CELLULAR ELECTROPHVSIOLOGY OF THE HEART 



245 



Generation of the Resting Potential 



It is clear, in principle, how the Na^-K"*" pump can 

 maintain internal ion concentrations. However, the 

 means whereby a neutral Na+-K+ exchange can 

 generate a transmembrane potential is not immedi- 

 ately apparent. If the pump were not operating, then 

 the potential across the membrane would be deter- 

 mined by the concentrations and relative membrane 

 permeabilities of the various ions. The voltage would 

 assume that value at which the net charge carried 

 through the membrane by all ions was zero, the 

 fluxes depending on voltage (equation 2c). In squid 

 axons the membrane is most permeable to K+ ions 

 and Pel is about 0.3 Pk (18). In frog skeletal muscle 

 at rest Pci is about twice Pk (55, 74). In both tissues 

 Pne is small, 0.05 Pk or less. Since the £k and Sci have 

 large negative values, it would be expected that, in 

 the absence of Na+-K+ pumping, a voltage would 

 develop at about the observed resting value, some- 

 where between Sn.i and £k, but closer to Sk- For at 

 this voltage, the net fluxes of K+ and Cl~ would not 

 be large, despite their relatively high permeabilities, 

 because the driving forces w^ould be small and the net 

 Na"*" influx would be the same magnitude, despite its 

 low permeability, because the driving force would be 

 large. In this situation, the cell would be slowly losing 

 K+ and slowly gaining Na"*" and Cl~. If the pump were 

 started and if the passive net fluxes of Na+ and K+ 

 were equal and opposite, then the pump would main- 

 tain the internal concentrations constant and, being 

 neutral, would not affect the voltage. It follows from 

 this argument that, in the steady state where all net 

 fluxes are zero and the potential is unchanging, Sr is 

 determined primarily by the relative permeabilities 

 of the membrane to Na+ and K^ and secondarily by 

 the pumping rate — e.g., the higher the value of 

 PNa/PK, the smaller Sr; the faster the pumping rate, 

 the greater Sr. In the steady state, CI"" must be dis- 

 tributed in equilibrium with the membrane voltage, 

 since it is not actively transported. Hence, Cl~ cannot 

 affect the steady-state voltage. Eccles' (38) diagram of 

 the driving forces and fluxes through the membrane 

 in the steady state (fig. 2) compactly summarizes the 

 foregoing discussion. The generation and maintenance 

 of the resting potential by a one-for-one Na+-K+ 

 exchange pump are treated in detail elsewhere (135). 



Effects of Changes in External Ion 

 Concentrations on Potential 



If the concentration of K"*" in the interstitial fluid 

 or in an artificial solution bathing a tissue is suddenlv 



EXTERIOR 



SURFACE 

 MEMBRANE I INTERIOR 



FIG. 2. Diagram of steady state passive and active fluxes 

 of Na* and K^ through the cell membrane of an excitable cell. 

 Vertical distance represents the electrochemical potential of 

 ion species. Downhill passise, or diff'usional, fluxes exceed 

 uphill passive fluxes. Net downhill diffusional fluxes are 

 matched by fluxes driven uphill by the energy consuming 

 Na^-K"*" pump. The height of a band indicates the relative 

 size of the flux in the direction of the arrow. £, — £k and £r — 

 SNa are the electrochemical potential diff'erences of K^ and 

 Na^, respectively, across the membrane. Inside the cell, the 

 electrochemical potential of K"*" is positive to the outside and 

 that of Na+ is negative. [After Eccles (38).] 



increased, the transmembrane potential immediately 

 decreases. This decrease results from the rise in K+ 

 influx, which reduces the charge on the membrane 

 until the increasing outflow of K+ and inflow of Cl~ 

 balance the increased K+ influx. The cells are now 

 in a nonsteady state, with the internal concentrations 

 slowly changing. The net current through the mem- 

 brane is zero, but the individual ionic fluxes are not. 

 For moderately large cells, the imbalance in individual 

 fluxes is so slight that the rate of change of internal 

 concentration is measured on a time scale of hours 

 and the voltage can be regarded as a constant in 

 short term experiments. 



The Goldman (49) constant field equation predicts 

 quite accurately membrane voltage as a function of 

 external ion concentrations. The equation for voltage 

 can be derived by writing the flux for each ion (equa- 

 tion 2C, generally limited to Na+, K+, Cl~), relating 

 these fluxes by the condition that the total membrane 

 cturent must be zero and solving for S: 



^„ [K-}o + |^[Na+]„ + |^[Cl-]. 



8=— In ?5 ^ (6) 



^ [K+],-|-5^[Na+Ji+-^[Cl-L 

 rK "k 



