Jianxiong Ye

Existence of equilibrium points and stability of the nonlinear dynamical system in microbial continuous cultures

In this paper, the nonlinear dynamical system of glycerol fermentations to 1,3-PD by Klebsiella pneumoniae in continuous cultures is investigated. We examine the existence of equilibrium points and deduce the permissible range of two main operating conditions (dilution rate and substrate concentration in feed) in continuous fermentations. Subsequently, algorithms are developed to calculate the equilibrium points and the upper boundary of dilution rate, respectively. The multiple steady states and stability of the system are also discussed.

Sensitivity analysis and identification of kinetic parameters in batch fermentation of glycerol

A nonlinear dynamical system was established in our preceding work to describe the batch and continuous bioconversions of glycerol to 1,3-propanediol by Klebsiella pneumoniae. The purpose of this article is to analyze the sensitivity of kinetic parameters of the dynamical system and identify their values from experiment. A global sensitivity analysis approach is constructed by combining the local technique with the Monte Carlo method. With only those parameters of higher sensitivity as design variables, we propose a parameter identification model and solve it by a gradient-based simulated annealing algorithm. Numerical results show that our methods are feasible and efficient.

Modeling and identification of a nonlinear hybrid dynamical system in batch fermentation of glycerol

A nonlinear hybrid dynamical system is established to describe the batch culture of glycerol to 1,3-propanediol (1,3-PD) by Klebsiella pneumoniae (K. pneumoniae), in which glycerol is assumed to pass the cell membrane by passive diffusion coupled with facilitated transport and transport mechanism of 1,3-PD is assumed to be uncertain. The existence, uniqueness and continuity of solutions are also discussed. To infer the most reasonable transport mechanism of 1,3-PD, a system identification model consisting of both discrete and continuous variables is proposed. Additionally, we construct a two-phase optimization algorithm on the basis of modified complex method together with very fast simulated annealing technology. Numerical results show that it is most reasonable for 1,3-PD to pass the cell membrane by passive diffusion coupled with facilitated transport and that the optimization algorithm is valid.

Modeling and Robustness Analysis of Biochemical Networks of Glycerol Metabolism by Klebsiella Pneumoniae

Glycerol bioconversion to 1,3-propanediol (1,3-PD) by Klebsiella pneumoniae (K. pneumoniae) can be characterized by an intricate network of interactions among biochemical fluxes, metabolic compounds, key enzymes and genetic regulatory. To date, there still exist some uncertain factors in this complex network because of the limitation in bio-techniques, especially in measuring techniques for intracellular substances. In this paper, among these uncertain factors, we aim to infer the transport mechanisms of glycerol and 1,3-PD across the cell membrane, which have received intensive interest in recent years. On the basis of different inferences of the transport mechanisms, we reconstruct various metabolic networks correspondingly and subsequently develop their dynamical systems (S-systems). To determine the most reasonable metabolic network from all possible ones, we establish a quantitative definition of biological robustness and undertake parameter identification and robustness analysis for each system. Numerical results show that it is most possible that both glycerol and 1,3-PD pass the cell membrane by active transport and passive diffusion.

Exponential and global stability of nonlinear dynamical systems relative to initial time difference

Specialized Research Fund for the Doctoral Program of Higher Education [20100121120018]; Natural Science Foundation of Fujian Province of China [2010J05013]; Fundamental Research Funds for the Central Universities [2010121004]

Automatic Control Design for Optimal Strategy in Fed-batch Culture with Coupled Feed of Glycerol and Alkali

In this paper, we study the production of 1,3-propanediol in fed-batch culture with coupled feed of glycerol and alkali. On the basis of the numerical solution to an optimal control problem subjected to a multi-stage nonlinear dynamical system, we propose a realizable optimal feeding strategy. Correspondingly, an automatic control system is designed for the fermenter, which involves the designs of control circuit, software flow control and computer monitored control system. This contribution successfully achieves a goal of combining a mathematically theoretical analysis with an automatic control design in the laboratory.

Modeling and Properties of Nonlinear Stochastic Dynamical System of Continuous Culture

The stochastic counterpart to the deterministic description of continuous fermentation with ordinary differential equation is investigated in the process of glycerol bio-dissimilation to 1,3-propanediol by Klebsiella pneumoniae. We briefly discuss the continuous fermentation process driven by three-dimensional Brownian motion and Lipschitz coefficients, which is suitable for the factual fermentation. Subsequently, we study the existence and uniqueness of solutions for the stochastic system as well as the boundedness of the Two-order Moment and the Markov property of the solution. Finally stochastic simulation is carried out under the Stochastic Euler-Maruyama method.

Optimal design of automatic control system for the fed-batch production of 1,3-propanediol with pH logic control

In this work, the fed-batch fermentation of glycerol by Klebsiella pneumoniae with pH logic control is discussed. We propose a hybrid system constrained optimal control problem with glycerol feeding instants as control variables to maximize the concentration of the objective product at the terminal time. Correspondingly, we explore an automatic control system to implement the optimal control strategy, in which the designs of control diagram, PLC control and supervisory computer control system are involved. This work achieves a goal of applying numerical optimal control analysis to the design of control system in glycerol fed-batch fermentation.