Article Contents
Article Contents

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

• 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.
Mathematics Subject Classification: Primary: 49J15, 49J35; Secondary: 90C30.

 Citation:

•  [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), 1162-1173. [2] H. Kitano, Biological robustness, Nat. Rev. Genet., 5 (2004), 826-837. [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), 79-96.doi: 10.1080/00207160903197187. [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), 2749-2757.doi: 10.1016/j.nonrwa.2008.08.014. [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), 265-280.doi: 10.1007/s10898-011-9663-8. [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), 1670-1680.doi: 10.1109/TAC.2005.858692. [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), 650-659.doi: 10.1016/j.sysconle.2005.09.014. [8] J. Stelling, U. Sauer and Z. Szallasi, Robustness of cellular functions, Cell, 118 (2004), 675-685. [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), 22-32. [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), 976-984. [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), 458-464. [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), 120-127.doi: 10.1016/j.jmaa.2008.09.054. [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), 102-112.doi: 10.1016/j.nahs.2010.10.002. [14] L. Wang, Determining the transport mechanism of an enzyme-catalytic complex metabolic network based on biological robustness, Bioprocess Biosyst. Eng., 36 (2013), 433-441.doi: 10.1007/s00449-012-0800-7. [15] L. Wang, Modelling and regularity of nonlinear impulsive switching dynamical system in fed-batch culture, Abstr. Appl. Anal., (2012), Article ID 295627, 15 pages. [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), 171-180. [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), 307-318.doi: 10.1016/j.amc.2008.10.046. [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, Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, 4 (2009), 446-457. [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), 237-257. [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), 561-571. [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), 2730-2741.doi: 10.1016/j.nonrwa.2011.03.018.