268 HANDBOOK OF PHYSIOLOGY ^^ CIRCULATION I 



® 



CmC-Ii -Ir 



FIG. 23. Hypothetical current, po- 

 tential relationships of a cell mem- 

 brane at one instant in time. Ordinate: 

 negative of capacitative membrane 

 current, — CmS = li — In.. Abscissa: 

 transmembrane voltage (6). .4.- — £,£ 

 curves for three values of the externally 

 applied current (Im). This current 

 shifts the curve in the vertical direc- 

 tion. Arrows show the movements of 

 the point (S,£) in time under various 

 circumstances. (See text for explana- 

 tion.) B: hypothetical !],£ curves for 

 the repolarization process in frog 

 ventricular cells with Im = o. Ik is 

 the curve of K"*" current, assumed 

 unchanging in time. The lNn,£ curve 

 has the same shape at all times but its 

 amplitude at any £ is decreasing 

 exponentially in time. The lNa,E curve 

 is drawn for the instant t = U. The 

 curves marked t,, t., , te show I, 



for successively later times. Dashed 

 line shows motion of the £,S point. 

 It is drawn with the same shape as 

 the actual £,£ curve of fig. 20C. (See 

 ext for explanation.) 



Im=-2 I'r 



^m"~^ m 



m 



applied current has no direct immediate effect on 

 the membrane conductances — a not completely 

 safe assumption (106) — the Ii,S curve is not altered 

 and the — C8,S curve is shifted vertically. The two 

 upper curves in figure 23.4 are for two different 

 applied currents, —I,,, and —2!^. If £ = £„ before 

 the application of — Im, the point on the — CmS,S 

 plane describing 8 and £ of the membrane will 

 immediately jump vertically to the Im = — Im 

 curve. Thereafter, £ will decrease toward a stable 

 equilibrium point (£2) as shown by the arrows. If 

 the current is turned off, the slope reverses in sign 

 and the membrane will then depolarize back to £0. 

 On the other hand, if — 2lm is applied, the point of 

 minimum current rises above the zero current axis 

 and repolarization proceeds all the way to fis- The 

 repolarization rate would be rapid at first, decline 

 to a minimum, increase to a maximum and, finally, 

 decrease to zero at Ss. This repolarization process 

 has two inflection points — one at a point of minimum 

 slope and one at a point of maximvim slope — and is 



thus similar in shape to repolarization in the heart. 

 The range of 8 wherein £ is increasing corresponds 

 to the region of negative G. If a sudden small change 

 in applied current is made during the repolarization 

 from £0 with — 2lm flowing, 8 would be changed in 

 magnitude but not in sign. FitzHugh (40) has dis- 

 cussed the Hodgkin-Huxley nerve equations in 

 terms of their behavior on various phase planes (e.g., 

 m,8; 1,8). References to the mathematical literature 

 and a clear discussion of the usefulness of the phase 

 plane method can be found in his paper. 



POSSIBLE MECHANISMS OF REPOLARIZATION. The prOCesS 



of repolarization can be profitably discussed in 

 terms of — £,£ diagrams (cf. fig. 23). For this purpose 

 it is useful to describe the repolarization process by 

 a family of Ii,fi curves at different times and to 

 determine how these vary with stimulus rate and 

 external ion concentrations. At present no such 

 family of curves can lie specified, but certain types 

 of curves can be excluded. The most evident Ii,£ curve 



