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Updated: Jun 6, 2026

The Use of Chemostats in Microbial Systems Biology
Published on: October 14, 2013
A general model for the dynamics of cell volume, global stability, and optimal control
James D Benson1, Carmen C Chicone, John K Critser
1Mathematical and Computational Sciences Division, National Institute of Standards and Technology, Gaithersburg, MD, USA. james.benson@nist.gov
None:
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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