Continuous culture models with intermediates

Abstract

The number of stability of steady states of minimal structured models are determined theoretically. Regulation of two "bottle-necks" of cell metabilism by extracellular or intracellular intermediates is suggested. The mechanisms of this regulation include substrate and product feed-forward inhibition as well as feedback product control. The most complex system behaviour is obtained in models with feed-forward intermediate inhibition. I n particular these models exhibit multistability and two limit cycles. The maximum number of steady states decreases from five to four when the extracellular intermediate is changed by the intracellular one. The number of non-zero steady states is changed from four to two. The relevant features of phase-portrait appear to be independent of the choice of reaction rates. Therefore our results are suitable for a large group of the third order models. The possibility to verify the theoretical predictions experimentally is also discussed.Mathematical models which describe dynamics of continuous and batch microbial cultures are often classified into structured and non-structured ones. Non-structured models based on the hypothesis of a single "bottle-neck" reaction of cell metabolism can be successfully used to describe balanced microbial growth of microorganisms. When the growth rate changes, the fractions of cell components can also change. Structured models can describe such unbalanced growth of microorganisms. Two key steps lead t o the synthesis of biomass X from substrate S reflected in the above structured models [l]. The first step corresponds to production of intermediate P and the second one t o the biomass production. These SPX models are the simplest structured models. Therefore, they can form the basis for mathematical description of unbalanced cell growth. The great advantage of models with few variables is the possibility of not only numerical computer analysis but also of an analytic study. Thus, these models clarify the real mechanisms of dynamic phenomena in microbial cultures.Using the S P X models it is possible to simulate different phases of batch growth such as the lag-phase and the long-term period of linear growth, the phenomenon of false diauxy, broken growth curves corresponding to the change of "bottle-necks". These models explain the synchronous yield and specific growth rate oscillations during transients in continuous culture of C. Utilis [2]. The S P X imitational models*) allows to * We call the models imitational if they are capable of describing the real microbial processes not only qualitatively but also quantitatively. 4 Acta Biotechnol. 10 (1990) 5