438 



The Molecular Basis of Nerve Conduction /24 : I 



Dialysis 

 Bag 



[Pi 



[cn-,< 



[Na + ] ; > 



[Clio 

 [Na1 



The second is based on biochemical experiments dealing with extracts 

 of nervous tissue. The third type of simplified system makes use of 

 electronic potential clamps to study the variations of current with time 

 at a fixed membrane potential or after a predetermined potential 

 change. 



Classically, the oldest type of simplified system used to attempt to 

 account for nerve potentials was the Donnan membrane potential. 



Because Donnan potentials are used in the 

 ideas presented in this chapter, they will be 

 developed here in detail. The Donnan 

 membrane potential arises when a semi- 

 permeable membrane separates two solu- 

 tions, one of which contains three ions, 

 two of which can permeate the membrane 

 and one of which cannot. 



This is pictured in Figure 1. Initially, 

 one may conceive of filling a dialysis bag 

 with a solution of sodium chloride and so- 

 dium proteinate. The dialysis bag is 

 placed in distilled water, resulting in the 

 configuration shown in Figure 1 , where some 

 of the Na + and Cl~ ions have left the 

 dialysis bag to enter into the surrounding 

 fluid. It seems intuitively clear that 

 because there are more Na + ions than CI ~ 

 ions, a few more of the Na + ions might 

 permeate the membrane, charging the out- 

 side positive relative to the inside. As soon 

 as the potential difference became appreci- 

 able, it would discriminate against Na + ions 

 coming out, so that the net external con- 

 centration of Na + and Cl~ would be almost 

 exactly equal and no appreciable error 

 would be made in neglecting the difference in these two concentrations. 

 Thermodynamics can be used to find the magnitude of the potential 

 developed across the membrane. According to the formulas developed 

 in Chapter 21, equilibrium will represent a minimum in the Gibbs' free 

 energy for the system; that is 



dG = 



In order that this be true, there must be no change in G when a few Na + 

 ions are moved from one side of the membrane to the other. This 

 implies that G Na + , the partial molal free energy of sodium ions, must be 



*AV- 



-AV + 



Figure I. Donnan membrane 

 potential. The potential 

 developed across a semi- 

 permeable membrane is used as 

 part of the explanation of 

 nerve membrane potentials in 

 Section 4 of this chapter. 



