254 



HANDBOOK OF PHYSIOLOGY 



CIRCULATION I 



mediately following a sudden repolarization cannot 

 produce an increase in gxa any greater than that 

 obtained immediately prior to the repolarization, 

 i.e., proportional to the fraction of H molecules in 

 position. This consideration suggests the experimental 

 method actually used by Hodgkin & Huxley {59) to 

 measure the kinetics of the activation-inactivation 

 process — a two-step x'oltage experiment analogous 

 to the classical conditioning-testing stimulus tech- 

 nique. 



The records obtained in one such experiment are 

 shown in figure 10. The testing stimulus is a main- 

 tained depolarization of 44 mv and the conditioning 

 stimulus is a 31 mv hyperpolarization of variable 

 duration. The response is the ratio of the conditioned 

 peak inward (Na+) current to the unconditioned 

 peak iNa- It can be seen in figure 10 that peak Ix„ 

 increases as the duration of the hyperpolarizing 

 conditioning step is increased. The ratio of con- 

 ditioned to unconditioned current is plotted as a 

 function of the duration of the conditioning step in 

 the upper curve of figure i i . The curve is exponential 

 with a time constant of about 4 msec (arrow). The 

 other curves in figure 1 1 were obtained for different 

 values of the conditioning step voltage (£1). This 







44 

 44 



31 



e-Er 



(mV) 



I — 'I 



44 



44 



31 

 44 



-44 



vf 



-44 



T^ 



V 



50 

 TIME (mSECl 



50 



FIG. 10. Time course of activation of available gna- Left 

 column: the time courses of membrane voltage which gave 

 rise to the corresponding current records at right. Top and 

 bottom current records are controls which show the Ij resulting 

 from a depolarization of 44 mv. In intervening records, the 

 44 mv depolarization was preceded by periods of 31 mv hyper- 

 polarization of progressively increasing duration. As the dura- 

 tion of the hyperpolarization increased, the peak Inj increased. 

 The vertical bar by each current curve is the height of the 

 pezik Inu obtained in the upper record. Relative peak Ixa 

 is plotted as a function of the duration of the hyperpolarizing 

 step in fig. II, curve labeled Si = —31 mv. [After Hodgkin & 

 Huxley (59).] 



figure illustrates the major properties of the activa- 

 tion-inactivation system: a) Hyperpolarization (Si 

 negative) increases and depolarization decreases the 

 amoimt of activation in the steady state, h) Steady- 

 state activation is highly sensiti\e to voltage, as shown 

 in figure 1:2 where the fractional amount of steady- 

 state activation is plotted as a function of S. r) The 

 time required to reach a steady state also depends 

 upon the voltage of the conditioning step; this feature 

 is shown by the arrows in figure 1 1 w^iich indicate 

 the time constant of the exponential change in the 

 current ratio. Hodgkin & Huxley (59, p. 505) describe 

 these effects of voltage on g.x;, as follows: 



The early effects of changes in membrane potential are a 

 rapid increase in sodium conductance when the fibre is de- 

 polarized and a rapid decrease when it is repolarized. The late 

 effects are a slow onset of a refractory or inactive condition 

 during a maintained depolarization and a slow recovery 

 following repolarization. A membrane in the refractory or 

 inactive condition resembles one in the resting state in having 

 a low sodium conductance. It differs in that it cannot undergo 

 an increase in sodium conductance if the fibre is depolarized. 

 The difference allows inactivation to be measured by methods 

 such as those described in this paper. The results show that 

 both the final level of inactivation and the rate at which this 

 level is approached are greatly influenced by membrane po- 

 tential. .At high membrane potentials inactivation appears to 

 be absent, at low membrane potentials it approaches comple- 

 tion with a time constant of about 1.5 msec at 6°C. 



QiianUlat'we Description of Xerve Behavior 



If gx:, and gK have been sufficiently characterized 

 bv the voltage-clamp analysis, it should be possible 

 to predict the excitable properties of the undamped 

 nerve fiber. This possibility is strengthened by the 

 evidence that changes in membrane permeability 

 depend on membrane voltage rather than on mem- 

 brane current — i.e., voltage clamping eliminates 

 regenerative behavior, the shapes of the current- 

 time curves are independent of the size and direction 

 of the current, and current-voltage curves are con- 

 tinuous. To test this possibility, Hodgkin & Huxley 

 (60) formulated mathematical descriptions of gsa 

 and gK under voltage-clamp conditions, and with 

 these were able to predict with astonishing success 

 the excitable properties, potential changes, and 

 ionic movements in a nerve fiber under many con- 

 ditions. 



KINETICS OF CONDUCTANCE CHANGES AT CONSTANT 



VOLTAGE. Hodgkin and Huxley developed the kinetic 

 model for gx„ described qualitatively above to predict 



