Impact of Fast Sodium Channel Inactivation on Spike Threshold Dynamics and Synaptic Integration

Neurons spike when their membrane potential exceeds a threshold value. In central neurons, the spike threshold is not constant but depends on the stimulation. Thus, input-output properties of neurons depend both on the effect of presynaptic spikes on the membrane potential and on the dynamics of the spike threshold. Among the possible mechanisms that may modulate the threshold, one strong candidate is Na channel inactivation, because it specifically impacts spike initiation without affecting the membrane potential. We collected voltage-clamp data from the literature and we found, based on a theoretical criterion, that the properties of Na inactivation could indeed cause substantial threshold variability by itself. By analyzing simple neuron models with fast Na inactivation (one channel subtype), we found that the spike threshold is correlated with the mean membrane potential and negatively correlated with the preceding depolarization slope, consistent with experiments. We then analyzed the impact of threshold dynamics on synaptic integration. The difference between the postsynaptic potential (PSP) and the dynamic threshold in response to a presynaptic spike defines an effective PSP. When the neuron is sufficiently depolarized, this effective PSP is briefer than the PSP. This mechanism regulates the temporal window of synaptic integration in an adaptive way. Finally, we discuss the role of other potential mechanisms. Distal spike initiation, channel noise and Na activation dynamics cannot account for the observed negative slope-threshold relationship, while adaptive conductances (e.g. K+) and Na inactivation can. We conclude that Na inactivation is a metabolically efficient mechanism to control the temporal resolution of synaptic integration

A Threshold Equation for Action Potential Initiation

In central neurons, the threshold for spike initiation can depend on the stimulus and varies between cells and between recording sites in a given cell, but it is unclear what mechanisms underlie this variability. Properties of ionic channels are likely to play a role in threshold modulation. We examined in models the influence of Na channel activation, inactivation, slow voltage-gated channels and synaptic conductances on spike threshold. We propose a threshold equation which quantifies the contribution of all these mechanisms. It provides an instantaneous time-varying value of the threshold, which applies to neurons with fluctuating inputs. We deduce a differential equation for the threshold, similar to the equations of gating variables in the Hodgkin-Huxley formalism, which describes how the spike threshold varies with the membrane potential, depending on channel properties. We find that spike threshold depends logarithmically on Na channel density, and that Na channel inactivation and K channels can dynamically modulate it in an adaptive way: the threshold increases with membrane potential and after every action potential. Our equation was validated with simulations of a previously published multicompartemental model of spike initiation. Finally, we observed that threshold variability in models depends crucially on the shape of the Na activation function near spike initiation (about −55 mV), while its parameters are adjusted near half-activation voltage (about −30 mV), which might explain why many models exhibit little threshold variability, contrary to experimental observations. We conclude that ionic channels can account for large variations in spike threshold

Dynamique de l'excitabilité neuronale: approches théorique et numérique

Neurons generate electrical spikes in an all-or-none manner: a stereotypical action potential is produced and propagated whenever the stimulus amplitude is large enough, and not triggered otherwise. The minimal amplitude above which a spike is initiated is called the excitability threshold. Recent in vivo experiments have shown that this threshold can be highly variable. Moreover, it has been observed that the threshold can be adapted to the recent membrane activity history. These observations were of particular interest because they seemed to challenge fundamental hypotheses in the biophysics of excitability, and classical conceptions of synaptic integration. We raised then the following questions: How and to what extent do the different biophysical excitability mechanisms contribute to threshold variability? More specifically, what is the impact of sodium channel inactivation on spike threshold dynamics? We have tackled these questions by analyzing and simulating different mathematical models of neuronal excitability. First, we have observed that standard models can account for the significant threshold variability. This variability can be predicted from the dynamics of the biophysical excitability variables. Secondly, we have confirmed that sodium channel inactivation can account for the different threshold characteristics. Thus, our work confirms the relevance of threshold models for describing the dynamics of neuronal excitability.Les neurones émettent des impulsions électriques suivant une loi dite ''tout-ou-rien'' : un potentiel d'action stéréotypé est généré et propagé pour des amplitudes suffisamment grandes du stimulus, autrement aucune décharge n'a lieu. L'amplitude minimale au-delà de laquelle une impulsion est générée est appelée seuil d'excitabilité. Des expériences in vivo récentes, dans lesquelles l'activité membranaire des neurones du système nerveux central a été enregistrée, ont mis en évidence une variabilité significative de ce seuil. De plus, il a été observé une adaptation du seuil à la dynamique de l'activité membranaire précédant l'initiation des impulsions. Ces observations nous ont intéressées car elles concernaient à la fois les hypothèses fondamentales de la biophysique de l'excitabilité et les conceptions classiques de l'intégration synaptique. Nous nous sommes alors demandé dans quelle mesure et comment les différents mécanismes biophysiques impliqués dans l'excitabilité contribuent à la variabilité du seuil. Nous nous sommes aussi demandé quelle est l'influence spécifique sur la dynamique du seuil d'un mécanisme classique de régulation de la décharge, l'inactivation du canal sodium. Nous avons abordé ces questions à partir d'analyses mathématiques et de simulations numériques de modèles d'excitabilité. Nous avons montré qu'il est possible d'obtenir un seuil variable dans le cadre des hypothèses classiques et de le prédire quantitativement à partir des variables biophysiques de l'excitabilité. Nous avons aussi confirmé que l'inactivation du canal sodium permet de rendre compte des différentes caractéristiques du seuil. Ainsi, notre travail confirme la pertinence des modèles à seuil pour décrire la dynamique de l'excitabilité neuronale

Dynamique de l'excitabilité neuronale (approches théorique et numérique)

PARIS5-BU Méd.Cochin (751142101) / SudocSudocFranceF