104 



HANDBOOK OF PHYSIOLOGY ^ NEUROPHYSIOLOGY I 



J_ 



-100 



IMPULSE 



Fig. 24 



r\f 1 



-J V 



V ^ 



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'''/////,V.\//////^/- 



LONGITUDINAL 

 CURRENT 



FIG. 23. Diagrams showing tiie spatial and temporal distribution of the membrane potential, V, 

 the longitudinal current, li, and the membrane current, Im- The curves for I^ and Im were obtained 

 from the upper curve for V by the graphical method of determining derivatives. 



FIG. i\. Simultaneous recording of the membrane action potential (V) and the membrane cur- 

 rent (Im). The width of the middle pool was about 2 mm. The potential drop across the resistor r 

 was taken as the measure of the meinbrane current. Temperature, 20°C. 



These equations show that the membrane current of 

 a uniform axon is proportional to the second deriva- 

 tive (with respect to either time or space) of the mem- 

 brane action potential [cf. Katz & Schmitt (73)]. It 

 should be pointed out in this connection that equa- 

 tions C9-2) were derived without any assumption as to 

 the behavior of the resting or active membrane. These 

 equations fail to hold only when the axoplasm dis- 

 obeys Ohm's law or when the propae;ation of the im- 

 pulse is macroscopicalh' nonuniform. 



Figure 23 shows the space and time patterns of the 

 membrane potential, the longitudinal current and the 

 membrane current as calculated by equations (9-1) 

 and (9-2). To emphasize the similarity between the 

 space pattern and the time course of the action po- 

 tential, the impulse is assumed in this figure to travel 

 from the right-hand end of the axon to the left. The 

 resistance r; is assumed to be 1.5X10^ ohm per cm 

 [cf. Schmitt (106)] and the velocity to be 15 m per sec. 

 It is seen that the longitudinal current is diphasic and 

 the membrane current is triphasic. It is simple to 

 prove that the total area under the curve for the longi- 



tudinal current or under the curve for the memijrane 

 current has to be equal to zero. 



The upper part of figure 24 shows an approximate 

 method of recording the membrane current of the 

 giant axon of the squid. A giant axon is mounted 

 across three pools of sea water separated by two nar- 

 row partitions. The large lateral pools are directly 

 grounded, and the small middle pool is grounded 

 through a small resistor. The membrane current flow- 

 ing through the portion of the fiber in the middle 

 pool is measured by amplifying a small potential drop 

 across the resistor between the middle pool and 

 ground. In order to obtain a simultaneous recording of 

 the membrane action potential, a microelectrode is 

 inserted into the portion of the axon in the middle 

 pool. The axon is excited by a shock applied near its 

 end. The record presented in the figure shows that 

 the temporal relation between the action potential 

 and the membrane current is very similar to what has 

 been expected from the results of the calculations in 

 figure 23. 



W^e shall now discuss the field of potential in the 



