Maximization of production of secreted recombinant proteins in Pichia pastoris fed-batch fermentation

Pontryagin's Maximum Principle has been applied for optimization of secreted proteins from Pichia pastoris fed-batch fermentation. The objective of this work is to maximize the total accumulated product per unit operation time under different given conditions and system constraints. To obtain optimal solutions, an automated curve-fitting software, Table Curve 2D, was employed to construct the necessary mathematical models and solve the complicated functions. In the solution processes, the end of the glycerol batch phase was defined as the initial state of the system, the end of the methanol fed-batch phase as the final state, the cell mass produced along with product accumulated as state variables, and the specific growth rate (mu) as the control variable. Initially, a relationship between the specific production rate (rho) and mu was established. Then, according to Pontryagin's Maximum Principle, the admissible range of mu and its trajectories for the optimal operations were determined. Four representative cases with different combinations of the operation time along with the initial and final states were evaluated. A close correlation was obtained between the predicted values of the model equation with the experimental results from the Pichia pastoris fed-batch fermentations producing secreted alpha-galactosidase. The approaches proposed here greatly simplify the computational processes and validate the optimization strategy as a generalized approach to maximize the yield from fed-batch fermentations.