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2014, 4(2): 103-113. doi: 10.3934/naco.2014.4.103

Parameter identification of nonlinear delayed dynamical system in microbial fermentation based on biological robustness

1. 

School of Mathematical Science, Dalian University of Technology, Dalian,116024, China, China, China

2. 

Fundamental Course Teaching Department, Hebei College of Industry and Technology, Shijiazhuang, 050000, China

3. 

School of Bioscience and Biotechnology, Dalian University of Technology, Dalian,116024, China

Received  February 2013 Revised  December 2013 Published  May 2014

In this paper, the nonlinear enzyme-catalytic kinetic system of batch and continuous fermentation in the process of glycerol bio-dissimilation is investigated. On the basis of both glycerol and 1,3-PD pass the cell membrane by active and passive diffusion under substrate-sufficient conditions, we consider the delay of concentration changes on both extracellular substances and intracellular substances. We establish a nonlinear delay dynamical system according to the batch and continuous fermentation of bio-dissimilation of glycerol to 1,3-propanediol(1,3-PD) and we propose an identification problem, in which the biological robustness is taken as a performance index, constrained with nonlinear delay dynamical system. An algorithm is constructed to solve the identification problem and the numerical result shows the values of time delays of glycerol, 3-HPA, 1,3-PD intracellular and extracellular substances. This work will be helpful for deeply understanding the metabolic mechanism of glycerol in batch and continuous fermentation.
Citation: Lei Wang, Jinlong Yuan, Yingfang Li, Enmin Feng, Zhilong Xiu. Parameter identification of nonlinear delayed dynamical system in microbial fermentation based on biological robustness. Numerical Algebra, Control & Optimization, 2014, 4 (2) : 103-113. doi: 10.3934/naco.2014.4.103
References:
[1]

A. Ashoori, B. Moshiri, A. Khaki-Sedigh and M. R. Bakhtiari, Optimal control of a nonlinear fed-batch fermentation process using model predictive approach,, J Process Contr., 19 (2009), 1162.   Google Scholar

[2]

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

[3]

X. F. Li, R. N. Qu and E. M. Feng, Hopf bifurcation of a five-dimensional delay differential system,, Int. J. Comput. Math., 88 (2011), 79.  doi: 10.1080/00207160903197187.  Google Scholar

[4]

H. S. Lian, E. M. Feng, J. X. Ye, X. F. Li and Z. L. Xiu, Oscillatory behavior in microbial continuous culture with discrete time delay,, Nonlinear Anal-real, 10 (2009), 2749.  doi: 10.1016/j.nonrwa.2008.08.014.  Google Scholar

[5]

C. Y. Liu, Z. H. Gong, E. M. Feng and H. C. Yin, Optimal switching control of a fed-batch fermentation process,, J. Global Optim., 52 (2012), 265.  doi: 10.1007/s10898-011-9663-8.  Google Scholar

[6]

P. Mhaskar, N. H. El-Farra and P. D. Christofides, Predictive control of switched nonlinear systems with scheduled mode transitions,, IEEE T. Automat. Contr., 50 (2005), 1670.  doi: 10.1109/TAC.2005.858692.  Google Scholar

[7]

P. Mhaskar, N. H. El-Farra, and P. D. Christofides, Stabilization of nonlinear systems with state and control constraints using lyapunov-based predictive control,, Syst. Control Lett., 55 (2006), 650.  doi: 10.1016/j.sysconle.2005.09.014.  Google Scholar

[8]

J. Stelling, U. Sauer and Z. Szallasi, Robustness of cellular functions,, Cell, 118 (2004), 675.   Google Scholar

[9]

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,, Biochem. Eng. J., 38 (2008), 22.   Google Scholar

[10]

Y. Tian, L. S. Chen and A. Kasperski, Modelling and simulation of a continuous process with feedback control and pulse feeding,, Comput. Chem. Eng., 34 (2010), 976.   Google Scholar

[11]

G. Wang, E. M. Feng and Z. L. Xiu, Modeling and parameter identification of microbial bioconversion in fed-batch cultures,, J. Process Contr., 18 (2008), 458.   Google Scholar

[12]

G. Wang, E. M. Feng and Z. L. Xiu, Vector measure as controls for explicit nonlinear impulsive system of fed-batch culture,, J. Math. Anal. Appl., 351 (2009), 120.  doi: 10.1016/j.jmaa.2008.09.054.  Google Scholar

[13]

J. Wang, J. X. Ye, E. M. Feng, H. C. Yin and B. Tan, Complex metabolic network of glycerol fermentation by klebsiella pneumoniae and its system identification via biological robustness,, Nonlinear Analysis: Hybrid Sys., 5 (2011), 102.  doi: 10.1016/j.nahs.2010.10.002.  Google Scholar

[14]

L. Wang, Determining the transport mechanism of an enzyme-catalytic complex metabolic network based on biological robustness,, Bioprocess Biosyst. Eng., 36 (2013), 433.  doi: 10.1007/s00449-012-0800-7.  Google Scholar

[15]

L. Wang, Modelling and regularity of nonlinear impulsive switching dynamical system in fed-batch culture,, Abstr. Appl. Anal., (2012).   Google Scholar

[16]

H. H. Yan, X. Zhang, J. X. Ye and E. M. Feng, Identification and robustness analysis of nonlinear hybrid dynamical system concerning glycerol transport mechanism,, Comput. Chem. Eng., 40 (2012), 171.   Google Scholar

[17]

J. X. Ye, E. M. Feng, H. S. Lian and Z. L. Xiu, Existence of equilibrium points and stability of the nonlinear dynamical system in microbial continuous cultures,, Appl. Math. Comput., 207 (2009), 307.  doi: 10.1016/j.amc.2008.10.046.  Google Scholar

[18]

J. X. Ye, E. M. Feng, L. Wang, Y. Q. Sun and Z. L. Xiu, Modeling and robustness analysis of biochemical networks of glycerol metabolism by Klebsiella pneumoniae,, Complex Sciences, 4 (2009), 446.   Google Scholar

[19]

A. P. Zeng and H. Biebl, Bulk-chemicals from biotechnology: the case of microbial production of 1,3-propanediol and the new trends,, Adv. Biochem. Eng. Biot., 74 (2002), 237.   Google Scholar

[20]

A. P. Zeng, K. Menzel and W. D. Deckwer, Kinetic, dynamic, and pathway studies of glycerol metabolism by Klebsiella pneumoniae in anaerobic continuous culture: II. Analysis of metabolic rates and pathways under oscillation and steady-state conditions,, Biotechnol. Bioeng., 52 (1996), 561.   Google Scholar

[21]

J. G. Zhai, J. X. Ye, L. Wang, E. M. Feng, H. C. Yin and Z. L. Xiu, Pathway identification using parallel optimization for a complex metabolic system in microbial continuous culture,, Nonlinear Anal-real, 12 (2011), 2730.  doi: 10.1016/j.nonrwa.2011.03.018.  Google Scholar

show all references

References:
[1]

A. Ashoori, B. Moshiri, A. Khaki-Sedigh and M. R. Bakhtiari, Optimal control of a nonlinear fed-batch fermentation process using model predictive approach,, J Process Contr., 19 (2009), 1162.   Google Scholar

[2]

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

[3]

X. F. Li, R. N. Qu and E. M. Feng, Hopf bifurcation of a five-dimensional delay differential system,, Int. J. Comput. Math., 88 (2011), 79.  doi: 10.1080/00207160903197187.  Google Scholar

[4]

H. S. Lian, E. M. Feng, J. X. Ye, X. F. Li and Z. L. Xiu, Oscillatory behavior in microbial continuous culture with discrete time delay,, Nonlinear Anal-real, 10 (2009), 2749.  doi: 10.1016/j.nonrwa.2008.08.014.  Google Scholar

[5]

C. Y. Liu, Z. H. Gong, E. M. Feng and H. C. Yin, Optimal switching control of a fed-batch fermentation process,, J. Global Optim., 52 (2012), 265.  doi: 10.1007/s10898-011-9663-8.  Google Scholar

[6]

P. Mhaskar, N. H. El-Farra and P. D. Christofides, Predictive control of switched nonlinear systems with scheduled mode transitions,, IEEE T. Automat. Contr., 50 (2005), 1670.  doi: 10.1109/TAC.2005.858692.  Google Scholar

[7]

P. Mhaskar, N. H. El-Farra, and P. D. Christofides, Stabilization of nonlinear systems with state and control constraints using lyapunov-based predictive control,, Syst. Control Lett., 55 (2006), 650.  doi: 10.1016/j.sysconle.2005.09.014.  Google Scholar

[8]

J. Stelling, U. Sauer and Z. Szallasi, Robustness of cellular functions,, Cell, 118 (2004), 675.   Google Scholar

[9]

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,, Biochem. Eng. J., 38 (2008), 22.   Google Scholar

[10]

Y. Tian, L. S. Chen and A. Kasperski, Modelling and simulation of a continuous process with feedback control and pulse feeding,, Comput. Chem. Eng., 34 (2010), 976.   Google Scholar

[11]

G. Wang, E. M. Feng and Z. L. Xiu, Modeling and parameter identification of microbial bioconversion in fed-batch cultures,, J. Process Contr., 18 (2008), 458.   Google Scholar

[12]

G. Wang, E. M. Feng and Z. L. Xiu, Vector measure as controls for explicit nonlinear impulsive system of fed-batch culture,, J. Math. Anal. Appl., 351 (2009), 120.  doi: 10.1016/j.jmaa.2008.09.054.  Google Scholar

[13]

J. Wang, J. X. Ye, E. M. Feng, H. C. Yin and B. Tan, Complex metabolic network of glycerol fermentation by klebsiella pneumoniae and its system identification via biological robustness,, Nonlinear Analysis: Hybrid Sys., 5 (2011), 102.  doi: 10.1016/j.nahs.2010.10.002.  Google Scholar

[14]

L. Wang, Determining the transport mechanism of an enzyme-catalytic complex metabolic network based on biological robustness,, Bioprocess Biosyst. Eng., 36 (2013), 433.  doi: 10.1007/s00449-012-0800-7.  Google Scholar

[15]

L. Wang, Modelling and regularity of nonlinear impulsive switching dynamical system in fed-batch culture,, Abstr. Appl. Anal., (2012).   Google Scholar

[16]

H. H. Yan, X. Zhang, J. X. Ye and E. M. Feng, Identification and robustness analysis of nonlinear hybrid dynamical system concerning glycerol transport mechanism,, Comput. Chem. Eng., 40 (2012), 171.   Google Scholar

[17]

J. X. Ye, E. M. Feng, H. S. Lian and Z. L. Xiu, Existence of equilibrium points and stability of the nonlinear dynamical system in microbial continuous cultures,, Appl. Math. Comput., 207 (2009), 307.  doi: 10.1016/j.amc.2008.10.046.  Google Scholar

[18]

J. X. Ye, E. M. Feng, L. Wang, Y. Q. Sun and Z. L. Xiu, Modeling and robustness analysis of biochemical networks of glycerol metabolism by Klebsiella pneumoniae,, Complex Sciences, 4 (2009), 446.   Google Scholar

[19]

A. P. Zeng and H. Biebl, Bulk-chemicals from biotechnology: the case of microbial production of 1,3-propanediol and the new trends,, Adv. Biochem. Eng. Biot., 74 (2002), 237.   Google Scholar

[20]

A. P. Zeng, K. Menzel and W. D. Deckwer, Kinetic, dynamic, and pathway studies of glycerol metabolism by Klebsiella pneumoniae in anaerobic continuous culture: II. Analysis of metabolic rates and pathways under oscillation and steady-state conditions,, Biotechnol. Bioeng., 52 (1996), 561.   Google Scholar

[21]

J. G. Zhai, J. X. Ye, L. Wang, E. M. Feng, H. C. Yin and Z. L. Xiu, Pathway identification using parallel optimization for a complex metabolic system in microbial continuous culture,, Nonlinear Anal-real, 12 (2011), 2730.  doi: 10.1016/j.nonrwa.2011.03.018.  Google Scholar

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