430 Diffusion, Permeability, and Active Transport /23 : 4 



In this fashion, the volume can be used to indicate the internal con- 

 centrations, and because the surface area remains constant, one may 

 compute the permeability constant k. In actual practice, the area is 

 constant and not measured; rather the permeability P is used. It is 

 defined by 



P = kA r (15) 



where A r is the surface area of the erythrocyte. 



Equation 10 is particularly suited to this case. If S is the mass of 

 substance s inside the cell, then Equation 10 becomes 



— = kA r (c t - c s ) (16) 



where c i and c s are the concentrations of s inside and outside the cell, 

 respectively. Because diffusion occurs rapidly as compared to penetra- 

 tion of the cell membrane, c x may be replaced using 



Ci -- -r 



S 

 V 



where V is the cell volume 4 . Equation 16 can then be rewritten 



As the concentration of substance s within the cell rises, there will 

 be a flow of water into the cell. This will result, in turn, in a change 

 of the cell volume V. The flow of water must also obey Equation 10 

 for the mass flow through the cell wall. It takes a few algebraic manipu- 

 lations to rewrite this equation for water flow as 



dV ( c V + S \ 



n = M — v — ' s ~ Cm ) (18) 



where c is the initial concentration of nonpenetrating solutes within 

 the cell, V the initial cell volume, and c M the concentration of non- 

 penetrating solutes in the external medium. If more than one pene- 

 trating solute is present, S and c s must be regarded as the sum of all the 

 various values. 



If the volume changes are observed, Equations 17 and 18 may be 

 used to compute values for P and P w . In the most general case, only 

 numerical solutions are possible. There exist, however, a number of 

 simplified conditions under which P and P w may be found. 



First, if there are no nonpenetrating solutes in the external medium, 



4 The symbol V is used for volume in this section. The same symbol is used for 

 electrical potential in Sections 2 and 5 of this chapter. 



