1 138 



HANDBOOK OF PHYSIOLOGY 



CIRCULATION II 



table 2. Relation 0} Ion Size to Mobility in an Electric Field 



Velocities of Ions Under Gradient of i 17cm or 0.5 17cm for Divalent Ions 



Relative Ion Diameters (Diameter of Potassium Ion = 1.00J 



From Conway (32). 



table 3. Relative Entrance Rates of Ions into 

 Muscle (Left Column) Compared with Their 

 Diffusion Constants, D, Though Water Relative to A 

 Taken as 100 (Right Column). 



From Conway (31). 



Special Properties of Ions in Biological Systems 



donnan equilibrium. By thermodynamic principles 

 it can be demonstrated that the product of diffusible 

 cations and anions on the two sides of a membrane 

 must attain equality at equilibrium. Thus: 



(cations), (anions), = (cations)<,(anions)e, 



When the cell is nonpermeable to some charged 

 material on one side of its membrane, a sufficient 

 number of diffusible ions of opposite charge is re- 

 quired to balance this. In the cell this fixed material 

 is mainly negative in charge so that it can be shown 

 that at equilibrium the sum of the diffusible cellular 

 cations must be rather larger than the sum of dif- 

 fusible anions. In brief, this shows up in the low 



intracellular and high extracellular CI - . It is im- 

 portant to realize that in determining an expected 

 Donnan equilibrium in a tissue only the diffusible 

 ions count. Thus, Na+ figures only to the small extent 

 that it penetrates the cell membrane. 



electrochemical gradients and membrane po- 

 tentials. It is beyond the scope of this article to at- 

 tempt to deal with this fascinating subject in any sort 

 of detail. Since our discussion of ions and smooth 

 muscle must make frequent reference to bioelectric 

 potentials, however, a brief outline will be presented. 

 Two different dilutions of a substance A' and A" 

 have necessarily different activities and different 

 chemical potentials stored in them. This may be 

 expressed as the change in free energy required to 

 move one mole of A' from the lower to the higher 

 activity or, conversely, the amount of free energy 

 liberated when A" slides from higher to lower activity. 

 This relation follows the very general form 



(A)' 

 (A) 



AG can be expressed in electrical terms as volt-cou- 

 lombs and factored into a potential difference E and 

 nF faradays so that : 



F _RT .(A)' 

 E — P ln 777" 

 nF (A) 



At 25 C this simplifies to 



E < mv i 58,0 'wr 



Clearly, the osmotic balancing of the nondiffusible 

 material in the cell and the associated Donnan rear- 

 rangement together produce a situation in which the 

 diffusible ions are distributed unequally on the two 

 sides of the membrane and so contain stored energy. 



