186 



A CONCEPTUAL INTRODUCTION TO BIOENERGETICS 



solutions of different concentrations separated by a suitable membrane. Fig- 

 ure 7-7) are allowed to interact, the difference in free enegery, AF, can be 

 manifested by transport or movement of molecules or ions. By a rather neat 

 argument involving the dependence of electrical potential upon concentra- 

 tion of ions, it can be shown that the A/ 7 can also be manifested as a poten- 

 tial difference in such a system. With suitable electrodes the value can be 

 measured. A form of the Nernst equation relates the emf of this concentra- 

 tion cell to the ratio of the salt activities. Thus 



0.060 



log (a, /a,; 



This equation shows the relationship between the potential and the activity 

 ratio for condition of no transport across the interface. For example, for a 

 cell composed of IN - NaCl:0.1A r - NaCl, in which the activity ratio is 

 about 10, the value of £ conc = 0.060 v ( = 60 mv). 



I 

 I 



salt in J water) 



membrane 



dif f use 

 interface 



a i greater than o 2 



Figure 7-7. Concentration Cell (left); with Transport (right). 



If flow or transport of ions or water occurs, and it usually does to some 

 extent across living membranes, the value observed, E, differs from E by 

 a "diffusion potential," E m , which can be approximated by either the Hen- 

 derson (1911) or Planck (1915) equations, and measured, approximately, 

 under certain rigorous experimental conditions. Thus, 



E = £ 



'diff 



Values 50 to 100 mv are found routinely in living systems, across the mem- 

 branes of nerve cells and red blood cells, for example (see Table 7-6). These 

 values are due principally to potassium chloride concentration differences 

 across the membranes. It is interesting to note that in the electric eel, simi- 

 lar cells are arranged in series, and potential differences of 200 to 1000 v are 

 usually observed! In nerve, the stationary values of about 80 mv are modi- 

 fied rapidly with passage of a stimulus, due to a change in permeability. 



