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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|
|PDF version:||Click here to retrieve PDF version of paper (254KB)|