CONDUCTION OF THE NERVE IMPULSE 



103 



FIG. 22. Demonstration ol the dependence of the conduction 

 velocity of a crab nerve fiber upon the resistance of the external 

 medium. A and C. Action potential recorded with sea water 

 covering 95 per cent of the intermediate conduction distance. 

 B and D. Fiber completely immersed in oil. Conduction 

 distance, 1 3 mm. Time in msec. [From Hodgkin (52).] 



velocity was prompt and completely reversiijle; there 

 seems to be little doubt, therefore, that the effect is due 

 to the increased electric resistance of the surrounding 

 medium. 



The velocity of a nerve impulse is determined by a 

 mechanism involving the interplay of many factors. In 

 a uniform axon immersed in a large volume of highly 

 conducting fluid medium, the mechanism determin- 

 ing the conduction velocity is as follows. In the inactive 

 area of the axon ahead of the active area, the mem- 

 brane is traversed by an outward current (see fig. 23) 

 the intensity of which depends on the velocity of the 

 impulse. This current is supplied by the active area 

 immediately behind the active-inactive boundary. 

 The membrane current in the active area is inward 

 (see fig. 23), and this inward current tends to delay 

 the rate of potential rise in the active region. If the 

 membrane is capable of developing an action poten- 

 tial rapidly in spite of the existence of a strong inward 

 current, the velocity tends to be high. If the capacity 

 and the conductance of the resting membrane are 

 large, the active area of the membrane has to supply 

 a strong current to bring the membrane potential of 

 the inactive area up to the critical level, and conse- 



quently the velocity tends to be small. A large longi- 

 tudinal resistance (small fiber diameter) is expected to 

 have the same effect upon the velocity as an increased 

 external resistance. 



Hodgkin & Huxley (59) determined the relation 

 between the membrane potential and the membrane 

 conductance on the squid axon. By using the cable 

 equation and a set of empirical formulae relating the 

 membrane potential and the membrane conductance, 

 they calculated the velocity and obtained a solution 

 of the right order of magnitude. 



We have discussed in a previous section (see p. 83) 

 the cable properties of a uniform invertebrate axon. 

 In a uniform axon carrying an impulse of a constant 

 velocity, there are certain features that deserve further 

 discussion. First of all, it should be pointed out that 

 there is an inseparable relationship between the 

 spatial distribution of the membrane potential and 

 the time course of the action potential. A diagram 

 representing the time course of an action potential 

 can be converted into a diagram showing the spatial 

 distribution simply by converting the time scale into 

 the distance scale by using the conduction velocity as 

 a conversion factor. This and the following statements 

 are not applicable to axons with any macroscopic 

 nonuniformity along their length in regard to the 

 size and shape of the action potential. 



Next to be discussed is the relationship between the 

 spatial distribution of the action potential and the dis- 

 tribution of the longitudinal and the membrane cur- 

 rent of the axon. According to Ohm's law, the longi- 

 tudinal current in the axoplasm is proportional to the 

 gradient of the potential in the axoplasm, i.e. 



_ -I dV 

 /"i dx 



-_i dV 



r,v at ' 



(9-1 a) 



(9-ib) 



where h is the longitudinal current, r, the axoplasm 

 resistance per unit length of axon, V the potential of 

 the axoplasm (as a function of time, t, and distance 

 along the axon, .v) and u the conduction velocity. A 

 variation in the longitudinal current with respect to 

 space is associated with the membrane current, /„, 

 (Kirchoff's law), i.e. 



(9-2 a) 

 (9-2b) 



(9-2c) 



