A Small Fraction of Strongly Cooperative Sodium Channels Boosts Neuronal Encoding of High Frequencies

Abstract

Generation of action potentials (APs) is a crucial step in neuronal information processing. Existing biophysical models for AP generation almost universally assume that individual voltage-gated sodium channels operate statistically independently, and their avalanche-like opening that underlies AP generation is coordinated only through the transmembrane potential. However, biological ion channels of various types can exhibit strongly cooperative gating when clustered. Cooperative gating of sodium channels has been suggested to explain rapid onset dynamics and large threshold variability of APs in cortical neurons. It remains however unknown whether these characteristic properties of cortical APs can be reproduced if only a fraction of channels express cooperativity, and whether the presence of cooperative channels has an impact on encoding properties of neuronal populations. To address these questions we have constructed a conductance-based neuron model in which we continuously varied the size of a fraction of sodium channels expressing cooperativity and the strength of coupling between cooperative channels . We show that starting at a critical value of the coupling strength , the activation curve of sodium channels develops a discontinuity at which opening of all coupled channels becomes an all-or-none event, leading to very rapid AP onsets. Models with a small fraction, , of strongly cooperative channels generate APs with the most rapid onset dynamics. In this regime APs are triggered by simultaneous opening of the cooperative channel fraction and exhibit a pronounced biphasic waveform often observed in cortical neurons. We further show that presence of a small fraction of cooperative Na+ channels significantly improves the ability of neuronal populations to phase-lock their firing to high frequency input fluctuation. We conclude that presence of a small fraction of strongly coupled sodium channels can explain characteristic features of cortical APs and has a functional impact of enhancing the spike encoding of rapidly varying signals.

Action potential initiation in a multi-compartmental model with cooperatively gating Na channels in the axon initial segment

“…Third, it is assumed that only a fraction (percentage, p) of the Na + channels cooperatively gate in the given membrane surface area. The activation kinetics of the cooperative Na V channels was explained in detail in the previous paper (Huang et al 2012). Our study extends the findings presented in the previous paper by implementing the framework for cooperative activity in each of the AIS segments in our multi-compartmental model.…”

“…in cortical neurons (Naundorf et al 2005a(Naundorf et al , 2006 can be associated high cut-off frequencies in physiological conditions. It is also reported that cooperative gating kinetics, when implemented in classical Hodgkin-Huxley formulations, can indeed reproduce two most important effects of the cortical neuron dynamics: rapid AP onsets and threshold variability (Huang et al 2012). Therefore, it is alluring to test this hypothesis on a more realistic neuron model, and i.e.…”

“…The basis of the model in this paper was previously established by Huang et al (2012) to study the effects of cooperativity on a single-compartment model. First of all, it is assumed that a Na V channel is coupled to K neighboring channels.…”

“…opening) of one channel triggers the activity (e.g. opening) of a certain fraction of its neighbors and hence, these groups of channels behave as a unit (Naundorf et al 2006;Huang et al 2012). Although there is no direct evidence supporting the hypothesis up to date, there are many reports of similar type of activity for various kinds of ion channels.…”

The interplay between cooperativity and diversity in model threshold ensembles

“…a particular potential window for the ion channels in a cell membrane [3,12,13]. A sigmoidal dependence between the system response (conductance, ligand binding, etc.)…”