Theoretical approach to modelling and analysis of the bioprocess with product inhibition and impulse effect

This work presents the first mathematical model of a bioprocess with product inhibition and impulse effect. To begin with, an exemplary mathematical bioprocess model with product inhibition and impulse effect is formulated. Then, according to the model, the analysis of bioprocess stability is presented. The article expresses the product oscillation period, which provides the precise feeding time frame for the regulator bioprocess to achieve an equivalent stable output as that of a bioprocess with impulse effect in the same production environment. Moreover, in this work, the optimization of the production process with respect to the tunable parameters is investigated, and analytical expressions of their optimal values are provided. Numerical simulations using biological data are presented to illustrate the main results.

[1]  Lansun Chen,et al.  Periodic solution of a chemostat model with Monod growth rate and impulsive state feedback control. , 2009, Journal of theoretical biology.

[2]  Lansun Chen,et al.  Nonlinear modelling of a synchronized chemostat with impulsive state feedback control , 2010, Math. Comput. Model..

[3]  Kaibiao Sun,et al.  New Approach to the Nonlinear Analysis of a Chemostat with Impulsive State Feedback Control , 2010 .

[4]  A. Herrero.  End-product inhibition in anaerobic fermentations , 1983 .

[5]  G. Zacchi,et al.  Modelling the influence of pH, temperature, glucose and lactic acid concentrations on the kinetics of lactic acid production by Lactococcus lactis ssp. lactis ATCC 19435 in whole-wheat flour , 1998, Applied Microbiology and Biotechnology.

[6]  Indra Mani Mishra,et al.  Modeling the growth of Corynebacterium glutamicum under product inhibition in l-glutamic acid fermentation , 2005 .

[7]  Lansun Chen,et al.  Periodic solution of a turbidostat system with impulsive state feedback control , 2009 .

[8]  D. Bainov,et al.  Impulsive Differential Equations: Periodic Solutions and Applications , 1993 .

[9]  Guangzhao Zeng,et al.  Existence of periodic solution of order one of planar impulsive autonomous system , 2006 .

[10]  H. Henzler.  Particle stress in bioreactors. , 2000, Advances in biochemical engineering/biotechnology.

[11]  Andrzej Kasperski,et al.  Optimization of pulsed feeding in a Baker's yeast process with dissolved oxygen concentration as a control parameter , 2008 .

[12]  S. Kumar Dutta,et al.  Effect of product inhibition on lactic acid fermentation: simulation and modelling , 1996, Applied Microbiology and Biotechnology.

[13]  I. M. Mishra,et al.  Kinetic Modeling and Sensitivity Analysis of Kinetic Parameters for L-Glutamic Acid Production Using Corynebacterium glutamicum , 2009 .

[14]  Lansun Chen,et al.  PERMANENCE AND COMPLEXITY OF THE ECO-EPIDEMIOLOGICAL MODEL WITH IMPULSIVE PERTURBATION , 2008 .

[15]  A. Moser,et al.  Modelling of the L-glutamic acid production with Corynebacterium glutamicum under biotin limitation , 1997 .

[16]  Y. Y. Lee,et al.  Product inhibition in simultaneous saccharification and fermentation of cellulose into lactic acid , 1999, Biotechnology Letters.

[17]  V. Lakshmikantham,et al.  Theory of Impulsive Differential Equations , 1989, Series in Modern Applied Mathematics.

[18]  R. Tengerdy,et al.  Inhibition of microbial growth and metabolism by excess turbulence. , 1991, Biotechnology and Bioengineering.

[19]  Antonio Delgado,et al.  Numerical simulation of the mechanics of a yeast cell under high hydrostatic pressure. , 2004, Journal of biomechanics.

[20]  Lansun Chen,et al.  Modelling and simulation of a continuous process with feedback control and pulse feeding , 2010, Comput. Chem. Eng..

[21]  Sanyi Tang,et al.  The effect of seasonal harvesting on stage-structured population models , 2004, Journal of mathematical biology.

[22]  Xianning Liu,et al.  Complex dynamics of Holling type II Lotka–Volterra predator–prey system with impulsive perturbations on the predator ☆ , 2003 .

[23]  Yusuf Chisti,et al.  Carboxymethyl cellulose protects algal cells against hydrodynamic stress , 2001 .

[24]  Lansun Chen,et al.  Studies on the dynamics of a continuous bioprocess with impulsive state feedback control , 2010 .

[25]  Guirong Jiang,et al.  Complex dynamics of a Holling type II prey–predator system with state feedback control , 2007 .

[26]  Andrzej Kasperski,et al.  Modelling of Cells Bioenergetics , 2008, Acta biotheoretica.

[27]  Xinzhu Meng,et al.  PERMANENCE AND GLOBAL STABILITY IN AN IMPULSIVE LOTKA–VOLTERRA N-SPECIES COMPETITIVE SYSTEM WITH BOTH DISCRETE DELAYS AND CONTINUOUS DELAYS , 2008 .

[28]  Sanyi Tang,et al.  Modelling and analysis of integrated pest management strategy , 2004 .

[29]  Guirong Jiang,et al.  Chaos and its control in an impulsive differential system , 2007 .

[30]  Lansun Chen,et al.  Density-dependent birth rate, birth pulses and their population dynamic consequences , 2002, Journal of mathematical biology.