454 The Molecular Basis of Nerve Conduction /24 : 4 



- = a h - (a ft + /%) ^ (H5) 



These equations summarize all their data in terms of six constants. 

 Functional forms for these constants are summarized in Table II. 



TABLE II 



A. Functional form of constants in Hodgkin and Huxley's differential equations 



a n = (0.01)(F+ 10)/(e (V + 10) ' 10 - 1) 



)8 n = 0.125^' 80 

 a m = (0.1)(F + 25)/(* (V + 25 >' 10 - 1) a h = 0.07^' 20 



j8 m = 4e V118 j8 h = («or + 8«>)/io + l)-i 



B. These values are all at 6°C. The constants all increase about threefold for a 

 10° rise in temperature (Qi = 3). 



C. It is doubtful if the functional forms of a and /3 have any theoretical significance. 



D. Alternative forms: If the membrane potential is changed from V to V at 

 t = 0, the equations H2, H4, and H5 have as solutions 



n — n x — (««, — n )e~ ilz n 

 m = m x — {m n — m )r f,I "i 

 A = h* - (A„ - h )e- tl \ 

 In these, the constants are given by 



"» = aj(a n + j8„) Woo = a m /(a m + /? m ) A*, = cc h j{a h + fi h ) 



Tn = («n + /3 n ) _1 T m = (a m + ^m)" 1 T h = (a h + £ h ) ~ 1 



The foregoing differential equations describe adequately the form of 

 the voltage clamp currents over a wide range of Fand [Na + ], as well as 

 for various axons and temperatures. They indicate the need for six 

 rate constants, all of which are functions of both V and temperature. 

 Any model failing to supply these constants is incomplete. Even 

 though the exact form chosen for the equations may be wrong, it does 

 not appear that the data can be fitted with fewer rate constants. This 

 discovery in itself makes the analytical effort worthwhile (although it 

 would not justify including its outline in this text). 



