(479c) Modelling and Bifurcation Studies of a Two-Stage Continuous Bioreactor for the Production of Poly-Beta-Hydroxybutyrate (PHB)

Biopolymers are gaining importance due to the potential for the production of biodegradable products and the use of renewable raw materials. Poly-β-hydroxybutyrate (PHB) is one such biopolymer whose production has been studied in detail (e.g., [1-3]). PHB belongs to the class of bacterial polyesters collectively called polyhydroxyalkanoates (PHAs). PHAs have properties similar to polypropylene and are important due to their complete biodegradability, with recognised potential applications in reducing disposable waste problems and in certain medical applications [2]. This paper will deal with the detailed mathematical modelling of microbial PHB production in an industrial reactor configuration, and the use of the model for steady-state and dynamic analysis of the process.

As mentioned above, the metabolic processes underlying the production of PHB are now reasonably well understood [1-3]. The biological function of PHAs in bacteria is similar to that of glycogen in mammals and starch in plants [1]. When subject to a large excess of carbon source (glucose) in relation to a second source such as nitrogen or phosphorous, most bacteria channel the excess carbon source to accumulate PHAs as a carbon and energy storage material [3]. When the carbon energy sources are exhausted, the accumulated PHAs will then be degraded to sustain cell growth. This phenomenon is exploited as a means of industrial production of PHAs, by subjecting microbial cells to growth under a large carbon source and a limiting secondary source. In practice, though the limiting nutrient could also be phosphorous, sulphur or oxygen, PHB production is normally induced with nitrogen as the second substrate, and by limiting its supply in comparison to that of glucose [2]. The bacterium Alcaligenes eutrophus is the most widely used organism for the production of PHAs as it is easy to grow, its physiology leading to PHA synthesis is well understood, and it accumulates large amounts of PHB (up to 80% of cell dry weight) in a simple medium under nitrogen-limited conditions [1]. The detailed information on the metabolic mechanisms leading to PHB synthesis in bacteria has led to the development of detailed models that consider the intracellular aspects of this process [4,5,6] . These have included mainly batch and fed-batch operating conditions [1,4,7,8,9], but also continuous conditions [2,5].

Biological processes are intrinsically complex and mathematical descriptions of them are proving invaluable in the chemical industry as they can aid in improving process design, operation and control [10]. A powerful methodology for describing the complex phenomena observed in biological cells is the cybernetic modelling framework. This technique hypothesises that cells have evolved optimal goal-oriented strategies as a result of evolutionary pressures [11]. Thus, unlike modelling based purely on kinetic considerations, cybernetic models consider biological cells to be optimal control systems that seek to maximise a specific performance index or goal [12]. The optimality hypothesis implies that cells direct the synthesis and activity of enzymes such that a nutritional objective (the goal) is achieved in an optimal manner [11]. This optimal resource allocation is attained by the introduction of the so-called cybernetic variables that modify the rates of enzyme production and of enzyme activation to tailor the metabolic reaction rates. Optimality is achieved by defining the cybernetic variables in accordance with the law of diminishing returns which states that, given a number of resources to be allocated among a certain number of alternatives, the amount of a resource allocated to a particular alternative is proportional to the ratio of the yield from that alternative to the resources allocated to it [13]. Depending on the nature of the metabolic pathway being examined, the definition of the cybernetic variables varies and this has been addressed in detail [11].

In this paper, the cybernetic model of continuous PHB production using Alcaligenes eutrophus  [5] is studied and extended to an industrial two-stage continuous process [14]. This model considers the three metabolic pathways - the glycolytic pathway, the pentose phosphate pathway and the TCA cycle - by which glucose and ammonium sulphate are assimilated by the cell and channelled into the production of precursors required for cell growth. It also accounts for the storage and degradation of excess carbon source in the form of PHB through the PHB synthesis and degradation pathways respectively. Two levels of cybernetic variables are defined ? one at the local level and the other at the global level [5]. The local cybernetic variables consider the individual strands of the metabolic pathways (production of growth precursors, production of PHB etc.) At the global level, competition between the different strands of the metabolic pathways such as between the production of cell growth precursors and of PHB are considered, resulting in the allocation of larger amount of resources for the synthesis of PHB when cells are exposed to an excess of glucose. Likewise, competition between pathways that account for the production of metabolites, one from glucose and the other from PHB, is also considered to account for the degradation of PHB when the carbon energy source is growth limiting.

The specific process considered in this study [14] consists of two reactors in series followed by a separation stage. In the first reactor, bacteria are grown on glucose and ammonium sulphate (the nitrogen source) in an environment where neither nutrient is limiting. This results in cell growth and appreciable cell mass levels. The output from this reactor is fed continuously to the second reactor to which only glucose substrate is fed. Any ammonium sulphate present in this reactor can come only through the stream fed from the first reactor. This results in the bacteria in the second reactor being supplied with an excess of glucose, which they channel preferentially into PHB than into the rest of the biomass. The output from the second reactor is sent to a separation unit where PHB is extracted from the biomass. In order to minimise wastage, the remaining biomass is broken down by various mechanisms (see [14] for details) to yield carbohydrate which is used as feed to the two reactors.

A bifurcation analysis will be presented employing the cybernetic model described above. Bifurcation analysis is a useful tool for studying the dynamic behaviour of a process [15] as it provides insight into features such as steady states and limit cycles, which information is valuable for efficient reactor design and control.   This study will specifically examine the effect of the amount of glucose fed to the two reactors on the productivity of PHB. The cost of glucose contributes significantly to the production cost of PHB [14], and is therefore an important consideration in process design. The analysis will also examine the effect of dilution rates on PHB productivity. These are the main process control variables and an understanding of their effect on the dynamic behaviour of the system will aid in designing robust control systems for the process.

References

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