Optimal control of a semibatch fermentation

Rational design and optimization of fed-batch and continuous fermentations

This chapter provides rational approaches to design and optimize fed-batch and continuous fermentations of both Mut+ and Muts (methanol utilization plus and slow) Pichia pastoris strains. The methods are described in detail for glycerol batch, glycerol fed-batch, transition, and methanol fed-batch/mixed feed/ continuous stirred tank reactor (CSTR) phases of the process based on glycerol and methanol consumption models. Cell density, broth volume, substrate feed rate, and the length of each phase are rationally designed to conduct runs with selected parameters for optimizing a process. The optimization is anchored by the impact of a specific growth rate/dilution time (for CSTRs) on productivity. Equations for simulation of a process with optimal parameters are derived for an optimal process design. This protocol can be used as a practical manual for process development of a P. pastoris recombinant fermentation, and also as a reference for fermentation of other microorganisms.

Versatile modeling and optimization of fed batch processes for the production of secreted heterologous proteins with Pichia pastoris

Background

Secretion of heterologous proteins depends both on biomass concentration and on the specific product secretion rate, which in turn is not constant at varying specific growth rates. As fed batch processes usually do not maintain a steady state throughout the feed phase, it is not trivial to model and optimize such a process by mathematical means.

Results

We have developed a model for product accumulation in fed batch based on iterative calculation in Microsoft Excel spreadsheets, and used the Solver software to optimize the time course of the media feed in order to maximize the volumetric productivity. The optimum feed phase consisted of an exponential feed at maximum specific growth rate, followed by a phase with linearly increasing feed rate and consequently steadily decreasing specific growth rate. The latter phase could be modeled also by exact mathematical treatment by the calculus of variations, yielding the explicit shape of the growth function, however, with certain indeterminate parameters. To evaluate the latter, one needs a numerical optimum search algorithm. The explicit shape of the growth function provides additional evidence that the Excel model results in correct data. Experimental evaluation in two independent fed batch cultures resulted in a good correlation to the optimized model data, and a 2.2 fold improvement of the volumetric productivity.

Conclusion

The advantages of the procedure we describe here are the ease of use and the flexibility, applying software familiar to every scientist and engineer, and rapid calculation which makes predictions extremely easy, so that many options can be tested in silico quickly. Additional options like further biological and technological constraints or different functions for specific productivity and biomass yield can easily be integrated.

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.

Unstructured model for L-lysine fermentation under controlled dissolved oxygen

An unstructured model was developed for batch cultivation of Corynebacterium lactofermentum (ATCC 21799) under controlled dissolved oxygen. The model is capable of predicting batch experiments performed at various initial substrate concentrations. By extending the batch culture model to a fed-batch model and using a heuristic approach to optimize the fed-batch cultivation, it is shown that fed-batch cultivation is superior to batch operation due to increased productivity at high substrate concentrations.

L-Lysine Production by Exponential Feeding of L-Threonine

The effect of L-threonine feeding in the production phase on L-lysine production by Brevibacterium flavum, which requires L-homoserine or L-threonine for cell growth, was investigated considering the concerted inhibition by L-threonine plus L-lysine, and the metabolism related to lysine production. Exponential feeding of L-threonine increased L-lysine production to 70 g/l about three times that without feeding. From the analysis of the metabolic flux, carbon flux of L-lysine synthesis pathway in the production phase after L-threonine feeding was higher than that in the growth phase. The results show that feeding of an inhibitory substance may increase the production, especially when the substance is necessary for the continuation of cell growth and/or production.

Suboptimal control of fed-batch bioprocesses using phase properties

A new method for the evaluation of suboptimal feeding strategies for fed-batch bioprocesses is introduced. This method is based on a time-local optimization of the process dynamics. To include global effects into the optimization, the process has to be partitioned into several phases with different local extremality conditions. The penicillin bioprocess is used to illustrate the method. One advantage of the proposed method is that the evaluated control function appears as a feedback law. Simultaneously, the new method allows the inclusion of constraints on the process states and the use of very complex models. Due to the simplicity and stability of the numerical procedure the method is robust against external perturbation. Therefore, it is suited for use in on-line controls.