2015, 5(4): 393-403. doi: 10.3934/naco.2015.5.393

Modeling and identification of dynamical system with Genetic Regulation in batch fermentation of glycerol

1. 

School of Mathematical Science, Dalian University of Technology, Linggong Road, Dalian, Liaoning 116024, China, China

Received  April 2015 Revised  October 2015 Published  October 2015

The background of this paper is the production of 1,3-PD by batch fermentation of glycerol, supposed that glycerol and 1,3-PD pass the cell membrane by passive diffusion with active transportation. We present a nonlinear enzyme-catalytic dynamical system with genetic regulation and our purpose is to identify these parameters in the dynamical system. Since the intracellular substance concentrations are immeasurable, we refer to the robustness definition of parameter disturbance in biological system, then we establish a parameter identification model. We prove the existence of the solution to the optimization model. At last, we get the parameters of dynamical systems by particle swarm algorithm. Numerical results show that the optimization algorithm is valid and the genetic regulations can help to understand the intracellular reaction process.
Citation: Xu Zhang, Xiang Li. Modeling and identification of dynamical system with Genetic Regulation in batch fermentation of glycerol. Numerical Algebra, Control & Optimization, 2015, 5 (4) : 393-403. doi: 10.3934/naco.2015.5.393
References:
[1]

C. X. Gao, Z. T. Wang, E. M. Feng and Z. L. Xiu, Parameter identification and optimization of process for bio-dissimilation of glycerol to 1,3-propanediol in batch culture,, \emph{Journal of Dalian University of Technology}, 46 (2006), 771.   Google Scholar

[2]

Z. H. Gong, E. M. Feng and Z. L. Xiu, Identification of specific growth rate and optimization algorithm in microbial batch culture,, \emph{Journal of Dalian University of Technology}, 49 (2009), 611.   Google Scholar

[3]

Z. G. Jiang, J. L. Yuan and E. M. Feng, Robust identification and its properties of nonlinear bilevel multi-stage dynamic system,, \emph{Applied Mathematics and Computation}, 219 (2013), 6979.  doi: 10.1016/j.amc.2012.12.082.  Google Scholar

[4]

H. Kitano, Biological robustness,, \emph{Nat. Rev. Genet.}, 5 (2004), 826.   Google Scholar

[5]

D. H. Liu, H. J. Liu and K. K. Cheng, Research progress on the production of l,3-propanediol by fermentation,, \emph{Journal of Microbiolog}, 4 (2000), 300.   Google Scholar

[6]

C. Y. Liu, L. Yin, E. M. Feng and Z. L. Xiu, Modeling of microbial continuous fermentations and identifying of intracellular kinetic parameters,, \emph{Journal of Dalian University of Technology}, 51 (2011), 458.   Google Scholar

[7]

Y. Q. Sun, W. T. Qi, H. Teng, Z. L. Xiu and A. P. Zeng, Mathematical modeling of glycerol fermentation by Klebsiella pneumoniae: concerning enzyme-catalytic reductive pathway and transport of glycerol and 1,3-propanediol across cell membrane,, \emph{Biochemical Engineering Journal, 38 (2008), 22.   Google Scholar

[8]

Y. Q. Sun, Nonlinear Mathematical Simulation and Analysis of Enzyme-Eatalytic Kinetics and Genetic Regulation for Glycerol Dissimilation by Klebsiella Pneumoniae,, Dalian: Dalian university of technology, (2010).   Google Scholar

[9]

L. Wang, J. X. Ye, E. M. Feng and Z. L. Xiu, An improved model for multistage simulation of glycerol fermentation in batch culture and its parameter identification,, \emph{Nonlinear Analysis: Hybrid Systems}, 3 (2009), 455.  doi: 10.1016/j.nahs.2009.03.003.  Google Scholar

[10]

J. Wang, J. X. Ye, E. M. Feng, H. C. Yin and Z. L. Xiu, Modelling and identification of a nonlinear hybrid dynamical system in batch fermentation of glycerol,, \emph{Mathematical and Computer Modelling}, 54 (2011), 618.  doi: 10.1016/j.mcm.2011.03.005.  Google Scholar

[11]

J. Wang, Modelling and Optimization of a Class of Nonlinear Enzyme-Catalysis Hybrid System,, Dalian: Dalian university of technology, (2012).   Google Scholar

[12]

Z. L. Xiu and A. P. Zeng, Mathematical modeling of kinetics and research on multiplicity of glycerol bioconversion to 1,3-propanediol,, \emph{Journal of Dalian University of Technology}, 40 (2000), 428.   Google Scholar

[13]

A. P. Zeng, H. Biebl and et al., Multiple product and growth modeling of clostridium butyicum and Klebsiella pneumoniae in fermentation,, \emph{Biotechnol.}, 44 (1994), 902.   Google Scholar

[14]

Y. D. Zhang, Y. J. Zhang and E. M. Feng, Robustness analysis of microbio continuous fermentation based on parallel computing,, \emph{Journal of Biomathematics}, 3 (2011), 524.   Google Scholar

[15]

C. Zhou, H. B. Gao and L. Gao, Particle swarm optimization (PSO) algorithm 3,, \emph{Application Research of Computers}, 12 (2003), 7.   Google Scholar

show all references

References:
[1]

C. X. Gao, Z. T. Wang, E. M. Feng and Z. L. Xiu, Parameter identification and optimization of process for bio-dissimilation of glycerol to 1,3-propanediol in batch culture,, \emph{Journal of Dalian University of Technology}, 46 (2006), 771.   Google Scholar

[2]

Z. H. Gong, E. M. Feng and Z. L. Xiu, Identification of specific growth rate and optimization algorithm in microbial batch culture,, \emph{Journal of Dalian University of Technology}, 49 (2009), 611.   Google Scholar

[3]

Z. G. Jiang, J. L. Yuan and E. M. Feng, Robust identification and its properties of nonlinear bilevel multi-stage dynamic system,, \emph{Applied Mathematics and Computation}, 219 (2013), 6979.  doi: 10.1016/j.amc.2012.12.082.  Google Scholar

[4]

H. Kitano, Biological robustness,, \emph{Nat. Rev. Genet.}, 5 (2004), 826.   Google Scholar

[5]

D. H. Liu, H. J. Liu and K. K. Cheng, Research progress on the production of l,3-propanediol by fermentation,, \emph{Journal of Microbiolog}, 4 (2000), 300.   Google Scholar

[6]

C. Y. Liu, L. Yin, E. M. Feng and Z. L. Xiu, Modeling of microbial continuous fermentations and identifying of intracellular kinetic parameters,, \emph{Journal of Dalian University of Technology}, 51 (2011), 458.   Google Scholar

[7]

Y. Q. Sun, W. T. Qi, H. Teng, Z. L. Xiu and A. P. Zeng, Mathematical modeling of glycerol fermentation by Klebsiella pneumoniae: concerning enzyme-catalytic reductive pathway and transport of glycerol and 1,3-propanediol across cell membrane,, \emph{Biochemical Engineering Journal, 38 (2008), 22.   Google Scholar

[8]

Y. Q. Sun, Nonlinear Mathematical Simulation and Analysis of Enzyme-Eatalytic Kinetics and Genetic Regulation for Glycerol Dissimilation by Klebsiella Pneumoniae,, Dalian: Dalian university of technology, (2010).   Google Scholar

[9]

L. Wang, J. X. Ye, E. M. Feng and Z. L. Xiu, An improved model for multistage simulation of glycerol fermentation in batch culture and its parameter identification,, \emph{Nonlinear Analysis: Hybrid Systems}, 3 (2009), 455.  doi: 10.1016/j.nahs.2009.03.003.  Google Scholar

[10]

J. Wang, J. X. Ye, E. M. Feng, H. C. Yin and Z. L. Xiu, Modelling and identification of a nonlinear hybrid dynamical system in batch fermentation of glycerol,, \emph{Mathematical and Computer Modelling}, 54 (2011), 618.  doi: 10.1016/j.mcm.2011.03.005.  Google Scholar

[11]

J. Wang, Modelling and Optimization of a Class of Nonlinear Enzyme-Catalysis Hybrid System,, Dalian: Dalian university of technology, (2012).   Google Scholar

[12]

Z. L. Xiu and A. P. Zeng, Mathematical modeling of kinetics and research on multiplicity of glycerol bioconversion to 1,3-propanediol,, \emph{Journal of Dalian University of Technology}, 40 (2000), 428.   Google Scholar

[13]

A. P. Zeng, H. Biebl and et al., Multiple product and growth modeling of clostridium butyicum and Klebsiella pneumoniae in fermentation,, \emph{Biotechnol.}, 44 (1994), 902.   Google Scholar

[14]

Y. D. Zhang, Y. J. Zhang and E. M. Feng, Robustness analysis of microbio continuous fermentation based on parallel computing,, \emph{Journal of Biomathematics}, 3 (2011), 524.   Google Scholar

[15]

C. Zhou, H. B. Gao and L. Gao, Particle swarm optimization (PSO) algorithm 3,, \emph{Application Research of Computers}, 12 (2003), 7.   Google Scholar

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