CELLULAR ELECTROPHVSIOLOGV OF THE HEART 



267 



The fall in G below its beginning diastolic value 

 (Gr) during the plateau (fig. 22) has been interpreted 

 to indicate that the total membrane chord con- 

 ductance, g = gN„ + gK + gel. falls below its diastolic 

 value (gr). The following arguments show how this 

 interpretation may be fallacious. The simultaneous 

 changes in 8 and G during the slow diastolic de- 

 polarization suggest a fall in gK. If this drop in gK is a 

 concomitant of the decrease in £ (depolarization) 

 rather than of the passage of time, then dgK '^S is 

 negative rather than zero. There is conflicting opinion 

 on this point. Dudel & Trautwein (37) adduce 

 powerful evidence that the slow diastolic decrease in 

 G is due entirely to a fall in Gk. They conclude, 

 however, that the slow depolarization results from a 

 slow, time-dependent drop in Gk — i.e., slow depolari- 

 zation is a positive afterpotential similar to that of 

 squid axon. Shanes (106) postulates the occurrence 

 of time-dependent changes in gK throughout the 

 cardiac cycle. On the other hand, Hutter & Noble 

 (75) have found about the same relationship be- 

 tween S and G by varying S with an applied current 

 in Na+-free media as was found bv Dudel and Traut- 

 wein during diastolic depolarization. It seems more 

 likely, therefore, that the fall in G results from the 

 decrease in S rather than vice versa. A further indica- 

 tion that gK depends on £ is Tanaka"s (i 1 1) finding 

 of a constant G during diastole in nonspontaneous 

 toad atrial tissue. Thus, it is not unreasonable to 

 suppose that dgn/dS < o at least in the neighborhood 

 of £r and, since £ — 8k is always positive, Gr < gn- 

 Similarly, depolarization increases gN;,; hence, 

 5gN.i'5£ > o but £ — 8n;, < o so that Gxa < gxa. 

 Consequently, finding a G less than Gr during the 

 plateau does not justify the conclusion that g is less 

 than gr. 



SLOPE CONDUCTANCE AND CURRENT, VOLTAGE RE- 

 LATIONSHIPS. Some further idea of the physical 

 significance of slope conductance can be obtained by 

 studying figure 23. The curve labeled Im = o (fig. 

 23/I) is a hypothetical relationship between li and 

 8 in the heart at a particular instant during the 

 action potential. Voltage-clamp experiments would 

 be the most accurate way for obtaining the actual 

 curves. Figure 6 consists of such curves from squid 

 axon, obtained shortly and considerably after a 

 sudden depolarization. The Ii,£ curve shifts con- 

 tinuously in time from the early curve to the late 

 one. Another way to get an Ii,£ curve would be to 

 apply currents of different strengths to a ceil at a 

 fixed time during the action potential and calculate 



li by subtracting C,„fi from the applied current, 

 Im. Membrane slope conductance at any time and 

 at any membrane voltage is defined as the slope of 

 the Ii,£ curve. The G, measured at various times 

 throughout repolarization, is for I,n ^: o (cf. 4); 

 consequently, I, = — CmS- Since conductances are 

 presumably changing with time and voltage, each 

 measurement of G at I„, = o gives the .slope of an 

 Ii,£ curve at one time and one voltage. 



If the membrane voltage were set to some par- 

 ticular voltage, say £1 (fig. 23/I), and then un- 

 damped, an ionic current (Ii) would have to flow 

 through the membrane. Since the external current 

 has been reduced to zero, all the ionic current must 

 go to charge the membrane capacitor; hence S 

 begins to change. Since Ij = — C,n£, the positive 

 current (Ii) will steadily decrease £. If the Ii,£ curve 

 does not change with time, this process will proceed 

 at a continually slowing rate and finally cease when 

 Ii reaches zero at £0. The (8, Ii) point describing the 

 membrane at each instant will traverse the Ii,£ curve 

 from (81, Ii) to (80, o). The point (£0, o) is a stable 

 equilibrium point, since displacement of the voltage 

 from £0 creates a current which tends to restore the 

 voltage to 80. The slope of the curve is positive, so 

 G is positive in the region of a stable equilibrium 

 point. The voltage-time curve is of the form of 

 ^-tG,c„i as £ approaches £0, showing that fi also 

 decreases with time. 



On the other hand 83 is an unstable equilibrium 

 voltage. Although Ii = o at this point, any displace- 

 ment from it would be regeneratively magnified 

 and the \oltage would quickly change until either 

 point (£4, o) or point (£0, o) was reached — i.e., if 

 for any reason the voltage decreased, an outward 

 ionic current would develop which would addi- 

 tionally decrease the voltage. Thus if the Ii, fi curve 

 crosses zero with a negative slope, the zero current 

 voltage is an unstable equilibrium. An unstable 

 equilibrium \oltage is the same as a threshold voltage. 

 If the Ii,£ cur\e has a negative slope l)ut does not 

 pass through zero (curve I,„ = 2lm in fig. 23i-l) no 

 threshold is involved, but the voltage-time curve 

 has the same form (e ' "") in either case. Conse- 

 quentlv, in regions where G < o, |£[ is increasing 

 with time, i.e., |£| > o. 



In the absence of external current, Ii can he re- 

 placed by — Cfi on the Ii,£ diagram. On a — Crn£,8 

 diagram the application of a constant negative 

 (hyperpolarizing) current to the membrane im- 

 mediately changes — £ by the amount Im/Cn,, since 

 all current initially must flow through C,„. If the 



