TRANSIENT BIOELECTRICS IN NERVE 271 



Each g t was then related by a phenomenological trick to time and voltage in 

 such a way as to fit the experimental results. Thus, for potassium ion, 



n . fj max„4. 



6K+ ~ &K + " 



and 



dn 



= a„n{\ — n) — B„n 

 at 



where n is a dimensionless parameter which has a value between and 1; 

 it is time-dependent and is related to voltage-dependent penetration con- 

 stants, a n and /? n . The first, a n , expresses the rate of K + movement into the 

 cell, and /? n expresses its rate out. Similar expressions have been devised for 

 Na + and the other ions of the system. From these expressions the total cur- 

 rent (/) can be expressed in terms of time-dependent and voltage-dependent 

 parameters related to permeability. With proper choice of the values of the 

 different parameters, the experimental values of conductance as a function 

 of time and voltage can be completely described. 



These two theories have been bright lights in the quantitative descrip- 

 tion of nerve propagation. The interested reader is referred to the analyti- 

 cal and summary papers 21,22 for the detailed arguments. The papers are 

 difficult, but rewarding. 



The charged-pore theory of membrane potential differences has been suc- 

 cessful with synthetic membranes of collodion, ion-exchanger resins, and 

 other synthetic polymers. It will not be developed here, although it has been 

 put into elegant quantitative form by Meyer and Siever and, more recently, 

 by Teorell. 



This is a very active and important part of biophysics today, and, as was 

 stated in Chapter 6, probably there is no part of the research in the subject 

 which will be more rewarding. Hodgkin's Croonian Lecture 14 is an excellent 

 statement of the state of the art, and Nachmansohn's recent, short review, 18 

 more from the biochemical viewpoint, will nicely balance the further devel- 

 opment of the reader's concepts. 



Is Semiconductivity Important? 



It may be. We saw in Chapter 4 that the tt electrons of many organic 

 compounds have a certain freedom and can move under the influence of an 

 electric field. Most vertebrate nerve is sheathed in myelin, the protein-and- 

 fat wrapping formed by the doubled membrane of the Schwann cells. This 

 is illustrated schematically in Figure 10-1, top right, and shown very dra- 

 matically by the electron micrograph, Figure 10-5. The myelin sheath offers 

 physical protection to the fine nerve fibers of vertebrates. But it has further 

 roles. For instance, since it completely covers the nerve fiber except at 

 certain interruptions about 1 mm apart, called the nodes of Ranvier (Fig- 



