Solving linear unbranched pathways with Michaelis–Menten kinetics using the Lambert W-function

In this paper, an n -step, linear and unbranched pathway with Michaelis–Menten kinetics is solved in a quasi-analytical way. The method, based on the optimal control theory, calculates the optimal enzyme concentrations while minimizing the operation time. In the computation of the solution, the Lambert W -function plays a fundamental role, due to the presence of a non-linear kinetic model. Our method allows us to obtain the generalized solution and to perform the sensitivity analysis of the catalytic parameters.