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.degree. C) were modified to approximate voltage clamp data from repetitive-firing crustacean [Callinectes sapidus and Cancer magister] walking leg axons, and activity in response to constant current stimulation was computed. The m.infin. and h.infin. [steady state values of membrane voltage functions] parameters of the Na 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 K conductance, n.infin. 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 5th branch was added to the circuit representing a transient K conductance system present in the repetitive walking leg axons and in other repetitive neurons. This model, with various parameter choices, fired repetitively down to .apprx. 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 1st spike latency (utilization time) were most strongly influenced by the inactivation time constant of the transient K conductance (.tau.B), the delayed K 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.