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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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Sufficiency of oppositely directed subthrehsold currents to explain                            excitability.(A) Responses from 3D model described in Figure 4B. Without                                Isub, the model operated at the                            interface between class 1 and 2 excitability (see (C)). Adding an                            outward current                            (Esub = −100                            mV) produced class 2 or 3 excitability, with the latter becoming more                            predominant (i.e. over a wider range of                            Istim) as                                ḡsub was increased. Adding an                            inward current                            (Esub = 50                            mV) produced class 1 excitability. (B) Bifurcation diagrams show voltage                            at fixed point and at max/min of limit cycle as                                Istim was increased. Class 1, 2, and 3                            versions of the 3D models exhibited exactly the same spike initiating                            dynamics seen in class 1, 2 and 3 versions of the 2D models (compare                            with Figure 2B). (C)                            Firing rate (color) is plotted against Istim                            and ḡsub. These data are                            qualitatively identical to those for the 2D model (see Figure 1D) and                            indicate that direction and magnitude of                            Isub are sufficient to explain different                            classes of excitability. The phasic-spiking that results from adaptation                            (see Figure 1C) can                            be understood in terms of slowly activating outward current (or                            inactivating inward current) causing a shift from class 2 to class 3                            excitability. (D) As with the 2D model (Figure 3A), the class 3 version of                            the 3D model exhibited significantly greater spike amplitude variability                            than the class 1 version when driven by noisy stimulation                            (p<0.001, respectively; Kolmogorov-Smirnov                            test). σnoise = 10                                µA/cm2.
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pcbi-1000198-g007: Sufficiency of oppositely directed subthrehsold currents to explain excitability.(A) Responses from 3D model described in Figure 4B. Without Isub, the model operated at the interface between class 1 and 2 excitability (see (C)). Adding an outward current (Esub = −100 mV) produced class 2 or 3 excitability, with the latter becoming more predominant (i.e. over a wider range of Istim) as ḡsub was increased. Adding an inward current (Esub = 50 mV) produced class 1 excitability. (B) Bifurcation diagrams show voltage at fixed point and at max/min of limit cycle as Istim was increased. Class 1, 2, and 3 versions of the 3D models exhibited exactly the same spike initiating dynamics seen in class 1, 2 and 3 versions of the 2D models (compare with Figure 2B). (C) Firing rate (color) is plotted against Istim and ḡsub. These data are qualitatively identical to those for the 2D model (see Figure 1D) and indicate that direction and magnitude of Isub are sufficient to explain different classes of excitability. The phasic-spiking that results from adaptation (see Figure 1C) can be understood in terms of slowly activating outward current (or inactivating inward current) causing a shift from class 2 to class 3 excitability. (D) As with the 2D model (Figure 3A), the class 3 version of the 3D model exhibited significantly greater spike amplitude variability than the class 1 version when driven by noisy stimulation (p<0.001, respectively; Kolmogorov-Smirnov test). σnoise = 10 µA/cm2.

Mentions: To demonstrate the sufficiency of subthreshold currents for determining excitability, we explicitly incorporated a subthreshold inward or outward current by adding an additional term for Isub to the 2D model with βw = −10 mV (see Equation 7); recall that the 2D model lies at the interface between class 1 and 2 excitability when βw = −10 mV (see Figure 1D). Adding an inward current produced class 1 excitability, whereas adding an outward current produced class 2 or 3 excitability depending on the magnitude of gsub (which is controlled by the maximal conductance, ḡsub) (Figure 7A). With βw = −13 mV (like the class 2 model in Figure 1B), the default 3D model was class 2; adding a subthreshold inward or outward current converted it to class 1 or 3, respectively (data not shown). The three classes of excitability can be readily identified from the bifurcation diagrams of the 3D model (Figure 7B; compare with 2D model in Figure 2B). Varying ḡsub affected the f–I curve in this 3D model in exactly the same manner as varying βw in the 2D model (compare Figure 7C with Figure 1D). The transition between class 1 and 2 excitability occurred at ḡsub = 0 mS/cm2, although that value varied depending on βw (see above). For a given value of Istim, class 1 and 2 excitability were mutually exclusive whereas class 2 and 3 excitability coexisted. Furthermore, the 3D model exhibited constant or variably sized spikes depending on whether the model was class 1 or 3, respectively (Figure 7D; compare with Figure 3A and 3B). This demonstrates the sufficiency of subthreshold inward and outward currents for producing class 1 and 3 excitability, respectively.


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

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

Sufficiency of oppositely directed subthrehsold currents to explain                            excitability.(A) Responses from 3D model described in Figure 4B. Without                                Isub, the model operated at the                            interface between class 1 and 2 excitability (see (C)). Adding an                            outward current                            (Esub = −100                            mV) produced class 2 or 3 excitability, with the latter becoming more                            predominant (i.e. over a wider range of                            Istim) as                                ḡsub was increased. Adding an                            inward current                            (Esub = 50                            mV) produced class 1 excitability. (B) Bifurcation diagrams show voltage                            at fixed point and at max/min of limit cycle as                                Istim was increased. Class 1, 2, and 3                            versions of the 3D models exhibited exactly the same spike initiating                            dynamics seen in class 1, 2 and 3 versions of the 2D models (compare                            with Figure 2B). (C)                            Firing rate (color) is plotted against Istim                            and ḡsub. These data are                            qualitatively identical to those for the 2D model (see Figure 1D) and                            indicate that direction and magnitude of                            Isub are sufficient to explain different                            classes of excitability. The phasic-spiking that results from adaptation                            (see Figure 1C) can                            be understood in terms of slowly activating outward current (or                            inactivating inward current) causing a shift from class 2 to class 3                            excitability. (D) As with the 2D model (Figure 3A), the class 3 version of                            the 3D model exhibited significantly greater spike amplitude variability                            than the class 1 version when driven by noisy stimulation                            (p<0.001, respectively; Kolmogorov-Smirnov                            test). σnoise = 10                                µA/cm2.
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pcbi-1000198-g007: Sufficiency of oppositely directed subthrehsold currents to explain excitability.(A) Responses from 3D model described in Figure 4B. Without Isub, the model operated at the interface between class 1 and 2 excitability (see (C)). Adding an outward current (Esub = −100 mV) produced class 2 or 3 excitability, with the latter becoming more predominant (i.e. over a wider range of Istim) as ḡsub was increased. Adding an inward current (Esub = 50 mV) produced class 1 excitability. (B) Bifurcation diagrams show voltage at fixed point and at max/min of limit cycle as Istim was increased. Class 1, 2, and 3 versions of the 3D models exhibited exactly the same spike initiating dynamics seen in class 1, 2 and 3 versions of the 2D models (compare with Figure 2B). (C) Firing rate (color) is plotted against Istim and ḡsub. These data are qualitatively identical to those for the 2D model (see Figure 1D) and indicate that direction and magnitude of Isub are sufficient to explain different classes of excitability. The phasic-spiking that results from adaptation (see Figure 1C) can be understood in terms of slowly activating outward current (or inactivating inward current) causing a shift from class 2 to class 3 excitability. (D) As with the 2D model (Figure 3A), the class 3 version of the 3D model exhibited significantly greater spike amplitude variability than the class 1 version when driven by noisy stimulation (p<0.001, respectively; Kolmogorov-Smirnov test). σnoise = 10 µA/cm2.
Mentions: To demonstrate the sufficiency of subthreshold currents for determining excitability, we explicitly incorporated a subthreshold inward or outward current by adding an additional term for Isub to the 2D model with βw = −10 mV (see Equation 7); recall that the 2D model lies at the interface between class 1 and 2 excitability when βw = −10 mV (see Figure 1D). Adding an inward current produced class 1 excitability, whereas adding an outward current produced class 2 or 3 excitability depending on the magnitude of gsub (which is controlled by the maximal conductance, ḡsub) (Figure 7A). With βw = −13 mV (like the class 2 model in Figure 1B), the default 3D model was class 2; adding a subthreshold inward or outward current converted it to class 1 or 3, respectively (data not shown). The three classes of excitability can be readily identified from the bifurcation diagrams of the 3D model (Figure 7B; compare with 2D model in Figure 2B). Varying ḡsub affected the f–I curve in this 3D model in exactly the same manner as varying βw in the 2D model (compare Figure 7C with Figure 1D). The transition between class 1 and 2 excitability occurred at ḡsub = 0 mS/cm2, although that value varied depending on βw (see above). For a given value of Istim, class 1 and 2 excitability were mutually exclusive whereas class 2 and 3 excitability coexisted. Furthermore, the 3D model exhibited constant or variably sized spikes depending on whether the model was class 1 or 3, respectively (Figure 7D; compare with Figure 3A and 3B). This demonstrates the sufficiency of subthreshold inward and outward currents for producing class 1 and 3 excitability, respectively.

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