Polyhydroxyalkanoates (PHAs) are microbial thermoplastics produced in a variety of micro-organisms as intracellular carbon and energy storage compounds. These compounds exhibit significant advantages over conventional polymeric materials as they are non-toxic, they come from renewable sources and they are 100% biodegradable. Polyhydroxybutyrate (PHB) constitutes the most important and widely studied representative of the PHAs. It is a biopolymer with mechanical properties similar to conventional commercial polymers like polypropylene or polyethylene. Despite the promise of these new materials, their introduction to the worldwide market is inhibited by a series of economic and engineering considerations. Commercially available biopolymers are at present, significantly more expensive than their synthetic alternatives. Therefore, there is an emerging need to reduce the overall cost of PHB production by designing novel processes and product separation/purification procedures in order to maximize its yield and productivity. Towards this direction, advanced mathematical models with simulation capabilities of the complex biochemical phenomena occurring in cell factories within a bioreactor, are of decisive importance.
The objective of the present work is to develop a structured, segregated modeling framework for the process design and optimization of the microbial PHB production process. The framework will comprise individual models at different length/time scales namely, metabolic and kinetic models at the single-cell level. At the present stage our focus is on the development of models at the cell-metabolism and polymerization-kinetics level in order to be able to predict both the concentration gradients of intracellular metabolites including PHB, as well as to account for the dynamics of the molecular build-up of polymer chains in terms of their molecular weight distribution (MWD), which in turn reflects the final mechanical properties of the produced biopolymer. Despite the fact that there is a large number of studies based on (structured and unstructured) metabolic models of biopolymer-producing bacteria, none of them has focused on the prediction of the MW properties of the produced polymer in microbial production systems.
Model Development
In the present study a mathematical model of different scales is developed for the description of the cell metabolism, in terms of substrate utilization, biomass growth and PHB accumulation, and at the same time, for the prediction of the molecular weight distribution of the produced biopolymer in Alcaligenes latus.
Sucrose, provided as carbon source, is assimilated by the cells by means of active transport and metabolized either for PHB accumulation and/or for biomass growth (synthesis of new cells) and maintenance.
The pathway of the central aerobic carbon metabolism that leads to the production of PHB and biomass growth in this bacterium consists of a large network of biochemical reactions. For the needs of this study part of the complex metabolic network is simplified into a single reaction step, since we are only interested in specific an not all the produced metabolites.
Initially, sucrose is converted into acetyl-coenzyme A (AcCoA) through the Entner-Doudoroff pathway. The main biosynthetic pathway of P(3HB) consists of three enzymic reactions. In the first reaction, two AcCoA molecules are condensed by 3-ketothiolase (PhaA) into one molecule of aceto-acetyl-coenzyme A (Ac-AcCoA). In the second reaction, the Ac-AcCoA is reduced by reductase (PhaB) to hydroxybutyryl-CoA (3-HBCoA) at the expense of NADH. In the final stage, the 3-HBCoA monomers are polymerized by synthase (PhaC) to form P(3HB).
Alcaligenes latus is a growth associated bacterium that has the ability to accumulate PHB even when biomass growth is not ceased. As long as the above three reactions take place, biomass growth from AcCoA occurs in parallel, in the presence of a nitrogen source, while catabolism of AcCoA also occurs through the Krebs cycle, where it is converted to CO2. The necessary energy for the synthesis of every molecule of residual biomass from AcCoA, is considered constant. The formula of the produced non-polymer biomass (residual) is assumed to be CH1.76O0.47N0.19, as determined by Yamane et al. (1995), through elemental analysis of A. latus cells containing PHB up to 45% of dry cell weight.
Finally, the accumulated P(3HB) can be hydrolysed into its building blocks (3-HB monomers) by the action of depolymerase (PhaZ) and then utilised by the bacteria as carbon and energy source, when carbon-limited conditions occur in the cells environment (i.e., depletion of carbon source).
The third stage of the enzymic reactions described above comprises a set of comprehensive, elementary reactions that constitute the enzymic polymerization mechanism of the monomer unit (3-HBCoA) into polymer P(3HB), which can be used as carbon source. The polymerization-depolymerization mechanism considered in this study consists of initiation, propagation, chain transfer to water and depolymerization reactions (Kawaguchi and Doi, 1992). The P(3HB) synthesis on the active site of polymerase is initiated by the reaction with the hydroxybutyryl-CoA monomer and is followed by the chain propagation reaction. The chain transfer reaction transforms the live (propagating) polymer chains into dead (inactive) polymer chains. Subsequently, under conditions of carbon starvation the produced (PHB) polymer chains degrade in order to be used as carbon source.
The rate of monomer production is assumed to be a constant fraction of the rate of substrate consumption, thereby associating the polymerization kinetic model with the metabolism of the cell. Notice that the connection point between the polymerization kinetic model and the central metabolism of A. latus bacteria is the metabolite 3-HBCoA. 3-HBCoA is produced from sucrose and at the same time is consumed for the formation and propagation of the PHB polymer chains. The dynamics of these two competing rates designate the accumulation of polymer within the bacterial cells. In order to calculate the rate of substrate consumption, a metabolically unstructured (lumped) model is employed, accounting for the dynamic production/consumption rates of biomass, carbon and nitrogen substrates and polyhydroxybutyrate.
Model Application
Initially, the metabolic and polymerization kinetic models are individually developed and verified. The unknown parameters (i.e., kinetic constants, monomer production rate, etc.) are estimated based on experimental data. At the first stage a uniform cell population is assumed and we focus on the single cell carbon metabolism (metabolic level) and the polymerization mechanism (kinetic level), with respect to the prediction of the molecular weight distribution of the produced biopolymer. In this framework and for the accurate development of the kinetic/polymerization model it is necessary to obtain information about the synthesis of monomer directly from the uptake rate of the carbon source and then its consumption rate in the polymerization process. The operation of the central carbon metabolism in A. latus for biomass growth and PHB accumulation is utilized, in order to obtain this kind of information. Furthermore the time evolution of the uptake rate of the carbon source derives from a lumped model of cell metabolism, comprising simple differential equations.
The developed mathematical model is able to predict the consumption rate of carbon and nitrogen sources, the dynamic evolution of biomass growth and polymer product accumulation and also the molecular weight distribution of the produced polymer, along the fermentation of A. latus bacteria.
References
• Beun J.J., Dircks K., van Loosdrecht M.C.M., Heijnen J.J., “Poly-b-hydroxybutyrate metabolism in dynamically fed mixed microbial cultures”, 2002, Wat. Res., vol. 36, pp. 1167–1180.
• Kawaguchi Y., Doi Y., “Kinetics and mechanism of synthesis and degradation of Poly(3-hydroxyburate) in Alcaligenes eutrophus”, Macromolecules, 1992, vol. 25, pp. 2324-2329.
• Yamane T., Fukunaga M., Lee Y.W., “Increased PHB productivity by high-cell-density fed-batch culture of Alcaligenes latus, a growth-associated PHB producer”, Biotechnol. Bioeng., 1995, vol. 50, pp. 197–202.