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Mathematical Problems in Engineering
Volume 2015, Article ID 673120, 9 pages
http://dx.doi.org/10.1155/2015/673120
Research Article

Dynamics Analysis and Prediction of Genetic Regulation in Glycerol Metabolic Network via Structural Kinetic Modelling

1School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, Fujian 350108, China
2School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China
3Department of Mathematics and Statistics, Curtin University, Perth, WA 6845, Australia
4School of Mathematical Sciences, Xiamen University, Xiamen, Fujian 361005, China
5College of Life Science, Fujian Normal University, Fuzhou, Fujian 350108, China
6School of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning 116024, China

Received 16 August 2014; Accepted 22 December 2014

Academic Editor: Carlo Cosentino

Copyright © 2015 Jianxiong Ye et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Glycerol can be biologically converted to 1,3-propanediol (1,3-PD) by Klebsiella pneumoniae. In the synthesis pathway of 1,3-PD, the accumulation of an intermediary metabolite 3-hydroxypropionaldehyde (3-HPA) would cause an irreversible cessation of the dynamic system. Genetic manipulation on the key enzymes which control the formation rate and consumption rate of 3-HPA would decrease the accumulation of 3-HPA, resulting in nonlinear regulation on the dynamic system. The interest of this work is to focus on analyzing the influence of 3-HPA inhibition on the stability of the dynamic system. Due to the lack of intracellular knowledge, structural kinetic modelling is applied. On the basis of statistical account of the dynamical capabilities of the system in the parameter space, we conclude that, under weak or no inhibition to the reaction of 3-HPA consumption, the system is much easier to obtain a stable state, whereas strong inhibition to its formation is in favor of stabilizing the system. In addition, the existence of Hopf bifurcation in this system is also verified. The obtained results are helpful for deeply understanding the metabolic and genetic regulations of glycerol fermentation by Klebsiella pneumoniae.