258 



HANDBOOK OF PHYSIOLOGY 



CIRCULATION I 



REFRACTORY PERIOD. The equations predict quite ac- 

 curately the size and shape of the action potential dur- 

 ing the refractory period (60, fig. 20). Two factors 

 determine the refractory period — inactivation of gxa 

 (decrease in hj and the persistent increase in gK follow- 

 ing repolarization. Inactivation reduces the gNa made 

 available hv depolarization and thus increases the 

 depolarization required to induce a regenerative ac- 

 tion. The delayed rise in gK following depolarization 

 speeds up the rate of repolarization tremendously and 

 the slowness of gK in falling during and after repolari- 

 zation lengthens and intensifies the refractory period, 

 because a stimulating current does not have as great 

 an effect on 6 when gK is above normal. Following the 

 upstroke of the action potential, h decreases from its 

 resting value of 0.6 to about o. i near the end of the 

 spike; thereafter, h increases to its resting value in 

 about 10 msec at 6°C. Slightly before h is minimum, 

 gK reaches its peak value and then decreases in a 

 roughly exponential manner, reaching its resting level 

 somewhat sooner than h (cf. 60, fig. 19). The abso- 

 lutelv refractory period ends when h becomes suffi- 

 ciently high that a depolarization causes a net Na+ 

 influx which exceeds the above normal net K+ efflux. 

 The relatively refractory period lasts until gK and h 

 have returned to their normal values. 



of such a calculation is shown in figure 15. The re- 

 quired conduction velocity was 18.8 m sec and the 

 comparable measured conduction velocity was 21.2 

 m sec. The values of gxa and gK during the action 

 potential are also plotted in figure 1 5. This figure is 

 a quantitative plot of the membrane conductance and 

 potential changes accompanying propagated activity. 

 It can be seen that considerable depolarization occurs 

 before gNa begins to change, but that thereafter g^a 

 rises steeply. This passive depolarization is caused by 

 local circuit flow into the advancing active region. 

 This passive depolarization proceeds until threshold 

 is reached (inflection of the S,t curve) where mem- 

 brane current flow reverses from outward to inward 

 owing to the rise in gxa- Peak gfja is reached shortly 

 before the peak of the action potential. Thereafter, 

 gxa decreases and gK increases rapidly; the conse- 

 quence is a rapid repolarization followed by the pro- 

 longed hyperpolarization, the effect on S of the 

 delayed fall in gK following repolarization. Total 

 conductance (gxa + gK) follows o time course closely 

 similar to that measured by Cole & Curtis [(18); cf. 

 (60, fig. 16)]. 



MEMBRANE PROPERTIES OF CARDIAC CELLS 



PROPAGATED ACTION POTENTIAL. The Calculation of 

 the response of a nerve to a current applied at a point 

 is difficult, since membrane current is a function of 

 distance along the fiber. In, = (i /rOa-S/St- (66, 88, 

 112) where rj is the resistance of a i cm length of 

 axoplasm, whereas ionic current is a function of time 

 and voltage as given by equation 12. This expression 

 for Ini can be substituted in the top equation of 12, 

 but the resulting partial diflferential equation is ex- 

 tremely laborious to solve. Considerable simplifica- 

 tion can be achieved, however, if it is assumed that 

 the theoretical nerve model is capable of propagating 

 an impulse of constant shape and speed (u) then, in 

 steady-state propagation, membrane current can be 

 expressed as a function of time, I,„ = (i /riU^)6^S/5t- 

 (60, 113). Thus in a propagating action potential Im 

 can be expressed as a function of time; and if tliis 

 expression for Im is substituted in equation 7b to re- 

 place the top equation of 12, there results a second 

 order ordinary differential equation in which t is the 

 only independent variable. This equation is much 

 easier to solve. However, since the conduction speed 

 of the model was not known, Hodgkin & Huxley (60) 

 tried difl"crent values of u until the calculated response 

 resembled a propagating action potential. The result 



The transmembrane action potential of a frog ven- 

 tricular cell at 20°C lasts about i sec, depending on 

 the rate of stimulation (fig. i). In contrast, the action 

 potential of a squid giant axon at the same tempera- 

 ture persists little more than i msec (fig. 15). Never- 

 theless, these two excitable tissues have a number of 

 electrophysiological features in common, e.g., high 

 [K+]i, [Na+]o, and [Cl-]o, and low [K+]o, [Na+]i, and 

 [Cl"]i; Na+ for K+ exchange pumps; resting poten- 

 tials in the range 60 to 80 mv; rising phases of the 

 action potentials brought about by a specific increase 

 of the membrane permeai^ility to Na+; and inactiva- 

 tion of gxa- These facts indicate that electrical activity 

 in cardiac tissue and the squid axon are attributable 

 to the same sorts of underlying mechanisms. The 

 major difference is in the repolarization process. Re- 

 polarization in heart cells is poorly understood, since 

 it has not been technically feasible to do voltage-clamp 

 experiments on single cardiac cells. Pacemaker ac- 

 ti\ ity is not unique to cardiac cells since a continued 

 sinall depolarizing current applied to a squid axon is 

 sufiicient to make the membrane model oscillate in- 

 definitely, although trains of spikes in real axons tend 

 to terminate (16, 77). Three aspects of the electrical 

 properties of cardiac cell membranes are discussed. 



