24 : 4/ The Molecular Basis of Nerve Conduction 



455 



As already mentioned, these same equations can be used to predict 

 the behavior of the conducting axon. To demonstrate this, consider 

 the following: As the spike poten- r 



tial travels down the axon a poten- 

 tial gradient exists along the axon. 

 To distinguish quantities outside 

 and within the axon, the subscripts 

 1 and 2 respectively are used as 

 shown in Figure 1 0. If r represents 

 the resistance per unit length, then 

 Ohm's law states that 



rJi = 



dx 



Figure 10. Current flow along an axon. 

 Some of the symbols used in the text to 

 develop Equation (H6) are illustrated. 



and 



Hh = 



8V, 



dx 



The internal and external currents can be altered only by the current / 

 flowing through the axon membrane (or else large charges would accumu- 

 late). Analytically, this is expressed by 



/ == d ll _ <?h 



dx dx 



Likewise, the membrane potential V is given by 



v = v x - v 2 



Combining the four preceding relationships leads to 



1 d 2 V 



I = 



In the squid axon experiments 



r l + r 2 dX* 



h < r 2 



so r x may be discarded from the last equation. It is convenient to dis- 

 cuss the current per unit area of membrane J and to replace r 2 by the 

 resistivity R' 2 . The last equation can then be rewritten 



J = 



a d 2 V 

 2R'o dx 2 



