Some Membrane Phenomena from the Point of View of Information Theory 201 



and carrying through an identical analysis as followed in deriving equation (7), 

 H becomes 



A --= k[{dNldt) In CJC, -f A^a] -]- {ZqlT)[cINldt(cf>, - - <f>,) ^ ^ 



where q is the numerical value of the charge on the electron, when the membrane 

 transports ions from the lower concentration to the higher concentration, 

 C, - Co. 



Application to a Nerve 



Data on the movement of ions across the nerve membrane may be substituted 

 into equation (11) to obtain numerical values for ff. The knowledge of the 

 transport of ions across the nerve membrane although quite extensive is still 

 not complete enough to permit unequivocal choice of a model. There are 

 two possibihties which suggest themselves for consideration. In the first, 

 following the transport of an impulse, the nerve returns to its resting condition 

 with respect to the concentration of Na+ or K+ before it can pass another 

 impulse. The resting potential is reached at the beginning of this period. 

 Calling this example model one, we have these data for a squid axon (6): 



[K+] Co =10 C, = 410 



[Na+] Co = 460 Q = 49 

 [C1-] Co = 540 Q = 40 



in units of millimoles/kg. At 300°K, (f)Q — (f)^ = 50 mV with the outside positive. 

 If the length of the recovery period is taken as 1 millisecond, the equation (11) 

 becomes* 



n = kidNjdt) [In Co/C, + (ZqlkT)(cf>, - cf>,)]. (12) 



The first term on the right yields for the concentration gradient above 



for K+, // = 5.3 bits/ion-unit time, 



for Na+, H — 3.3 bits/ion-unit time, 

 for Cl~, li = 3.7 bits/ion-unit time. 



* In applying equation (1 1) the second and fourth terms contribute negligibly. Examining 

 the two terms with the data that 3.7 /iju moles of Na+ enter per impulse per cm*, a cylindrical 

 nerve of 100 ^i radius with unit surface area would have, 



Area = iTrrl = 1 cm^ 



Vol = 7Tr^l= 5 X 10-' cm'; 



and assuming that the nerve has the density of water, the section would weigh 5 x 10' gm. 

 So 49 m mole/kg would correspond to 2.5 x 10^ jufi mole/cm', whereupon for sodium 



H = 2.25 k{dNldt) + 1.5 x 10"° kN per millisecond 



= 2.25 kidNjdt), 

 since 



AAT = N and A/ is taken as 1 millisecond. 



