Benson, J.
(2011),
A General Model for the Dynamics of Cell Volume, Global Stability, and Optimal Control, Journal of Mathematical Biology, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=904647
(Accessed March 13, 2025)
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A General Model for the Dynamics of Cell Volume, Global Stability, and Optimal Control
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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
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Journals
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Keywords
Cellular mass transport , optimization , stability , cryobiology , sufficiency theorem
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Created February 11, 2011, Updated February 19, 2017