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A general model for the dynamics of cell volume, global stability, and optimal control. (English) Zbl 1230.92014
Summary: Cell volume and concentration regulation in the presence of changing extracellular environments has been studied for centuries, and recently a general non-dimensional 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. 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 V.G. Boltyanskij [SIAM J. Control 4, 326–362 (1966; Zbl 0143.32004)] prove sufficient conditions for these controls in the commonly encountered two-solute case.

92C37 Cell biology
49N90 Applications of optimal control and differential games
49K15 Optimality conditions for problems involving ordinary differential equations
34D23 Global stability of solutions to ordinary differential equations
Full Text: DOI
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