Structure analysis of continuous cultures subject to periodic medium tuning

Continuous bioprocesses subject to time-invariant external influences are attractive due to ease of operation and control. In many bacterial, plant and animal cell cultures, culture conditions that favor high growth rates of cells or cell aggregates are frequently not conducive for formation of valuable metabolites and vice versa. A plausible solution to the problem of maximization of bioprocess productivity in such situations is a forced periodic operation of continuous bioreactors with cell growth being promoted over a portion of each cycle and formation of the desired product(s) being promoted over the remainder of the cycle. Such shift from cell growth stage to product formation stage and vice versa can be accomplished by altering a key culture parameter. A systematic analysis of dynamics of continuous bioreactors subject to periodic medium tuning is presented in this article. The limiting substrate is considered to be utilized partly for cell growth and partly for synthesis of desired metabolites. Periodic solutions are classified on the basis of their stability characteristics and other properties of these and conditions for their admissibility are identified. Existence of and stability characteristics of various types of periodic states are examined in detail for few specific examples and the transient behavior arising for each example is classified. Structural changes such as bifurcation of periodic states (limit, Hopf and period-doubling bifurcations) and appearance/disappearance of periodic states resulting from variations in operating parameters are examined for each specific example. The superiority of forced periodic operation of continuous cultures over steady-state operations of continuous cultures is demonstrated via appropriate numerical illustrations.