Abstract
Cell volume and concentration regulation in the presence of changing extracellular environments has been studied for centuries, and recently a general nondimensional model was introduced that encompassed solute and solvent transmembrane flux for a wide variety of solutes and flux mechanisms. Moreover, in many biological applications it is of considerable interest to understand optimal controls for both volume and solute concentrations. Here we examine a natural extension of this general model to an arbitrary number of solutes or solute pathways, show that this system is globally asymptotically stable and controllable, define necessary conditions for time-optimal controls in the arbitrary-solute case, and using a theorem of Boltyanski prove sufficient conditions for these controls in the commonly encountered two-solute case.
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This work appeared as part of a doctoral dissertation (Benson 2009).
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Benson, J.D., Chicone, C.C. & Critser, J.K. A general model for the dynamics of cell volume, global stability, and optimal control. J. Math. Biol. 63, 339–359 (2011). https://doi.org/10.1007/s00285-010-0374-4
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DOI: https://doi.org/10.1007/s00285-010-0374-4