Unidirectional Flux Balance of Monovalent Ions in Cells with Na/Na and Li/Na Exchange: Experimental and Computational Studies on Lymphoid U937 Cells

Monovalent ion traffic across the cell membrane occurs via various pathways. Evaluation of individual fluxes in whole cell is hampered by their strong interdependence. This difficulty can be overcome by computational analysis of the whole cell flux balance. However, the previous computational studies disregarded ion movement of the self-exchange type. We have taken this exchange into account. The developed software allows determination of unidirectional fluxes of all monovalent ions via the major pathways both under the balanced state and during transient processes. We show how the problem of finding the rate coefficients can be solved by measurement of monovalent ion concentrations and some of the fluxes. Interdependence of fluxes due to the mandatory conditions of electroneutrality and osmotic balance and due to specific effects can be discriminated, enabling one to identify specific changes in ion transfer machinery under varied conditions. To test the effectiveness of the developed approach we made use of the fact that Li/Na exchange is known to be an analogue of the coupled Na/Na exchange. Thus, we compared the predicted and experimental data obtained on U937 cells under varied Li+ concentrations and following inhibition of the sodium pump with ouabain. We found that the coupled Na/Na exchange in U937 cells comprises a significant portion of the entire Na+ turnover. The data showed that the loading of the sodium pump by Li/Na exchange involved in the secondary active Li+ transport at 1–10 mM external Li+ is small. This result may be extrapolated to similar Li+ and Na+ flux relationships in erythrocytes and other cells in patients treated with Li+ in therapeutic doses. The developed computational approach is applicable for studying various cells and can be useful in education for demonstrating the effects of individual transporters and channels on ion gradients, cell water content and membrane potential.