252 



HANDBOOK OF PHYSIOLOGY 



CIRCULATION I 



current by the driving force on the ion. From equation 

 4c In:, can be written in the I'orm: 



iNa = gNa(S — SNa) 



(8) 



where the permeabihty term (gNa, unit, mhos/cm-) is 

 called the sodium chord conductance and is defined 

 by equation 8. A similar expression can be written for 

 all other ions. There are other ways of expressing 

 the current through the membrane, e.g., equation 2C, 

 so the justification for using equation 8, aside from its 

 simplicity, is its usefulness in describing the experi- 

 mental results. In this regard Hodgkin & Huxley (57) 

 found that in normal [Na+]o, gNa is constant for in- 

 stantaneous changes in S, i.e., the current-voltage 

 curve is a straight line if the current is measured 

 immediately after 6 is changed. Thus, at a fixed S, 

 gNa must vary with time in the same manner as Inb 

 and similarly for gK and Ik- The constancy of g^a 

 over brief periods indicates that conductances cannot 

 change instantaneously, the implication being that 

 changes in conductance result from time-consuming 

 physical or chemical alterations in the membrane. 



One consequence of the finding that conductances 

 do not change instantaneously is a simple method 

 for checking the reliability of the separation of Ii 

 into I^a and Ik components and the consequent 

 calculation of gNa and gK from equation 8. It can be 

 seen in figure 8 that Ins is at its peak before Ik begins 

 to rise appreciably. If the membrane were suddenly 

 repolarized to the resting level at about the time of 

 the peak iNa (ca. 0.6 msec in figs. 8 and 9), gNa 

 would not have had time to change. Consequently 

 Ine = gNa(Sr — SNa) will bc larger because the 

 driving force has increased. The gNa calculated from 

 equation 8 for the new voltage and current should 

 equal the gNa calculated just before repolarization. 

 The agreement between the two methods of calcu- 

 lating gNa is good and is a further reason for defining 

 membrane ionic currents by equation 8 (58). How- 

 ever, Dodge & Frankenhaeuser (33) have found it 

 necessary to express the iNa of myelinated nerve 

 fibers in terms of a permeability and a driving force 

 defined by Goldman's constant field integration of the 

 membrane flux equation (equation 2c). 



For any particular clamping voltage gNa and gK 

 vary in time in the same way as Inb and Ik- However, 

 the variations of the conductances with voltage at 

 any particular time are much less than the correspond- 

 ing variation of the currents (fig. 13). Like iNa, gNa 

 rises to a peak in 0.5 to 1.5 msec, depending on 8, 

 and then falls to low values in another i or 2 msec. 

 In contrast, gK does not start rising for perhaps 0.6 



msec but continues to a sustained high value (fig. 9, 

 solid lines). The analysis of the conductance changes 

 consequent to a rapid, maintained depolarization is 

 the basis of the statements made above concerning 

 the permeability changes during activity in squid 

 nerve. Since the ionic current under voltage-clamp 

 conditions is a continuous function of \-oltage and 

 time, the behavior of the action potential of an 

 undamped nerve fiber should be predictable from an 

 adequate description of the voltage and time varia- 

 tions of gNa and gK under voltage clamp. However, 

 an adequate description must also include information 

 on how a sudden repolarization alters the con- 

 ductances and on the nature of the gNa inactivation 

 process. The first of these bits of information can be 

 deduced from the data in figure 9. In marked con- 

 trast to S-shaped rising curves of both gNa and gg 

 they fall exponentially after a sudden repolarization 

 (dashed lines). The time constants describing the fall 

 of the conductances depend on the final voltage. 



INACTIVATION AND ACTIVATION OF SODIUM CON- 

 DUCTANCE. The activation-inactivation process is 

 perhaps the most difficult and certainly the most 

 crucial concept involved in understanding the genesis 

 of the action potential and refractory period (59). 

 Hodgkin & Huxley (60) have described hypo- 

 thetically the variation of g^a with time and voltage 

 in terms of two separate but interacting rate processes. 

 These authors supposed that a membrane channel or 

 pathway through which Na+ can pass relatively 

 easily is formed when three M molecules and one H 

 molecule are in particular positions in the membrane. 

 Na+ conductance was then assumed to be propor- 

 tional to the number of these channels per cm-. The 

 probability that an M or H molecule is in the proper 

 position for channel formation would depend on the 

 transmembrane voltage. This variation can be ex- 

 plained by supposing that M and H are charged or 

 dipolar. 



The kinetics of the M substance is such that most 

 of these molecules are not in the effective position at 

 the resting potential — i.e., if M designates molecules 

 in the proper position and M', the molecules in other 

 regions of the membrane, then the equilibrium 

 between the two, M ^ M', is far to the right. A 

 large depolarization markedly increases the rate of 

 movement from M' to M positions and decreases 

 the rate of movement from M to M', so that the 

 equilibrium shifts far to the left. The time required 

 for this reaction to reach equilibrium following a 

 depolarization is less than i msec, but is very de- 



