Neural repetitive firing: modifications of the Hodgkin-Huxley axon suggested by experimental results from crustacean axons

Abstract

The Hodgkin-Huxley equations for space-clamped squid axon (18 degrees C) have been modified to approximate voltage clamp data from repetitive-firing crustacean walking leg axons and activity in response to constant current stimulation has been computed. The m infinity and h infinity parameters of the sodium conductance system were shifted along the voltage axis in opposite directions so that their relative overlap was increased approximately 7 mV. Time constants tau m and tau h, were moved in a similar manner. Voltage-dependent parameters of delayed potassium conductance, n infinity and tau n, were shifted 4.3 mV in the positive direction and tau n was uniformly increased by a factor of 2. Leakage conductance and capacitance were unchanged. Repetitive activity of this modified circuit was qualitatively similar to that of the standard model. A fifth branch was added to the circuit representing a transient potassium conductance system present in the repetitive walking leg axons and in other repetitive neurons. This model, with various parameter choices, fired repetitively down to approximately 2 spikes/s and up to 350/s. The frequency vs. stimulus current plot could be fit well by a straight line over a decade of the low frequency range and the general appearance of the spike trains was similar to that of other repetitive neurons. Stimulus intensities were of the same order as those which produce repetitive activity in the standard Hodgkin-Huxley axon. The repetitive firing rate and first spike latency (utilization time) were found to be most strongly influenced by the inactivation time constant of the transient potassium conductance (tau b), the delayed potassium conductance (tau n), and the value of leakage conductance (gL). The model presents a mechanism by which stable low frequency discharge can be generated by millisecond-order membrane conductance changes.

Ion channel degeneracy enables robust and tunable neuronal firing rates

“…Model equations are described in ref. 3. Briefly, the model is composed of a leak current I leak , a transient sodium current I Na , a delayed-rectifier potassium current I Kd , and a transient A-type potassium current I A .…”

“…Experimentally, this means the frequency-input current (or FI) curve has a specific shape, called Type I, such that firing frequency smoothly approaches zero at current threshold (1-6). By contrast, so-called Type II neurons have a lower bound in their firing frequency and move abruptly from quiescence to fast spiking, with this transition visible as a sharp jump in the FI curve at threshold (1,3,5).Type I behavior is physiologically unlikely with a minimal set of membrane currents such as the voltage-gated sodium and delayed-rectifier potassium currents in the standard squid giant axon Hodgkin-Huxley model, which is Type II. Classic experimental (1, 7) and theoretical studies (3-5, 8, 9) revealed that a Type II membrane (such as a squid giant axon) can be turned into a Type I membrane by adding an inactivating (A-type) potassium conductance, I A .…”

“…For a neuron to represent continuously varying signals in its firing rate, it must be able to fire at low, high, and all intermediate frequencies. Experimentally, this means the frequency-input current (or FI) curve has a specific shape, called Type I, such that firing frequency smoothly approaches zero at current threshold (1)(2)(3)(4)(5)(6). By contrast, so-called Type II neurons have a lower bound in their firing frequency and move abruptly from quiescence to fast spiking, with this transition visible as a sharp jump in the FI curve at threshold (1,3,5).…”

Responses of cutaneous mechanoreceptors within fingerpad to stimulus information for tactile softness sensation of materials

“…channels in higher organisms have been shown to regulate the discharge patterns of neurons, and the transient K? channels (Connor and Stevens 1971;Connor et al 1977;Wellnitz 2010) were then added to the original HH model. Thus, the modulation model from the HH equation systems (Hodgkin and Huxley 1952) GðV; m; n; hÞ ¼ G Na m…”

“…channels were referred to Hodgkin and Huxley (1952) and Connor et al (1977), and e(t) the normal Gaussian noises. The drive current I c was the sensing current by external stimulus (lA/cm 2 ), which was calculated by Eq.…”