126 ELECTROLYTES IN BIOLOGICAL SYSTEMS 



Flux Ratio Analysis. Ussing (113) has derived the following relation for all 

 ions which move through a membrane by the process of diffusion. 



'M a™ , . 



'M and °M are influx and outflux respectively, and Sc and am are the electro- 

 chemical activities in inside and outside solution (in this case inside and out- 

 side the red cell). The most important basic assumptions underlying this formu- 

 lation are i) that the driving force for movement of the ion at any point within 

 the membrane is its electro-chemical potential gradient at that point, and 2} 

 that the resistance to diffusion as well as the electrical potential at any one 

 point in the membrane is the same for ions which originated in either of the 

 solutions bathing the two sides of the membrane. We may rewrite equation 2 

 assuming that activity coefficients for the ion are equal inside and outside the 

 cell, 



^M ^ Cm fzFE' 



exp [^^] (3) 



where Cc and Cm are concentrations of the transported ion per kg cell and 

 medium water respectively, and E is the electrical potential difference across, 

 the membrane. For red cells, we may write, 



RT [Cl]m / \ 



where the bracketed terms indicate the concentrations of CI per kg of medium 

 and cell water (35, 100). This statement is reasonable because the chloride ion 

 traverses the red cell membrane very rapidly (16, 54) and is probably at all 

 times at thermodynamic equilibrium across the cell membrane (39, 114). 



Now, defining the rate constant for inward transport, 'k, and outward 

 transport, Ok , as follows, 



•k = p^ (5«) 



°k = — (56) 



we obtain, 



'k [CI], 



{6) 



°k [Cl]e 



Thus, for cation diffusion across the red cell membrane, the ratio of the rate 

 constants should equal the chloride concentration ratio. 



If cation transport involves some chemical combination with another 



