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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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Hodgkin's three classes of neuronal excitability. (A) Sample                            responses from spinal lamina I neurons representing each of                            Hodgkin's three classes. Hodgkin's classification is                            based on the f–I curve which is continuous                            (class 1), discontinuous (class 2), or undefined because measurement of                            firing rate requires at least two spikes (class 3). Data points                            comprising a single spike (ss) are indicated with open                            symbols in (A) or gray shading in (B–D). (B) Each cell class                            could be reproduced in a Morris-Lecar model by varying a single                            parameter, in this case βw. Like in                            (A), rheobasic stimulation (minimum Istim                            eliciting ≥1 spike) elicited a single spike at short latency in                            class 2 and 3 neurons compared with slow repetitive spiking in class 1                            neurons. Despite reproducing the discontinuous                            f–I curve, the 2D model could not reproduce                            the phasic-spiking pattern. (C) Phasic-spiking was generated by adding                            slow adaptation, thus giving a 3D model described by C                                dV/dt = Istim−g¯fast                            m∞(V)(V−ENa)−g¯sloww(V−EK)−gleak(V−Eleak)−gadapta(V−EK)                            and  where a controls activation of                            adaptation and                            g¯adapt = 0.5                                mS/cm2,                            φa = 0.05                                ms−1,                            βa = −40                            mV, and                            γa = 10                            mV. Bottom traces show single-spike elicited by second stimulus applied                            shortly after the end of first stimulus, which suggests that adaptation                            slowly shifts the neuron from class 2 towards class 3 excitability. (D)                            Firing rate (color) is plotted against Istim                            and βw. Separable regions of the                            graph correspond to different classes of excitability. Neuronal                            classification is based on which class of excitability is predominant                            (i.e., exhibited over the broadest range of                            Istim) and is indicated above the                        graph.
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pcbi-1000198-g001: Hodgkin's three classes of neuronal excitability. (A) Sample responses from spinal lamina I neurons representing each of Hodgkin's three classes. Hodgkin's classification is based on the f–I curve which is continuous (class 1), discontinuous (class 2), or undefined because measurement of firing rate requires at least two spikes (class 3). Data points comprising a single spike (ss) are indicated with open symbols in (A) or gray shading in (B–D). (B) Each cell class could be reproduced in a Morris-Lecar model by varying a single parameter, in this case βw. Like in (A), rheobasic stimulation (minimum Istim eliciting ≥1 spike) elicited a single spike at short latency in class 2 and 3 neurons compared with slow repetitive spiking in class 1 neurons. Despite reproducing the discontinuous f–I curve, the 2D model could not reproduce the phasic-spiking pattern. (C) Phasic-spiking was generated by adding slow adaptation, thus giving a 3D model described by C dV/dt = Istim−g¯fast m∞(V)(V−ENa)−g¯sloww(V−EK)−gleak(V−Eleak)−gadapta(V−EK) and where a controls activation of adaptation and g¯adapt = 0.5 mS/cm2, φa = 0.05 ms−1, βa = −40 mV, and γa = 10 mV. Bottom traces show single-spike elicited by second stimulus applied shortly after the end of first stimulus, which suggests that adaptation slowly shifts the neuron from class 2 towards class 3 excitability. (D) Firing rate (color) is plotted against Istim and βw. Separable regions of the graph correspond to different classes of excitability. Neuronal classification is based on which class of excitability is predominant (i.e., exhibited over the broadest range of Istim) and is indicated above the graph.

Mentions: Spinal sensory neurons fall into several categories based on spiking pattern [14]–[18]. Tonic-, phasic-, and single-spiking lamina I neurons exhibit the characteristic features of class 1, 2, and 3 excitability, respectively, based on their f–I curves (Figure 1A). Spiking pattern is related to, but not synonymous with, Hodgkin's classification scheme. For instance, phasic-spiking neurons are not class 2 because they stop spiking before the end of stimulation, but the fact that they stop spiking so abruptly suggests that they cannot maintain spiking below a certain rate, which is consistent with a discontinuous (class 2) f–I curve; in contrast, adaptation causes tonic-spiking neurons to spike more slowly but without stopping, consistent with a continuous (class 1) f–I curve.


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

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

Hodgkin's three classes of neuronal excitability. (A) Sample                            responses from spinal lamina I neurons representing each of                            Hodgkin's three classes. Hodgkin's classification is                            based on the f–I curve which is continuous                            (class 1), discontinuous (class 2), or undefined because measurement of                            firing rate requires at least two spikes (class 3). Data points                            comprising a single spike (ss) are indicated with open                            symbols in (A) or gray shading in (B–D). (B) Each cell class                            could be reproduced in a Morris-Lecar model by varying a single                            parameter, in this case βw. Like in                            (A), rheobasic stimulation (minimum Istim                            eliciting ≥1 spike) elicited a single spike at short latency in                            class 2 and 3 neurons compared with slow repetitive spiking in class 1                            neurons. Despite reproducing the discontinuous                            f–I curve, the 2D model could not reproduce                            the phasic-spiking pattern. (C) Phasic-spiking was generated by adding                            slow adaptation, thus giving a 3D model described by C                                dV/dt = Istim−g¯fast                            m∞(V)(V−ENa)−g¯sloww(V−EK)−gleak(V−Eleak)−gadapta(V−EK)                            and  where a controls activation of                            adaptation and                            g¯adapt = 0.5                                mS/cm2,                            φa = 0.05                                ms−1,                            βa = −40                            mV, and                            γa = 10                            mV. Bottom traces show single-spike elicited by second stimulus applied                            shortly after the end of first stimulus, which suggests that adaptation                            slowly shifts the neuron from class 2 towards class 3 excitability. (D)                            Firing rate (color) is plotted against Istim                            and βw. Separable regions of the                            graph correspond to different classes of excitability. Neuronal                            classification is based on which class of excitability is predominant                            (i.e., exhibited over the broadest range of                            Istim) and is indicated above the                        graph.
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC2551735&req=5

pcbi-1000198-g001: Hodgkin's three classes of neuronal excitability. (A) Sample responses from spinal lamina I neurons representing each of Hodgkin's three classes. Hodgkin's classification is based on the f–I curve which is continuous (class 1), discontinuous (class 2), or undefined because measurement of firing rate requires at least two spikes (class 3). Data points comprising a single spike (ss) are indicated with open symbols in (A) or gray shading in (B–D). (B) Each cell class could be reproduced in a Morris-Lecar model by varying a single parameter, in this case βw. Like in (A), rheobasic stimulation (minimum Istim eliciting ≥1 spike) elicited a single spike at short latency in class 2 and 3 neurons compared with slow repetitive spiking in class 1 neurons. Despite reproducing the discontinuous f–I curve, the 2D model could not reproduce the phasic-spiking pattern. (C) Phasic-spiking was generated by adding slow adaptation, thus giving a 3D model described by C dV/dt = Istim−g¯fast m∞(V)(V−ENa)−g¯sloww(V−EK)−gleak(V−Eleak)−gadapta(V−EK) and where a controls activation of adaptation and g¯adapt = 0.5 mS/cm2, φa = 0.05 ms−1, βa = −40 mV, and γa = 10 mV. Bottom traces show single-spike elicited by second stimulus applied shortly after the end of first stimulus, which suggests that adaptation slowly shifts the neuron from class 2 towards class 3 excitability. (D) Firing rate (color) is plotted against Istim and βw. Separable regions of the graph correspond to different classes of excitability. Neuronal classification is based on which class of excitability is predominant (i.e., exhibited over the broadest range of Istim) and is indicated above the graph.
Mentions: Spinal sensory neurons fall into several categories based on spiking pattern [14]–[18]. Tonic-, phasic-, and single-spiking lamina I neurons exhibit the characteristic features of class 1, 2, and 3 excitability, respectively, based on their f–I curves (Figure 1A). Spiking pattern is related to, but not synonymous with, Hodgkin's classification scheme. For instance, phasic-spiking neurons are not class 2 because they stop spiking before the end of stimulation, but the fact that they stop spiking so abruptly suggests that they cannot maintain spiking below a certain rate, which is consistent with a discontinuous (class 2) f–I curve; in contrast, adaptation causes tonic-spiking neurons to spike more slowly but without stopping, consistent with a continuous (class 1) f–I curve.

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