The effect of maintenance on steady-state behavior in continuous cell cultures is studied theoretically with particular emphasis on stability and multiplicity characteristics. Bifurcation theory and stability analysis is applied to determine how the number and stability of steady-states depend on dilution rate and feed composition for Klebsiella pneumoniae feeding on mixed glucose-xylose substrates. The biological system is analyzed using a cybernetic modeling approach. We propose a numerical strategy which enables us to determine all possible steady-states for a given set of operating conditions. The algorithm exploits the polynomial nature of the equations. Results for a model without maintenance are compared to the predictions of a model with maintenance. It is shown that the model without maintenance effects and constitutive enzyme synthesis rate admits spurious steady-state solutions, which disappear when these effects are taken into account. In both cases multiple steady-states are observed over a range of dilution rates. In addition, the model with maintenance also predicts dynamic instability in the form of self-sustained oscillations. We have also investigated the effect of various parameters on the region of multiplicity to determine operating conditions which would enable experimental verification of our predictions. © 2008 IMACS.

Subramaniam Pushpavanam

Department Of Chemical Engineering

Mantravadi Vasudeva Kumar

Bifurcation (mathematics)

Biological systems

Cell culture

CONTINUOUS CELL CULTURE

Forecasting

glucose

Maintenance

Nonlinear analysis

System stability

Bifurcation analysis

Cybernetic modeling

Homotopy continuation

MAINTENANCE EFFECTS

metabolic regulation

Modal analysis

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IIT Madras

Mathematics and Computers in Simulation

In this work, the nonlinear behavior of a bioreactor coupled to a separator is analyzed. The main focus is on the effect of kinetics on the stability and multiplicity of the coupled system using a cybernetic modeling approach. One example of such a system is the activated sludge process. In this work we consider the growth of a culture of Pseudomonas putida in a medium containing phenol and glucose. We propose a cybernetic model which accounts for the regulatory features in the microorganism in a qualitative way in the aerator. These regulatory features control the rate of uptake of the substrates by the cells in the aerator. We use kinetics with self-substrate inhibition and cross-substrate inhibition effects. We observe a strong dependence of the window of multiplicity on kinetics. We depict that introduction of the more detailed kinetics into the model considerably widens the multiplicity region and helps the experimentalist to design the experiments. We use flocculation kinetics in the bioreactor which is the key for the settling of the suspended solids. The more realistic limiting flux condition is also introduced in the settler. We depict that under such conditions the resulting model of the coupled system exhibits nongrowth associated maintenance phenomena which occur at low dilution rates. The model equations governing the system behavior are ordinary differential equations and algebraic equations. In this work we vary the dilution rate and study the behavior of the system. We observe a shift in the uptake rates of the substrates as we vary the dilution rate. A two parameter continuation is also carried out to investigate the effect of other operating parameters on the nonlinear behavior. © 2009 American Chemical Society.

Industrial and Engineering Chemistry Research

Conceptual analysis of the effect of kinetics on the stability and multiplicity of a coupled bioreactor-separator system using a cybernetic modeling approach

Microbiology

Metabolic flux analysis of Escherichia coli in glucose-limited continuous culture. II. Dynamic response to famine and feast, activation of the methylglyoxal pathway and oscillatory behaviour

Journal of Process Control

On modeling of bioreactors for control

Chemical Engineering Science

Steady-state multiplicity in bioreactors: bifurcation analysis of cybernetic models

Biotechnology and Bioengineering

Unveiling steady-state multiplicity in hybridoma cultures: The cybernetic approach

Multiplicity and stability of steady states in continuous bioreactors: dissection of cybernetic models

Nonlinear analysis of the effect of maintenance in continuous cell cultures

Journal	Mathematics and Computers in Simulation
ISSN	03784754
Open Access	No