CELLULAR ELECTROPHVSIOLOGV OF THE HEART 



273 



hypothesis of the repolarization process in frog 

 ventricle quite similar to Weidmann's suggestions 

 (125) and the hypotheses of Shanes (106) and 

 Coraboeuf et al. (24), but the consequences of the 

 hypothesis have been examined in considerably 

 greater detail. As in other hypotheses, rapid 

 repolarization is regenerative in this model. Despite 

 this failure it easily integrates a number of experi- 

 mental observations. Since the model was analyzed 

 in some detail, it is perhaps worth presenting to 

 demonstrate the nature of the phenomena which give 

 rise to negative G's. In accord with Weidmann (125), 

 the starting point for the hypothesis was the Hodgkin- 

 Huxley Na+-K+ theory and an eflfort was made to 

 explain repolarization in the heart with a minimal 

 number of additional postulates concerning the 

 underlying changes in conductance. 



The postulates are as follows: /) Inactivation and 

 activation of gNa are described by two tiine-constants, 

 one short and one long. More precisely, in heart the 

 equation describing h as a function of time should 

 be written; hf = at(\ — hf) — /Sfhf and hg = a^ii 

 — hs) — /3sh, where h = hf + h^ (compare with 

 equation 9). The rate constants ai, /3f are large so 

 that the hf reaction is fast, being completed in a 

 matter of milliseconds, whereas the hs reaction takes 

 seconds to reach completion. More simply, there are 

 fast and slow components of inactivation and activa- 

 tion in the heart instead of only a fast component as 

 in the squid axon. This postulate is a simple explana- 

 tion for the tAP-ts relationship. 2) The kinetics of gK 

 change are about the same as in squid except that 

 depolarization decreases g^ instead of increasing it; 

 also, the changes occur somewhat more slowly than 

 in squid axons. This mechanism would reduce Na+-K+ 

 interchange during activity and could account for the 

 double peak of the action potential seen frequently 

 in papillary muscle from dogs and cats (fig. 21), and 

 occasionally in frog ventricle. The principal reason 

 for this postulate is derived from Hodgkin & 

 Horowicz' (55) recent investigations concerning the 

 nature of anomalous rectification in skeletal muscle. 

 In this tissue, depolarization reduces gK tremendously, 

 i.e., outflux of K+ is reduced. The functional signifi- 

 cance of this anomalous rectification in skeletal 

 muscle is not known, but such behavior in cardiac 

 muscle, which is depolarized about half the time, 

 would be efficient. Hutter & Noble (75) have recentlv 

 found evidence for anomalous rectification in heart. 

 A subsidiary assumption that gci remains constant 

 throughout activity is likely true, but is made here 

 entirely for convenience. 



On the basis of these assumptions, the events during 

 a frog ventricular action potential would he as 

 follows: After a threshold depolarization, gN.i and S 

 increase regeneratively. However, because of fast 

 inactivation and the relatively slow depolarization 

 rate, gNa reaches its peak value considerably before 

 the peak of the action potential and has declined to 

 about four times gK plus gci at the peak (4, 80). In 

 Purkinje cells the initial spike on the action potential 

 is clearly attributable to a higher peak gNa with a 

 consequent faster rate of rise and closer approach of 

 8 to Sn„. The "reason" for this behavior in Purkinje 

 fibers evidently is to increase conduction velocity. 

 At the start of the plateau, fast inactivation is nearly 

 complete and gK is still decreasing. This circumstance 

 could lead to first a decrease and then an increase in 

 8 depending on the relative rates of change of g^^ 

 and gK. Once gK has reached its final value, 8 will 

 slowly fall because of slow inactivation of gN.,- It is 

 assumed that at the plateau voltage gNa and gK do 

 not vary greatly with 8, so the plateau continues 

 until 8 enters a region where one or both conductances 

 vary rapidly with voltage. At this time repolarization 

 speeds up because of increasing gg and/or decreasing 

 gNa. The shape of fast repolarization is thus deter- 

 mined principally by the voltage dependencies of the 

 conductances, and trailing edges will be .super- 

 imposable regardless of the duration of the action 

 potential. Slow inactivation is incomplete at the 

 termination of the plateau, but any remaining gNa 

 is turned off by repolarization. Following repolariza- 

 tion, the fast moiety (hf) increases, or activates, 

 rapidly and hence excitability quickly returns. How- 

 ever, the slow moiety (hs) reactivates slowly, with a 

 time constant of about i sec (10). Thus, the overshoot 

 of an action potential evoked shortly after the return 

 of excitability will be nearly normal but the duration 

 will be much shorter than normal (fig. 20^4) because 

 hs has increased only slightly. After the upstroke, gNa 

 falls rapidly to a low level and fast repolarization 

 ensues immediately. As time passes, more and more 

 slow gNa (hs) becomes available, so that the plateau 

 becomes higher and the Iap longer. Thus the slow 

 gNa activation process accounts for the existence of 

 a plateau and for the dependence of Iap on the 

 stimulus interval. 



Like all hypotheses of repolarization which have 

 been advanced, this scheme has major defects. Its 

 greatest one is that the repolarization process is 

 regenerative. Another is that the kinetics of the 

 activation process must be different from those of the 

 squid axon. FitzHugh (40) has demonstrated two 



