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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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Biophysical correlate of differences inβw.(A) The w-cline (inset) corresponds to thevoltage-dependent activation curve forIslow. Horizontal positioning of that curveis controlled by βw. Differencesbetween class 1, 2, and 3 models may thus reflect differences in thevoltage-dependency of Islow. (B) It is morelikely, however, that the components ofIslow vary between cells of differentclasses (see Results).Islow may comprise multiple currentswith similar kinetics. IfIslow = IK,dr+Isub,the position of the net I–V curve can bechanged in qualitatively the same way as in (A) by changing thedirection and magnitude of Isub (see insets)without changing the voltage-dependencies ofIsub(βz = −21mV,γz = 15mV) or of IK,dr(βy = −10mV,γy = 10mV); voltage-dependencies of Isub andIK,dr are different, however, with theformer being more strongly activated at subthreshold potentials. Theseresults predict that tonic-spiking neurons express a subthreshold inwardcurrent and/or that single-spiking neurons express a subthresholdoutward current.
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pcbi-1000198-g004: Biophysical correlate of differences inβw.(A) The w-cline (inset) corresponds to thevoltage-dependent activation curve forIslow. Horizontal positioning of that curveis controlled by βw. Differencesbetween class 1, 2, and 3 models may thus reflect differences in thevoltage-dependency of Islow. (B) It is morelikely, however, that the components ofIslow vary between cells of differentclasses (see Results).Islow may comprise multiple currentswith similar kinetics. IfIslow = IK,dr+Isub,the position of the net I–V curve can bechanged in qualitatively the same way as in (A) by changing thedirection and magnitude of Isub (see insets)without changing the voltage-dependencies ofIsub(βz = −21mV,γz = 15mV) or of IK,dr(βy = −10mV,γy = 10mV); voltage-dependencies of Isub andIK,dr are different, however, with theformer being more strongly activated at subthreshold potentials. Theseresults predict that tonic-spiking neurons express a subthreshold inwardcurrent and/or that single-spiking neurons express a subthresholdoutward current.

Mentions: In the process of building the model (see Methods), βw was identified as animportant parameter given its capacity to convert the model between all threeclasses of excitability. The biophysical meaning ofβw is deferred until Figure 4, after its functionalsignificance has been established. See Figure 8 for the effects of changing otherparameters. Therefore, to begin, we explored the effects on the model'sf–I curve of systematically varyingβw (Figure 1D). The model exhibited class 1excitability for βw>−10 mV,but class 2 and 3 excitability coexisted for allβw<−10 mV; in otherwords, class 2 or 3 excitability was exhibited depending on stimulus intensityIstim. This is evident in Figure 1B where, in the model withβw = −13mV, rheobasic stimulation elicited a single spike while stronger stimulationelicited repetitive spiking. This pattern is characteristic of phasic-spikingspinal lamina I neurons (Figure1A) and is commonly observed in other “class 2”neurons including the squid giant axon [2], trigeminalmotoneurons [19], and fast-spiking neocortical interneurons[10],[20]. Conversely,“class 3” neurons should theoretically begin spikingrepetitively if given extremely strong stimulation. In reality, strongstimulation elicits, at most, a burst of 2–4 high frequency spikes insingle-spiking spinal lamina I neurons [14], which isconsistent with Hodgkin's classification in which class 3 neurons aresaid to “repeat only with difficulty or not atall” [5]. Responses to strong stimulation can be moreaccurately reproduced in the model by incorporating slow processes likecumulative Na+ channel inactivation, but such processes werenot included in the models analyzed here in order to keep the model as simple aspossible and because such strong stimulation is arguably unphysiological in thefirst place.


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

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

Biophysical correlate of differences inβw.(A) The w-cline (inset) corresponds to thevoltage-dependent activation curve forIslow. Horizontal positioning of that curveis controlled by βw. Differencesbetween class 1, 2, and 3 models may thus reflect differences in thevoltage-dependency of Islow. (B) It is morelikely, however, that the components ofIslow vary between cells of differentclasses (see Results).Islow may comprise multiple currentswith similar kinetics. IfIslow = IK,dr+Isub,the position of the net I–V curve can bechanged in qualitatively the same way as in (A) by changing thedirection and magnitude of Isub (see insets)without changing the voltage-dependencies ofIsub(βz = −21mV,γz = 15mV) or of IK,dr(βy = −10mV,γy = 10mV); voltage-dependencies of Isub andIK,dr are different, however, with theformer being more strongly activated at subthreshold potentials. Theseresults predict that tonic-spiking neurons express a subthreshold inwardcurrent and/or that single-spiking neurons express a subthresholdoutward current.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1000198-g004: Biophysical correlate of differences inβw.(A) The w-cline (inset) corresponds to thevoltage-dependent activation curve forIslow. Horizontal positioning of that curveis controlled by βw. Differencesbetween class 1, 2, and 3 models may thus reflect differences in thevoltage-dependency of Islow. (B) It is morelikely, however, that the components ofIslow vary between cells of differentclasses (see Results).Islow may comprise multiple currentswith similar kinetics. IfIslow = IK,dr+Isub,the position of the net I–V curve can bechanged in qualitatively the same way as in (A) by changing thedirection and magnitude of Isub (see insets)without changing the voltage-dependencies ofIsub(βz = −21mV,γz = 15mV) or of IK,dr(βy = −10mV,γy = 10mV); voltage-dependencies of Isub andIK,dr are different, however, with theformer being more strongly activated at subthreshold potentials. Theseresults predict that tonic-spiking neurons express a subthreshold inwardcurrent and/or that single-spiking neurons express a subthresholdoutward current.
Mentions: In the process of building the model (see Methods), βw was identified as animportant parameter given its capacity to convert the model between all threeclasses of excitability. The biophysical meaning ofβw is deferred until Figure 4, after its functionalsignificance has been established. See Figure 8 for the effects of changing otherparameters. Therefore, to begin, we explored the effects on the model'sf–I curve of systematically varyingβw (Figure 1D). The model exhibited class 1excitability for βw>−10 mV,but class 2 and 3 excitability coexisted for allβw<−10 mV; in otherwords, class 2 or 3 excitability was exhibited depending on stimulus intensityIstim. This is evident in Figure 1B where, in the model withβw = −13mV, rheobasic stimulation elicited a single spike while stronger stimulationelicited repetitive spiking. This pattern is characteristic of phasic-spikingspinal lamina I neurons (Figure1A) and is commonly observed in other “class 2”neurons including the squid giant axon [2], trigeminalmotoneurons [19], and fast-spiking neocortical interneurons[10],[20]. Conversely,“class 3” neurons should theoretically begin spikingrepetitively if given extremely strong stimulation. In reality, strongstimulation elicits, at most, a burst of 2–4 high frequency spikes insingle-spiking spinal lamina I neurons [14], which isconsistent with Hodgkin's classification in which class 3 neurons aresaid to “repeat only with difficulty or not atall” [5]. Responses to strong stimulation can be moreaccurately reproduced in the model by incorporating slow processes likecumulative Na+ channel inactivation, but such processes werenot included in the models analyzed here in order to keep the model as simple aspossible and because such strong stimulation is arguably unphysiological in thefirst place.

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