452 



The Molecular Basis of Nerve Conduction /24 : 4 



Outside 



^i 



Membrane 



although not to the original value. When the membrane polarization 

 is increased, both the permeability to Na + and the permeability to K + 

 drop rapidly. The time dependence of the changes as well as the size 

 of the changes are uniquely determined by the original and final values 

 of V. All of these permeabilities and rates are temperature dependent. 

 Hodgkin and Huxley accumulated a vast array of data; however, 

 they went further in that they summarized these data in terms of a 

 minimum number of formulas. Although this minimum presented 

 on page 454 may seem large, it is nevertheless small compared to the 

 original data. 



Figure 9 shows the 

 equivalent circuit of an 

 axon. This circuit was 

 used to describe the 

 permeability changes in 

 electrical terminology. 

 Note that the sodium 

 emf is directed opposite 

 to the potassium and 

 leakage emf 's. Accord- 

 ing to this picture, at 

 the resting potential 

 currents would flow 

 within the membrane. 

 This is equivalent to 

 saying that the mem- 

 brane, at its resting po- 

 tential, must use energy 

 to keep its "pumps" 

 going, thereby maintain- 

 ing £" Na . Note that R K 

 and i? Na are variable to include the fact that they must depend on E 

 and on the time t. 



Through the use of mathematical symbols, it is possible to develop 

 differential equations which summarize all the books of data on one or 

 two pages, and which permit a simple comparison with data of other 

 investigators. Moreover, this summary, with one additional assumption, 

 allows one to predict the form of the transmitted spike potential in the 

 normal axon. 



The development of these equations is quite straightforward. It is 

 reviewed here because it illustrates the power of mathematical tools 

 when applied to quantitative biological data. Nonetheless, some 

 readers may feel that their mathematical interests are too limited to 



Inside 



Figure 9. Equivalent membrane circuit. The sym- 

 bol E is used for the absolute value of the potentials; 

 whereas V is used for the differences from the resting 

 potential. The symbol R is an areal resistance in 

 ohm • cm 2 and C u is an areal capacitance in fd/cm 2 . 

 After A. L. Hodgkin and A. F. Huxley, "A Quanti- 

 tative Description of Membrane Current and its 

 Application to Conduction and Excitation in Nerve," 

 J. Physiol. 117: 500 (1952). 



