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Mathematical Modeling and Control of Bioprocesses

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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) | Viewed by 36960

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Special Issue Editors

Prof. Dr. Philippe Bogaerts

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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

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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
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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

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Keywords

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

Published Papers (14 papers)

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Editorial

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3 pages, 181 KiB

Open AccessEditorial

Special Issue: Mathematical Modeling and Control of Bioprocesses

by Philippe Bogaerts and Alain Vande Wouwer

Processes 2022, 10(7), 1372; https://0-doi-org.brum.beds.ac.uk/10.3390/pr10071372 - 14 Jul 2022

Viewed by 1199

Abstract

This Special Issue (SI) of Processes on Mathematical Modeling and Control of Bioprocesses (MMCB) contains papers focusing, on the one hand, on mathematical modeling of biological processes at different scales ranging from microscopic to macroscopic levels and, on the other hand, on model-based [...] Read more.

(This article belongs to the Special Issue Mathematical Modeling and Control of Bioprocesses)

Research

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20 pages, 1716 KiB

Open AccessArticle

Design, Implementation and Simulation of a Small-Scale Biorefinery Model

by Mihaela Sbarciog, Viviane De Buck, Simen Akkermans, Satyajeet Bhonsale, Monika Polanska and Jan F. M. Van Impe

Processes 2022, 10(5), 829; https://0-doi-org.brum.beds.ac.uk/10.3390/pr10050829 - 22 Apr 2022

Cited by 5 | Viewed by 2062

Abstract

Second-generation biomass is an underexploited resource, which can lead to valuable products in a circular economy. Available locally as food waste, gardening and pruning waste or agricultural waste, second-generation biomass can be processed into high-valued products through a flexi-feed small-scale biorefinery. The flexi-feed and the use of local biomass ensure the continuous availability of feedstock at low logistic costs. However, the viability and sustainability of the biorefinery must be ensured by the design and optimal operation. While the design depends on the available feedstock and the desired products, the optimisation requires the availability of a mathematical model of the biorefinery. This paper details the design and modelling of a small-scale biorefinery in view of its optimisation at a later stage. The proposed biorefinery comprises the following processes: steam refining, anaerobic digestion, ammonia stripping and composting. The models’ integration and the overall biorefinery operation are emphasised. The simulation results assess the potential of the real biowaste collected in a commune in Flanders (Belgium) to produce oligosaccharides, lignin, fibres, biogas, fertiliser and compost. This represents a baseline scenario, which can be subsequently employed in the evaluation of optimised solutions. The outlined approach leads to better feedstocks utilisation and product diversification, raising awareness on the impact and importance of small-scale biorefineries at a commune level. Full article

(This article belongs to the Special Issue Mathematical Modeling and Control of Bioprocesses)

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23 pages, 1245 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Optimal Darwinian Selection of Microorganisms with Internal Storage

by Walid Djema, Térence Bayen and Olivier Bernard

Processes 2022, 10(3), 461; https://0-doi-org.brum.beds.ac.uk/10.3390/pr10030461 - 24 Feb 2022

Cited by 6 | Viewed by 1137

Abstract

In this paper, we investigate the problem of species separation in minimal time. Droop model is considered to describe the evolution of two distinct populations of microorganisms that are in competition for the same resource in a photobioreactor. We focus on an optimal control problem (OCP) subject to a five-dimensional controlled system in which the control represents the dilution rate of the chemostat. The objective is to select the desired species in minimal-time and to synthesize an optimal feedback control. This is a very challenging issue, since we are are dealing with a ten-dimensional optimality system. We provide properties of optimal controls allowing the strain of interest to dominate the population. Our analysis is based on the Pontryagin Maximum Principle (PMP), along with a thorough study of singular arcs that is crucial in the synthesis of optimal controls. These theoretical results are also extensively illustrated and validated using a direct method in optimal control (via the Bocop software for numerically solving optimal control problems). The approach is illustrated with numerical examples with microalgae, reflecting the complexity of the optimal control structure and the richness of the dynamical behavior. Full article

(This article belongs to the Special Issue Mathematical Modeling and Control of Bioprocesses)

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45 pages, 1687 KiB

Open AccessFeature PaperArticle

Best Operating Conditions for Biogas Production in Some Simple Anaerobic Digestion Models

by Tewfik Sari

Processes 2022, 10(2), 258; https://0-doi-org.brum.beds.ac.uk/10.3390/pr10020258 - 28 Jan 2022

Cited by 7 | Viewed by 2539

Abstract

We consider one-step and two-step simple models of anaerobic digestion that are able to adequately capture the main dynamical behaviour of the full anaerobic digestion model ADM1. We do not consider specific growth functions. We only require them to satisfy certain qualitative assumptions. These assumptions are satisfied for concave growth functions, but they are also satisfied for a large class of growth functions found in many applications. We consider the maximisation of the biogas production with respect to the operating parameters of the model, which are the dilution rate and the substrate input concentration. We give the best operating conditions and we describe them as a subset of the set of operating parameters. Our models incorporate biomass decay terms, corresponding to maintenance. Numerical plots with specified growth functions and biological parameters illustrate the obtained results. Full article

(This article belongs to the Special Issue Mathematical Modeling and Control of Bioprocesses)

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16 pages, 3160 KiB

Open AccessFeature PaperArticle

Dynamic Model for Biomass and Proteins Production by Three Bacillus Thuringiensis ssp Kurstaki Strains

by Tatiana Segura Monroy, Nouha Abdelmalek, Souad Rouis, Mireille Kallassy, Jihane Saad, Joanna Abboud, Julien Cescut, Nadia Bensaid, Luc Fillaudeau and César Arturo Aceves-Lara

Processes 2021, 9(12), 2147; https://0-doi-org.brum.beds.ac.uk/10.3390/pr9122147 - 28 Nov 2021

Cited by 2 | Viewed by 1794

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) 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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20 pages, 1421 KiB

Open AccessFeature PaperArticle

Metabolic Flux Analysis of VERO Cells under Various Culture Conditions

by Georges Bastin, Véronique Chotteau and Alain Vande Wouwer

Processes 2021, 9(12), 2097; https://0-doi-org.brum.beds.ac.uk/10.3390/pr9122097 - 23 Nov 2021

Cited by 4 | Viewed by 2156

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 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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23 pages, 4245 KiB

Open AccessArticle

Off-Gas-Based Soft Sensor for Real-Time Monitoring of Biomass and Metabolism in Chinese Hamster Ovary Cell Continuous Processes in Single-Use Bioreactors

by Tobias Wallocha and Oliver Popp

Processes 2021, 9(11), 2073; https://0-doi-org.brum.beds.ac.uk/10.3390/pr9112073 - 19 Nov 2021

Cited by 3 | Viewed by 4336

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 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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20 pages, 1814 KiB

Open AccessArticle

Set Membership Estimation with Dynamic Flux Balance Models

by Xin Shen and Hector Budman

Processes 2021, 9(10), 1762; https://0-doi-org.brum.beds.ac.uk/10.3390/pr9101762 - 01 Oct 2021

Cited by 2 | Viewed by 1507

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 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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12 pages, 3309 KiB

Open AccessFeature PaperArticle

Simple Gain-Scheduled Control System for Dissolved Oxygen Control in Bioreactors

by Mantas Butkus, Donatas Levišauskas and Vytautas Galvanauskas

Processes 2021, 9(9), 1493; https://0-doi-org.brum.beds.ac.uk/10.3390/pr9091493 - 25 Aug 2021

Cited by 6 | Viewed by 2210

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. 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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19 pages, 1536 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Advanced Kinetic Modeling of Bio-co-polymer Poly(3-hydroxybutyrate-co-3-hydroxyvalerate) Production Using Fructose and Propionate as Carbon Sources

by Stefanie Duvigneau, Robert Dürr, Jessica Behrens and Achim Kienle

Processes 2021, 9(8), 1260; https://0-doi-org.brum.beds.ac.uk/10.3390/pr9081260 - 21 Jul 2021

Cited by 10 | Viewed by 2555

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 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 CO

_{2}

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 CO

_{2}

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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23 pages, 2336 KiB

Open AccessArticle

FPGA-Based Implementation of an Optimization Algorithm to Maximize the Productivity of a Microbial Electrolysis Cell

by José de Jesús Colín-Robles, Ixbalank Torres-Zúñiga, Mario A. Ibarra-Manzano and Víctor Alcaraz-González

Processes 2021, 9(7), 1111; https://0-doi-org.brum.beds.ac.uk/10.3390/pr9071111 - 25 Jun 2021

Cited by 2 | Viewed by 2306

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 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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19 pages, 1465 KiB

Open AccessFeature PaperArticle

Global Stability Analysis of a Bioreactor Model for Phenol and Cresol Mixture Degradation

by Neli Dimitrova and Plamena Zlateva

Processes 2021, 9(1), 124; https://0-doi-org.brum.beds.ac.uk/10.3390/pr9010124 - 08 Jan 2021

Cited by 8 | Viewed by 1856

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 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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22 pages, 958 KiB

Open AccessFeature PaperReview

Application of Optimization and Modeling for the Composting Process Enhancement

by Tea Sokač, Davor Valinger, Maja Benković, Tamara Jurina, Jasenka Gajdoš Kljusurić, Ivana Radojčić Redovniković and Ana Jurinjak Tušek

Processes 2022, 10(2), 229; https://0-doi-org.brum.beds.ac.uk/10.3390/pr10020229 - 25 Jan 2022

Cited by 9 | Viewed by 5628

Abstract

Composting is a more environmentally friendly and cost-effective alternative to digesting organic waste and turning it into organic fertilizer. It is a biological process in which polymeric waste materials contained in organic waste are biodegraded by fungi and bacteria. Temperature, pH, moisture content, C/N ratio, particle size, nutrient content and oxygen supply all have an impact on the efficiency of the composting process. To achieve optimal composting efficiency, all of these variables and their interactions must be considered. To this end, statistical optimization techniques and mathematical modeling approaches have been developed over the years. In this paper, an overview of optimization and mathematical modeling approaches in the field of composting processes is presented. The advantages and limitations of optimization and mathematical modeling for improving composting processes are also addressed. Full article

(This article belongs to the Special Issue Mathematical Modeling and Control of Bioprocesses)

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18 pages, 886 KiB

Open AccessFeature PaperEditor’s ChoiceReview

How to Tackle Underdeterminacy in Metabolic Flux Analysis? A Tutorial and Critical Review

by Philippe Bogaerts and Alain Vande Wouwer

Processes 2021, 9(9), 1577; https://0-doi-org.brum.beds.ac.uk/10.3390/pr9091577 - 02 Sep 2021

Cited by 2 | Viewed by 2679

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 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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