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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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Depolarization-induced inactivation of a subthreshold outward current                            can also produce class 1 excitability.(A) Inactivation of an A-type K+ current by                            subthreshold depolarization should shift the balance of inward and                            outward currents the same way that depolarization-induced activation of                            an inward current does, and is therefore predicted to encourage class 1                            excitability. To test this, we warped the w-cline                            to give it a region of negative slope at subthreshold potentials (see                                [55]); this was done by changing Equation                            5 so that  where                            βw = −10                            mV,                            γw = 10                            mV,                            βw* = −60                            mV,                            γw* =  = 20                            mV, and ξ = 0.1. Under these                            conditions, the V- and w-clines                            intersected tangentially at rheobasic stimulation. (B) This phase plane                            geometry resulted in an SNIC bifurcation and class 1 excitability, as                            predicted. (C) Inactivation of the A-type K+ current                            at subthrehsold potentials gave a region of negative slope on the steady                            state I–V curve that                            overlapped the apex of the instantaneous                                I–V curve.
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pcbi-1000198-g010: Depolarization-induced inactivation of a subthreshold outward current can also produce class 1 excitability.(A) Inactivation of an A-type K+ current by subthreshold depolarization should shift the balance of inward and outward currents the same way that depolarization-induced activation of an inward current does, and is therefore predicted to encourage class 1 excitability. To test this, we warped the w-cline to give it a region of negative slope at subthreshold potentials (see [55]); this was done by changing Equation 5 so that where βw = −10 mV, γw = 10 mV, βw* = −60 mV, γw* =  = 20 mV, and ξ = 0.1. Under these conditions, the V- and w-clines intersected tangentially at rheobasic stimulation. (B) This phase plane geometry resulted in an SNIC bifurcation and class 1 excitability, as predicted. (C) Inactivation of the A-type K+ current at subthrehsold potentials gave a region of negative slope on the steady state I–V curve that overlapped the apex of the instantaneous I–V curve.

Mentions: If the balance of fast and slow currents at perithreshold potentials is the crucial determinant of excitability, then perithreshold inactivation of a slow outward current (e.g., an A-type K+ current, IK,A) should encourage class 1 excitability the same way perithreshold activation of a slow inward current does. To test this, we incorporated IK,A by warping the w-cline to create a 2D model similar to that of Wilson [29]. Rather than initiating spikes through a Hopf bifurcation, the V-cline intercepted the negatively sloping region of the w-cline tangentially (Figure 10A) and repetitive spiking was generated through an SNIC bifurcation (Figure 10B), which resulted in a continuous f–I curve (not shown) typical of class 1 excitability. Furthermore, inactivation of IK,A introduced a region of negative slope into the steady state I–V curve that overlapped the apex of the instantaneous I–V curve (Figure 10C; compare with Figure 9). The same results were found if IK,A was explicitly incorporated to produce a 3D model (data not shown). Thus, IK,A increased rheobase but its slow inactivation as voltage passed through threshold amounted to a slow positive feedback process that encouraged class 1 excitability. The converse has been shown in medial superior olive neurons, where inactivation of INa encourages coincidence detection associated with class 3 excitability [30].


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

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

Depolarization-induced inactivation of a subthreshold outward current                            can also produce class 1 excitability.(A) Inactivation of an A-type K+ current by                            subthreshold depolarization should shift the balance of inward and                            outward currents the same way that depolarization-induced activation of                            an inward current does, and is therefore predicted to encourage class 1                            excitability. To test this, we warped the w-cline                            to give it a region of negative slope at subthreshold potentials (see                                [55]); this was done by changing Equation                            5 so that  where                            βw = −10                            mV,                            γw = 10                            mV,                            βw* = −60                            mV,                            γw* =  = 20                            mV, and ξ = 0.1. Under these                            conditions, the V- and w-clines                            intersected tangentially at rheobasic stimulation. (B) This phase plane                            geometry resulted in an SNIC bifurcation and class 1 excitability, as                            predicted. (C) Inactivation of the A-type K+ current                            at subthrehsold potentials gave a region of negative slope on the steady                            state I–V curve that                            overlapped the apex of the instantaneous                                I–V curve.
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pcbi-1000198-g010: Depolarization-induced inactivation of a subthreshold outward current can also produce class 1 excitability.(A) Inactivation of an A-type K+ current by subthreshold depolarization should shift the balance of inward and outward currents the same way that depolarization-induced activation of an inward current does, and is therefore predicted to encourage class 1 excitability. To test this, we warped the w-cline to give it a region of negative slope at subthreshold potentials (see [55]); this was done by changing Equation 5 so that where βw = −10 mV, γw = 10 mV, βw* = −60 mV, γw* =  = 20 mV, and ξ = 0.1. Under these conditions, the V- and w-clines intersected tangentially at rheobasic stimulation. (B) This phase plane geometry resulted in an SNIC bifurcation and class 1 excitability, as predicted. (C) Inactivation of the A-type K+ current at subthrehsold potentials gave a region of negative slope on the steady state I–V curve that overlapped the apex of the instantaneous I–V curve.
Mentions: If the balance of fast and slow currents at perithreshold potentials is the crucial determinant of excitability, then perithreshold inactivation of a slow outward current (e.g., an A-type K+ current, IK,A) should encourage class 1 excitability the same way perithreshold activation of a slow inward current does. To test this, we incorporated IK,A by warping the w-cline to create a 2D model similar to that of Wilson [29]. Rather than initiating spikes through a Hopf bifurcation, the V-cline intercepted the negatively sloping region of the w-cline tangentially (Figure 10A) and repetitive spiking was generated through an SNIC bifurcation (Figure 10B), which resulted in a continuous f–I curve (not shown) typical of class 1 excitability. Furthermore, inactivation of IK,A introduced a region of negative slope into the steady state I–V curve that overlapped the apex of the instantaneous I–V curve (Figure 10C; compare with Figure 9). The same results were found if IK,A was explicitly incorporated to produce a 3D model (data not shown). Thus, IK,A increased rheobase but its slow inactivation as voltage passed through threshold amounted to a slow positive feedback process that encouraged class 1 excitability. The converse has been shown in medial superior olive neurons, where inactivation of INa encourages coincidence detection associated with class 3 excitability [30].

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