23 : 5/ Diffusion, Permeability, and Active Transport 433 



transport certain substances. In Chapters 4 and 8, it was stated that 

 the concentration of potassium ions within nerve axons and muscle 

 fibers is higher than in the surrounding solution, whereas the concentra- 

 tion of sodium ions was lower. Because these membranes are charged, 

 it is not sufficient to merely measure concentration differences; the 

 concentrations must be compared with those predicted for the electrical 

 potential differences measured across the membrane. This reasoning 

 shows that the Na + ions, although demonstrated by tracer techniques to 

 pass from the outside medium into the cell, must be continually pumped 

 out against an electrochemical gradient to maintain equilibrium. 



Whenever molecules and ions are pumped against an electrochemical 

 gradient, the phenomenon may be called active transport. This has been 

 demonstrated to occur in the kidney tubules, in the epithelium of the 

 stomach mucosa (H + transport), in the epithelium of the intestines 

 (transport of ions, water, simple sugars, fatty acids, amino acids, and 

 so on), and in frog skin. Active transport may involve this pumping 

 against an electrochemical gradient, or it may involve pumping to 

 increase the net flow in the direction of an electrochemical gradient, as 

 perhaps the entrance of urea into the red blood cell. In either case, the 

 cell expends metabolic work and alters the relative rates of flux of a 

 molecular species in passing through the membrane in the two directions. 

 The detailed molecular mechanisms are not known in any case so far 

 studied, although ATP (adenosine triphosphate) appears to be an 

 energy source for some of them. 



A mathematical theory has been developed by Ussing to determine 

 whether active transport occurs. This theory seems particularly 

 important because the detailed mechanisms are not known on a molec- 

 ular basis. The mathematical theory involves the relative rates of 

 transport of tracer-labeled molecules across the membrane in the two 

 directions. These are compared with actually measured values. 



At equilibrium the rate of transport of molecules across the membrane 

 in the two directions must be equal, or else the concentrations would 

 not be at their equilibrium values. If the membrane is uncharged, the 

 concentrations on both sides must be equal at equilibrium. If the flux 

 from the right to the left is called J RL and in the opposite direction J LR , 

 then probability considerations dictate that, in the absence of active 

 transport or of membrane potentials 



J_RL __ C _R (21) 



Jlr c l 

 where c R is the concentration on the right side of the membrane and 



c 



that on the left. This same conclusion can be reached from consider- 



ations of Gibbs' free energy, or of chemical potentials. 



