The threshold conditions for initiation of action potentials by excitable cells.

1. The relation between the strength and duration of a just threshold stimulus (strength-duration curve) is analysed for an excitable membrane polarized uniformly and for an excitable cable polarized at one point.2. The effect on the strength-duration curve of non-linearity in the membrane current-voltage curve has been analysed. The strength-duration curve can be derived if the membrane current-voltage relation is independent of time. The effects of changes in the current-voltage curve with time due to the existence of a finite membrane activation time and membrane accommodation are analysed.3. The strength-duration curve for the Hodgkin-Huxley membrane equations (Hodgkin & Huxley, 1952) is compared to that of Hill's (1936) two-time constant model.4. The relation between membrane current-voltage curves and those for a point-polarized cable are derived for the steady-state condition. The cable properties tend to linearize the current-voltage curve and to sharpen the voltage threshold.5. The strength-duration curve for a point-polarized cable whose membrane obeys the Hodgkin-Huxley equations is computed numerically. There is an additional large effect on the cable strength-duration curve arising from the redistribution of charge during passage of a constant current; and the resulting strength-duration curve lies within the range of curves predicted by Hill's model.6. The conditions required for a constant charge threshold (Hodgkin & Rushton, 1946) are shown to be satisfied for short, intense stimuli applied to a cable at one point.7. The results are discussed with reference to the experimental studies available.