Upper and lower bounds from the maximum principle. Intracellular diffusion with Michaelis-Menten kinetics.

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.