144; MEMBRANES {PLASM AH iUT) 



a terrier and a spaniel, on the other hand, similarly united might 

 pass into the field together. One woidd then find that the con- 

 centration of terriers on either side of the fence would bear a 

 definite relationship to the number of spaniels on that side. 



Following Donnan's plan and indicating the membrane by a 

 vertical line and molecular concentrations by square brackets, we 

 have, to begin with : 



(1) Na+ : Na+ 



R- Cl- 



[i) inside outside (o) 



The NaCl diffuses readily into the cell, so that when equilibrium is 

 established we have : 



(2) Na 



R 

 CI 



Na 



CI 



It can be calculated that at this point 



[NaJ [CI,] 



[Nao] "^ [Cy 



Since the concentration of the cation Na inside the cell must be 

 equal to the sum of the anions (R and CI) present in order to 

 maintain electrical equilibrium, whereas on the outside the con- 

 centration of Na is only equal to that of CI, it follows that 



[Na,] > [Nao] and [CI,] < [Clo] 



i.e. there is more cation (positive charge) inside the cell than out- 

 side. This difference of electrical potential is intensified by the 

 smaller amount of mobile anion (negative charge) inside than 

 outside. The potential difference thus created is balanced by the 

 osmotic energy developed in the opposite sense, i.e. the energy 

 which can be gained in this way is zero. Donnan has shown that 

 the potential difference developed is 



[Na.] [CL] „ , 



58 log Y^J^^ ^ ^^ ^°S YtT] milli'^olts (at room temperature). 



Where the amount of NaR is large compared with the amount of 

 NaCl, the P.D.- would be 58 log [NaR]/[NaCl] millivolts, 

 where [NaR] = initial concentration inside the cell 

 and [NaCl] = initial concentration outside the cell. 



As a matter of fact, as we shall see in Chap. XXIII., other 

 balancing factors come into play as well {e.g. hydrostatic pressure). 



Since many compounds in the cell are of the form NaR, and, as 

 readily diffusible substances and membranes permeable to them 

 abound both in the cell and forming a boundary to the cell, it 



