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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 explainexcitability.(A) Responses from 3D model described in Figure 4B. WithoutIsub, the model operated at theinterface between class 1 and 2 excitability (see (C)). Adding anoutward current(Esub = −100mV) produced class 2 or 3 excitability, with the latter becoming morepredominant (i.e. over a wider range ofIstim) asḡsub was increased. Adding aninward current(Esub = 50mV) produced class 1 excitability. (B) Bifurcation diagrams show voltageat fixed point and at max/min of limit cycle asIstim was increased. Class 1, 2, and 3versions of the 3D models exhibited exactly the same spike initiatingdynamics seen in class 1, 2 and 3 versions of the 2D models (comparewith Figure 2B). (C)Firing rate (color) is plotted against Istimand ḡsub. These data arequalitatively identical to those for the 2D model (see Figure 1D) andindicate that direction and magnitude ofIsub are sufficient to explain differentclasses of excitability. The phasic-spiking that results from adaptation(see Figure 1C) canbe understood in terms of slowly activating outward current (orinactivating inward current) causing a shift from class 2 to class 3excitability. (D) As with the 2D model (Figure 3A), the class 3 version ofthe 3D model exhibited significantly greater spike amplitude variabilitythan the class 1 version when driven by noisy stimulation(p<0.001, respectively; Kolmogorov-Smirnovtest). σnoise = 10µA/cm2.
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pcbi-1000198-g007: Sufficiency of oppositely directed subthrehsold currents to explainexcitability.(A) Responses from 3D model described in Figure 4B. WithoutIsub, the model operated at theinterface between class 1 and 2 excitability (see (C)). Adding anoutward current(Esub = −100mV) produced class 2 or 3 excitability, with the latter becoming morepredominant (i.e. over a wider range ofIstim) asḡsub was increased. Adding aninward current(Esub = 50mV) produced class 1 excitability. (B) Bifurcation diagrams show voltageat fixed point and at max/min of limit cycle asIstim was increased. Class 1, 2, and 3versions of the 3D models exhibited exactly the same spike initiatingdynamics seen in class 1, 2 and 3 versions of the 2D models (comparewith Figure 2B). (C)Firing rate (color) is plotted against Istimand ḡsub. These data arequalitatively identical to those for the 2D model (see Figure 1D) andindicate that direction and magnitude ofIsub are sufficient to explain differentclasses of excitability. The phasic-spiking that results from adaptation(see Figure 1C) canbe understood in terms of slowly activating outward current (orinactivating inward current) causing a shift from class 2 to class 3excitability. (D) As with the 2D model (Figure 3A), the class 3 version ofthe 3D model exhibited significantly greater spike amplitude variabilitythan the class 1 version when driven by noisy stimulation(p<0.001, respectively; Kolmogorov-Smirnovtest). σnoise = 10µA/cm2.

Mentions: To demonstrate the sufficiency of subthreshold currents for determiningexcitability, we explicitly incorporated a subthreshold inward or outwardcurrent by adding an additional term for Isub to the2D model withβw = −10mV (see Equation 7); recall that the 2D model lies at the interface betweenclass 1 and 2 excitability whenβw = −10mV (see Figure 1D). Addingan inward current produced class 1 excitability, whereas adding an outwardcurrent produced class 2 or 3 excitability depending on the magnitude ofgsub (which is controlled by the maximalconductance, ḡsub) (Figure 7A). Withβw = −13mV (like the class 2 model in Figure 1B), the default 3D model was class 2; adding a subthresholdinward or outward current converted it to class 1 or 3, respectively (data notshown). The three classes of excitability can be readily identified from thebifurcation diagrams of the 3D model (Figure 7B; compare with 2D model in Figure 2B). Varyingḡsub affected thef–I curve in this 3D model in exactly the samemanner as varying βw in the 2D model(compare Figure 7C withFigure 1D). Thetransition between class 1 and 2 excitability occurred atḡsub = 0mS/cm2, although that value varied depending onβw (see above). For a given value ofIstim, class 1 and 2 excitability were mutuallyexclusive whereas class 2 and 3 excitability coexisted. Furthermore, the 3Dmodel exhibited constant or variably sized spikes depending on whether the modelwas class 1 or 3, respectively (Figure 7D; compare with Figure 3A and 3B). This demonstrates the sufficiency of subthresholdinward 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 explainexcitability.(A) Responses from 3D model described in Figure 4B. WithoutIsub, the model operated at theinterface between class 1 and 2 excitability (see (C)). Adding anoutward current(Esub = −100mV) produced class 2 or 3 excitability, with the latter becoming morepredominant (i.e. over a wider range ofIstim) asḡsub was increased. Adding aninward current(Esub = 50mV) produced class 1 excitability. (B) Bifurcation diagrams show voltageat fixed point and at max/min of limit cycle asIstim was increased. Class 1, 2, and 3versions of the 3D models exhibited exactly the same spike initiatingdynamics seen in class 1, 2 and 3 versions of the 2D models (comparewith Figure 2B). (C)Firing rate (color) is plotted against Istimand ḡsub. These data arequalitatively identical to those for the 2D model (see Figure 1D) andindicate that direction and magnitude ofIsub are sufficient to explain differentclasses of excitability. The phasic-spiking that results from adaptation(see Figure 1C) canbe understood in terms of slowly activating outward current (orinactivating inward current) causing a shift from class 2 to class 3excitability. (D) As with the 2D model (Figure 3A), the class 3 version ofthe 3D model exhibited significantly greater spike amplitude variabilitythan the class 1 version when driven by noisy stimulation(p<0.001, respectively; Kolmogorov-Smirnovtest). σnoise = 10µA/cm2.
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Related In: Results  -  Collection

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

pcbi-1000198-g007: Sufficiency of oppositely directed subthrehsold currents to explainexcitability.(A) Responses from 3D model described in Figure 4B. WithoutIsub, the model operated at theinterface between class 1 and 2 excitability (see (C)). Adding anoutward current(Esub = −100mV) produced class 2 or 3 excitability, with the latter becoming morepredominant (i.e. over a wider range ofIstim) asḡsub was increased. Adding aninward current(Esub = 50mV) produced class 1 excitability. (B) Bifurcation diagrams show voltageat fixed point and at max/min of limit cycle asIstim was increased. Class 1, 2, and 3versions of the 3D models exhibited exactly the same spike initiatingdynamics seen in class 1, 2 and 3 versions of the 2D models (comparewith Figure 2B). (C)Firing rate (color) is plotted against Istimand ḡsub. These data arequalitatively identical to those for the 2D model (see Figure 1D) andindicate that direction and magnitude ofIsub are sufficient to explain differentclasses of excitability. The phasic-spiking that results from adaptation(see Figure 1C) canbe understood in terms of slowly activating outward current (orinactivating inward current) causing a shift from class 2 to class 3excitability. (D) As with the 2D model (Figure 3A), the class 3 version ofthe 3D model exhibited significantly greater spike amplitude variabilitythan the class 1 version when driven by noisy stimulation(p<0.001, respectively; Kolmogorov-Smirnovtest). σnoise = 10µA/cm2.
Mentions: To demonstrate the sufficiency of subthreshold currents for determiningexcitability, we explicitly incorporated a subthreshold inward or outwardcurrent by adding an additional term for Isub to the2D model withβw = −10mV (see Equation 7); recall that the 2D model lies at the interface betweenclass 1 and 2 excitability whenβw = −10mV (see Figure 1D). Addingan inward current produced class 1 excitability, whereas adding an outwardcurrent produced class 2 or 3 excitability depending on the magnitude ofgsub (which is controlled by the maximalconductance, ḡsub) (Figure 7A). Withβw = −13mV (like the class 2 model in Figure 1B), the default 3D model was class 2; adding a subthresholdinward or outward current converted it to class 1 or 3, respectively (data notshown). The three classes of excitability can be readily identified from thebifurcation diagrams of the 3D model (Figure 7B; compare with 2D model in Figure 2B). Varyingḡsub affected thef–I curve in this 3D model in exactly the samemanner as varying βw in the 2D model(compare Figure 7C withFigure 1D). Thetransition between class 1 and 2 excitability occurred atḡsub = 0mS/cm2, although that value varied depending onβw (see above). For a given value ofIstim, class 1 and 2 excitability were mutuallyexclusive whereas class 2 and 3 excitability coexisted. Furthermore, the 3Dmodel exhibited constant or variably sized spikes depending on whether the modelwas class 1 or 3, respectively (Figure 7D; compare with Figure 3A and 3B). This demonstrates the sufficiency of subthresholdinward 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