Stability analysis of several non-dilute multiple solute transport equations

Abstract

Recently a new solute and solvent transmembrane cellular transport model accounting for non-dilute solute concentrations was introduced. This model depends on a second or third order polynomial expansion in mole fraction of Gibbs energy for solutes and solvents along with a mixing term that depends only on single solute data. This model is applicable to cells in so called semi-dilute anisosmotic conditions. The extents of these conditions are not immediately clear from within the theory. Therefore, in order to provide an estimate of the upper concentration bound of this model we rederive the original model in the practical molality form, apply a natural extension of the model to an arbitrary number of solutes, and provide concrete bounds on the maximal concentrations where the model may be stable, and thus likely physiologically relevant. Moreover, we apply a similar stability analysis for a simpler, and more classic model based on similar Gibbs energy. The results show that the classical model has an asymptotically stable rest point for all parameter values, whereas the new model does in fact become unstable at very high solute concentrations. This instability, however, occurs at concentrations that are most likely well beyond the intended applicability of the model.