title: Upper and lower bounds from the maximum principle. Intracellular diffusion with Michaelis-Menten kinetics.
abstract: Analytical bounding functions for diffusion problems with Michaelis-Menten kinetics were recently presented by Anderson an Arthurs, 1985 (Bull. math. Biol. 47, 145-153). Their method, successful to some extent for a small range of parameters, has the disadvantage of providing a weak upper bound. The optimal approach for the use of one-line bounding kinetics is presented. The use of two-line bounding kinetics is also shown, in order to give sufficient accuracy in those cases where the one-line approach does not provide satisfactory results. The bounding functions provide excellent upper and lower bounds on the true solution for the entire range of kinetic and transport parameters.
authors.forename: M C
authors.initials: MC
authors.lastname: Regalbuto
authors.forename: W
authors.initials: W
authors.lastname: Strieder
authors.forename: A
authors.initials: A
authors.lastname: Varma
mesh_terms: D001692:Biological Transport; D002477:Cells / Q000378:metabolism; D007700:Kinetics; D008433:Mathematics; D008962:Models, Theoretical