Abstract
Analytical bounding functions for diffusion problems with Michaelis-Menten kinetics were recently presented by Anderson and Arthurs, 1985 (Bull. math. Biol. 47, 145–153). Their methods, 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.
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Literature
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Regalbuto, M.C., Strieder, W. & Varma, A. Upper and lower bounds from the maximum principle. Intracellular diffusion with Michaelis-Menten kinetics. Bltn Mathcal Biology 51, 325–335 (1989). https://doi.org/10.1007/BF02460111
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DOI: https://doi.org/10.1007/BF02460111