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

Area of Science:

• Biomathematics
• Biochemical Engineering
• Mathematical Biology

Background:

• Previous analytical bounding functions for diffusion with Michaelis-Menten kinetics provided limited accuracy.
• Existing methods offered weak upper bounds for a narrow parameter range.

Purpose of the Study:

• To present an optimal one-line bounding kinetics approach for diffusion problems.
• To introduce a two-line bounding kinetics method for enhanced accuracy when one-line is insufficient.
• To develop bounding functions providing excellent accuracy for all kinetic and transport parameters.

Main Methods:

• Development of a novel one-line bounding kinetics approach.
• Implementation of a two-line bounding kinetics strategy for complex cases.
• Validation of bounding functions across the full spectrum of kinetic and transport parameters.

Main Results:

• The one-line bounding kinetics approach offers an optimal solution for diffusion problems.
• The two-line bounding kinetics method significantly improves accuracy where the one-line approach is inadequate.
• The developed bounding functions yield excellent upper and lower bounds for the true solution.

Conclusions:

• The presented one-line and two-line bounding kinetics methods significantly advance the analytical treatment of diffusion problems.
• These improved bounding functions provide robust and accurate estimations for a wide range of parameters.
• The study offers a more reliable tool for analyzing diffusion with Michaelis-Menten kinetics.