Theoretical Effect of Temperature on Threshold in the Hodgkin-Huxley Nerve Model

Abstract

In the squid giant axon, Sjodin and Mullins, using 1 msec duration pulses, found a decrease of threshold with increasing temperature, while Guttman, using 100 msec pulses, found an increase. Both results are qualitatively predicted by the Hodgkin-Huxley model. The threshold versus temperature curve varies so much with the assumptions made regarding the temperature-dependence of the membrane ionic conductances that quantitative comparison between theory and experiment is not yet possible. For very short pulses, increasing temperature has 2 effects. (1) At lower temperatures the decrease of relaxation time of Na activation (m) relative to the electrical (RC) relaxation time favors excitation and decreases threshold. (2) For higher temperatures, effect (1) saturates, but the decreasing relaxation times of Na inactivation (h) and K activation (n) favor accommodation and increased threshold. The result is a U-shaped threshold temperature curve. R. Guttman has obtained such U-shaped curves for 50 usec pulses. Assuming higher ionic conductances decreases the electrical relaxation time and shifts the curve to the right along the temperature axis. Making the conductances increase with temperature flattens the curve. Using very long pulses favors effect (2) over (1) and makes threshold increase monotonically with temperature.