On the Mathematical Modelling of EPS Production by a Thermophilic Bacterium

Abstract

This paper presents experimental data coming from a batch fermentation process and theoretical models aiming to explain various aspects of these data. The studied process is the production of exopolysaccharides (EPS) by a thermophilic bacterium, Aeribacillus pallidus 418, isolated from the Rupi basin in South-West Bulgaria. The modelling approach chosen here is: first, biochemical reaction schemes are formulated, comprising several reaction steps; then the reaction schemes are translated into systems of ordinary differential equations (ODE) using the mass action law; then the ODE systems are studied by means of numerical simulations. The latter means that the ODE systems are parametrically identified in order to possibly fit the experimental data. A main peculiarity of the proposed reaction schemes, resp. models, is the assumption that the cell biomass consist of two dynamically interacting cell fractions (dividing and non-dividing cells). This assumption allows us to implement certain modelling ideas borrowed from enzyme kinetics. The proposed models are compared to a classical model used as reference. It is demonstrated that the introduction of the two cell fractions allows a much better fit of the experimental data. Moreover, our modelling approach allows to draw conclusions about the underlying biological mechanisms, formulating the latter in the form of simple biochemical reaction steps.

Keywords

• batch fermentation processes, thermophilic