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Publication Citation: A General Model for the Dynamics of Cell Volume, Global Stability, and Optimal Control

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Author(s): James D. Benson;
Title: A General Model for the Dynamics of Cell Volume, Global Stability, and Optimal Control
Published: February 11, 2011
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 Boltayanski prove sufficient conditions for these controls in the commonly encountered two-solute case.
Citation: Journal of Mathematical Biology
Keywords: Cellular mass transport ; optimization ;stability ;cryobiology ; sufficiency theorem
Research Areas: Life Sciences Research, Modeling
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