Special Issue "Mathematical Modeling and Control of Bioprocesses"

A special issue of Processes (ISSN 2227-9717). This special issue belongs to the section "Biological Processes and Systems".

Deadline for manuscript submissions: closed (30 November 2021).

Special Issue Editors

Prof. Dr. Philippe Bogaerts
E-Mail Website
Guest Editor
Biosystems Modeling and Control, Université Libre de Bruxelles, CP 165/61, Roosevelt Ave. 50, 1050 Brussels, Belgium
Interests: mathematical modeling; parameter estimation; network analysis; model-based optimization; control and state estimation with application to biological systems and bioprocesses
Prof. Dr. Alain Vande Wouwer
E-Mail Website
Guest Editor
Automatic Control Laboratory, University of Mons, 31 Boulevard Dolez, 7000 Mons, Belgium
Interests: mathematical modeling; metabolic flux analysis; numerical simulation; identification; data-driven techniques; process control; model predictive control
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue on Mathematical Modeling and Control of Bioprocesses aims at presenting novel scientific contributions to mathematical modeling in major areas of biotechnologies, including biological cultures in biopharmaceutical or in agro-food industries, environmental bioprocesses, biomass valorization processes, etc. Contributions may focus either on the development of the mathematical model itself and/or the modeling procedure (new model structures, model identification), or on the use of mathematical models for bioprocess supervision, diagnosis, state observation, operation, optimization, and control. Mathematical models at macroscopic or at microscopic levels may be considered. In this latter category, the analysis of metabolic networks is a topic of particular interest.

Mathematical models or, in contrast, data-driven techniques can be the basis to determine desirable operating conditions and to design optimizing control strategies, which is the second set of topics of this Special Issue.

New methods (or method extensions) in mathematical modeling and control should be validated with experimental or simulated data.

Areas of interest include:

  • Modeling and identification
  • Parameter and state estimation
  • Optimal experiment design
  • Fault diagnosis and monitoring
  • Model-based optimization and control
  • Data-driven control
  • Metabolic networks, metabolic flux analysis, flux variability analysis, elementary flux modes

with applications to

  • Microbial (bacteria or yeast) cultures
  • Mammalian and insect cell cultures
  • Microalgae cultures
  • Biopharmaceutical processes (vaccines, monoclonal antibodies production)
  • Food engineering
  • Environmental bioprocesses (waste water treatment, bioremediation)
  • Biomass valorization processes (biohydrogen, biofuel, biopolymers production)

Prof. Dr. Philippe Bogaerts
Prof. Dr. Alain Vande Wouwer
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Processes is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2000 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Bioprocesses
  • Mathematical modeling
  • Parameter estimation
  • State estimation
  • Model-based optimization
  • Model-based control
  • Data-driven control
  • Metabolic network
  • Metabolic Flux Analysis

Published Papers (9 papers)

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Research

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Article
Dynamic Model for Biomass and Proteins Production by Three Bacillus Thuringiensis ssp Kurstaki Strains
Processes 2021, 9(12), 2147; https://0-doi-org.brum.beds.ac.uk/10.3390/pr9122147 - 28 Nov 2021
Viewed by 274
Abstract
Bacillus thuringiensis is a microorganism used for the production of biopesticides worldwide. In the present paper, different kinetic models were analyzed to study and compare three different strains of Bt ssp kurstaki (LIP, BLB1, and HD1). Bioperformances (vegetative cell, spore, substrate, and protein) [...] Read more.
Bacillus thuringiensis is a microorganism used for the production of biopesticides worldwide. In the present paper, different kinetic models were analyzed to study and compare three different strains of Bt ssp kurstaki (LIP, BLB1, and HD1). Bioperformances (vegetative cell, spore, substrate, and protein) and successive culture phases (oxidative growth, limitation and sporulation, and protein release) were depicted with an overarching aim to estimate total protein productivity, yield, and titer. In the end, two models were calibrated using experimental dataset (11 batches culture in 3 L bioreactor with semisynthetic medium), subsequently validated, and statistically compared. Both models satisfactorily followed the dynamics of the experimental data. Finally, a dynamic model was selected following the Akaike information criterion (AIC). Full article
(This article belongs to the Special Issue Mathematical Modeling and Control of Bioprocesses)
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Article
Metabolic Flux Analysis of VERO Cells under Various Culture Conditions
Processes 2021, 9(12), 2097; https://0-doi-org.brum.beds.ac.uk/10.3390/pr9122097 - 23 Nov 2021
Viewed by 238
Abstract
Although the culture of VERO cells in bioreactors is an important industrial bioprocess for the production of viruses and vaccines, surprisingly few reports on the analysis of the flux distribution in the cell metabolism have been published. In this study, an attempt is [...] Read more.
Although the culture of VERO cells in bioreactors is an important industrial bioprocess for the production of viruses and vaccines, surprisingly few reports on the analysis of the flux distribution in the cell metabolism have been published. In this study, an attempt is made to fill this gap by providing an analysis of relatively simple metabolic networks, which are constructed to describe the cell behavior in different culture conditions, e.g., the exponential growth phase (availability of glucose and glutamine), cell growth without glutamine, and cell growth without glucose and glutamine. The metabolic networks are kept as simple as possible in order to avoid underdeterminacy linked to the lack of extracellular measurements, and a unique flux distribution is computed in each case based on a mild assumption that the macromolecular composition of the cell is known. The result of this computation provides some insight into the metabolic changes triggered by the culture conditions, which could support the design of feedback control strategies in fed batch or perfusion bioreactors where the lactate concentration is measured online and regulated by controlling the delivery rates of glucose and, possibly, of some essential amino acids. Full article
(This article belongs to the Special Issue Mathematical Modeling and Control of Bioprocesses)
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Article
Off-Gas-Based Soft Sensor for Real-Time Monitoring of Biomass and Metabolism in Chinese Hamster Ovary Cell Continuous Processes in Single-Use Bioreactors
Processes 2021, 9(11), 2073; https://0-doi-org.brum.beds.ac.uk/10.3390/pr9112073 - 19 Nov 2021
Viewed by 347
Abstract
In mammalian cell culture, especially in pharmaceutical manufacturing and research, biomass and metabolic monitoring are mandatory for various cell culture process steps to develop and, finally, control bioprocesses. As a common measure for biomass, the viable cell density (VCD) or the viable cell [...] Read more.
In mammalian cell culture, especially in pharmaceutical manufacturing and research, biomass and metabolic monitoring are mandatory for various cell culture process steps to develop and, finally, control bioprocesses. As a common measure for biomass, the viable cell density (VCD) or the viable cell volume (VCV) is widely used. This study highlights, for the first time, the advantages of using VCV instead of VCD as a biomass depiction in combination with an oxygen-uptake- rate (OUR)-based soft sensor for real-time biomass estimation and process control in single-use bioreactor (SUBs) continuous processes with Chinese hamster ovary (CHO) cell lines. We investigated a series of 14 technically similar continuous SUB processes, where the same process conditions but different expressing CHO cell lines were used, with respect to biomass growth and oxygen demand to calibrate our model. In addition, we analyzed the key metabolism of the CHO cells in SUB perfusion processes by exometabolomic approaches, highlighting the importance of cell-specific substrate and metabolite consumption and production rate qS analysis to identify distinct metabolic phases. Cell-specific rates for classical mammalian cell culture key substrates and metabolites in CHO perfusion processes showed a good correlation to qOUR, yet, unexpectedly, not for qGluc. Here, we present the soft-sensoring methodology we developed for qPyr to allow for the real-time approximation of cellular metabolism and usage for subsequent, in-depth process monitoring, characterization and optimization. Full article
(This article belongs to the Special Issue Mathematical Modeling and Control of Bioprocesses)
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Article
Set Membership Estimation with Dynamic Flux Balance Models
Processes 2021, 9(10), 1762; https://doi.org/10.3390/pr9101762 - 01 Oct 2021
Viewed by 357
Abstract
Dynamic flux balance models (DFBM) are used in this study to infer metabolite concentrations that are difficult to measure online. The concentrations are estimated based on few available measurements. To account for uncertainty in initial conditions the DFBM is converted into a variable [...] Read more.
Dynamic flux balance models (DFBM) are used in this study to infer metabolite concentrations that are difficult to measure online. The concentrations are estimated based on few available measurements. To account for uncertainty in initial conditions the DFBM is converted into a variable structure system based on a multiparametric linear programming (mpLP) where different regions of the state space are described by correspondingly different state space models. Using this variable structure system, a special set membership-based estimation approach is proposed to estimate unmeasured concentrations from few available measurements. For unobservable concentrations, upper and lower bounds are estimated. The proposed set membership estimation was applied to batch fermentation of E. coli based on DFBM. Full article
(This article belongs to the Special Issue Mathematical Modeling and Control of Bioprocesses)
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Article
Simple Gain-Scheduled Control System for Dissolved Oxygen Control in Bioreactors
Processes 2021, 9(9), 1493; https://0-doi-org.brum.beds.ac.uk/10.3390/pr9091493 - 25 Aug 2021
Viewed by 399
Abstract
An adaptive control system for the set-point control and disturbance rejection of biotechnological-process parameters is presented. The gain scheduling of PID (PI) controller parameters is based on only controller input/output signals and does not require additional measurement of process variables for controller-parameter adaptation. [...] Read more.
An adaptive control system for the set-point control and disturbance rejection of biotechnological-process parameters is presented. The gain scheduling of PID (PI) controller parameters is based on only controller input/output signals and does not require additional measurement of process variables for controller-parameter adaptation. Realization of the proposed system does not depend on the instrumentation-level of the bioreactor and is, therefore, attractive for practical application. A simple gain-scheduling algorithm is developed, using tendency models of the controlled process. Dissolved oxygen concentration was controlled using the developed control system. The biotechnological process was simulated in fed-batch operating mode, under extreme operating conditions (the oxygen uptake-rate’s rapidly and widely varying, feeding and aeration rate disturbances). In the simulation experiments, the gain-scheduled controller demonstrated robust behavior and outperformed the compared conventional PI controller with fixed parameters. Full article
(This article belongs to the Special Issue Mathematical Modeling and Control of Bioprocesses)
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Article
Advanced Kinetic Modeling of Bio-co-polymer Poly(3-hydroxybutyrate-co-3-hydroxyvalerate) Production Using Fructose and Propionate as Carbon Sources
Processes 2021, 9(8), 1260; https://0-doi-org.brum.beds.ac.uk/10.3390/pr9081260 - 21 Jul 2021
Cited by 1 | Viewed by 540
Abstract
Biopolymers are a promising alternative to petroleum-based plastic raw materials. They are bio-based, non-toxic and degradable under environmental conditions. In addition to the homopolymer poly(3-hydroxybutyrate) (PHB), there are a number of co-polymers that have a broad range of applications and are easier to [...] Read more.
Biopolymers are a promising alternative to petroleum-based plastic raw materials. They are bio-based, non-toxic and degradable under environmental conditions. In addition to the homopolymer poly(3-hydroxybutyrate) (PHB), there are a number of co-polymers that have a broad range of applications and are easier to process in comparison to PHB. The most prominent representative from this group of bio-copolymers is poly(3-hydroxybutyrate-co-3-hydroxyvalerate) (PHBV). In this article, we show a new kinetic model that describes the PHBV production from fructose and propionic acid in Cupriavidus necator (C. necator). The developed model is used to analyze the effects of process parameter variations such as the CO2 amount in the exhaust gas and the feed rate. The presented model is a valuable tool to improve the microbial PHBV production process. Due to the coupling of CO2 online measurements in the exhaust gas to the biomass production, the model has the potential to predict the composition and the current yield of PHBV in the ongoing process. Full article
(This article belongs to the Special Issue Mathematical Modeling and Control of Bioprocesses)
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Article
FPGA-Based Implementation of an Optimization Algorithm to Maximize the Productivity of a Microbial Electrolysis Cell
Processes 2021, 9(7), 1111; https://0-doi-org.brum.beds.ac.uk/10.3390/pr9071111 - 25 Jun 2021
Viewed by 457
Abstract
In this work, the design of the hardware architecture to implement an algorithm for optimizing the Hydrogen Productivity Rate (HPR) in a Microbial Electrolysis Cell (MEC) is presented. The HPR in the MEC is maximized by the golden section search algorithm in conjunction [...] Read more.
In this work, the design of the hardware architecture to implement an algorithm for optimizing the Hydrogen Productivity Rate (HPR) in a Microbial Electrolysis Cell (MEC) is presented. The HPR in the MEC is maximized by the golden section search algorithm in conjunction with a super-twisting controller. The development of the digital architecture in the implementation step of the optimization algorithm was developed in the Very High Description Language (VHDL) and synthesized in a Field Programmable Gate Array (FPGA). Numerical simulations demonstrated the feasibility of the proposed optimization strategy embedded in an FPGA Cyclone II. Results showed that only 21% of the total logic elements, 5.19% of dedicated logic registers, and 64% of the total eight-bits multipliers of the FPGA were used. On the other hand, the estimated power consumption required by the FPGA-embedded optimization algorithm was only 146 mW. Full article
(This article belongs to the Special Issue Mathematical Modeling and Control of Bioprocesses)
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Article
Global Stability Analysis of a Bioreactor Model for Phenol and Cresol Mixture Degradation
Processes 2021, 9(1), 124; https://0-doi-org.brum.beds.ac.uk/10.3390/pr9010124 - 08 Jan 2021
Cited by 3 | Viewed by 597
Abstract
We propose a mathematical model for phenol and p-cresol mixture degradation in a continuously stirred bioreactor. The model is described by three nonlinear ordinary differential equations. The novel idea in the model design is the biomass specific growth rate, known as sum [...] Read more.
We propose a mathematical model for phenol and p-cresol mixture degradation in a continuously stirred bioreactor. The model is described by three nonlinear ordinary differential equations. The novel idea in the model design is the biomass specific growth rate, known as sum kinetics with interaction parameters (SKIP) and involving inhibition effects. We determine the equilibrium points of the model and study their local asymptotic stability and bifurcations with respect to a practically important parameter. Existence and uniqueness of positive solutions are proved. Global stabilizability of the model dynamics towards equilibrium points is established. The dynamic behavior of the solutions is demonstrated on some numerical examples. Full article
(This article belongs to the Special Issue Mathematical Modeling and Control of Bioprocesses)
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Review

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Review
How to Tackle Underdeterminacy in Metabolic Flux Analysis? A Tutorial and Critical Review
Processes 2021, 9(9), 1577; https://0-doi-org.brum.beds.ac.uk/10.3390/pr9091577 - 02 Sep 2021
Viewed by 456
Abstract
Metabolic flux analysis is often (not to say almost always) faced with system underdeterminacy. Indeed, the linear algebraic system formed by the steady-state mass balance equations around the intracellular metabolites and the equality constraints related to the measurements of extracellular fluxes do not [...] Read more.
Metabolic flux analysis is often (not to say almost always) faced with system underdeterminacy. Indeed, the linear algebraic system formed by the steady-state mass balance equations around the intracellular metabolites and the equality constraints related to the measurements of extracellular fluxes do not define a unique solution for the distribution of intracellular fluxes, but instead a set of solutions belonging to a convex polytope. Various methods have been proposed to tackle this underdeterminacy, including flux pathway analysis, flux balance analysis, flux variability analysis and sampling. These approaches are reviewed in this article and a toy example supports the discussion with illustrative numerical results. Full article
(This article belongs to the Special Issue Mathematical Modeling and Control of Bioprocesses)
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