Special Issue "Modelling and Optimal Design of Complex Biological Systems"

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

Deadline for manuscript submissions: closed (15 June 2021).

Special Issue Editors

Dr. Jérôme Harmand
E-Mail Website
Guest Editor
INRA, Université de Montpellier, LBE, Avenue des étangs, 11100 Narbonne, France
Interests: modelling and control of microbial ecosystems and bioprocesses; dynamic systems, optimal design, interconnections of bioprocesses; observer design, control design, modelling and control for reuse of non conventional waters; optimal control of bioreactors
Dr. Alain Rapaport
E-Mail Website
Guest Editor
MISTEA (Univ. Montpellier, INRA, Montpellier SupAgro), 34060 Montpellier, France
Interests: dynamical systems, differential equations, control and observation of dynamical systems; optimization and optimal control, modelling, optimization and control for microbial ecology; modelling and control for the management of renewable natural resources
Prof. Dr. Neli Dimitrova
E-Mail Website
Guest Editor
Institute of Mathematics and Informatics (IMI), Bulgarian Academy of Sciences, Acad. G. Bonchev, block 8, Sofia 1113, Bulgaria
Interests: computer-oriented numerical analysis; dynamical systems; mathematical modelling in engineering and bioscience
Prof. Dr. Ivan Simeonov
E-Mail Website
Guest Editor
Institute of microbiology “Stephan Angeloff”, Bulgarian Academy of Sciences, Acad. G. Bonchev str., bl 26, Sofia 1113, Bulgaria
Interests: anaerobic digestion; mathematical modeling; automatic control; bioprocess engineering; environmental engineering

Special Issue Information

Dear Colleagues,

Complex biological processes are currently used in many industrial areas, and are being used increasingly within real environmental refineries whose objectives are the production of biomolecules or the recovery of nutrients and energy within circular economy cycles. The use of modelling has become very common to optimize bioprocesses. Recently, optimal design that aims at conciving optimal configurations of processes or the best way to interconnect several reactors has developed rapidly in order to minimize building and/or operational costs. To this end, tools from modeling and control; simulation; and, in a more general way, dynamical systems theory, are essential tools to address these optimization challenges.

This Special Issue “Modelling and Optimal Design of Complex Biological Systems“ aims at collecting research studies related to these important research areas. Topics include but are not limited to the following:

  • Aerobic and anaerobic systems for nutrient removal;
  • Bioprocesses for energy recovery;
  • Biorefinery used for the production of biomolecules;
  • Microalgae systems for the treatment of water and the production of biomolecules;
  • Complex interconnections of biosystems for energy production.

Dr. Jérôme Harmand
Dr. Alain Rapaport
Prof. Dr. Neli Dimitrova
Prof. Dr. Ivan Simeonov
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

  • Modelling, control, and simulation for minimizing the size of biological systems
  • Optimal control of bioprocesses
  • Constrained optimization for the minimization of process retention time
  • New process configurations for energy and nutrient recovery
  • Flexible systems for water reuse.

Published Papers (11 papers)

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Research

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Article
Mathematical Study of a Two-Stage Anaerobic Model When the Hydrolysis Is the Limiting Step
Processes 2021, 9(11), 2050; https://0-doi-org.brum.beds.ac.uk/10.3390/pr9112050 - 16 Nov 2021
Viewed by 247
Abstract
A two-step model of the anaerobic digestion process is mathematically and numerically studied. The focus of the paper is put on the hydrolysis and methanogenesis phases when applied to the digestion of waste with a high content of solid matter: existence and stability [...] Read more.
A two-step model of the anaerobic digestion process is mathematically and numerically studied. The focus of the paper is put on the hydrolysis and methanogenesis phases when applied to the digestion of waste with a high content of solid matter: existence and stability properties of the equilibrium points are investigated. The hydrolysis step is considered a limiting step in this process using the Contois growth function for the bacteria responsible for the first degradation step. The methanogenesis step being inhibited by the product of the first reaction (which is also the substrate for the second one), and the Haldane growth rate is used for the second reaction step. The operating diagrams with respect to the dilution rate and the input substrate concentrations are established and discussed. Full article
(This article belongs to the Special Issue Modelling and Optimal Design of Complex Biological Systems)
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Article
Optimum Design of N Continuous Stirred-Tank Bioreactors in Series for Fermentation Processes Based on Simultaneous Substrate and Product Inhibition
Processes 2021, 9(8), 1419; https://0-doi-org.brum.beds.ac.uk/10.3390/pr9081419 - 16 Aug 2021
Viewed by 423
Abstract
Optimization of the continuous fermentation process is important for increasing efficiency and decreasing cost, especially for complicated biochemical processes described by substrate and product inhibition. The optimum design (minimum volume) of CSTRs in series assuming substrate and product inhibition was determined in this [...] Read more.
Optimization of the continuous fermentation process is important for increasing efficiency and decreasing cost, especially for complicated biochemical processes described by substrate and product inhibition. The optimum design (minimum volume) of CSTRs in series assuming substrate and product inhibition was determined in this study. The effect of operating parameters on the optimum design was investigated. The optimum substrate concentration in the feed to the first reactor was determined for N reactors in series. The nonlinear, constrained optimization problem was solved using the MATLAB function “fmincon”. It was found that the optimum design is more beneficial at high substrate conversion and at a medium level of feed substrate concentration. The best number of reactors is two to three for optimum arrangements and two for equal-size arrangements. The presence of biomass in the feed to the first reactor reduces the reactor volume, while the presence of product in the feed slightly increases the required total volume. The percentage reduction in the total volume using the optimum design compared to equal-volume design (R%) was determined as a function of substrate conversion and substrate concentration in the feed to the first reactor. The obtained R% values agree with experimental data available in the literature for ethanol fermentation. Full article
(This article belongs to the Special Issue Modelling and Optimal Design of Complex Biological Systems)
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Article
Multivariable Robust Regulation of Alkalinities in Continuous Anaerobic Digestion Processes: Experimental Validation
Processes 2021, 9(7), 1153; https://0-doi-org.brum.beds.ac.uk/10.3390/pr9071153 - 02 Jul 2021
Viewed by 623
Abstract
A multivariable adaptive feedback control for highly uncertain continuous anaerobic digestion processes is proposed to regulate the volatile fatty acids (VFA) concentration, the strong ions concentrations, and the total and intermediate alkalinities. The multivariable control scheme includes a Luenberger observer to estimate both [...] Read more.
A multivariable adaptive feedback control for highly uncertain continuous anaerobic digestion processes is proposed to regulate the volatile fatty acids (VFA) concentration, the strong ions concentrations, and the total and intermediate alkalinities. The multivariable control scheme includes a Luenberger observer to estimate both the unmeasured variables (i.e., VFA) and unknown microbial growth kinetics. The control approach is designed using an exponential Lyapunov function to resemble the typical exponential biological growth of the involved microbial consortia. Taking into account physicochemical equilibrium, alkalinities are represented as a function of the state variables. As a result, the control problem becomes a regulation problem on alkalinities, and in turn, a tracking control problem on the state variables, with two manipulated variables—the dilution rate and the feed rate of a strong alkali solution—while the state variables’ set-points are given as a function of pH. The implementation of this multivariable control scheme was experimentally tested and validated in a 0.982 m3 pilot plant treating agro-industrial wastewater and demonstrated to be robust in the face of unknown microbial growth kinetics. Results showed the potential for practical application and optimization of industrial digesters. Full article
(This article belongs to the Special Issue Modelling and Optimal Design of Complex Biological Systems)
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Article
Modeling the Influence of Temperature, Light Intensity and Oxygen Concentration on Microalgal Growth Rate
Processes 2021, 9(3), 496; https://0-doi-org.brum.beds.ac.uk/10.3390/pr9030496 - 09 Mar 2021
Viewed by 754
Abstract
Dissolved oxygen plays a key role in microalgal growth at high density. This effect was so far rarely quantified. Here we propose a new model to represent the combined effect of light, oxygen concentration and temperature (LOT-model) on microalgae growth. The LOT-model introduces [...] Read more.
Dissolved oxygen plays a key role in microalgal growth at high density. This effect was so far rarely quantified. Here we propose a new model to represent the combined effect of light, oxygen concentration and temperature (LOT-model) on microalgae growth. The LOT-model introduces oxygen concentration in order to represent the oxidative stress affecting the cultures, adding a toxicity term in the expression of the net growth rate. The model was validated with experimental data for several species such as Chlorella minutissima, Chlorella vulgaris, Dunaliella salina, Isochrysis galbana. It successfully predicted experimental records with an average error lower than 5.5%. The model was also validated using dynamical data where oxygen concentration varies. It highlights a strong impact of oxygen concentration on productivity, depending on temperature. The model quantifies the sensitivity to oxidative stress of different species and shows, for example, that Dunaliella salina is much less affected than Chlorella vulgaris by oxidative stress. The modeling approach can support an optimization strategy to improve productivity, especially for managing high oxygen levels. Full article
(This article belongs to the Special Issue Modelling and Optimal Design of Complex Biological Systems)
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Article
Experimental Study of Substrate Limitation and Light Acclimation in Cultures of the Microalgae Scenedesmus obliquus—Parameter Identification and Model Predictive Control
Processes 2020, 8(12), 1551; https://0-doi-org.brum.beds.ac.uk/10.3390/pr8121551 - 27 Nov 2020
Viewed by 781
Abstract
In this study, the parameters of a dynamic model of cultures of the microalgae Scenedesmus obliquus are estimated from datasets collected in batch photobioreactors operated with various initial conditions and light illumination conditions. Measurements of biomass, nitrogen quota, bulk substrate concentration, as well [...] Read more.
In this study, the parameters of a dynamic model of cultures of the microalgae Scenedesmus obliquus are estimated from datasets collected in batch photobioreactors operated with various initial conditions and light illumination conditions. Measurements of biomass, nitrogen quota, bulk substrate concentration, as well as chlorophyll concentration are achieved, which allow the determination of parameters with satisfactory confidence intervals and model cross-validation against independent data. The dynamic model is then used as a predictor in a nonlinear model predictive control strategy where the dilution rate and the incident light intensity are simultaneously manipulated in order to optimize the cumulated algal biomass production. Full article
(This article belongs to the Special Issue Modelling and Optimal Design of Complex Biological Systems)
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Article
Adaptive Monitoring of Biotechnological Processes Kinetics
Processes 2020, 8(10), 1307; https://0-doi-org.brum.beds.ac.uk/10.3390/pr8101307 - 17 Oct 2020
Cited by 1 | Viewed by 911
Abstract
In this paper, an approach for the monitoring of biotechnological process kinetics is proposed. The kinetics of each process state variable is presented as a function of two time-varying unknown parameters. For their estimation, a general software sensor is derived with on-line measurements [...] Read more.
In this paper, an approach for the monitoring of biotechnological process kinetics is proposed. The kinetics of each process state variable is presented as a function of two time-varying unknown parameters. For their estimation, a general software sensor is derived with on-line measurements as inputs that are accessible in practice. The stability analysis with a different number of inputs shows that stability can be guaranteed for fourth- and fifth-order software sensors only. As a case study, the monitoring of the kinetics of processes carried out in stirred tank reactors is investigated. A new tuning procedure is derived that results in a choice of only one design parameter. The effectiveness of the proposed procedure is demonstrated with experimental data from Bacillus subtilis fed-batch cultivations. Full article
(This article belongs to the Special Issue Modelling and Optimal Design of Complex Biological Systems)
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Article
Water Cycle Algorithm for Modelling of Fermentation Processes
Processes 2020, 8(8), 920; https://0-doi-org.brum.beds.ac.uk/10.3390/pr8080920 - 02 Aug 2020
Viewed by 744
Abstract
The water cycle algorithm (WCA), which is a metaheuristic method inspired by the movements of rivers and streams towards the sea in nature, has been adapted and applied here for the first time for solving such a challenging problem as the parameter identification [...] Read more.
The water cycle algorithm (WCA), which is a metaheuristic method inspired by the movements of rivers and streams towards the sea in nature, has been adapted and applied here for the first time for solving such a challenging problem as the parameter identification of fermentation process (FP) models. Bacteria and yeast are chosen as representatives of FP models that are subjected to parameter identification due to their impact in different industrial fields. In addition, WCA is considered in comparison with the genetic algorithm (GA), which is another population-based technique that has been proved to be a promising alternative of conventional optimisation methods. The obtained results have been thoroughly analysed in order to outline the advantages and disadvantages of each algorithm when solving such a complicated real-world task. A discussion and a comparative analysis of both metaheuristic algorithms reveal the impact of WCA on model identification problems and show that the newly applied WCA outperforms GA with regard to the model accuracy. Full article
(This article belongs to the Special Issue Modelling and Optimal Design of Complex Biological Systems)
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Article
Impact of Dual Substrate Limitation on Biodenitrification Modeling in Porous Media
Processes 2020, 8(8), 890; https://0-doi-org.brum.beds.ac.uk/10.3390/pr8080890 - 24 Jul 2020
Viewed by 981
Abstract
In this work, we consider a model of the biodenitrification process taking place in a spatially-distributed bioreactor, and we take into account the limitation of the kinetics by both the carbon source and the oxidized nitrogen. This model concerns a single type of [...] Read more.
In this work, we consider a model of the biodenitrification process taking place in a spatially-distributed bioreactor, and we take into account the limitation of the kinetics by both the carbon source and the oxidized nitrogen. This model concerns a single type of bacteria growing on nitrate, which splits into adherent bacteria or free bacteria in the liquid, taking all interactions into account. The system obtained consists of four diffusion-convection-reaction equations for which we show the existence and uniqueness of a global solution. The system is approximated by a standard finite element method that satisfies an optimal a priori error estimate. We compare the results obtained for three forms of the growth function: single substrate limiting, “multiplicative” form, and “minimum” form. We highlight the limitation of the ‘ single substrate limiting model”, where the dependency of the bacterial growth on the nitrate is neglected, and find that the “minimum” model gives numerical results closer to the experimental results. Full article
(This article belongs to the Special Issue Modelling and Optimal Design of Complex Biological Systems)
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Article
Mathematical Modeling and Stability Analysis of a Two-Phase Biosystem
Processes 2020, 8(7), 791; https://0-doi-org.brum.beds.ac.uk/10.3390/pr8070791 - 06 Jul 2020
Cited by 2 | Viewed by 746
Abstract
We propose a new mathematical model describing a biotechnological process of simultaneous production of hydrogen and methane by anaerobic digestion. The process is carried out in two connected continuously stirred bioreactors. The proposed model is developed by adapting and reducing the well known [...] Read more.
We propose a new mathematical model describing a biotechnological process of simultaneous production of hydrogen and methane by anaerobic digestion. The process is carried out in two connected continuously stirred bioreactors. The proposed model is developed by adapting and reducing the well known Anaerobic Digester Model No 1 (ADM1). Mathematical analysis of the model is carried out, involving existence and uniqueness of positive and uniformly bounded solutions, computation of equilibrium points, investigation of their local stability with respect to practically important input parameters. Existence of maxima of the input–output static characteristics with respect to hydrogen and methane is established. Numerical simulations using a specially elaborated web-based software environment are presented to demonstrate the dynamic behavior of the model solutions. Full article
(This article belongs to the Special Issue Modelling and Optimal Design of Complex Biological Systems)
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Article
Effect of Delays on the Response of Microalgae When Exposed to Dynamic Environmental Conditions
Processes 2020, 8(1), 87; https://0-doi-org.brum.beds.ac.uk/10.3390/pr8010087 - 09 Jan 2020
Cited by 1 | Viewed by 926
Abstract
During mathematical representation of microbial cultures, it is normally assumed that changes in the environment produce instantaneous effects on growth. However, reports are available indicating that sometimes this may not be the case. This work studied the existence of delays on the response [...] Read more.
During mathematical representation of microbial cultures, it is normally assumed that changes in the environment produce instantaneous effects on growth. However, reports are available indicating that sometimes this may not be the case. This work studied the existence of delays on the response of a population of microalgae when subjected to changes in energy and carbon sources, and when exposed to a growth inhibitor. Results show that no appreciable delays exist when microalgae undergo changes in the incident light intensity. For changes in carbon source concentration (inorganic carbon), a small delay in the range of minutes was detected. Finally, when exposing microalgae to inhibitory concentrations of ammonia, a significant delay of several hours was observed. Full article
(This article belongs to the Special Issue Modelling and Optimal Design of Complex Biological Systems)
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Review

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Review
Not Just Numbers: Mathematical Modelling and Its Contribution to Anaerobic Digestion Processes
Processes 2020, 8(8), 888; https://0-doi-org.brum.beds.ac.uk/10.3390/pr8080888 - 24 Jul 2020
Cited by 11 | Viewed by 1726
Abstract
Mathematical modelling of bioprocesses has a long and notable history, with eminent contributions from fields including microbiology, ecology, biophysics, chemistry, statistics, control theory and mathematical theory. This richness of ideas and breadth of concepts provide great motivation for inquisitive engineers and intrepid scientists [...] Read more.
Mathematical modelling of bioprocesses has a long and notable history, with eminent contributions from fields including microbiology, ecology, biophysics, chemistry, statistics, control theory and mathematical theory. This richness of ideas and breadth of concepts provide great motivation for inquisitive engineers and intrepid scientists to try their hand at modelling, and this collaboration of disciplines has also delivered significant milestones in the quality and application of models for both theoretical and practical interrogation of engineered biological systems. The focus of this review is the anaerobic digestion process, which, as a technology that has come in and out of fashion, remains a fundamental process for addressing the global climate emergency. Whether with conventional anaerobic digestion systems, biorefineries, or other anaerobic technologies, mathematical models are important tools that are used to design, monitor, control and optimise the process. Both highly structured, mechanistic models and data-driven approaches have been used extensively over half a decade, but recent advances in computational capacity, scientific understanding and diversity and quality of process data, presents an opportunity for the development of new modelling paradigms, augmentation of existing methods, or even incorporation of tools from other disciplines, to ensure that anaerobic digestion research can remain resilient and relevant in the face of emerging and future challenges. Full article
(This article belongs to the Special Issue Modelling and Optimal Design of Complex Biological Systems)
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