D. C. TOSTESON' 1 27 



molecule in ihe membrane, the tlux ratio will, in general, not conform to that 

 jiredicted for diffusion. Deviation of the flux ratio from the theoretical value 

 for diffusion may or may not be associated with transport of an ion against 

 its electro-chemical potential gradient (114). In the former case, the term 

 active transport has been applied to the process, whereas in the latter instance 

 some term such as exchange diffusion has been used (114). In both circum- 

 stances, transport involves some chemical combination between the trans- 

 ported ion and another molecule. As noted above, deviation of the flux ratio 

 from the diffusion value may also occur due to the interaction between flow- 

 ing solvent and transported solute. In red cells, this complication can usually 

 be avoided since measurements of cation fluxes can be made in the absence of 

 a change in cell volume. 



Variation of Fluxes With Concentration in the Solution of Origin. For the 

 case of electrolyte diffusion through a charged membrane, the relation between 

 tlux and concentration in the solution of origin is complicated. This becomes 

 clear upon examination of the following general flux equation, 



M=Z^(RT^ + ^^ + zFCg (7) 



where M is flux, A is the area available for diffusion, G is the frictional re- 

 sistance to diffusion, f the activity coefficient, C the concentration, V the 

 electrical potential. It is assumed that C, f and V vary only in the x direction, 

 i.e. normal to the surface of the membrane. It is clear that M is determined by 

 the gradients of f and V^ as well as of C. Since both f, and particularly V, are 

 likely to vary with C, the relation of flux to C will be complicated. In the case 

 of cation diffusion across the red cell membrane, however, a reasonable simpli- 

 fying assumption is possible. As mentioned in the previous section, the red 

 cell membrane is highly permeable to anions such as chloride. Chloride prob- 

 ably penetrates the membrane 10^ times more rapidly than sodium or potas- 

 sium (16). Therefore, it can reasonably be assumed thatdV/dx is independent 

 of the concentrations of Na and K inside and outside the cell provided that 

 the anion concentration is not altered, e.g. by substitution of KCl for NaCl in 

 the outside solution. If, as a first approximation, we also assume that f is in- 

 variant with C, it can be shown that the unidirectional cation flux across the 

 red cell membrane will vary linearly wath the concentration of the ion in the 

 solution of origin, i.e. diffusion influx will vary linearly with concentration in 

 the medium. 



In order to evaluate theoretically the rate constant for diffusion, it is neces- 

 sary to integrate the flux equation. This requires some assumption regarding 

 the variation of V and of f with x. Several examples of such integrations are 

 av^ailable in the literature (26, 79). For a somewhat different mathematical ap- 

 proach, see the paper of Parlin and Eyring (74). 



