TRANSIENT BIOELECTRICS IN NERVE 267 



(2) Concentration Ratio: Table 7-12 gave data which show that the resting 

 potential measured across living membranes is in substantial agreement 

 with the value calculated from the ratio of the two concentrations of salt, 

 outside and inside the membrane. Calculation is done via the Nernst equa- 

 tion, suitably modified to express the voltage of a concentration cell: 



E = 60/n log (a,/<3 2 ) mv 



where n is the number of charges carried on the ions of the salt, and a, 

 and a-, are the effective concentrations (activities) on opposite sides of the 

 membrane. 



However, such a relationship as that shown above between the potential 

 of a concentration cell and the ratio of the activities of the salt on the two 

 sides of the membrane is actually a special simplified case, used here for 

 introductory purposes. More generally, when two such salt solutions with 

 activities (effective concentrations) a, and a 2 abut each other, and if diffusion 

 is restricted so that salt cannot flow, 



E = 2 —=- In a x /a 2 

 nF 



or 



E = 2 x 60 log a } /a 2 



The 2 comes from the fact that work is potentially available from the con- 

 centration ratios of both the positive and negative ions. 



If salt can diffuse, a new factor, /_ , the transference number of the anions, 

 enters (for reasons which will not be developed here) so that 



£ = 2 L x 60 log a, /a 2 



Here /_ = /u_/(/*+ + M- ), where the yu's are the mobilities, or speeds, of the 

 ions in centimeters per second when the voltage gradient is 1 v/cm. Intro- 

 duction of the expression for <_ , and rearrangement, gives 



E = 60 log a, /a 2 - 60 M+ ~ M ~ log aja 2 



M+ + M- 



This expression gives the potential if cations and anions are not restricted in 

 their motion. When both move with the same speed (KC1 in water, for ex- 

 ample) n + = M- (or t_ = 1/2), and the second term drops out. If the mo- 

 tion of one is completely restricted, there can be no motion of the other if 

 micro-neutrality is to be maintained, and the potential is given by the first 

 term only. In such a case — charged protein ions plus salt in water, the 

 Donnan case, for example — the values of a, and a 2 are the activities of the 

 unrestricted ion. 



