Membrane structure as revealed by permeability studies 



The meanings of M in , M out and A w have been defined above. Z) w is the diffusion 

 coefficient for water diffusing in water, A is the fraction of the total area of the 

 membrane which is available to water diffusion, x is the distance from the inside 

 boundary, and x is the total thickness of the membrane. 



Evidently the flux ratio for water may vary profoundly, and depends on the shape 

 of the pores inside the membrane. 



In the case of the action of posterior lobe on the toad skin, in which the net water 

 flux increased by more than ioo per cent, without the influx's changing by more 

 than a few per cent., it turns out that the equation is satisfied if the diffusion area 

 remains constant while, at the same time, a larger number of narrow pores is replaced 

 by a smaller number of large pores. The results therefore do not necessarily indicate 

 an active transport of water. But the alternative to the active transport hypothesis 

 is the acceptance of pores in the membrane. In order to see what the pore hypothesis 

 means in terms of pore dimensions it may be useful to consider an 'equivalent' 

 membrane with uniform cylindrical pores. Furthermore it is assumed that the only 

 force available for the transfer of water is the difference of osmotic pressure across 

 the membrane. We then get the following simple expression : 



^/^out=(^ ) ) GW/ ' W ( 2) 



\<2 w(i ) / 



where G' w is the frictional coefficient for water diffusing in water, and is equal to 

 RTjD^. D w has been determined by Orr & Butler (1935) and more precisely by 

 Rogener (1941). At 17-5° C. the numerical value of G w is 1 36 x io 15 . The term g' w 

 represents the frictional coefficient for water flowing through the membrane. It is a 

 function of the pore diameter, and works out as 



_ 14477 



S w ^2 



where 77 is the viscosity of water. At 17-5° C. we have 



g' =- 5 . 



5 w r 2 



It is seen that G w becomes equal to g' w for r = 3 5 x io -8 cm. Since this is less than 

 the average distance between water molecules, we must conclude that at all real pore 

 sizes water flow takes place with a lower resistance than water diffusion. As one might expect, 

 the difference between the two frictional coefficients vanishes when one gets down 

 to molecular dimensions, and one obtains the classical equation as applied by 

 Hevesy et al. (I.e.) and Visscher et al. (I.e.). With increasing pore size, however, the 

 frictional resistance for flow gradually becomes insignificant as compared with that 

 for diffusion. 



Inserting the numerical values for G w and g' w in equation (2), we obtain: 



log (MJM out ) = 0-9 x io% 2 x log(fl w(o) /a w(i) ) ... (3) 



In one of the toad-skin experiments mentioned above, after the hormone had been 

 added, the water influx was 532 /xl./hr. and the net flux 30 /xl. Taking the water 

 activities to be equal to the water concentrations we had 



^w(i) = 55'3 mol./l. and <r w(o) = 55-5 mol./l. 

 37 



