Solute transport with Michaelis–Menten kinetics for in vitro cell culture.

The article focuses on developing and analyzing a mathematical model of solute transport with Michaelis–Menten (M-M) kinetics in traditional static in vitro cell culture setups, where a monolayer of cells at the base of a petri dish metabolizes solutes such as oxygen or drugs. The model reduces the reaction-diffusion system to nonlinear Volterra integral equations, enabling derivation of approximate analytical solutions valid for small and large values of the parameter β (the ratio of initial solute concentration to the M-M constant), as well as for small time and steady-state conditions. These analytical solutions, validated against numerical computations, clarify how key parameters influence solute concentration at the cell surface, offering practical tools to optimize experimental design, such as determining solute metabolism rates, maintaining desired solute levels, and estimating time to steady state. The work aims to assist experimental researchers by providing accessible mathematical insights into solute dynamics within in vitro cell culture environments without requiring extensive computational resources.