Network thermodynamic analysis and stimulation of isotonic solute-coupled volume flow in leaky epithelia: an example of the use of network theory to provide the qualitative aspects of a complex system and its verification by stimulation.

A network thermodynamic model was developed to provide insights into the nature of isotonic solute-coupled volume flow in "leaky" epithelia, where the transepithelial volume flow is assumed to be primarily through the cellular pathway. The coupled flows of solute and volume at each membrane in this four membrane model are described by the practical phenomenological equations as developed by Kedem & Katchalsky (1958). The model contains one permeable non-electrolyte solute (s) and a fixed amount of an impermeable non-electrolyte (i) inside the cell. The cell is assumed to be capable of volume regulation under the steady-state experimental conditions simulated. A solute-pump, located in the basolateral membrane, uses feedback regulation to adjust Cs in the cell in order to maintain cell volume at or near control levels in all simulations. Model behavior is, in general, very consistent with experimental observations with respect to tonicity and magnitude of volume flow over a wide range of experimental conditions. Examination of the parameter space suggests the following important features when isotonic solute-coupled volume flow moves primarily through the cellular pathway: (1) the apical membrane reflection coefficient must be less than that of the basolateral membrane; (2) the basement membrane reflection coefficient must be small; (3) the apical membrane solute permeability and reflection coefficient are the two most "sensitive" parameters and need to vary in an inverse manner in order to maintain isotonicity when both solute and volume flows increase; and (4) relationships (1) and (3) above imply the need for at least two separate solute pathways in the apical membrane, one that is shared with volume flow and one that is not.

Effect of sodium content on sodium efflux from human red cells suspended in sodium-free media containing potassium, rubidium, caesium or lithium chloride.

1. Human red cells treated with lactose solution and loaded with NaCl and BCl subsequently exchange cation with a nutrient BCl medium. B is the same in cells and medium, and is either K, Rb, Cs or Li. In these circumstances Na always moves outwards with the concentration gradient, but the efflux is largely active.2. With suspensions in media containing Ca(2+), the total Na efflux depends on the amount of Na in the cells and on the nature of cation B. Thus for any given value of mean cell Na (Na(m)) in excess of 30 m-equiv/l. cells, the effect of B on the amount of Na efflux is K > Cs > Rb > Li, while with Na(m) between 0.7 and 5 m-equiv/l. cells, the sequence is Cs > Li > K, Rb. With Na(m) between 5 and 30 m-equiv/l. cells, intermediate sequences may be demonstrated for the effects of B on Na efflux. This applies both to the efflux itself and to the flux: concentration ratio, FCR.3. FCR for passive Na efflux in these circumstances is determined by adding strophanthin G to the medium. It varies inversely with the duration of exposure to Ca(2+) in the exchange and nutrient media, but not with the nature of cation B. FCR for passive efflux is probably little affected by the value of Na(m).4. By deducting passive from total Na efflux, active Na efflux is obtained, and variations in the latter with cell Na content, and with B, result in FCR curves similar to those obtained with total Na efflux.5. Total and passive Na efflux have also been measured in Ca-free media. Here the passive efflux is considerable, and with Na + K cells in KCl media FCR increases with Na(m), but in other systems this change is not significant. However, the rate of passive efflux into LiCl media is less than that for KCl or CsCl media. Owing to the magnitude of passive flux in Ca-free systems, the total Na efflux is also increased, but FCR for active Na efflux is quantitatively and qualitatively similar to that occurring in systems containing Ca(2+).6. The effects of B and Na(m) on Na efflux give a series of sequences for B which recall some of those obtainable when chemically modified glass membranes separate solutions of salts, and which are attributable to the charge on the membrane and the hydration of the cations involved. However, certain sequences obtained with red cells do not occur with glass membranes. This difficulty is resolved if it be assumed that throughout the range of Na(m) (0-80 m-equiv/l. cells) active B influx at the external cell face modifies linked Na efflux according to the series K > Rb, Cs > Li, while with Na(m) between 0 and 30 m-equiv/l. cells (and high complementary B), cations escaping passively compete with active efflux of Na inhibiting the latter according to the series K, Rb > Li > Cs. Both these series could theoretically be explained in terms of surface charges and hydration of cations.7. Li-loaded cells in nutrient KCl or other media failed to show active Li efflux.