248 



HANDBOOK OF PHYSIOLOGY 



CIRCULATION I 



ments of li and the driving forces on the ions (equa- 

 tions 2C, 4c). 



Since it is desirable to measure Ii, it would be 

 experimentally convenient if Im and Ic could be 

 eliminated or controlled. Im can be made zero by 

 stimulating the whole axon simultaneously so that 

 the potential does not vary with distance along the 

 fiber. For this purpose a long, thin electrode is in- 

 serted axially in a squid axon (fig. 4J). Any current 

 from this electrode flows radially so that membrane 

 current den.sity is uniform. If the membrane prop- 

 erties are uniform, the change in S will be the same 

 everywhere. This procedure is referred to as "space 



'INTERNAL ELECTRODE 



EXTRACELLULAR 

 FLUID 



y 



EXTERNAL 

 ELECTRODE 



§5^ 



(mV) 



FIG. 4. Voltage clamping. A : principle of the voltage clamp- 

 A squid axon is equipped with long internal and external 

 electrodes and a fixed potential source (battery) is connected 

 between them. Switch (S) permits a sudden change of voltage 

 between the electrodes from one value, usually the resting 

 potential (Sr) to any other value (£), typically less than St. 

 An ammeter connected in series with the battery-electrode 

 system measures membrane current (Im). In this simplified 

 diagram, it is assumed that there is no resistance in the internal 

 and external electrodes or in the junctions between the elec- 

 trode and the extracellular and intracellular fluids. These 

 idealized conditions are unobtainable in practice, and elabo- 

 rate measures are required to achieve voltage clamping. 

 [After Woodbury (137)]. B: typical current records from a 

 clamped squid a.\on. At time zero, the switch was thrown 

 (from position i to position 2 in A). In the upper two records 

 S was 65 mv less than Sr so that the membrane voltage followed 

 the time course shown in the uppermost record. The ionic 

 current during this same period is shown immediately below. 

 Outward flow through the membrane is defined as positive. 

 The current surge that charged the membrane capacity 

 to the new voltage was too large and brief to show on the record, 

 which shows only ionic current. The lower two traces show 

 the same experiment, except that the membrane was suddenly 

 hypcrpolarized by 65 mv at time zero. The current is small 

 and steady throughout the hyperpolarization. Temperature, 

 3.8°C. [After Hodgkin H al. (62).] 



clamping." In a space-clamped axon I,,, = o, so that 

 equation 7a becomes 



0= Ic-h I 



(S=") 



(7b) 



The activity resulting from a suprathreshold stimulus 

 to a space-clamped axon is termed a membrane action 

 potential, as opposed to a propagated action potential 

 (62). 



CAPACITATIVE CURRENT. It might be supposed that 

 current cannot flow through a capacitor since there is 

 an insulator in the current flow pathway. However, 

 the flow of charges through the conductor to the sur- 

 face of the dielectric pushes charges of equal sign 

 away from the other conductor. So, although diff"erent 

 charges are moving, the same amount of charge 

 moves away from the capacitor as moves toward it. 

 Hence, a current flows "through"' the capacitor. A 

 current flowing into a capacitor alters the amount of 

 charge on it. The rate of change of charge (dq/dt) 

 must equal the current flowing in, i.e., capacitative 

 current is defined as dq/dt like any other current flow. 

 There is, however, a slight difiference in the meaning 

 of the term. In the conductor, dq dt refers to the 

 amount of charge passing a particular cross section 

 per unit time; in a capacitor, dq/dt refers to the rate 

 of change of charge stored on either conductor. Since 

 q = CS, the current through a capacitor is CdS/dt. 

 However, the membrane is not an ideal capacitor and 

 this equation is not exact (17, 61). The error is not 

 great for the present applications. Assuming that C,„ 

 is ideal. 



iZ . /9S \ 



(7c) 



In words, membrane ionic current is proportional to 

 the time rate of change of voltage in a space-clamped 

 axon. 



Just as keeping S invariant with distance eliminates 

 local current, so keeping S invariant in time eliminates 

 capacitative current. Since the membrane is capable 

 of changing its voltage via changes in permeability 

 and in Ii, it is necessary to supply an external source 

 or sink for Ii if the transmembrane voltage is to be 

 kept constant. In this case equation 7c simplifies to 



, /as as \ , ., 



Ii = I J — = — = o ) (7d) 



\ax at / 



where le is the current supplied by the external source. 

 There is another, overriding advantage accruing 



