INFER OBJECTIVE FUNCTION OF GLYCEROL METABOLISM IN KLEBSIELLA PNEUMONIAE BASING ON BILEVEL PROGRAMMING

Mathematical modelling of cellular metabolism plays an important role in understandingbiological functions and providing identification of targets for biotechnological modification.This paperproposes a nonlinear bilevel programming(NBP)model to infer the objective function of anaerobicglycerol metabolism in Klebsiella Pneumoniae(K.Pneumoniae)for 1,3-propanediol(1,3-PD)production.Based on the Kuhn-Tucker optimality condition of the lower level problem,NBP is transformedinto a nonlinear programming with complementary and slackness conditions.The authors give the existencetheorem of solutions to NBP.An efficient algorithm is proposed to solve NBP and its convergenceis also simply analyzed.Numerical results reveal some interesting conclusions,e.g.,biomass productionis the main force to drive glycerol metabolism,and the objective functions,which are obtained in termof several different groups of flux distributions,are similar.

The uncoupled microbial fed-batch fermentation optimization based on state-dependent switched system

In the actual microbial fermentation process,excessive or insufficient substrate can produce inhibitory effects on cells growth.The artificial substrate feeding rules by past experiences have great blindness to keep substrate concentration in a given appropriate range.This paper considers that alkali feed depends on pH value of the solution and glycerol feed depends on glycerol concentration of the solution in the uncoupled microbial fed-hatch fermentation process,and establishes a state-dependent switched system in which the flow rates of glycerol and alkali,the number of mode switches,the mode sequence and the switching times are prior unknown.To maximize the yield of target product 1,3-Propanediol(1,3-PD),we formulate a switching optimal control problem with the flow rates of glycerol and alkali,the number of mode switches,the mode sequence and the switching times as decision variables,which is a mixed-integer dynamic programming problem.For solving the mixed-integer dynamic programming problem,the control parametrization technique,the time scaling transformation and the embedded system technology are used to obtain an approximate parameter optimization problem.By using a parallel optimization algorithm,we obtain the optimal control strategies.Under the obtained optimal control strategies,the 1,3-PD yield at the terminal time is increased significantly compared with the previous results.

MULTISTAGE DYNAMIC SYSTEM OF MICROBIAL BATCH FERMENTATION AND ITS PARAMETER IDENTIFICATION

Based on 1,3-propanediol production from batch fermentation of glycerol by Klebsiella pneurnoniae, a multistage dynamic system and its parameter identification are discussed in this paper. The batch fermentation process is divided into three stages exhibiting different dynamic behaviors and characteristics, from which a corresponding nonlinear multistage dynamic system is built. We then propose a parameter identification optimization model whose objective function is the average relative error. The model is solved by particle swarm optimization weighted by inertia, and the result shows that the relative error of our proposed model is 2-10%smaller than those of existing models.

Strong stability of an optimal control hybrid system in fed-batch fermentation

In this paper, we consider a nonlinear hybrid dynamic （NHD） system to describe fedbatch culture where there is no analytical solutions and no equilibrium points. Our goal is to prove the strong stability with respect to initial state for the NHD system. To this end, we construct corresponding linear variational system （LVS） for the solution of the NHD system, also prove the boundedness of fundamental matrix solutions for the LVS. On this basis, the strong stability is proved by such boundedness.

Strong stability of optimal design to dynamic system for the fed-batch culture

Most economic and industrial processes are governed by inherently nonlinear dynamic system in which mathematical analysis （with few exceptions） is unable to provide general solutions; even the conditions to the existence of equilibrium point for the nonlinear dynamic system are simply not established in some special cases. In this paper, based on numerical solution of a nonlinear multi-stage automatic control dynamic （NMACD） in fed-batch culture of glycerol bioconversion to 1,3-propanediol （1,3-PD） induced by KlebsieUa pneumoniae （K. pneumoniae）, we consider an optimal design of the NMACD system. For convenience, the NMACD system is reconstructed together with the existence, uniqueness and continuity of solutions are discussed. Our goal is to prove the strong stability with respect to the perturbation of initial state for the solution to the NMACD system. To this end, we construct corresponding linear variational system for the solution to the NMACD system, and also prove the boundedness of fundamental matrix solutions to the linear variational system. On this basis, we prove the strong stability appearing above through the application of this boundedness.

IDENTIFICATION OF HYBRID DYNAMICAL SYSTEM IN GLYCEROL FERMENTATION： ESTIMATING THE INHIBITION RANGE OF 3-HPA ONTO TWO KEY ENZYMES BASED ON BIOLOGICAL ROBUSTNESS

As an important intermediate substance in the process of producing 1,3-propanediol （1, 3-PD） by bio-dissimilation of glycerol, the concentration of 3-hydroxypropionaldehyde （3-HPA） has inhibitory action on glycerol dehydratase （GDHt） and 1, 3-propanediol oxi- doreductase （PDOR）. Considering the transmission of glycerol and 1,3-PD across cell membrane by both passive diffusion and active transmission as well as the inhibitory action of 3-HPA on the specific rate of growth, this paper aims to establish and dis- cuss a nonlinear hybrid dynamical system model to ascertain the concentration range of 3-HPA where it does exhibit an inhibitory action on GDHt and PDOR. A quantita- tive definition of biological robustness is presented and an identification model is estab- lished based on biological robustness. An algorithm procedure is constructed to solve the identification problem. Numerical results show that only within a proper concentration range 3-HPA can have inhibitory action on the two enzymes mentioned above.

IMPULSIVE CONTROL IN MICROORGANISMS CONTINUOUS FERMENTATION

This work presents the nonlinear dynamical system of continuous fermentation from glycerol to 1,3-propanediol. The impulsive control scheme of continuous culture is intro- duced. By employing impulsive control, Lyapunov＇s method and comparison technique, sufficient conditions are established for the asymptotical stability and synchronization of the dynamical system of continuous fermentation. The upper bound of the impulse interval is also estimated. An example will illustrate the effectiveness of the results in Sec. 4.

MODELING AND PARAMETER IDENTIFICATION FOR MULTISTAGE SIMULATION OF MICROBIAL BIOCONVERSION IN BATCH CULTURE

The bioconversion of glycerol to 1,3-propanediol is a complex bioprocess. The item of product inhibition in the equation of Specific rate of cell growth is overlapped in [L. Wang, J. X. Ye, E. M. Feng and Z. L. Xiu, An improved model for multistage simula- tion of glycerol fermentation in batch culture and its parameter identification, Nonlinear Anal. Hybrid Syst. 3（4） （2009） 455462]. Therefore, in this work, the specific rate of cell growth is modified by the mechanism of multistage simulation of microbial bioconversion and the previous time-dependent model is converted to the autonomous standard form. The properties of the solutions for the nonlinear dynamic system are discussed and the identifiability of the parameters is proved. Finally the feasible optimization algorithm is constructed to find the optimal parameters for the system. Numerical result shows that the improved model with identified parameters can describe the batch culture better, compared with the previous results.