title: Global stability and exact solution of an arbitrary-solute nonlinear cellular mass transport system.
abstract: The prediction of the cellular state as a function of extracellular concentrations and temperatures has been of interest to physiologists for nearly a century. One of the most widely used models in the field is one where mass flux is linearly proportional to the concentration difference across the membrane. These fluxes define a nonlinear differential equation system for the intracellular state, which when coupled with appropriate initial conditions, define the intracellular state as a function of the extracellular concentrations of both permeating and nonpermeating solutes. Here we take advantage of a reparametrization scheme to extend existing stability results to a more general setting and to a develop analytical solutions to this model for an arbitrary number of extracellular solutes.
authors.affiliation: Department of Mathematical Sciences, Northern Illinois University, Dekalb, IL 60178, USA. Electronic address: benson@math.niu.edu.
authors.forename: James D
authors.initials: JD
authors.lastname: Benson
mesh_terms: D001692:Biological Transport / Q000502:physiology*; D002462:Cell Membrane / Q000502:physiology*; D008954:Models, Biological
keywords: Cryobiology; Global stability; Jacobs model; Membrane mass transport; Nonionic transport; Two parameter model