240 



HANDBOOK OF PHYSIOLOGY 



CIRCULATION I 



force acting on a unit charge placed between the con- 

 ductors of a capacitor is directly proportional to the 

 amount of charge on the conductors. Therefore, the 

 potential difference between the conductors is also 

 directly proportional to the charge on them, the pro- 

 portionality constant being i/C. Since charges of 

 opposite sign are on the conductors, the charges on 

 one conductor will distribute themselves as closely as 

 possible to their counter charges on the other conduc- 

 tor, i.e., the charges are at the conductor-insulator 

 boundary. Capacity depends only on the geometry 

 of tlie conductors and the dielectric constant of the 

 insulating material between them. The capacity of 

 1 cm" of Purkinje cell membrane is about 10 ixF (126). 



Since ions can penetrate the membrane it obviously 

 is not a perfect insulator. This fact can be represented 

 by a capacitor shunted by a resistor. Thus, there must 

 be an electromotive force in the membrane-bathing- 

 solution system to supply charge to the membrane 

 capacitor as fast as it leaks off through the membrane 

 resistor. From the definitions of potential and capacity 

 it follows that the existence of a potential difiference 

 between the interstitial fluid and the cell plasm is 

 simply a reflection of the fact that unlike electrical 

 charges have been separated across the membrane by 

 nonelectrical forces. The formal expedient of repre- 

 senting the transmembrane potential in series with the 

 membrane capacity (112) thus has no precise physical 

 meaning in this system. In the absence of changing 

 magnetic fields, potentials can arise only from separa- 

 tion of charges, i.e., the creation of a double layer. 



Clearly, the separation of charge across the mem- 

 brane creates an electric field which will exert a force 

 on any ion within the membrane. For example, there 

 is a net tendency for K+ to diffuse from the inside of 

 the cell where its concentration is high to the outside 

 where it is low, but the excess positive charges on the 

 outside of the membrane repel and the negative 

 charges on the inside attract any cation within the 

 membrane. Consequently, K+ tends to diffuse out- 

 ward due to its concentration gradient and inward due 

 to the potential gradient. Thus, the net movement of 

 K+ through the membrane is determined by the 

 difference between these two factors. If the concen- 

 tration and potential gradients exert ecjual and oppo- 

 site forces on an ion, it is distributed at equilibrium 

 across a membrane. 



somewhat uncertain due to the difficulty of apportion- 

 ing the total ion content of a tissue between the intra- 

 cellular and interstitial spaces. Nevertheless, this un- 

 certainty does not obscure the direction nor greatly 

 alter the magnitude of the concentration gradients 

 In skeletal muscle, where the analysis is more precise, 

 the ion distribution is approximately the same. Since 

 radioactive tracer experiments show that these ions 

 can penetrate the membrane, it is necessary to con- 

 sider the forces that drive ions through the mem- 

 brane. 



The net diffusional flux (Mg; unit, mole/cm- sec) 

 of any substance (S) is proportional to the concentra- 

 tion gradient (grad [S]) where [S] is the concentration 

 of S but is in the opposite direction, i.e., substances 

 diffuse from regions of higher concentration to regions 

 of lower concentration.- The ease of movement of an 

 ion through a region is measured by the diffusion 

 constant (Dg; unit, cm'-/ sec). To a first approximation 

 the concentration gradient across a cell membrane is 

 the difference between interstitial ([S]o) and intra- 

 cellular ([S]i) concentrations divided by the thickness 

 of the membrane (5) 



Ms = -Dssrad [S] = -Ds([S]o - [S],)/6 



= Ps([S]i - [S]„) (i) 



where a net outflux is defined as positive and the 

 expression Pg = Ds/6 (cm/sec) is defined as the 

 permeability of the membrane to S. Mg is a vector 

 whose direction is that of —grad [S]. The one-way 

 flux is formally defined as the net flux when the other 

 concentration is zero, all other conditions remaining 

 the same. The permeability of a skeletal muscle cell 

 membrane to K""" is of the order of io~^ cm/sec and 

 that of an equal thickness of water about 10 cm/sec, a 

 contrast indicating the relatively great impermeability 

 of the membrane to ions. 



Equation i is useful for describing the movements 

 of nonionized substances through the membrane. 

 However, since ions are electrically charged particles 

 and there is a voltage gradient in the membrane, the 

 equation must be modified to take into account effects 

 of the electric field on ion movements. It is usually 

 assumed that the effects of concentration and poten- 

 tial gradients on ion fluxes are additive, i.e., that 

 equation i can be made applicable to ions by adding 

 a term on the right for the flux due to the electric 



ION EQUILIBRIUM POTENTIAL. Table I gives the approxi- 

 mate concentrations of Na+, K+, and Cl~ in the in- 

 terstitial and intracellular water of the frog ventricle. 

 The values for the intracellular concentrations are 



- Strictly speaking, activity not concentration should be 

 used throughout this section. However, in most cases the 

 important quantities are ratios of external to internal con- 

 centrations and these ratios are nearly equal to the corre- 

 sponding activity ratios. 



