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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 in                                βw.(A) The w-cline (inset) corresponds to the                            voltage-dependent activation curve for                            Islow. Horizontal positioning of that curve                            is controlled by βw. Differences                            between class 1, 2, and 3 models may thus reflect differences in the                            voltage-dependency of Islow. (B) It is more                            likely, however, that the components of                            Islow vary between cells of different                            classes (see Results).                                Islow may comprise multiple currents                            with similar kinetics. If                                Islow = IK,dr+Isub,                            the position of the net I–V curve can be                            changed in qualitatively the same way as in (A) by changing the                            direction and magnitude of Isub (see insets)                            without changing the voltage-dependencies of                            Isub                            (βz = −21                            mV,                            γz = 15                            mV) or of IK,dr                                (βy = −10                            mV,                            γy = 10                            mV); voltage-dependencies of Isub and                                IK,dr are different, however, with the                            former being more strongly activated at subthreshold potentials. These                            results predict that tonic-spiking neurons express a subthreshold inward                            current and/or that single-spiking neurons express a subthreshold                            outward current.
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pcbi-1000198-g004: Biophysical correlate of differences in βw.(A) The w-cline (inset) corresponds to the voltage-dependent activation curve for Islow. Horizontal positioning of that curve is controlled by βw. Differences between class 1, 2, and 3 models may thus reflect differences in the voltage-dependency of Islow. (B) It is more likely, however, that the components of Islow vary between cells of different classes (see Results). Islow may comprise multiple currents with similar kinetics. If Islow = IK,dr+Isub, the position of the net I–V curve can be changed in qualitatively the same way as in (A) by changing the direction and magnitude of Isub (see insets) without changing the voltage-dependencies of Isub (βz = −21 mV, γz = 15 mV) or of IK,dr (βy = −10 mV, γy = 10 mV); voltage-dependencies of Isub and IK,dr are different, however, with the former being more strongly activated at subthreshold potentials. These results predict that tonic-spiking neurons express a subthreshold inward current and/or that single-spiking neurons express a subthreshold outward current.

Mentions: In the process of building the model (see Methods), βw was identified as an important parameter given its capacity to convert the model between all three classes of excitability. The biophysical meaning of βw is deferred until Figure 4, after its functional significance has been established. See Figure 8 for the effects of changing other parameters. Therefore, to begin, we explored the effects on the model's f–I curve of systematically varying βw (Figure 1D). The model exhibited class 1 excitability for βw>−10 mV, but class 2 and 3 excitability coexisted for all βw<−10 mV; in other words, class 2 or 3 excitability was exhibited depending on stimulus intensity Istim. This is evident in Figure 1B where, in the model with βw = −13 mV, rheobasic stimulation elicited a single spike while stronger stimulation elicited repetitive spiking. This pattern is characteristic of phasic-spiking spinal lamina I neurons (Figure 1A) and is commonly observed in other “class 2” neurons including the squid giant axon [2], trigeminal motoneurons [19], and fast-spiking neocortical interneurons [10],[20]. Conversely, “class 3” neurons should theoretically begin spiking repetitively if given extremely strong stimulation. In reality, strong stimulation elicits, at most, a burst of 2–4 high frequency spikes in single-spiking spinal lamina I neurons [14], which is consistent with Hodgkin's classification in which class 3 neurons are said to “repeat only with difficulty or not at all” [5]. Responses to strong stimulation can be more accurately reproduced in the model by incorporating slow processes like cumulative Na+ channel inactivation, but such processes were not included in the models analyzed here in order to keep the model as simple as possible and because such strong stimulation is arguably unphysiological in the first 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 in                                βw.(A) The w-cline (inset) corresponds to the                            voltage-dependent activation curve for                            Islow. Horizontal positioning of that curve                            is controlled by βw. Differences                            between class 1, 2, and 3 models may thus reflect differences in the                            voltage-dependency of Islow. (B) It is more                            likely, however, that the components of                            Islow vary between cells of different                            classes (see Results).                                Islow may comprise multiple currents                            with similar kinetics. If                                Islow = IK,dr+Isub,                            the position of the net I–V curve can be                            changed in qualitatively the same way as in (A) by changing the                            direction and magnitude of Isub (see insets)                            without changing the voltage-dependencies of                            Isub                            (βz = −21                            mV,                            γz = 15                            mV) or of IK,dr                                (βy = −10                            mV,                            γy = 10                            mV); voltage-dependencies of Isub and                                IK,dr are different, however, with the                            former being more strongly activated at subthreshold potentials. These                            results predict that tonic-spiking neurons express a subthreshold inward                            current and/or that single-spiking neurons express a subthreshold                            outward current.
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Related In: Results  -  Collection

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pcbi-1000198-g004: Biophysical correlate of differences in βw.(A) The w-cline (inset) corresponds to the voltage-dependent activation curve for Islow. Horizontal positioning of that curve is controlled by βw. Differences between class 1, 2, and 3 models may thus reflect differences in the voltage-dependency of Islow. (B) It is more likely, however, that the components of Islow vary between cells of different classes (see Results). Islow may comprise multiple currents with similar kinetics. If Islow = IK,dr+Isub, the position of the net I–V curve can be changed in qualitatively the same way as in (A) by changing the direction and magnitude of Isub (see insets) without changing the voltage-dependencies of Isub (βz = −21 mV, γz = 15 mV) or of IK,dr (βy = −10 mV, γy = 10 mV); voltage-dependencies of Isub and IK,dr are different, however, with the former being more strongly activated at subthreshold potentials. These results predict that tonic-spiking neurons express a subthreshold inward current and/or that single-spiking neurons express a subthreshold outward current.
Mentions: In the process of building the model (see Methods), βw was identified as an important parameter given its capacity to convert the model between all three classes of excitability. The biophysical meaning of βw is deferred until Figure 4, after its functional significance has been established. See Figure 8 for the effects of changing other parameters. Therefore, to begin, we explored the effects on the model's f–I curve of systematically varying βw (Figure 1D). The model exhibited class 1 excitability for βw>−10 mV, but class 2 and 3 excitability coexisted for all βw<−10 mV; in other words, class 2 or 3 excitability was exhibited depending on stimulus intensity Istim. This is evident in Figure 1B where, in the model with βw = −13 mV, rheobasic stimulation elicited a single spike while stronger stimulation elicited repetitive spiking. This pattern is characteristic of phasic-spiking spinal lamina I neurons (Figure 1A) and is commonly observed in other “class 2” neurons including the squid giant axon [2], trigeminal motoneurons [19], and fast-spiking neocortical interneurons [10],[20]. Conversely, “class 3” neurons should theoretically begin spiking repetitively if given extremely strong stimulation. In reality, strong stimulation elicits, at most, a burst of 2–4 high frequency spikes in single-spiking spinal lamina I neurons [14], which is consistent with Hodgkin's classification in which class 3 neurons are said to “repeat only with difficulty or not at all” [5]. Responses to strong stimulation can be more accurately reproduced in the model by incorporating slow processes like cumulative Na+ channel inactivation, but such processes were not included in the models analyzed here in order to keep the model as simple as possible and because such strong stimulation is arguably unphysiological in the first 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