Three-step linear pathway with mass action kinetics. A) Schematic representation of the three-step linear pathway. The pathway converts the substrate (S
1) into the product (S
4) using three steps, each one catalyzed by a specific enzyme (e
). B) Metabolite dynamics and enzyme profiles that minimize the time needed to reach a certain amount of product with buffered concentration of substrate (LPN3B) as presented in Equation (10). C) Pareto front obtained for the minimization of time needed to reach a certain amount of product and the intermediates concentrations as shown in Equation (15). D) Enzyme profiles for the selected points of the Pareto front. Control variables have been approximated using ρ=120 steps with fixed duration. Metabolites and enzymes are expressed in concentration units and time in seconds (s).