Biophysical basis for three distinct dynamical mechanisms of action potential initiation.
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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.
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PubMed Central - PubMed
Affiliation: Computational Neurobiology Laboratory, Salk Institute, La Jolla, California, United States of America. prescott@neurobio.pitt.edu
ABSTRACT
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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. Related in: MedlinePlus |
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Mentions: In the process of building the model (see Methods), βw was identified as an important parameter given its capacity to convert the model between all three classes of excitability. The biophysical meaning of βw is deferred until Figure 4, after its functional significance has been established. See Figure 8 for the effects of changing other parameters. Therefore, to begin, we explored the effects on the model's f–I curve of systematically varying βw (Figure 1D). The model exhibited class 1 excitability for βw>−10 mV, but class 2 and 3 excitability coexisted for all βw<−10 mV; in other words, class 2 or 3 excitability was exhibited depending on stimulus intensity Istim. This is evident in Figure 1B where, in the model with βw = −13 mV, rheobasic stimulation elicited a single spike while stronger stimulation elicited repetitive spiking. This pattern is characteristic of phasic-spiking spinal lamina I neurons (Figure 1A) and is commonly observed in other “class 2” neurons including the squid giant axon [2], trigeminal motoneurons [19], and fast-spiking neocortical interneurons [10],[20]. Conversely, “class 3” neurons should theoretically begin spiking repetitively if given extremely strong stimulation. In reality, strong stimulation elicits, at most, a burst of 2–4 high frequency spikes in single-spiking spinal lamina I neurons [14], which is consistent with Hodgkin's classification in which class 3 neurons are said to “repeat only with difficulty or not at all” [5]. Responses to strong stimulation can be more accurately reproduced in the model by incorporating slow processes like cumulative Na+ channel inactivation, but such processes were not included in the models analyzed here in order to keep the model as simple as possible and because such strong stimulation is arguably unphysiological in the first place. |
View Article: PubMed Central - PubMed
Affiliation: Computational Neurobiology Laboratory, Salk Institute, La Jolla, California, United States of America. prescott@neurobio.pitt.edu