further from the quasi-separatrix (produced bylarger Istim fluctuations). Spikes initiatedthrough an SNIC bifurcation exhibit little variability (pink shading)because all trajectories follow the invariant circle once theheteroclinic trajectories (green curves) fuse at the moment of the SNICbifurcation to form a single homoclinic orbit. Histogram showsdistribution of voltage maxima; maxima above cutoff (*) areconsidered spikes. Distributions differed significantly between cellclasses after normalizing by maximum or by average spike amplitude(p<0.005 andp<0.001, respectively; Kolmogorov-Smirnov test).(B) As predicted, class 3 (single-spiking) neurons showed significantlygreater variability in spike amplitude than class 1 (tonic-spiking)neurons (p<0.001 regardless of normalization bypeak or average; Kolmogorov-Smirnov test).σnoise = 10 pA.
Mentions: Since model parameters were chosen to produce one or another spiking pattern,simply reproducing a given pattern is not necessarily informative—thisconstitutes an inverse problem akin to circular reasoning. To ensure that themodel does not simply mimic spiking pattern, it must predict behaviors separatefrom those used to choose parameters. The model makes such a prediction: spikesinitiated through different dynamical mechanisms are predicted to exhibitdifferent variability in their amplitudes. Specifically, spikes initiatedthrough an SNIC bifurcation should have uniform amplitudes because allsuprathreshold trajectories follow the invariant circle formed when the stablemanifolds (green curves on Figure3A) fuse at the moment of the bifurcation. In contrast, spikesinitiated through a QSC are predicted to have variable amplitudes that aresensitive to stimulus intensity because each trajectory (including how far itextends on the abscissa) depends on where that trajectory starts relative to thequasi-separatrix.

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