an:06004481
Zbl 1230.92014
Benson, James D.; Chicone, Carmen C.; Critser, John K.
A general model for the dynamics of cell volume, global stability, and optimal control
EN
J. Math. Biol. 63, No. 2, 339-359 (2011).
00288503
2011
j
92C37 49N90 49K15 34D23
Cellular mass transport; Optimization; Stability; Cryobiology; Sufficiency theorem
Summary: Cell volume and concentration regulation in the presence of changing extracellular environments has been studied for centuries, and recently a general non-dimensional 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. 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 \textit{V.G. Boltyanskij} [SIAM J. Control 4, 326--362 (1966; Zbl 0143.32004)] prove sufficient conditions for these controls in the commonly encountered two-solute case.
Zbl 0143.32004