Modelling and parameter identification for a two-stage fractional dynamical system in microbial batch process

In this paper, we consider mathematical modelling and parameter identification problem in bioconversion of glycerol to 1,3-propanediol by Klebsiella pneumoniae. In view of the dynamic behavior with memory and heredity and experimental results in batch culture, a two-stage fractional dynamical system with unknown fractional orders and unknown kinetic parameters is proposed to describe the fermentation process. For this system, some important properties of the solution are discussed. Then, taking the weighted least-squares error between the computational values and the experimental data as the performance index, a parameter identification model subject to continuous state inequality constraints is presented. An exact penalty method is introduced to transform the parameter identification problem into the one only with box constraints. On this basis, we develop a parallel Particle Swarm Optimization algorithm to find the optimal fractional orders and kinetic parameters. Finally, numerical results show that the model can reasonably describe the batch fermentation process, as well as the effectiveness of the developed algorithm. Keywords: fractional dynamical system, parameter identification, parallel optimization

Modeling nonlinear stochastic kinetic system and stochastic optimal control of microbial bioconversion process in batch culture

In this paper, we analyze a stochastic model representing batch fermentation in the process of glycerol bio-dissimilation to 1,3-propanediol by klebsiella pneumoniae. The stochasticity in the model is introduced by parameter perturbation which is a standard technique in stochastic population modelling. Thus, based on the nonlinear deterministic dynamical system of glycerol bioconversion to 1,3-propanediol in batch culture, we present the stochastic version of the batch fermentation process driven by a five-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 and Markov property of solutions. Moveover a stochastic optimal control model is constructed and the sufficient and necessary conditions for optimality are proved via dynamic programming principle. Finally we present computer simulation for the stochastic system by using Stochastic Euler–Maruyama scheme. Compared with the results from the deterministic system, numerical results reveal the peculiar role of stochasticity in the dynamical responses of the batch culture

Optimization of a fed-batch bioreactor for 1,3-propanediol production using hybrid nonlinear optimal control

A nonlinear hybrid system was proposed to describe the fed-batch bioconversion of glycerol to 1,3-propanediol with substrate open loop inputs and pH logic control in previous work [47]. The current work concerns the optimal control of this fed-batch process. We slightly modify the hybrid system to provide a more convenient mathematical description for the optimal control of the fed-batch culture. Taking the feeding instants and the terminal time as decision variables, we formulate an optimal control model with the productivity of 1,3-propanediol as the performance index. Inequality path constraints involved in the optimal control problem are transformed into a group of end-point constraints by introducing an auxiliary hybrid system. The original optimal control problem is associated with a family of approximation problems. The gradients of the cost functional and the end-point constraint functions are derived from the parametric sensitivity system. On this basis, we construct a gradient-based algorithm to solve the approximation problems. Numerical results show that the productivity of 1,3-propanediol can be increased considerably by employing our optimal control policy

A linear optimal feedback control for producing 1,3-propanediol via microbial fermentation

In this paper, we consider a multistage feedback control strategy for the production of 1,3-propanediol(1,3-PD) in microbial fermentation. The feedback control strategy is widely used in industry, and to the best of our knowledge, this is the first time it is applied to 1,3-PD. The feedback control law is assumed to be linear of the concentrations of biomass and glycerol, and the coefficients in the controller are continuous. A multistage feedback control law is obtained by using the control parameterization method on the coefficient functions. Then, the optimal control problem can be transformed into an optimal parameter selection problem. The time horizon is partitioned adaptively. The corresponding gradients are derived, and finally, our numerical results indicate that the strategy is flexible and efficient

Advances and Future Perspectives

Agharafeie , R., Ramos, J. R. C., Mendes, J. M., & Oliveira, R. M. F. (2023). From Shallow to Deep Bioprocess Hybrid Modeling: Advances and Future Perspectives. Fermentation, 9(10), 1-22. [922]. https://doi.org/10.20944/preprints202310.0107.v1, https://doi.org/10.3390/fermentation9100922--- This work was supported by the Associate Laboratory for Green Chemistry - LAQV which is financed by national funds from FCT/MCTES (UIDB/50006/2020 and UIDP/50006/2020). This work received funding from the European Union’s Horizon 2020 research and innovation program under the grant agreement no. 101099487- BioLaMer-HORIZON-EIC-2022-PATHFINDEROPEN-01 (BioLaMer)Deep learning is emerging in many industrial sectors in hand with big data analytics to streamline production. In the biomanufacturing sector, big data infrastructure is lagging comparatively to other industries. A promising approach is to combine Deep Neural Networks (DNN) with prior knowledge in Hybrid Neural Network (HNN) workflows that are less dependent on the quality and quantity of data. This paper reviews published articles over the past 30 years on the topic of HNN applications to bioprocesses. It revealed that HNNs were applied to various bioprocesses, including microbial cultures, animal cells cultures, mixed microbial cultures, and enzyme biocatalysis. HNNs were mainly applied for process analysis, process monitoring, development of software sensors, open- and closed-loop control, batch-to-batch control, model predictive control, intensified design of experiments, quality-by-design, and recently for the development of digital twins. Most previous HNN studies combined shallow Feedforward Neural Networks (FFNNs) with physical laws, such as macroscopic material balance equations, following the semiparametric design principle. Only recently, deep HNNs based on deep FFNNs, Convolution Neural Networks (CNN), Long Short-Term Memory (LSTM) networks and Physics Informed Neural Networks (PINNs) have been reported. The biopharma sector is currently a major driver but applications to biologics quality attributes, new modalities, and downstream processing are significant research gaps.publishersversionpublishe

Modeling and optimization of extracellular polysaccharides production by Enterobacter A47

Polysaccharides are gaining increasing attention as potential environmental friendly and sustainable building blocks in many fields of the (bio)chemical industry. The microbial production of polysaccharides is envisioned as a promising path, since higher biomass growth rates are possible and therefore higher productivities may be achieved compared to vegetable or animal polysaccharides sources. This Ph.D. thesis focuses on the modeling and optimization of a particular microbial polysaccharide, namely the production of extracellular polysaccharides (EPS) by the bacterial strain Enterobacter A47. Enterobacter A47 was found to be a metabolically versatile organism in terms of its adaptability to complex media, notably capable of achieving high growth rates in media containing glycerol byproduct from the biodiesel industry. However, the industrial implementation of this production process is still hampered due to a largely unoptimized process. Kinetic rates from the bioreactor operation are heavily dependent on operational parameters such as temperature, pH, stirring and aeration rate. The increase of culture broth viscosity is a common feature of this culture and has a major impact on the overall performance. This fact complicates the mathematical modeling of the process, limiting the possibility to understand, control and optimize productivity. In order to tackle this difficulty, data-driven mathematical methodologies such as Artificial Neural Networks can be employed to incorporate additional process data to complement the known mathematical description of the fermentation kinetics. In this Ph.D. thesis, we have adopted such an hybrid modeling framework that enabled the incorporation of temperature, pH and viscosity effects on the fermentation kinetics in order to improve the dynamical modeling and optimization of the process. A model-based optimization method was implemented that enabled to design bioreactor optimal control strategies in the sense of EPS productivity maximization. It is also critical to understand EPS synthesis at the level of the bacterial metabolism, since the production of EPS is a tightly regulated process. Methods of pathway analysis provide a means to unravel the fundamental pathways and their controls in bioprocesses. In the present Ph.D. thesis, a novel methodology called Principal Elementary Mode Analysis (PEMA) was developed and implemented that enabled to identify which cellular fluxes are activated under different conditions of temperature and pH. It is shown that differences in these two parameters affect the chemical composition of EPS, hence they are critical for the regulation of the product synthesis. In future studies, the knowledge provided by PEMA could foster the development of metabolically meaningful control strategies that target the EPS sugar content and oder product quality parameters

Hybrid physics-based and data-driven modeling for bioprocess online simulation and optimization

Model‐based online optimization has not been widely applied to bioprocesses due to the challenges of modeling complex biological behaviors, low‐quality industrial measurements, and lack of visualization techniques for ongoing processes. This study proposes an innovative hybrid modeling framework which takes advantages of both physics‐based and data‐driven modeling for bioprocess online monitoring, prediction, and optimization. The framework initially generates high‐quality data by correcting raw process measurements via a physics‐based noise filter (a generally available simple kinetic model with high fitting but low predictive performance); then constructs a predictive data‐driven model to identify optimal control actions and predict discrete future bioprocess behaviors. Continuous future process trajectories are subsequently visualized by re‐fitting the simple kinetic model (soft sensor) using the data‐driven model predicted discrete future data points, enabling the accurate monitoring of ongoing processes at any operating time. This framework was tested to maximize fed‐batch microalgal lutein production by combining with different online optimization schemes and compared against the conventional open‐loop optimization technique. The optimal results using the proposed framework were found to be comparable to the theoretically best production, demonstrating its high predictive and flexible capabilities as well as its potential for industrial application

Fermentation: Metabolism, Kinetic Models, and Bioprocessing

Biochemical and metabolic interpretation of microbial growth is an important topic in bioreactor design. We intend to address valuable information about the relation of critical operation variables and the simulation of bioprocesses with unstructured and structured kinetic models. Process parameters such as nutrient supply, pH, dissolved oxygen, and metabolic end-products directly impact the physiology and metabolism of microorganisms. Changes in the membrane as well as cell viability are of interest since protein expression and maturation in prokaryota are directly related to membrane integrity. This chapter intends to deliver an insight of different alternatives in kinetic modeling

Kinetic models in industrial biotechnology - Improving cell factory performance

An increasing number of industrial bioprocesses capitalize on living cells by using them as cell factories that convert sugars into chemicals. These processes range from the production of bulk chemicals in yeasts and bacteria to the synthesis of therapeutic proteins in mammalian cell lines. One of the tools in the continuous search for improved performance of such production systems is the development and application of mathematical models. To be of value for industrial biotechnology, mathematical models should be able to assist in the rational design of cell factory properties or in the production processes in which they are utilized. Kinetic models are particularly suitable towards this end because they are capable of representing the complex biochemistry of cells in a more complete way compared to most other types of models. They can, at least in principle, be used to in detail understand, predict, and evaluate the effects of adding, removing, or modifying molecular components of a cell factory and for supporting the design of the bioreactor or fermentation process. However, several challenges still remain before kinetic modeling will reach the degree of maturity required for routine application in industry. Here we review the current status of kinetic cell factory modeling. Emphasis is on modeling methodology concepts, including model network structure, kinetic rate expressions, parameter estimation, optimization methods, identifiability analysis, model reduction, and model validation, but several applications of kinetic models for the improvement of cell factories are also discussed