CELLULAR ELECTROPHVSIOLOGY OF THE HEART 



249 



from holding membrane voltage constant. The re- 

 generative interaction between P^.i and S which 

 gives rise to the rising phase of the action potential is 

 prevented because S is controlled by the experimenter 

 and is not the consequence of uncontrolled changes in 

 li. Historically speaking, it was found that holding S 

 constant eliminates threshold and all-or-nothing 

 behavior, i.e., at £ = constant, I; is a continuous 

 function of time and at t = constant, li is a continuous 

 function of £. Such experiments led to the conclusion 

 that some membrane permeabilities depend on 8 in a 

 regenerative manner. 



MEMBRANE VOLTAGE CLAMPING. The experimental 

 procedure for holding the membrane voltage constant 

 in space and time at a value determined by the experi- 

 menter is called voltage clamping. Figure 4A is a 

 highly simplified diagram illustrating the principle of 

 voltage clamping. A giant axon is equipped with 

 long internal and external electrodes. If a battery is 

 suddenly connected between these electrodes, the 

 membrane voltage must change until it is equal to the 

 battery voltage, the battery supplying the required 

 membrane current. A switch is provided so that the 

 membrane voltage can be abruptly changed from one 

 value — usually 8r — to any other value. An ammeter 

 in series with one of the battery leads is used to 

 measure the current. An idea of the factors which 

 determine the current generated by the membrane 

 can be obtained by substituting the equivalent circuit 

 of figure 3B for the membrane in figure 4A. 



The voltage clamp is the latest step in a sequence of 

 increasing sophistication in experimental design. The 

 historical and logical sequences coincide and are 

 somewhat as follows: a) External electrodes were used 

 to record propagated action potentials, a crushed end 

 being used to secure a monophasic record, h) Intra- 

 cellularly placed electrodes permitted the quantitative 

 recording of resting and action potentials, c) Long 

 intracellular electrodes were used to eliminate local 

 circuit current flow, ionic current being calculated 

 from — CmdS/dt (90). d) Membrane voltage was held 

 constant, permitting the direct measurement of ionic 

 current and the elimination of regenerative interac- 

 tions between S and li (19, 62). 



In practice, voltage clamping is extremely difficult. 

 Successful clamping of a "healthy" axon is attainable 

 with present techniques only if meticulous attention is 

 paid to the significant details (19). The experimental 

 technique utilizes at least two internal electrodes, one 

 of which is long (62, 90, 112, 115). One electrode is 

 used to measure £ and the other to supply the required 



current over the length of the axon. The mea.sured 

 membrane voltage is subtracted from the desired 

 value. This difference is then amplified electronically 

 and the output is applied to the current electrode in 

 the direction which reduces the error. Electrode 

 polarization is the principal reason for using two 

 internal electrodes, i.e., the voltage at the internal 

 electrode supplying current may be far different from 

 that measured by the other electrode in the axoplasm. 

 In "healthy" axons, spatial nonuniformity of mem- 

 brane current further complicates the situation (19, 

 no, 115). 



With £ artificially held constant, the only independ- 

 ent variable in the nerve-electrode feed-back system 

 is time. The important experimental parameters are fi 

 and the external ion concentrations. The experimental 

 procedure is to measure membrane ionic current as a 

 fimction of the time following a sudden shift of S from 

 one value, usually £r, to another (fig. 4S). A series of 

 such records is obtained for different values of the 

 step voltage change (fig. 6). From these records the 

 dependence of 1 1 on voltage at different times can be 

 obtained (fig. 7). The contribution of Na+ to Ii can be 

 determined by measuring the effects of changes in 

 [Na+]o (fig. 6)'. 



Extensive voltage-clamp experiments on squid 

 axons have been conducted by Hodgkin et al. (62) and 

 Hodgkin & Huxley (57-61). Frankenhaeuser and his 

 colleagues (32, 33, 43) have recently obtained similar 

 results in a study of myelinated nerve fibers. The 

 Cole (19, 20) and Tasaki (iio, 115) groups have 

 recorded peak ionic currents considerably larger 

 than those observed by Hodgkin and Huxley. Since 

 these larger currents have much the same characteris- 

 tics (20) as those recorded by Hodgkin and Huxley, 

 there are no strong reasons for asserting that their 

 analysis does not apply in principle to these "hotter" 

 axons. Certainly, the analysis does give an accurate 

 description of the somewhat "deteriorated" axons on 

 which the original experiments were performed. The 

 voltagc-clamp experiments of Hodgkin et al. will now 

 be described in some detail. 



Ion Currents at Constant Voltage 



Figure i^B shows a recording of the current through 

 a membrane under a voltage clamp. At t = o, the 

 membrane was abruptly hyperpolarized (lower 

 record) or depolarized (upper record) by 65 mv and 

 then maintained at a constant voltage. In an\ real 

 system, the charge on a capacity and hence its voltage 

 cannot be changed instantaneouslv, since an infinite 



