CONDUCTION OF THE NERVE IMPULSE 



97 



Fio. 1 8. Variations of the membrane potential of a single 

 node (V) caused by linearly rising voltage pulses (S). The 

 arrangement of fig. i6 was used. In records A' and B' the miss- 

 ing portions of the potential trace (V) indicate production of 

 action potentials of about lOO mv in amplitude. The trace for 

 the stimulating voltage (S) was blanked at too cps. Large 

 motor nerve fiber of the toad. Temperatine, 1 1 °C. [From 

 Tjisaki (127).] 



nodes No and Ni and since the time constant of the 

 membrane is far shorter than the time scale employed 

 in these observations, the time course of the current 

 through the nodal membrane is similar to that of the 

 applied \0lta5e. In records .-1, B, Cand D, an accoino- 

 dative fall in the membrane potential is evident. 

 Each of the paired records. A- A' or B-B', was taken 

 at almost the same stimulus intensity; in one QA or 5) 

 the node failed to respond, and in the other (J' or 

 B') a large action potential was evoked. The peak 

 value of the subthreshold membrane potential in 

 these cases is more erratic than in the experiment of 

 figure 16; it is roughly independent of the rise time of 

 these stimuli. 



In most classical theories of nerve excitation [e.g. 

 Hill C48)], the process of accommodation has been 

 regarded as a gradual rise in the threshold level of 

 the nerve during the period of prolonged d.c. stimula- 

 tion. The direct observations mentioned above 

 indicate that this is not exactly the case. It is due to a 

 secondary change in the property of the membrane 

 which decreases the effectiveness of the current to 

 raise the membrane potential. Undoubtedly, this is 

 related to the phenomenon of delayed rectification 

 described first by Cole (18); he found that the axon 

 membrane of the squid shows a resistance to an 

 outward directed maintained current far smaller than 



that measured with an inward current [see also 

 Hodgkin (53)]. Hodgkin & Huxley (59) attributed 

 this process mainly to an increased permeability of 

 the membrane to potassium ions. In the nodal mem- 

 brane, there is some e\idence indicating that there is 

 a change in the resting potential when the membrane 

 undergoes an accommodative change (127). 



Strength-Duialion Rilalum 



The relation between the threshold intensity of a 

 stimulus and its duration is called a strength-duration 

 or intensity-time relation. In the squid giant axon 

 excited by means of a long internal metal wire elec- 

 trode, the significance of this relation is now very 

 clear. When a rectangular pulse of current is applied 

 to the membrane through the internal electrode, the 

 inembrane potential rises exponentially as described 

 by equation (4-2). If a stimulus which lasts no longer 

 than about 2 msec' (at i4°C) is to initiate an action 

 potential, the membrane potential has to reach the 

 critical level, l\, at the end of the pulse. This leads to 

 the relation 



F, = IRii - e-J-'Rf), 



in which T is the duration of the current pulse, / is 

 the current intensity and RC the time constant of the 

 membrane. Rearranging the terms, we have 



/ 



T = RC log . 



This is known as Blair's equation for strength- 

 duration relation (15). Because of the interaction 

 between the stimulating current and the response of 

 the membrane mentioned abo\e, this equation is 

 only a poor approximation near the rheobase. 



Stimulation of a squid giant a.xon through a glass 

 pipette can be treated in a similar fashion by using the 

 solution of the cable equation for the corresponding 

 conditions. Again the rheobase will be slightly (20 

 to 30 per cent) smaller than that expected from the 

 space and time constants of the resting axon mem- 

 brane. When the duration becomes far shorter than 

 the membrane time constant, another complication 

 (related to the phenomenon of abolition of an action 

 potential to be discussed in the next section) prob- 

 ably sets in. When the current pulse is extremely 

 short, the uncharged membrane on both sides of the 

 site of stimulation is expected to prevent a further rise 

 in potential at the site of stimulation and to suppress 

 the start of an action potential. These factors have 

 not yet been carefully investigated. 



' This figure was kindly supplied by Dr. S. Hagiwara. 



