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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 currentcan also produce class 1 excitability.(A) Inactivation of an A-type K+ current bysubthreshold depolarization should shift the balance of inward andoutward currents the same way that depolarization-induced activation ofan inward current does, and is therefore predicted to encourage class 1excitability. To test this, we warped the w-clineto give it a region of negative slope at subthreshold potentials (see[55]); this was done by changing Equation5 so that  whereβw = −10mV,γw = 10mV,βw* = −60mV,γw* =  = 20mV, and ξ = 0.1. Under theseconditions, the V- and w-clinesintersected tangentially at rheobasic stimulation. (B) This phase planegeometry resulted in an SNIC bifurcation and class 1 excitability, aspredicted. (C) Inactivation of the A-type K+ currentat subthrehsold potentials gave a region of negative slope on the steadystate I–V curve thatoverlapped the apex of the instantaneousI–V curve.
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pcbi-1000198-g010: Depolarization-induced inactivation of a subthreshold outward currentcan also produce class 1 excitability.(A) Inactivation of an A-type K+ current bysubthreshold depolarization should shift the balance of inward andoutward currents the same way that depolarization-induced activation ofan inward current does, and is therefore predicted to encourage class 1excitability. To test this, we warped the w-clineto give it a region of negative slope at subthreshold potentials (see[55]); this was done by changing Equation5 so that whereβw = −10mV,γw = 10mV,βw* = −60mV,γw* =  = 20mV, and ξ = 0.1. Under theseconditions, the V- and w-clinesintersected tangentially at rheobasic stimulation. (B) This phase planegeometry resulted in an SNIC bifurcation and class 1 excitability, aspredicted. (C) Inactivation of the A-type K+ currentat subthrehsold potentials gave a region of negative slope on the steadystate I–V curve thatoverlapped the apex of the instantaneousI–V curve.

Mentions: If the balance of fast and slow currents at perithreshold potentials is thecrucial determinant of excitability, then perithresholdinactivation of a slow outward current (e.g., an A-typeK+ current, IK,A) shouldencourage class 1 excitability the same way perithreshold activation of a slowinward current does. To test this, we incorporatedIK,A by warping the w-cline tocreate a 2D model similar to that of Wilson [29]. Rather thaninitiating spikes through a Hopf bifurcation, the V-clineintercepted the negatively sloping region of the w-clinetangentially (Figure 10A)and repetitive spiking was generated through an SNIC bifurcation (Figure 10B), which resulted ina continuous f–I curve (not shown) typical of class 1excitability. Furthermore, inactivation of IK,Aintroduced a region of negative slope into the steady stateI–V curve that overlapped the apex of theinstantaneous I–V curve (Figure 10C; compare with Figure 9). The same results were found ifIK,A was explicitly incorporated to produce a 3Dmodel (data not shown). Thus, IK,A increasedrheobase but its slow inactivation as voltage passed through threshold amountedto a slow positive feedback process that encouraged class 1 excitability. Theconverse has been shown in medial superior olive neurons, where inactivation ofINa encourages coincidence detection associatedwith 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 currentcan also produce class 1 excitability.(A) Inactivation of an A-type K+ current bysubthreshold depolarization should shift the balance of inward andoutward currents the same way that depolarization-induced activation ofan inward current does, and is therefore predicted to encourage class 1excitability. To test this, we warped the w-clineto give it a region of negative slope at subthreshold potentials (see[55]); this was done by changing Equation5 so that  whereβw = −10mV,γw = 10mV,βw* = −60mV,γw* =  = 20mV, and ξ = 0.1. Under theseconditions, the V- and w-clinesintersected tangentially at rheobasic stimulation. (B) This phase planegeometry resulted in an SNIC bifurcation and class 1 excitability, aspredicted. (C) Inactivation of the A-type K+ currentat subthrehsold potentials gave a region of negative slope on the steadystate I–V curve thatoverlapped the apex of the instantaneousI–V curve.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-1000198-g010: Depolarization-induced inactivation of a subthreshold outward currentcan also produce class 1 excitability.(A) Inactivation of an A-type K+ current bysubthreshold depolarization should shift the balance of inward andoutward currents the same way that depolarization-induced activation ofan inward current does, and is therefore predicted to encourage class 1excitability. To test this, we warped the w-clineto give it a region of negative slope at subthreshold potentials (see[55]); this was done by changing Equation5 so that whereβw = −10mV,γw = 10mV,βw* = −60mV,γw* =  = 20mV, and ξ = 0.1. Under theseconditions, the V- and w-clinesintersected tangentially at rheobasic stimulation. (B) This phase planegeometry resulted in an SNIC bifurcation and class 1 excitability, aspredicted. (C) Inactivation of the A-type K+ currentat subthrehsold potentials gave a region of negative slope on the steadystate I–V curve thatoverlapped the apex of the instantaneousI–V curve.
Mentions: If the balance of fast and slow currents at perithreshold potentials is thecrucial determinant of excitability, then perithresholdinactivation of a slow outward current (e.g., an A-typeK+ current, IK,A) shouldencourage class 1 excitability the same way perithreshold activation of a slowinward current does. To test this, we incorporatedIK,A by warping the w-cline tocreate a 2D model similar to that of Wilson [29]. Rather thaninitiating spikes through a Hopf bifurcation, the V-clineintercepted the negatively sloping region of the w-clinetangentially (Figure 10A)and repetitive spiking was generated through an SNIC bifurcation (Figure 10B), which resulted ina continuous f–I curve (not shown) typical of class 1excitability. Furthermore, inactivation of IK,Aintroduced a region of negative slope into the steady stateI–V curve that overlapped the apex of theinstantaneous I–V curve (Figure 10C; compare with Figure 9). The same results were found ifIK,A was explicitly incorporated to produce a 3Dmodel (data not shown). Thus, IK,A increasedrheobase but its slow inactivation as voltage passed through threshold amountedto a slow positive feedback process that encouraged class 1 excitability. Theconverse has been shown in medial superior olive neurons, where inactivation ofINa encourages coincidence detection associatedwith 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