Biophysical Basis for Three Distinct Dynamical Mechanisms of Action Potential Initiation

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.

Ion channel degeneracy enables robust and tunable neuronal firing rates

“…7A, Middle Insets) leading to slow spiking characteristic of a Type I membrane. Spiking occurs through a Saddle Node on Invariant Circle (SNIC) bifurcation, as reported in the literature (5,8,28). Fig.…”

“…At low g A , Type II firing (Fig. 7, Left) occurs due to an Andronov-Hopf bifurcation at a critical value of applied current, I Hopf , as is widely known from previous analyses (5,8,19,20,24,25,28,42,43).…”

“…The task of relating the shape of an FI curve to the dynamics of individual conductances is complicated by the nonlinear nature of voltage-gated conductances, and a large literature on this problem exists (2,5,8,9,(22)(23)(24)(25)(26)(27)(28)(29)(30). However, the observation that two completely different currents can induce qualitatively similar changes in FI curve shape suggests a general underlying mechanism.…”

“…The sign, magnitude, and voltage dependence of g f and g s account for the dynamics of a spike. In particular, the sign of the DIC curve determines whether it is restorative or regenerative, that is, whether it tends to provide negative or positive feedback, respectively, via membrane potential variations (8,21,22,28).…”

“…Previous work relies on planar reductions of conductance-based models to analyze dynamics in a phase plane (4,5,8,24,25,28,(38)(39)(40)(41). Our approach here is quite different and, we hope, more intuitive to physiologists who think about neuronal dynamics in terms of contributions of voltagedependent ionic currents at different timescales.…”