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J Math Biol. 2011 Aug;63(2):339-59. doi: 10.1007/s00285-010-0374-4. Epub 2010 Nov 10.

A general model for the dynamics of cell volume, global stability, and optimal control.

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1
Mathematical and Computational Sciences Division, National Institute of Standards and Technology, Gaithersburg, MD, USA. james.benson@nist.gov

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.

PMID:
21063873
DOI:
10.1007/s00285-010-0374-4
[Indexed for MEDLINE]
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