Nonlinear Mathematical Simulation and Analysis of Dha Regulon for Glycerol Metabolism in Klebsiella pneumoniae

Glycerol may be converted to 1,3-propanediol (1,3-PD) by Klebsiella pneumoniae under anaerobic conditions and glycerol dismutation involves two parallel pathways controlled by the dha regulon. In this study, a fourteen-dimensional nonlinear dynamic system is presented to describe the continuous culture and multiplicity analysis, in which two regulated negative-feedback mechanisms of repression and enzyme inhibition are 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 indicate that the model can be used to describe the production of 1,3-PD under continuous fermentation. The new model is translated into the corresponding S-system version. The robustness of this model is discussed by using the S-system model and the sensitivity analysis shows that the model is sufficiently robust. The influences of initial glycerol concentration and dilution rate on the biosynthesis of 1,3-PD and the stability of the dha regulon model are investigated. The intracellular concentrations of glycerol, 1,3-PD, 3-HPA, repressor mRNA, repressor, mRNA and protein levels of glycerol dehydratase (GDHt) and 1,3-PD oxydoreductase (PDOR) can be predicted for continuous cultivation. The results of simulation and analysis indicate that 3-HPA accumulation will repress the expression of the dha regulon at the transcriptional level. This model gives new insights into the regulation of glycerol metabolism in K. pneumoniae and explain some of the experimental observations.