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: To demonstrate the sufficiency of subthreshold currents for determiningexcitability, we explicitly incorporated a subthreshold inward or outwardcurrent by adding an additional term for Isub to the2D model withβw = −10mV (see Equation 7); recall that the 2D model lies at the interface betweenclass 1 and 2 excitability whenβw = −10mV (see Figure 1D). Addingan inward current produced class 1 excitability, whereas adding an outwardcurrent produced class 2 or 3 excitability depending on the magnitude ofgsub (which is controlled by the maximalconductance, ḡsub) (Figure 7A). Withβw = −13mV (like the class 2 model in Figure 1B), the default 3D model was class 2; adding a subthresholdinward or outward current converted it to class 1 or 3, respectively (data notshown). The three classes of excitability can be readily identified from thebifurcation diagrams of the 3D model (Figure 7B; compare with 2D model in Figure 2B). Varyingḡsub affected thef–I curve in this 3D model in exactly the samemanner as varying βw in the 2D model(compare Figure 7C withFigure 1D). Thetransition between class 1 and 2 excitability occurred atḡsub = 0mS/cm2, although that value varied depending onβw (see above). For a given value ofIstim, class 1 and 2 excitability were mutuallyexclusive whereas class 2 and 3 excitability coexisted. Furthermore, the 3Dmodel exhibited constant or variably sized spikes depending on whether the modelwas class 1 or 3, respectively (Figure 7D; compare with Figure 3A and 3B). This demonstrates the sufficiency of subthresholdinward and outward currents for producing class 1 and 3 excitability,respectively. |
View Article: PubMed Central - PubMed
Affiliation: Computational Neurobiology Laboratory, Salk Institute, La Jolla, California, United States of America. prescott@neurobio.pitt.edu