Optimization of a continuous fermentation process producing 1,3-propane diol with Hopf singularity and unstable operating points as constraints

Kinetics-based development of two-stage continuous fermentation of 1,3-propanediol from crude glycerol by Clostridium butyricum

BACKGROUND

Glycerol, as a by-product, mainly derives from the conversion of many crops to biodiesel, ethanol, and fatty ester. Its bioconversion to 1,3-propanediol (1,3-PDO) is an environmentally friendly method. Continuous fermentation has many striking merits over fed-batch and batch fermentation, such as high product concentration with easy feeding operation, long-term high productivity without frequent seed culture, and energy-intensive sterilization. However, it is usually difficult to harvest high product concentrations.

RESULTS

In this study, a three-stage continuous fermentation was firstly designed to produce 1,3-PDO from crude glycerol by Clostridium butyricum, in which the first stage fermentation was responsible for providing the excellent cells in a robust growth state, the second stage focused on promoting 1,3-PDO production, and the third stage aimed to further boost the 1,3-PDO concentration and reduce the residual glycerol concentration as much as possible. Through the three-stage continuous fermentation, 80.05 g/L 1,3-PDO as the maximum concentration was produced while maintaining residual glycerol of 5.87 g/L, achieving a yield of 0.48 g/g and a productivity of 3.67 g/(L·h). Based on the 14 sets of experimental data from the first stage, a kinetic model was developed to describe the intricate relationships among the concentrations of 1,3-PDO, substrate, biomass, and butyrate. Subsequently, this kinetic model was used to optimize and predict the highest 1,3-PDO productivity of 11.26 g/(L·h) in the first stage fermentation, while the glycerol feeding concentration and dilution rate were determined to be 92 g/L and 0.341 h-1, separately. Additionally, to achieve a target 1,3-PDO production of 80 g/L without the third stage fermentation, the predicted minimum volume ratio of the second fermenter to the first one was 11.9. The kinetics-based two-stage continuous fermentation was experimentally verified well with the predicted results.

CONCLUSION

A novel three-stage continuous fermentation and a kinetic model were reported. Then a simpler two-stage continuous fermentation was developed based on the optimization of the kinetic model. This kinetics-based development of two-stage continuous fermentation could achieve high-level production of 1,3-PDO. Meanwhile, it provides a reference for other bio-chemicals production by applying kinetics to optimize multi-stage continuous fermentation.

Bifurcation Control on the Un-Linearizable Dynamic System via Washout Filters

Information fusion integrates aspects of data and knowledge mostly on the basis that system information is accumulative/distributive, but a subtle case emerges for a system with bifurcations, which is always un-linearizable and exacerbates information acquisition and presents a control problem. In this paper, the problem of an un-linearizable system related to system observation and control is addressed, and Andronov-Hopf bifurcation is taken as a typical example of an un-linearizable system and detailed. Firstly, the properties of a linear/linearized system is upon commented. Then, nonlinear degeneracy for the normal form of Andronov-Hopf bifurcation is analyzed, and it is deduced that the cubic terms are an integral part of the system. Afterwards, the theoretical study on feedback stabilization is conducted between the normal-form Andronov-Hopf bifurcation and its linearized counterpart, where stabilization using washout-filter-aided feedback is compared, and it is found that by synergistic controller design, the dual-conjugate-unstable eigenvalues can be stabilized by single stable washout filter. Finally, the high-dimensional ethanol fermentation model is taken as a case study to verify the proposed bifurcation control method.

Optimization and feedback control system of dilution rate for 1,3-propanediol in two-stage fermentation: A theoretical study

In utilizing glycerol to produce 1,3-propanediol by microbial fermentation, the problems of low utilization rate and poor production performance need to be addressed. Based on the analysis of a mathematical model for 1,3-propanediol production from glycerol by Klebsiella pneumoniae, this study theoretically investigated the effects of the dilution rate and the initial glycerol concentration in a two-stage fermentation process and the feasibility of applying the feedback control methods. First, the optimal operation conditions of initial glycerol concentration and dilution rate were obtained. Through the use of feedback control theory, a control strategy for dilution rate was designed and optimized to shorten the settling time (time required for fermentation to reach stability) from 60.92 to 36.68 h for the first reactor, and from 53.66 to 22.68 h for the second reactor. In addition, the yield of 1,3-propanediol in both two reactors reached up to 0.5 g·g^-1 . The simulation results indicated that the feedback control strategy for dilution rate increased the product concentration, reduced the residual glycerol in the fermentation broth, and greatly improved the performance of the fermentation. A feeding strategy of automatic control for dilution rate has been established and will be applied as an effective guiding scheme in automatic continuous fermentations for production of 1,3-propanediol.

Robustness analysis and identification for an enzyme-catalytic complex metabolic network in batch culture

Bioconversion of glycerol to 1,3-propanediol is a promising way to mitigate the shortage of energy. To maximize the production of 1,3-propanediol, it needs to control precisely microbial fermentation process. However, it might consume lots of human and material resources when conducting experimental tests many times. In this study, a nonlinear enzyme-catalytic dynamical system is developed to describe the bioconversion process of glycerol to 1,3-propanediol, especially continuous piecewise linear functions are used as identification parameters. The existence, uniqueness and continuity of solutions are also discussed. Then, considering the fact that the concentration of intracellular substances is difficult to measure in experiments, a new quantitative definition of biological robustness is introduced as a performance index to determine the identification parameters related to intracellular substances. Meanwhile, a two-phase optimization algorithm is constructed to solve the identification model. By comparison with the experimental data, it can be found that the present nonlinear dynamical system can describe the fermentation process very well. Finally, the present nonlinear dynamical system and the corresponding optimal identification parameters might be useful in future studies on the batch culture of glycerol to 1,3-propanediol.

Ensemble optimization of microbial conversion of glycerol into 1, 3-propanediol by Klebsiella pneumoniae

Using mathematical model and computer simulation to predict biological processes and optimize the target production is an important strategy for optimizing fermentation process. However, the inherent uncertainty of the kinetic model severely limits the predictive capability. In this study, optimize target production, such as productivity and yield of 1, 3-propanediol produced by Klebsiella pneumoniae using glycerol as substrate, the ensemble modeling approach was used to reduce the model's uncertainty for fermentation process as much as possible, and effectively improve its prediction performance. Firstly, through sensitivity analysis, the parameters having significant influence on the model were determined as the adjustable parameters for the ensemble modeling. After comparison, the appropriate threshold coefficient of the model error was determined, and the sampling method was used to generate as many equivalent parameter sets as possible. Each set of parameters was separately applied for the simulation, and all the predicted values were integrated for the weighted average. Therefore, the expected value of the prediction was obtained. Compared with the traditional simulation using single parameter set, the ensemble modeling method achieved the lower relative error between the prediction and the experimental value and the greatly improved model prediction performance. Moreover, the optimal productivity and yield of 1, 3-propanediol and the corresponding operating conditions were obtained, respectively. The ensemble modeling approach effectively compensates for the uncertainties of the model, making its prediction performance more practical, which is important for computer simulations to predict and guide the actual production process.