CELLULAR ELECTROPHYSIOLOGY OF THE HEART 



255 



1.0 -r 



er-31mV 



£,= -16mV 



20 25 mSEC 



FIG. II. Kinetics of the g^tj, activation-inactivation process 

 determined from conditioning, testing step voltage experi- 

 ments on voltage-clamped squid giant axon. Inset shows the 

 time course of membrane voltage and method of measuring the 

 peak Na"*" current (Inb) which developed following the testing 

 step depolarization to (S — £,) = 44 mv from the conditioning 

 potential, fii. The ordinate is the ratio of the peak Na* current, 

 (INa)^l, developed by the 44 mv depolarization when pre- 

 ceded by a depolarization of £1 to the Na^ current developed 

 by the 44 mv depolarization alone, (lNs)£r. The abscissa is 

 the duration of the conditioning step. Curves for both plus 

 (depolarizing) and minus (hyperpolarizing) values of the 

 parameter £1 are given and these values serve to identify the 

 curves. Note that a preceding hyperpolarization increases the 

 iNa made available by a depolarization. Curve £i = —31 mv 

 was obtained from data shown in fig. 10. .\rrow by each curve 

 indicates the time-constant of the change in (lNa)£i/(lNa)5,. 



The greater the absolute value of £1, the shorter the time-con- 

 stant of the resulting changes in available iNa- [After Hodgkin 

 & Huxley (59).] 



FIG. 12. Steady-State activation of Na* conductance as a 

 function of transmembane potential. The open circles were 

 obtained by measuring the values of (lNa)£i/(lNa)Er at t = 30 

 msec for the various values of £1 in fig. 1 1 and plotting this 

 \alue against £1 = £ — £,. However, the ordinate has been 

 normalized, the quantity h having a maximum value of i.o 

 for £ — £r < — 40 mv. The horizontal dashed line shows the 

 value of h at the resting potential (£r) shown by the vertical 

 dashed line. Thus, at the £ , of the a.xon used in these experi- 

 ments, 0.6 of the maximum possible increase in gfja is made 

 available by a sudden depolarization. The solid curve is a 

 plot of the equation h = [i + exp (£ — £h)/7]~', where £h 

 is the value of £ at which h = 0.5. [.\fter Hodgkin & Hu.xley 

 (39)-] 



the S-shaped rise in gxa on depolarization and the 

 exponential fall on repolarization (fig. 9). The kinetics 

 of the changes in gK are the same except the changes 

 are much slower. Hodgkin and Huxley postulated 

 that a channel for K+ ions to mo\e through the mem- 

 brane is formed when four N molecules are in place 

 simultaneously and that the movements of N mole- 

 cules into and out of each position follows first order 

 kinetics. If n is the probability that any one of the 

 four sites is occupied, then the total probability that 

 a K+ channel exists is n^. Since each site follows 

 first order kinetics with the rate constants depending 

 on £, the time course of n following a sudden de- 

 polarization is of the form ( i — e"''*) because de- 

 polarization increases the probability that a site will 

 be occupied. Similarly, repolarization causes a 

 change in n of the form e"*". Since gK is proportional 

 to n^ the increase in gK on depolarization is S-shaped 



e '"". Hodgkin and Huxley described the kinetics 

 of gK changes by the equation 



n) - (3„n (9) 



gic 



gxn^ 



and 



where li — dn dt and the rate constants On and ^n 

 are functions of S but not of time. The latter defini- 

 tion means that a„ and /i,i instantly assume the 

 appropriate value when 8 is changed. The rate 

 constants also depend on temperature with a Qio 

 of about 3 (60) and calcium concentration (45). 

 Depolarization increases an and decreases /?„. 



Similar equations were used to describe the kinetics 

 of gxa changes. If m is the probability that an M 

 molecule is in place and h the probability that an H 

 molecule is in place, then the total probability for 

 the existence of a Na"*" pathway is m% since three M 

 molecules and one H molecule are required. Thus, 



SXa 



is described bv 



of the form (i — e ' 



changes gK along a curve that is proportional to 



whereas repolarization ^ ~ _3h ^ 



«„,( I — m ) — 3mm, 



h = ai,(i — h) — /3iih (10) 



