23 : 4/ Diffusion, Permeability, and Active Transport 



429 



plotted as a function of oxygen pressure fail to fit these theoretical 

 predictions. The steady-state, spherical model can be brought closer 

 to the experimental data by including several steps in the utilization of 

 2 ; these alter the values for q. Mathematically, if one is willing to 

 include enough arbitrary constants, one can fit any experimental curve. 

 The model in Figure 5 is supported by some biochemical evidence and 

 can fit any measured curve merely by juggling parameters. 



LA = Lactic Acid 

 G- Glucose 



Figure 5. Spherical-cell model. This model with its numerous 

 constants can account for 2 diffusion into living cells. The 

 model is also supported by metabolic studies of other types. 



The spherical-cell model shows that a simple assumption such as the 

 constancy of the rate of oxygen utilization cannot be maintained. More 

 complex chemical reactions and equilibria must be included to fit the 

 2 -uptake data. Although diffusion and permeability play an import- 

 ant role, they are not the only rate-limiting steps in the intracellular 

 use of On. 



4. Permeability of Red Blood Cells 



The mathematical problems of analyzing diffusion into biological cells 

 can be greatly simplified if the rate at which a substance penetrates the 

 cell membrane is slow compared to its rate of diffusion on cither side of 

 this membrane. Mammalian red blood cells haw proved very useful 

 for studies of this nature. They are especially convenient because the 

 cells act as "osmometers," swelling or shrinking accordingly as their 

 internal osmotic pressure varies. In spite of very large variations in 

 the volume, the surface area of the erythrocytes remains almost constant. 



