| The bioconversion of glycerol to 1,3-propanediol (1,3-PD) was particularly attractive to industry because of renewable feedbacks and potential uses of 1,3-PD.1,3-PD was discussed as a bifunctional chemical on a large commercial scale, especially as a monomer for polyesters, polyethers and polyurethanes. In this paper, nonlinear mathematical equations of the enzyme-catalytic kinetics and genetic regulation were set up to describe the continuous and batch fermentations of glycerol by Klebsiella pneumoniae. The main work of this paper was summarized as follows:Firstly, a nonlinear dynamical system was presented to describe the continuous and batch fermentations of glycerol metabolism in K. pneumoniae, in which the enzyme-catalytic kinetics on the reductive and oxidative pathway, the inhibition of 3-hydroxypropionaldehyde (3-HPA) to glycerol dehydratase (GDHt),1,3-PD oxydoreductase (PDOR) and glycerol dehydrogenase (GDH), and the transport of glycerol and diffusion of products across cell membrane were all taken into consideration. Moreover, the enzyme-catalytic kinetics of GDHt, PDOR, GDH, pyruvate kinase (PK), pyruvate formate-lyase (PFL) and pyruvate dehydrogenase (PDH) were also investigated. Comparisons between simulated and experimental results indicated that the model could be used to describe the continuous fermentation under steady states reasonably. The intracellular concentrations of glycerol, 1,3-propanediol,3-HPA, succinic acid, lactic acid,2,3-butanediol (2,3-BD), format, ethanol and acetate acid could also be predicted for continuous cultivations. Multiplicity analysis for continuous cultures was developed. The simulation results disclosed that dihydroxyacetone, dihydroxyacetone phosphate, phosphoenolpyruvate, acetyl coenzyme A were not accumulated under continuous culture and all entered into the following step. Furthermore,3-HPA accumulation was disadvantageous for the formation of the target product 1,3-PD and the inhibition of 3-HPA to PDOR was stronger than that to GDHt and GDH which indicated that PDOR might be the rate-limit enzyme. This model would give new insights into the metabolic and genetic regulation of dha regulon of glycerol metabolism in K. pneumoniae.Thirdly, an expended mathematical model for the tryptophan operon regulation on the effects of repression, feedback enzyme inhibition, attenuation, interaction among genes and excretion of tryptophan was presented. The new model was first translated into the corresponding S-system version. The robustness of this model was then discussed by using the S-system model and the sensitivity analysis showed that the model is robust enough. The influences of cell growth rate on the biosynthesis of tryptophan, stability and dynamic behavior of the trp operon were also well investigated. Furthermore, a steady-state optimization model was established based on trp operon models according to indirect optimization method. The optimization results indicated that it was possible to attain a stable and robust steady state with a rate of tryptophan production increased more than 4.8 times in which the growth rate was kept as 0.00624h-1 and some key parameters were modulated.Fourthly, the fourteen-dimensional nonlinear dynamical system was presented to describe the continuous cultures and multiplicity analysis of the dha regulon for glycerol metabolism in K. pneumoniae, in which two regulated negative-feedback mechanisms of repression and enzyme inhibition were well investigated. The model describing the expression of gene-mRNA-enzyme-product was established according to the repression of the dha regulon by 3-hydroxypropionaldehy (3-HPA). Comparisons between simulated and experimental results indicated that the model could be used to describe the production of 1,3-PD in continuous fermentations. The new model was first translated into the corresponding S-system version. The robustness of this model was then discussed by using the S-system model and the sensitivity analysis showed that the model was sufficiently robust. Moreover, multiplicity analysis for continuous cultures was developed, and application of this analysis to the regulation of the dha regulon revealed two regions of multiplicity. The influences of initial glycerol concentration and dilution rate on the biosynthesis of 1,3-PD and the stability of the dha regulon model were also well investigated. The intracellular concentrations of glycerol,1,3-PD,3-HPA, repressor mRNA, repressor, mRNA and protein levels of GDHt and PDOR could also be predicted for continuous cultivations. The results of simulation and analysis indicated that 3-HPA accumulation would repress the expression of the dha regulon at the transcriptional level.Finally, the bioconversion processes such as 1,3-PD,2,3-butanediol (2,3-BD) and hydrogen were stoichiometrically analyzed according to mass, energy (ATP) and reducing equivalent balances. Atom economy was used for optimization of 1,3-PD,2,3-BD and hydrogen production. The results indicated that the regulation of reducing equivalents balance would directly affect the yields of products to substrate, especially under microaerobic conditions. The ratio between two substrates was an important parameter in microbial cofermentation which also affected the yields of products to substrate. Respiratory quotient was proved to be a control parameter for optimum production of 1,3-PD,2,3-BD and hydrogen. The theoretical analysis of the glycerol-glucose cometabolism by K. pneumoniae to 1,3-PD indicated that the maximum ratio of 0.32 mol glucose per mol glycerol was needed to convert glycerol completely to 1,3-propanediol under anaerobic conditions if glycerol neither entered oxidation pathways nor formed biomass. The theoretical analysis of glycerol-glucose cometabolism to 1,3-PD and 2,3-BD revealed that the ratio of 1.13 mol glucose per mol glycerol was needed to convert glycerol completely to 1,3-PD under anaerobic conditions if glucose was used for cell growth and reducing equivalent formation, whereas the yield of 2,3-BD to glucose was 0.88mol/mol. The optimal theoretical mass yield of 2,3-butanediol and hydrogen to glucose could reach to 0.50 g/g and 0.008 g/g at the respiratory quotient value of 14, respectively. Supposed that substrate was glucose or xylose alone, the molar yield of hydrogen to substrate was 0.71 mol/mol and 0.60mol/mol, respectively, whereas the optimal theoretical molar yield of hydrogen to glucose by Klebsiella pneumoniae could reach 6.68 mol/mol at the respiratory quotient value of 2.26 if no formation of 2,3-butanediol under microaerobic condition. The theoretical analysis could help us understand the metabolic principles and control the bioprocess.
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