CARDIAC MUSCLE CONTRACTILITY 



159 



On the other hand, it does not seem that the 

 chemical activity of the bulk of intracellular potassium 

 can be greatly different from what it would be in free 

 solution, since studies on osmotic pressure of cells in 

 which the principle cation is potassium show that the 

 cells are in osmotic equilibrium with the medium (54), 

 and therefore the potassium must be osmoticaily ac- 

 tive. The high electrical conductiviy of the proto- 

 plasm of cells leads to the same conclusion (141, 

 p. 281). Direct measurements of the mobility of K^'- 

 in the longitudinal axis of cell protoplasm also give 

 values not greatly different from that in free solution 

 (118, 145). Although some of these physical chemical 

 measurements show that the bulk of the potassium 

 must have a chemical activity the same as in free 

 solution and the potassium is completely exchangeable 

 under physiological conditions, nonuniform localiza- 

 tion or binding of a certain fraction of the potassium 

 cannot be ruled out. 



Ion Concentrations and Bioelectrical Potentials 



The luiequal distribution of inorganic ions across 

 the plasma membrane of living cells gives rise to an 

 electrical potential difference between the cell in- 

 terior and its environment. This has been appreciated 

 since the time of Bernstein (15), who suggested that 

 the membrane potential was due to the concentration 

 difference of potassium inside and outside the cell, 

 assuming that the membrane was permeable to po- 

 tassium ions but impermeable to all other ions present. 

 The theory required modification when Boyle & 

 Conway (28) showed that the cell membrane of the 

 frog sartorius was permeable not only to potassium, 

 but also to chloride and bicarbonate ions. The changes 

 in the membrane potential with changes in concen- 

 tration of sodium and potassium in the bathing fluid 

 were interpreted by Boyle and Conway as consistent 

 with the theory that the muscle was in a true Gibb.s- 

 Donnan equilibrium, the muscle membrane being 

 completely impermeable to protein and certain other 

 multivalent anions as well as to extracellular sodium. 

 The nondiffusibility of a fraction of intracellular anion 

 on one side of the membrane and of sodium on the 

 other thus gave rise to a "double-Donnan" potential, 

 the distribution of such permeating ions as K, CI, and 

 HCO3 following a relationship of the form (Nernst 

 equation) 



^ RT [CIJ. 

 E = In ; — - 



/•■ [Cl]„ 



RT [KL 



their usual significance, and / and refer to cell in- 

 terior and extracellular space. 



Although the cell membrane of the frog sartorius 

 appears to be virtually impermeable to sodium at 4°C, 

 this is not the case at higher temperatures, and in 

 general resting cell membranes probably have some 

 low degree of permeability to the sodium ion. This, 

 combined with the fact that sodium ions are thought 

 to enter the cell during the action potential, requires a 

 mechanism for the active transport of sodium ions 

 out of the cell. Therefore it is now not usualK' con- 

 sidered that the distribution of all the ions can be re- 

 garded as a true thermodynamic equilibrium in- 

 volving an inert membrane with selective permea- 

 bility for different ionic species (Gibbs-Donnan equi- 

 librium). Instead, a steady state exists in which 

 sodium diffuses into the cell at a rate determined by 

 the magnitude of the membrane permeability for 

 .sodium and the electrochemical potential gradient of 

 sodium across the membrane, and is then pumped 

 out of the cell by some kind of active transport system. 

 The pump is considered to be nonelectrogenic (see 

 299, p. 57), i.e., no net charge transfer across the 

 membrane occurs with active transport. The passive 

 diffusion of sodium into the cell can be considered to 

 affect the membrane potential according to the equa- 

 tion 



RT [K]„ + *[Na]„ 

 E = In 



E [K], -I- 6[NaJ. 



(3) 



(2) 



where E is the membrane potential, R, T, and F ha\'e 



where b is the ratio of the membrane permeability for 

 Na and K, PNa/PK- Since h is thouglit to be about o.oi 

 for muscle and nerve, fe[Na] , is small compared to 

 [K],, and at high [K]„ and low [Na]o, ^[Na],, can be 

 neglected also and the equation reduces to the form of 

 equation 2 .so that £ is a linear function of [K]„. At 

 low [K](, in the physiological range, i[Na]o becomes a 

 significant fraction of the sum [K]o + 6[Na]o and the 

 linear relationship between E and K„ no longer exists 

 (142). An example of experimental data on this point 

 is shown in figure 8. The nontransported but permeat- 

 ing anions, such as chloride and bicarbonate, will be 

 distributed passively according to their electrochemi- 

 cal potential gradients. 



It is perhaps worth pointing out that the magni- 

 tude of the potential difference across the membrane 

 in this system is influenced by the difference in mem- 

 brane permeabilitN' to sodiimi and potassium ions. If, 

 for example, the membrane exhibits little selectivity 

 between sodium and potassium in regard to passive 

 diffusion (i.e., h becomes much larger, approaching 

 the ratio of the diffusibility of the ions in free solution), 



