Limits...
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.

Show MeSH

Related in: MedlinePlus

Hodgkin's three classes of neuronal excitability. (A) Sampleresponses from spinal lamina I neurons representing each ofHodgkin's three classes. Hodgkin's classification isbased on the f–I curve which is continuous(class 1), discontinuous (class 2), or undefined because measurement offiring rate requires at least two spikes (class 3). Data pointscomprising a single spike (ss) are indicated with opensymbols in (A) or gray shading in (B–D). (B) Each cell classcould be reproduced in a Morris-Lecar model by varying a singleparameter, in this case βw. Like in(A), rheobasic stimulation (minimum Istimeliciting ≥1 spike) elicited a single spike at short latency inclass 2 and 3 neurons compared with slow repetitive spiking in class 1neurons. Despite reproducing the discontinuousf–I curve, the 2D model could not reproducethe phasic-spiking pattern. (C) Phasic-spiking was generated by addingslow adaptation, thus giving a 3D model described by CdV/dt = Istim−g¯fastm∞(V)(V−ENa)−g¯sloww(V−EK)−gleak(V−Eleak)−gadapta(V−EK)and  where a controls activation ofadaptation andg¯adapt = 0.5mS/cm2,φa = 0.05ms−1,βa = −40mV, andγa = 10mV. Bottom traces show single-spike elicited by second stimulus appliedshortly after the end of first stimulus, which suggests that adaptationslowly shifts the neuron from class 2 towards class 3 excitability. (D)Firing rate (color) is plotted against Istimand βw. Separable regions of thegraph correspond to different classes of excitability. Neuronalclassification is based on which class of excitability is predominant(i.e., exhibited over the broadest range ofIstim) and is indicated above thegraph.
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC2551735&req=5

pcbi-1000198-g001: Hodgkin's three classes of neuronal excitability. (A) Sampleresponses from spinal lamina I neurons representing each ofHodgkin's three classes. Hodgkin's classification isbased on the f–I curve which is continuous(class 1), discontinuous (class 2), or undefined because measurement offiring rate requires at least two spikes (class 3). Data pointscomprising a single spike (ss) are indicated with opensymbols in (A) or gray shading in (B–D). (B) Each cell classcould be reproduced in a Morris-Lecar model by varying a singleparameter, in this case βw. Like in(A), rheobasic stimulation (minimum Istimeliciting ≥1 spike) elicited a single spike at short latency inclass 2 and 3 neurons compared with slow repetitive spiking in class 1neurons. Despite reproducing the discontinuousf–I curve, the 2D model could not reproducethe phasic-spiking pattern. (C) Phasic-spiking was generated by addingslow adaptation, thus giving a 3D model described by CdV/dt = Istim−g¯fastm∞(V)(V−ENa)−g¯sloww(V−EK)−gleak(V−Eleak)−gadapta(V−EK)and where a controls activation ofadaptation andg¯adapt = 0.5mS/cm2,φa = 0.05ms−1,βa = −40mV, andγa = 10mV. Bottom traces show single-spike elicited by second stimulus appliedshortly after the end of first stimulus, which suggests that adaptationslowly shifts the neuron from class 2 towards class 3 excitability. (D)Firing rate (color) is plotted against Istimand βw. Separable regions of thegraph correspond to different classes of excitability. Neuronalclassification is based on which class of excitability is predominant(i.e., exhibited over the broadest range ofIstim) and is indicated above thegraph.

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 class1, 2, and 3 excitability, respectively, based on theirf–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 endof stimulation, but the fact that they stop spiking so abruptly suggests thatthey cannot maintain spiking below a certain rate, which is consistent with adiscontinuous (class 2) f–I curve; in contrast,adaptation causes tonic-spiking neurons to spike more slowly but withoutstopping, consistent with a continuous (class 1) f–Icurve.


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) Sampleresponses from spinal lamina I neurons representing each ofHodgkin's three classes. Hodgkin's classification isbased on the f–I curve which is continuous(class 1), discontinuous (class 2), or undefined because measurement offiring rate requires at least two spikes (class 3). Data pointscomprising a single spike (ss) are indicated with opensymbols in (A) or gray shading in (B–D). (B) Each cell classcould be reproduced in a Morris-Lecar model by varying a singleparameter, in this case βw. Like in(A), rheobasic stimulation (minimum Istimeliciting ≥1 spike) elicited a single spike at short latency inclass 2 and 3 neurons compared with slow repetitive spiking in class 1neurons. Despite reproducing the discontinuousf–I curve, the 2D model could not reproducethe phasic-spiking pattern. (C) Phasic-spiking was generated by addingslow adaptation, thus giving a 3D model described by CdV/dt = Istim−g¯fastm∞(V)(V−ENa)−g¯sloww(V−EK)−gleak(V−Eleak)−gadapta(V−EK)and  where a controls activation ofadaptation andg¯adapt = 0.5mS/cm2,φa = 0.05ms−1,βa = −40mV, andγa = 10mV. Bottom traces show single-spike elicited by second stimulus appliedshortly after the end of first stimulus, which suggests that adaptationslowly shifts the neuron from class 2 towards class 3 excitability. (D)Firing rate (color) is plotted against Istimand βw. Separable regions of thegraph correspond to different classes of excitability. Neuronalclassification is based on which class of excitability is predominant(i.e., exhibited over the broadest range ofIstim) and is indicated above thegraph.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1000198-g001: Hodgkin's three classes of neuronal excitability. (A) Sampleresponses from spinal lamina I neurons representing each ofHodgkin's three classes. Hodgkin's classification isbased on the f–I curve which is continuous(class 1), discontinuous (class 2), or undefined because measurement offiring rate requires at least two spikes (class 3). Data pointscomprising a single spike (ss) are indicated with opensymbols in (A) or gray shading in (B–D). (B) Each cell classcould be reproduced in a Morris-Lecar model by varying a singleparameter, in this case βw. Like in(A), rheobasic stimulation (minimum Istimeliciting ≥1 spike) elicited a single spike at short latency inclass 2 and 3 neurons compared with slow repetitive spiking in class 1neurons. Despite reproducing the discontinuousf–I curve, the 2D model could not reproducethe phasic-spiking pattern. (C) Phasic-spiking was generated by addingslow adaptation, thus giving a 3D model described by CdV/dt = Istim−g¯fastm∞(V)(V−ENa)−g¯sloww(V−EK)−gleak(V−Eleak)−gadapta(V−EK)and where a controls activation ofadaptation andg¯adapt = 0.5mS/cm2,φa = 0.05ms−1,βa = −40mV, andγa = 10mV. Bottom traces show single-spike elicited by second stimulus appliedshortly after the end of first stimulus, which suggests that adaptationslowly shifts the neuron from class 2 towards class 3 excitability. (D)Firing rate (color) is plotted against Istimand βw. Separable regions of thegraph correspond to different classes of excitability. Neuronalclassification is based on which class of excitability is predominant(i.e., exhibited over the broadest range ofIstim) and is indicated above thegraph.
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 class1, 2, and 3 excitability, respectively, based on theirf–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 endof stimulation, but the fact that they stop spiking so abruptly suggests thatthey cannot maintain spiking below a certain rate, which is consistent with adiscontinuous (class 2) f–I curve; in contrast,adaptation causes tonic-spiking neurons to spike more slowly but withoutstopping, consistent with a continuous (class 1) f–Icurve.

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