Ion Channel Density Regulates Switches between Regular and Fast Spiking in Soma but Not in Axons

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-I_stim) and, thus, an arbitrarily low frequency at threshold current; Type 2 (fast spiking) shows a discontinuous f-I_stim 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. All activity of the brain is manifested in electrical oscillatory patterns, shaped by the firing dynamics of the many neurons forming the brain networks. The underlying mechanisms of the firing pattern in the single neurons are still not fully understood. The distribution and identity of different channel types have been suggested as critical factors. We have suggested that the density of channels in the membrane is a fundamental complementary mechanism. 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. Here we extend the analysis to two axon membranes. Unexpectedly, both show that channel density alterations do not cause switches between different firing behaviours. We believe that this is an important property of axon membranes, explaining their limited flexibility.