O

Dilution rate (h-1)

Figure 5. Comparison of steady-state behavior of a chemostat (solid lines) and a chemostat with recycle (dotted lines) using the following parameters: YX/S = 0.5 g DCW/g substrate, imax = 1.0 h— 1, KS = 0.02 g/L, S0 = 30 g/L, C = 2, and a = 0.5.

CSTRs in Series

In the single CSTR, the constant, controlled environment gives the advantage of being able to control the cellular-enzyme environment for maximum utility. Sometimes, however, a particular cell system will exhibit multiple properties of interest that can only be realized in different environments. The optimal environments for cell growth and product formation, for example, may be characterized by different temperatures, pH, and limiting nutrients. The configuration of CSTRs in series lends itself to those applications in which multiple environments are required.

Cell Growth. Bacterial growth in the presence of multiple carbon substrates often results in diauxic growth, in which cells preferentially metabolize a single substrate over all others. In a waste treatment application, the preferred substrate would be consumed by the microorganisms and the remaining substrates would pass through the system untreated. Configuring CSTRs in series provides a partitioning of cell metabolism so that less-favored substrates are consumed in subsequent stages.

CSTRs in series have been used to improve recombinant protein fermentations in which performance is threatened by plasmid instability (56,57) and lethal protein overproduction (30). Cells are grown to high density in the first stage without inducer so that plasmid-free cells have little growth advantage over plasmid-containing cells. Induction in the second stage results in higher productivity than the simple CSTR because the continuous introduction of plasmid-containing cells from the first stage reduces the ability of nonproductive cells to dominate the culture.

Consider the two-stage system for biomass production in Figure 6, in which a separate feedstream can be added to the second stage. The steady-state material balances for cells and substrate in the first reactor are identical to the single CSTR case (equations 1 and 3), with steady-state solutions as equations 5 and 8 for Monod growth. Considering the case without the second feedstream, the material balances on cell mass and growth-limiting substrate in the second stage can be written as

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