Oscillations in continuous cultures of microorganisms: Criteria of utility of mathematical models

Abstract

This article proposes a new approach to the modeling of continuous cultures of microorganisms based on the concept of universality classes. Instead of analysis of concrete sets of equations, vast classes including models with identical qualitative features should be studied. The class of models of the second order is the simplest one, and it is analyzed in order to demonstrate the mathematical methods used. The authors have shown that the simplest model usually used for the description of continuous cultures is sensitive to even slight modifications. The modified model changes its properties and gives rise to a class of models that are applicable to the description of damped and nondamped oscillations of biomass and substrate concentrations in a fermenter. Irrespective of the mode of the initial model modification, the oscillations have a number of common features. These features can be used as the criteria of utility of this class of models for simulation of culture behavior. Two models of the class in question (with nonzero maintenance coefficient and nonconstant yield) are analyzed using these criteria.

Multiplicity and stability analysis of microorganisms in continuous culture: Effects of metabolic overflow and growth inhibition

“…To cope with these requirements, a quantitative knowledge of culture dynamics and stability is needed which can help to understand, optimize and control a process, particularly in continuous culture. Although the dynamic behavior of microorganisms in continuous culture has been the objective of a number of theoretical works since the late sixties (Chen and Chang, 1984;Ivanitskaya et al, 1989;Koga and Humphrey, 1967;Luong, 1987;Mihail and Straja, 1988;Ramkrishna et al, 1967;Williams 1967;Yang and Humphrey, 1975;Koga, 1969, 1973), more thorough and comprehensive experimental studies have been reported only recently (Axelsson et al, 1992;Chen et al, 1990aChen et al, , 1990bClarke et al, 1988;Ghommidh et al, 1989;Grotz and Stephanopoulos, 1990;Javanmardian and Palsson, 1992;Jöbses et al, 1986a;Menzel et al, 1996;Zeng et al, 1996). These experimental studies revealed several phenomena, such as sustained oscillation and multiple stable steady states which can hardly be explained by previous theoretical studies.…”

Continuous culture models with intermediates

“…5 b) is characterized by the lack of steady states in some interval of biomass concentration. We consider the theoretical study of the class of S-P-X models of continuous culture as a necessary step in developement of general theory of biotechnological processes on the line of [7]. Particular results map be used in investigation of growth regulation of particular microorganisms.…”

An Alternative Approach for Oscillatory Behaviour Control in a Nonlinear Bioprocess

“…In (Crooke et al, 1980;Crooke and Tanner, 1982) it has been shown that for the model described by (1)-(3) with constant yield coefficient (Y=const) there is no SSO. However, a slight modification in the model may result in qualitatively different behaviour of the system (Ivanitskaya et al, 1989). Hence, to describe the oscillatory behaviour, it is often assumed that the yield coefficient is dependent on substrate concentration S in the following fashion (Essajee and Tanner, 1979;Huang, 1990):…”