24 : 4/ The Molecular Basis of Nerve Conduction 453 



justify following even this simplified presentation. If they skip to 

 page 457, they will find the conclusion of the mathematical analysis listed 

 without having to struggle through the intervening details and symbols. 

 In order to analyze the behavior of the equivalent circuit of the 

 membrane shown in Figure 9, it is convenient to use some additional 

 symbols. Let the areal conductances be given by g K , g Na , and g h 

 respectively, for the potassium, the sodium, and the leakage conduct- 

 ances. The units of g are mhos/cm 2 . Because all potentials are 

 measured relative to the resting potential E r , all of the equations are 

 written referring to the potential change V; that is 



V = E - E r 



Similarly, one may define relative potentials for sodium, potassium, and 

 leakage; that is 



^Na = -^Na "~ E r 



Vk = E K - E r 



and V h = E h — E r 



Let J represent the current density flowing through the membrane. 

 This current density will consist of a part which charges the membrane 

 capacitance and of an ionic-current density J x ; that is 



J-C -+J 



~ (It 



In turn, J { may be represented as 



•J i — 4a + 4 + Jj_, 



where the different ionic currents are given as noted previously by 



Jk =Mk(V- v k ) 



From the preceding definitions, curves for the variation of g Na and 

 g K with V and time can be calculated. This still leaves a massive 

 catalog of data. To compress this catalog, Hodgkin and Huxley 

 developed differential equatins wohich would fit all the data. If such 

 differential equations are to be useful, it should be possible to show that 

 the equations also predict other properties of the system. Hodgkin and 

 Huxley were successful in predicting the behavior of the conducting 

 axon from their differential equations based on voltage clamp experiments. 



They found that the following five equations could predict all their 

 results. These are labeled H1-H5. 



