2 74 



HANDBOOK OF PHYSIOLOCi' 



CIRCULATION I 



Stable values of £ for which h= o in the squid, one at 

 the resting level and the other about 50 mv more 

 positive (depolarized). Hence, recovery to the resting 

 state occurs only because g^ increases concurrently. 

 Otherwise, following the upstroke, S reaches a plateau 

 at the second stable state. This situation is accentuated 

 in the heart by the postulated decrease in gK- It is not 

 known whether the kinetics of the gN,, activation- 

 inactivation system can be modified to eliminate this 

 deficiency without destroying other important prop- 

 erties of the h system. The type of change required 

 would appear to be a reduction in the rate of change 

 of the rate constants as and jS. and proljably at and 

 /3f with voltage. Such a change would also reduce the 

 negativity of G during the regenerative phase of 

 repolarization. 



This scheme of repolarization in the Ii, S plane is 

 represented in figure 23B. The lines labeled ti, 

 t2,....,t6 are instantaneous Ii,£ curves at roughly equal 

 time intervals of the order of 0.2 sec. These curves are 

 the .sum of I^a (shown for one instant, t^) and Ik- 

 For the sake of simplicity gci is taken as zero. Ik 

 is assumed to vary linearly with S near Sk, and to 

 level off and become constant at larger depolariza- 

 tions, a variation conforming roughly with Hutter 

 & Noble's findings (75). In,, is assumed to vary with 

 S at any fixed time in the same manner as the Inj 

 curve at t = ts except that the magnitude of Ix,, at 

 any voltage decreases exponentially with time. This 

 decreasing In^, when added to Ik, leads to the series 

 of Ii,8 curves shown for different times. At any time, 

 G is positive for large depolarizations but there is a 

 region of negative G at lesser depolarizations. S will 

 pursue S(.q until the Ii,S curve is just tangent to the 

 S axis. At this time the threshold point disappears, 

 Seq jumps suddenly to the left and the third phase 

 ensues. If, prior to this time, a hyperpolarizing current 

 is applied which carries 8 to the unstable point, early 

 repolarization will be induced. Thus liie hypothesis 

 fails in this respect. The dashed line shows the path 

 the (8,-8) point would follow during spontaneous 

 repolarization. The shape of the curve is drawn about 

 the same as the experimental curve in figure 20C. 

 Behavior of this sort is described l)y Moore (92) for 

 the squid axon in isosmotic KCl. 



Another set of assumptions slightly different from 

 those shown in figure 23B was quantitatively 

 analyzed by Brady & Woodbury (4). With a digital 

 computer 8 and G were calculated as functions of 

 time. The results of one such calculation are shown 

 in figure 24, where calculated 8 and G Gr are plotted 

 against time. A measured action potential, scaled 



40-1 



ri.5 



(mV) 



FIG. 24. Comparison of the behavior of the model of re- 

 polarization shown in fig. 23S with a measured action po- 

 tential from frog ventricle. S (theory) and G/G r were calculated 

 from the model. For ease in comparison, £ (measured) was 

 scaled to the same peak height and duration as S (theory). 

 The negative values of G/Gr occur just after the !],£ curve 

 becomes tangent to the S axis (fig. 23S). Left hand ordinate 

 scale applies to potential curves and right hand ordinate 

 scale to the G/Gr curve. Abscissa: time in sec. [After Brady & 

 Woodbury (4).] 



to the same amplitude and duration, is sliown for 

 comparison. There is reasonably good agreement 

 between theory and experiment for 8. However, G 

 goes rapidly and markedly negative during the third 

 phase. The divergence between theoretical and 

 calculated 8 probably could be eliminated by adjust- 

 ment of the parameters in the equation, but the 

 negative G in tlie third phase is inherent in the 

 model. 



Using an analogue computer, FitzHugh (40) made 

 extensive calculations to demonstrate the properties 

 of the Hodgkin-Huxley equations. He also predicted 

 with reasonable success the behavior of squid giant 

 axon injected with tetraethylammonium chloride 

 (TEA). Tasaki >& Hagiwara (114) found great elonga- 

 tion of tlie action potential, to 20 msec or more, when 

 the squid axon was treated with TEA. FitzHugh 

 predicted this behavior by assuming that the time 

 course of the rise of gK was more than too times 

 slower than normal. Potential-time curves could be 

 reproduced accurately, but the measured slope con- 

 ductances could not be explained on this basis. 

 Although Tasaki and Hagiwara likened tlie TEA- 

 treated axon to a cardiac cell because a plateau was 

 induced, the likeness is only superficial since, in 

 marked contrast to heart cells, there is a distinct, 

 sharp threshold for repolarization in this tissue. The 

 resemblance is somewhat closer to cardiac cells in 

 low [Ca++] .sokuions. 



In summary, all the hypotheses of repolarization 



