# Studies on generalized kinetic model and Pareto optimization of a product-driven self-cycling bioprocess

- 177 Downloads
- 1 Citations

## Abstract

The aim of this study is the optimization of a product-driven self-cycling bioprocess and presentation of a way to determine the best possible decision variables out of a set of alternatives based on the designed model. Initially, a product-driven generalized kinetic model, which allows a flexible choice of the most appropriate kinetics is designed and analysed. The optimization problem is given as the bi-objective one, where maximization of biomass productivity and minimization of unproductive loss of substrate are the objective functions. Then, the Pareto fronts are calculated for exemplary kinetics. It is found that in the designed bioprocess, a decrease of emptying/refilling fraction and an increase of substrate feeding concentration cause an increase of the biomass productivity. An increase of emptying/refilling fraction and a decrease of substrate feeding concentration cause a decrease of unproductive loss of substrate. The preferred solutions are calculated using the minimum distance from an ideal solution method, while giving proposals of their modifications derived from a decision maker’s reactions to the generated solutions.

## Keywords

Generalized kinetic model Optimization Pareto front Preferred solution Self-cycling bioprocess## Notes

### Acknowledgments

Kaibiao Sun would like to thank the China Scholarship Council and Dalian University of Technology for financial support during the period of his overseas study, and to express his gratitude to the Department of Mathematics and Statistics, Memorial University of Newfoundland for its kind hospitality. This work was supported in part by the National Natural Science Foundation of China (No. 11101066) and the Fundamental Research Funds for the Central Universities (No. DUT13LK32).

## References

- 1.Bainov D, Simeonov P (1993) Impulsive differential equations: periodic solutions and applications. Longman Scientific Technical Group Limited, New YorkGoogle Scholar
- 2.Bizukojc M, Ledakowicz S (2006) A kinetic model to predict biomass content for
*Aspergillus niger*germinating spores in the submerged culture. Process Biochem 41:1063–1071CrossRefGoogle Scholar - 3.Bona R, Moser A (1997) Modeling of growth of
*Corynebacterium glutamicum*under biotin limitation. Bioprocess Eng 17:121–125Google Scholar - 4.Bona R, Moser A (1997) Modeling of L-glutamic acid production with
*Corynebacterium glutamicum*under biotin limitation. Bioprocess Eng 17:139–142Google Scholar - 5.Clementschitsch F, Bayer K (2006) Improvement of bioprocess monitoring: development of novel concepts. Microb Cell Fact 5:19CrossRefGoogle Scholar
- 6.Guo HJ, Chen LS (2009) Periodic solution of a chemostat model with Monod growth rate and impulsive state feedback control. J Theor Biol 260:502–509CrossRefGoogle Scholar
- 7.Kasperski A (2008) Modelling of cells bioenergetics. Acta Biotheor 56:233–247CrossRefGoogle Scholar
- 8.Kasperski A, Miskiewicz T (2008) Optimization of pulsed feeding in a Baker’s yeast process with dissolved oxygen concentration as a control parameter. Biochem Eng J 40:321–327CrossRefGoogle Scholar
- 9.Khan NS, Mishra IM, Singh RP, Prasad B (2005) Modeling the growth of
*Corynebacterium glutamicum*under product inhibition in L-glutamic acid fermentation. Biochem Eng J 25:173–178CrossRefGoogle Scholar - 10.Lenbury Y, Chiaranai C (1987) Bifurcation analysis of a product inhibition model of a continuous fermentation process. Appl Microbiol Biotechnol 25:532–534Google Scholar
- 11.Liwarska E, Bizukojc M, Ledakowicz S (2001) Kinetic model for the process of aerobic biodegradation of organic fraction of municipal solid waste. Bioprocess Biosyst Eng 24(3):195–202CrossRefGoogle Scholar
- 12.Liwarska E, Bizukojc M, Ledakowicz S (2002) Kinetic model for the process of aerobic biodegradation of organic fraction of shredded municipal solid waste in liquid phase. Water Res 36(8):2124–2132CrossRefGoogle Scholar
- 13.Mandenius CF (2004) Recent developments in the monitoring, modeling and control of biological production systems. Bioprocess Eng 26(6):347–351CrossRefGoogle Scholar
- 14.Pareto V (1986) Cours dEconomie Politique. Droz, GenevaGoogle Scholar
- 15.Smith R (2011) Impulsive differential equations with applications to self-cycling fermentation, Open Access Dissertations and Theses, Paper 1526Google Scholar
- 16.Sun KB, Tian Y, Chen LS, Kasperski A (2010) Nonlinear modelling of a synchronized chemostat with impulsive state feedback control. Math Comput. Modell 52:227–240CrossRefGoogle Scholar
- 17.Sun KB, Kasperski A, Tian Y, Chen LS (2010) New approach to the nonlinear analysis of a chemostat with impulsive state feedback control. Int J Chem Reactor Eng 8:1–40Google Scholar
- 18.Sun KB, Tian Y, Chen LS, Kasperski A (2011) Universal modelling and qualitative analysis of an impulsive bioprocess. Comput Chem Eng 35(3):492–501CrossRefGoogle Scholar
- 19.Sun KB, Kasperski A, Tian Y, Chen LS (2011) Modelling and optimization of a continuous stirred tank reactor with feedback control and pulse feeding. Chem Eng Process Process Intensif 50:675–686CrossRefGoogle Scholar
- 20.Sun KB, Kasperski A, Tian Y, Chen LS (2011) Modelling of the
*Corynebacterium glutamicum*biosynthesis under aerobic fermentation conditions. Chem Eng Sci 66(18):4101–4110CrossRefGoogle Scholar - 21.Sun KB, Kasperski A, Tian Y (2013) Theoretical study and optimization of the biochemical reaction process by means of feedback control strategy. J Chem 2013:1–18. doi: 10.1155/2010/640594
- 22.Suresh S, Khan NS, Srivastava VC, Mishra IM (2009) Kinetic modeling and sensitivity analysis of kinetic parameters for L-Glutamic acid production using
*Corynebacterium glutamicum*. Int J Chem Reactor Eng 7:1–16Google Scholar - 23.Tian Y, Chen LS, Kasperski A (2010) Modelling and simulation of a continuous process with feedback control and pulse feeding. Comput Chem Eng 34:976–984CrossRefGoogle Scholar
- 24.Tian Y, Sun KB, Chen LS, Kasperski A (2010) Studies on the dynamics of a continuous bioprocess with impulsive state feedback control. Chem Eng J 157:558–567CrossRefGoogle Scholar
- 25.Tian Y, Sun KB, Kasperski A, Chen LS (2010) Nonlinear modelling and qualitative analysis of a real chemostat with pulse feeding. Discrete Dyn Nat Soc, 2010, Article ID 640594Google Scholar
- 26.Tian Y, Kasperski A, Sun KB, Chen LS (2011) Theoretical approach to modelling and analysis of the bioprocess with product inhibition and impulse effect. BioSystems 104:77–86CrossRefGoogle Scholar
- 27.Yano T, Koga S (1973) Dynamic behavior of the chemostat subject to product inhibition. J Gen Appl Microbiol 19:97–114CrossRefGoogle Scholar
- 28.Zaiat M, Passig FH, Foresti E (2000) A mathematical model and criteria for designing horizontal-flow anaerobic immobilized biomass reactors for wastewater treatment. Bioresour Technol 71(3):235–243CrossRefGoogle Scholar
- 29.Wincure BM, Cooper DG, Rey A (1995) Mathematical model of self-cycling fermentation. Biotechnol Bioeng 46:180–183CrossRefGoogle Scholar