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Abstract
The threshold firing frequency of a neuron is a characterizing feature of its dynamical behaviour, in turn determining its role in the oscillatory activity of the brain. Two main types of dynamics have been identified in brain neurons. Type 1 dynamics (regular spiking) shows a continuous relationship between frequency and stimulation current (f-Istim) and, thus, an arbitrarily low frequency at threshold current; Type 2 (fast spiking) shows a discontinuous f-Istim relationship and a minimum threshold frequency. In a previous study of a hippocampal neuron model, we demonstrated that its dynamics could be of both Type 1 and Type 2, depending on ion channel density. In the present study we analyse the effect of varying channel density on threshold firing frequency on two well-studied axon membranes, namely the frog myelinated axon and the squid giant axon. Moreover, we analyse the hippocampal neuron model in more detail. The models are all based on voltage-clamp studies, thus comprising experimentally measurable parameters. The choice of analysing effects of channel density modifications is due to their physiological and pharmacological relevance. We show, using bifurcation analysis, that both axon models display exclusively Type 2 dynamics, independently of ion channel density. Nevertheless, both models have a region in the channel-density plane characterized by an N-shaped steady-state current-voltage relationship (a prerequisite for Type 1 dynamics and associated with this type of dynamics in the hippocampal model). In summary, our results suggest that the hippocampal soma and the two axon membranes represent two distinct kinds of membranes; membranes with a channel-density dependent switching between Type 1 and 2 dynamics, and membranes with a channel-density independent dynamics. The difference between the two membrane types suggests functional differences, compatible with a more flexible role of the soma membrane than that of the axon membrane.
Highlights
It is more than 60 years since Alan Hodgkin categorized the firing behaviour in his classical study of isolated axons from the crab Carcinus maenas [1]
Using threshold dynamics and maximum frequency as parameters, he identified two major classes of repetitively firing axons: Class 1 axons start firing with very low frequency at threshold stimulation, yielding a continuous f-Istim relationship, whereas Class 2 axons start firing abruptly with a relatively high frequency at threshold, yielding a discontinuous f-Istim relationship
In a hippocampal soma membrane model study we have shown that altering the ion channel densities can cause the membrane to switch between two qualitatively different firing patterns
Summary
It is more than 60 years since Alan Hodgkin categorized the firing behaviour in his classical study of isolated axons from the crab Carcinus maenas [1]. In accordance with the notation of Tateno and Robinson [7], we in the following use the terms Type 1 and Type 2 dynamics when referring to continuous and discontinuous f-Istim relationships, respectively. This classification takes the threshold dynamics of the regular and fast spiking neurons, and that of the Class 1 and 2 axons, into account, but not all behavioural aspects of these classes [8]
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