266 



HANDBOOK OF PHYSIOLOGY 



CIRCULATION I 



depolarization and then falls rapidly. It reaches its 

 resting level, maximum diastolic conductance (Gr), 

 in less than loo msec and decreases to its minimum 

 level, 0.3 Gr, just before the onset of rapid repolariza- 

 tion at 400 msec. During the third phase, G increases 

 rapidly to Gr- During the slow diastolic depolariza- 

 tion G falls with £. If the distinction between slope 

 and chord conductance is kept in mind, the results 

 shown in figures 21 and 22 severely limit the possible 

 mechanisms of repolarization. Because of the con- 

 fusion in the literature and the apparent stringency 

 of the limitations imposed by Weidmann's data, the 

 relationships between chord and slope conductances 

 will be discussed further. 



SLOPE AND CHORD coNDUCT.'\NCES. The relationship 

 between G (slope) and g (chord) conductances 

 can be obtained by writing Ij as the sum of the in- 

 dividual ionic currents, writing each ionic current 

 as the product of a chord conductance and the cor- 

 responding driving force (equation 8), and then 

 differentiating with respect to £. The equation for 

 liis 



li = gNa(S - £n») -t- gK(S - Sk) -I- gci(S - Sci) (13) 



It will be assumed that gci is constant throughout the 

 action potential and that gxa and gK are functions 

 of time and voltage, possibly of the same type as in 

 squid axons. Differentiating equation 13 with respect 

 to S, holding time fixed gives 



aim 

 as 



ai; 

 as 



-1-c, 



as 



'as 



aim 

 as 



as 

 'ae 



(■5) 



G = al,/as = gxa + (S - En.) -f- 



-f gK -I- (S - Sk) — - + gci 

 oS 



(14) 



Thus, generally speaking, the relationship between 

 g and G is not simple and it is difiicult to draw any 

 unequivocal conclusions about chord conductance 

 from measurements of slope conductance. In parallel 

 with the definition of specific ionic chord con- 

 ductance, a specific ionic slope conductance can be 

 defined — e.g., the slope conductance for Na+ is 



Gnb = ,gNa + (fi — fiN-a)c>gN:, (IF,. Gj^n is CqUal tO 



gNa only if gjjii does not vary with 8. 



There is one further complication in estimating G 

 from experimental data. Part of the applied current 

 may flow through the memi)rane capacitor even 

 after the "transient" is "over" — i.e., S may be 

 altered by an applied current. The necessary cor- 

 rection can be obtained in differentiating I,,, = 

 li + C'.,„£; ec[uation 7a, c, with respect to S. 



Both terms on the right hand side of the expression 

 for G can be measured experimentally and thus G 

 can be calculated. The need for this type of correction 

 is apparent in figure 2 1^4. For depolarizing pulses it is 

 intuitively apparent that the "transient" is over 

 before the pulse is ended. Nevertheless, the final 

 slope is considerably less than the corresponding 

 slope at the same time in the zero current record. 

 The difference ijetween these two slopes (AS), divided 

 by the difference between the corresponding voltages 

 (AS), is an approximation to dt/dZ. The situation is 

 worse for hyperpolarizing pulses; here the "transient" 

 is persisting even at the end of the pulse and calcula- 

 tion of G from the final AS without using the cor- 

 rection indicated by equation 15 is inaccurate. 

 However, it should be noted that estimates of G based 

 on measurements made with two intracellular 

 microelectrodes are subject to large errors. The 

 corrections for the cal^le properties of the ti.ssue are 

 quite large and uncertain, particularly since the 

 correction depends importantly on the space con- 

 stant (66, 112, 122) which, in turn, depends on the 

 membrane conductance. Nevertheless, the large 

 corrections do not ob.scure the direction of the 

 changes in G during repolarization. 



The foregoing discussion shows why the long cur- 

 rent pulse method gives an estimate of total G rather 

 than total g. The change in £ is measured a con- 

 siderable time after the application of the current. 

 If the voltage-dependent conductance changes in 

 the heart are like those in the squid axon in re- 

 quiring time to reach completion, the final S is 

 reached only after the g changes are "'completed." 

 Since the change in S persists long enough to change g 

 (if it is voltage sensitive), G rather than g is measured 



(19)- 



Weidmann's estimates of slope conductances were 



not corrected for the capacitati\e component nor 

 can such a correction ije made from his puijlished 

 record, which shows the superposed effects of 20 

 unsynchronized current pulses. However, measure- 

 ments on the data obtained h\ I. Tanaka (iii) and 

 Cranefield & Hoffman (28, cf. fig. 21) indicate that 

 the capacitati\c term is of the order of 10 to 20 per 

 cent of the conducti\e term and thus is well within 

 the limits of error of the measurements. It will be 

 assumed, therefore, that \Veidmann's results are 

 indicative of G, but llic rectifying properties of the 

 meml)rane should be kept in mind. 



