434 Diffusion, Permeability, and Active Transport /23 : 5 



Likewise, if the membrane is charged, one may start from any of these 

 bases and arrive at the formula 



Jul _ C _R gsFV/RT /oo) 



Jlr c l 



In this, F'\s the Faraday, z, the charge on the molecule, and Fthe potential 

 difference between the right and left sides; RT has its usual meaning. 

 As mentioned earlier, the exponential factor appears because the partial 

 molal free energies on the two sides of the membrane differ by zFV 

 when the concentrations are equal. When the two fluxes are equal, 

 equilibrium is established although the concentrations need not be 

 equal. By using two different labeled isotopes on the two sides of the 

 membrane, one may measure the ratio of the fluxes. 



Equations 21 and 22 are sometimes referred to as Ussing's equations. 

 Their theoretical basis is sound except for the point that chemical 

 activities rather than concentrations should be used. Although this 

 difference is highly significant in many concentrated solutions, there is 

 little evidence that it is important in most biological systems. 



Equations 21 and 22 have been used to design experiments to test 

 for active transport across many membranes. If the flux ratio is different 

 than predicted, it implies that the assumption of passive transport 

 necessary to derive Equation 22 must be wrong. Somehow, the mem- 

 brane must be pumping or forcing the molecules in a preferred direction. 

 One of the easiest examples to discuss is the isolated frog skin. The 

 experimental arrangement is diagrammed in Figure 6. Perhaps this is 

 a rather poor example, for the membrane (or membranes) responsible 

 for the pumping action are not known. However, the frog skin can be 

 used to demonstrate active transport because it can separate two media 

 whose concentrations can be controlled. 



If an isolated live frog skin is used to separate two containers of 

 Ringers' solution, it develops a 60 millivolt potential difference between 

 the two solutions, the outside of the skin being negative relative to the 

 inside. For equal Ringers' solutions, and a 60 mv potential across 

 the membrane, a direct substitution of numbers into Equation 22 shows 

 that actually the efflux may be as low as one tenth of the influx, a factor 

 of 100 difference between theory and experiment, if active transport is 

 omitted. Accordingly, it is concluded that Na + is actively transported 

 inwardly. It is known that frogs can take up sodium ions from their sur- 

 roundings even if the external concentration is as low as 10 ~ 5 M. 

 Similar tests show that Cl" and HC0 3 ~ are not actively transported 

 by frog skins, whereas if Li + is present, it is actively transported. 



Because the frog skin actively transports Na + and develops an electrical 

 potential, it may be used as a battery to drive a current through an 



