202 Herman Branson 



The term ^ (<^o -«/•.)= 1 -94 



at 300°K. Using this value, the combined rates for both the concentration and 

 electrical terms are 



K+: H = 2.5 bits/ion-unit time, 



Na+: //= 6. 1 bits/ion-unit time, (13) 



C1-: H = 0.9 bits/ion-unit time. 



log2 e 

 These values have been arrived at by multiplying equation (11) by — j — to 



convert from k units to entropy units. 



[The conversion factor was derived in a previous paper by the author in 



considering proteins (2). It is easily shown that log,, x logj, y = 1, which means 



that this conversion factor is the same as that derived by Linshitz (!) and others 



(8).] 



On the basis of the first model the 3.7 /^/^ moles of Na+ entering during 

 the impulse would be extruded during the millisecond following the return 

 to the resting potential. This time interval requires that the nerve produce 

 information at the rate 



7^ = 9.3 X 10^5 ergs/°K cm^ sec, 

 or (14) 



fl=\35 X 1016 bits/cm^sec. 



The alternative model is that the nerve does not extrude the Na+ in so short 

 a time. Rather the nerve passes it from within to the outside at a rate of 

 20 i^fjL mole/cm^ second (9). However, the acceptance of this view does not 

 alter equations (13). Inserting this value for Na+ in equation (12) results in 



if = 7.3 X 1013 bits/cm2 sec. (15) 



The experimental results seem to favor this model; thus equation (15) is the 

 more reasonable result in comparison with equation (14).* 



The alternative mode of viewing the nerve according to information theory 

 makes use of the concept that the sodium ions are chosen from the pool of ions 

 within the nerve by some mechanism. Within the nerve the ratios are 

 Na+ : CI" : K+ = 1 : 1 : 10. The mechanism chooses the Na+ from this group, 

 requiring logg 12 bits of infomiation for each Na+ selected. This value, 

 3.57 bits/ion, leads to 



i^ = 4.3 X 1013 bits/cm2 sec, (16) 



for the nerve based on the second model which transports 20/^// moles cm^ sec. 

 of Na+ against the concentration and electrical gradient. Assuming that the 



* Dr Leroy Augenstine made the astute observation with respect to equation (14) in the 

 discussion that it is consistent with a value of 10^ A" for the area of a protein and that on 1 cm^ 

 of nerve there could be 10^^ proteins transporting one ion per millisecond. It may weaken the 

 argument to assume that the nerve surface has that many protein molecules. The lower value 

 1.20 X lO^ions/cm^ second is consistent with any combination of rates and numbers of 

 protein molecules responsible for transport such that the product equals this numerical value. 

 Thus 1 .20 X 10" protein molecules transporting an ion per miUisecond are suitable and require 

 that only 0.001 of the nerve surface consists of such proteins, each of 10* A^ area. 



