772 AGGREGATES AND MEMBRANE POTENTIALS 



hydrogen ion concentrations inside and outside, as we should expect 

 if the membrane potentials are due to a membrane equilibrium. The 

 pH inside and outside was therefore measured with the aid of the 

 hydrogen electrode and the value 58 (pH inside minus pH outside) 

 millivolts is called the calculated p.d. The reader will notice that 

 the difference between the observed membrane potential (measured 

 with indifferent electrodes) and the calculated p.d. is not more than 

 0.5 millivolt. This leaves no doubt that the observed p.d, is deter- 

 mined by the difference in the hydrogen ion concentration on the 

 opposite sides of the collodion membrane and that this p.d. obeys 

 Donnan's equilibrium equation.'* 



These facts then show that the protein aggregates participate in 

 the Donnan equilibrium almost to the same extent as do the 

 isolated molecules or ions of gelatin, and this participation finds 

 expression in the fact that the membrane potentials are lowered 

 comparatively little when dissolved gelatin is replaced by powdered 

 gelatin. The same particles, however, do not contribute to the 

 osmotic pressure for the reason that their share in the excess of 

 chlorine ions is contained inside the solid particles, where it serves 

 to increase the swelling of the particles. The swelling of solid protein 

 particles is, as Procter and Wilson have shown,' due to the increase 

 of osmotic pressure inside the particles caused by the Donnan equilib- 

 rium. In our experiment there exists inside of each particle of 

 powdered gelatin a Donnan equilibrium whereby the concentration 

 of CI ions inside is greater than outside and this causes an osmotic 

 pressure. Water will, therefore, diffuse into each granule until the 

 cohesion pressure of the solid particles of gelatin equals the osmotic 

 pressure inside the particles due to the Donnan equilibrium, and the 

 particles will swell. When we therefore have a mixture of dissolved 

 gelatin and powdered particles (micellae) we have two different ost 

 motic pressures; namely, first, the osmotic pressure of the gelatin in 

 true solution, and, second, the osmotic pressure inside each solid 

 particle of gelatin. The former is measured by the hydrostatic 

 pressure of the column of water required to equalize the rate of dif- 



^ Loeb, J., Proteins and the theory of colloidal behavior, New York and Lon- 

 don, 1922, 120; J. Gen. Physiol, 1920-21, iii, 557, 667; 1921-22, iv, 351, 463. 

 * Procter, H. R., and Wilson, J. A., /. Chem. Soc, 1916, cix, 307. 



