CELLULAR ELECTROPHYSIOLOGY OF THE HEART 



269 



that might be used to explain repolarization is the 

 upper record in figure 20C, where — S is plotted 

 against S for two normal repolarizations of different 

 durations. For — S > o, these curves have the same 

 form as the curve labeled I,„ = 2I,,, in figure 2^A. 

 The action potential would be "explained" by as- 

 suming that the Ii,S curve is initially like the one for 

 squid axons at short times (fig. 7), changes rapidly 

 at the peak of the action potential to one like figure 

 23.-1 (I,„ = — 2lni) or figure 20 and remains in this 

 form. Repolarization would then proceed along this 

 fixed Ii,S curve and hence would have the correct 

 shape. Aside from the difficulty in explaining the 

 ta,t.4i> relationship from these assumptions, the fact 

 that G measured experimentally is always positive 

 whereas these Ii,£ curves contain a region of negative 

 slope rules them out. Also, a depolarizing current 

 strong enough to change the sign of S (i.e., no larger 

 than the currents used in fig. 21. 4) would shift the 

 1 1,8 curve downward so that it would cross the S axis 

 (i.e., as the In, = o curve at So does in fig. 23.4). 

 The voltage then would approach an equilibrium 

 value and stay there for the duration of the current. 

 Maintained depolarizing currents prolong repolari- 

 zation but not indefinitely (28). 



Repolarization in squid axon is somewhat like the 

 process described above. The Ij,S curve during 

 depolarization is the early time curve in figure 7 

 which has two stable and one unstable equilibrium 

 points. The system transits from the resting stable 

 equilibrium to the active stable equilibrium when an 

 applied current from an external source or an ad- 

 jacent active area depolarizes the membrane to the 

 unstable equilibrium or threshold point. Once 

 threshold is reached, 8 accelerates toward the active 

 stable point (m and 8 interacting regeneratively). 

 However, as the active stable point is approached, 

 gNa starts to decrease owing to inactivation and gK 

 begins to increase, slowly at first and then more 

 rapidly (fig. 15). These two changes act to move the 

 unstable and the active stable points toward each 

 other, £ following the latter quite closely. Eventually, 

 these points meet and vanish, leaving only one stable 

 point which is near Sk (long-time curve fig. 7) but 

 remote from 8. Repolarization then rapidly ensues 

 along a path relatively unchanging in time. [See 

 FitzHugh (40) for a more accurate and detailed 

 description.] 



These considerations suggest that the slow re- 

 polarization rate of heart results from a slow move- 

 ment of an equilibrium point (8,.q), which is stable 

 since G is always positive (fig. 22) and that the speed 



of this movement gradually increases as repolariza- 

 tion proceeds. In the second phase when 6 is small, 

 £ should be only a few millivolts more positive than 

 £,q. If there were no membrane capacity, S would 

 always equal £,.,. Since there actually is capacity, 

 S, in FitzHugh's picturesque words (40), "pursues" 

 £eq as it changes slowly in time. To a first approxima- 

 tion, S is sufficiently more positive than 8c.q to make 

 li just large enough to charge the membrane ca- 

 pacitor, so that 6 = 8,.q, i.e., I; = -C„,S = — C„,£pq 

 (fig. 235). A more exact relationship between 8 and 

 S,.q follows from the definition of G. Over a small 

 range of £ around 8,q, li = G(8 — 8^q) = — C,„8; 

 therefore, £,.q = 8 + C,„8/G. Weidmann's experi- 

 ments on Purkinje fibers (125, 126) furnish estimates 

 of G, Cm, and £ as functions of time throughout 

 repolarization so that 8,q can be calculated ap- 

 proximately. The results of such an estimation of 

 8eq are plotted in figure 22 along with 8 and G Gr 

 as a function of time. Aside from the approximation 

 involved in assuming G is constant over the large 

 voltage range involved, the values of Seq are not 

 accurate because the graphical estimates of 8 and 

 G at any time during the third phase are subject to 

 considerable error. Nevertheless, the time course of 

 8cq plotted in figure 22 is reasonable: 8eq stays near 

 8 during the second phase and then drops rapidly 

 but does not jump to the neighborhood of 8k at the 

 beginning of the third phase. Thereafter 8 and 8pq 

 are close to each other until the succeeding depolari- 

 zation. 



The rapid fall in 8,.q at the beginning of the third 

 phase suggests even more strongly than does tiie 

 action potential itself that gNa falls rapidly, or gK 

 increases rapidly, or botli events occur at this voltage 

 or time. There seems little doubt that such con- 

 ductance changes occur. However, if these changes 

 are assumed to be voltage-dependent as they are in 

 squid axon, a difficulty arises. It has already been 

 shown that g changes of this type (g^a increasing and 

 gK decreasing with S) have slope conductances less 

 than their respective chord conductances. Further 

 analysis shows that the values of dg/d& have to be 

 inordinately small in order to prevent the values of G 

 from becoming negative at some voltages. The values 

 of dg/d& required to make S^q change as rapidly as 

 it does would make total G become negative in this 

 voltage range. There will be an unstable point on 

 the Ii,8 curve until rapid repolarization commences. 

 However, even after the point of instability has 

 disappeared G remains negative. A G < o is contrary 

 to experiment. There is no sign of regenerative 



