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A Physiologically Structured Equation to Consider Quota Heterogeneity in the Droop Model ArchiMer
Mairet, Francis; Baron, Regis.
The Droop model allows to represent microalgae growth limited by a nutrient, using a cell quota (also referred to as variable-yield) approach. Single-cell measurements have revealed quota heterogeneity in phytoplankton collected from field studies. Such heterogeneity can be due, among other factors, to spatial structure (e.g. in biogeochemical cycles in the ocean, or for photobioreactors connected in series). Nonetheless, quota heterogeneity is generally omitted in modelling studies, using an average quota approach, or included in size-structured or individual-based models. Here, we propose a distributed Droop equation to tackle this problem, considering subpopulation growth -in line with Droop macroscopic view- rather than cell division dynamics. We...
Tipo: Text Palavras-chave: Population Balance Model; Variable-yield model; Cell Quota; Phytoplankton; Microalgae.
Ano: 2019 URL: https://archimer.ifremer.fr/doc/00600/71187/69542.pdf
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Maximizing microalgae productivity in a light-limited chemostat ArchiMer
Martinez, Carlos; Bernard, Olivier; Mairet, Francis.
Light supply is one of the most important parameters to be considered for enhancing microalgae growth in photobioreactors (PBR) with artificial light. However, most of the mathematical works do not consider incident light as a parameter to be optimized. In this work based on a simple model of light-limited growth, we determine optimal values for the dilution rate and the incident light intensity in order to maximize the steady-state microalgal surface productivity in a continuous culture. We also show that in optimal conditions there is a minimal initial microalgal concentration (and we give a simple expression to determine it) to guarantee the persistence of the population. Finally, in the context of enhancing microalgae productivity by reducing light...
Tipo: Text Palavras-chave: Dynamics and control; Industrial biotechnology; Photoinhibition; Biomass productivity; Microalgae; Photoacclimation; Chlorophyll.
Ano: 2018 URL: https://archimer.ifremer.fr/doc/00439/55091/56653.pdf
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How haptophytes microalgae mitigate vitamin B-12 limitation ArchiMer
Nef, Charlotte; Jung, Sebastien; Mairet, Francis; Kaas, Raymond; Grizeau, Dominique; Garnier, Matthieu.
Vitamin B-12 (cobalamin) can control phytoplankton development and community composition, with around half of microalgal species requiring this vitamin for growth. B-12 dependency is determined by the absence of cobalamin-independent methionine synthase and is unrelated across lineages. Despite their important role in carbon and sulphur biogeochemistry, little is known about haptophytes utilization of vitamin B-12 and their ability to cope with its limitation. Here we report the first evaluation of B-12 auxotrophy among this lineage based on molecular data of 19 species from 9 families. We assume that all species encode only a B-12-dependent methionine synthase, suggesting ubiquitous B-12 auxotrophy in this phylum. We further address the effect of...
Tipo: Text
Ano: 2019 URL: https://archimer.ifremer.fr/doc/00504/61523/65398.pdf
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A biomolecular proportional integral controller based on feedback regulations of protein level and activity ArchiMer
Mairet, Francis.
Homeostasis is the capacity of living organisms to keep internal conditions regulated at a constant level, despite environmental fluctuations. Integral feedback control is known to play a key role in this behaviour. Here, I show that a feedback system involving transcriptional and post-translational regulations of the same executor protein acts as a proportional integral (PI) controller, leading to enhanced transient performances in comparison with a classical integral loop. Such a biomolecular controller-which I call a level and activity-PI controller (LA-PI)-is involved in the regulation of ammonium uptake by Escherichia coli through the transporter AmtB. The P-II molecules, which reflect the nitrogen status of the cell, inhibit both the production of...
Tipo: Text Palavras-chave: Homeostasis; Perfect adaptation; Regulatory motif; Transcriptional and post-translational regulations.
Ano: 2018 URL: https://archimer.ifremer.fr/doc/00434/54598/55968.pdf
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Modeling and Analysis of an Absorption Column Connected to a Microalgae Culture ArchiMer
Martinez, Carlos; Ávila, Andrés; Mairet, Francis; Meier, Leslie; Jeison, David.
We build and analyze a mathematical model of a system for biogas upgrading: an absorption column connected to a microalgae culture. The construction of the model is based on a chemical engineering approach and classical models of microalgae cultures. In our analysis, we prove the existence and uniqueness of solutions of a boundary value problem describing the absorption column. Some properties of this solution are also proved. Then, we use these results to study the long-term behavior of the mathematical model describing the coupled system. We state sufficient conditions for the existence of a globally attracting steady state characterized by the presence of microalgae. Finally, we find numerically the steady states of the system to test the efficiency of...
Tipo: Text Palavras-chave: Biogas upgrading; Absorption column; Boundary value problem; Global asymptotic behavior; Shooting method; Microalgae.
Ano: 2020 URL: https://archimer.ifremer.fr/doc/00617/72899/71912.pdf
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Theory of turbid microalgae cultures. ArchiMer
Martinez, Carlos; Mairet, Francis; Bernard, Olivier.
Microalgae can be cultivated in closed or open photobioreactors (PBR). In these systems, light rapidly decreases as it passes through the culture due to the turbidity of the medium. Thus, microalgae experiment different light intensities depending on their position in the medium. In this paper, we study theoretically how the growth rate of microalgae is affected by different factors; incident light intensity, form of the PBR, microalgae population density, turbidity of non-microalgae components, and light path-length of the reactor. We show that for different types of PBR the average growth rate is completely determined by the incident light intensity and the optical depth. In the case of vertical cylindrical PBRs illuminated from above (e.g. race-way or...
Tipo: Text Palavras-chave: Photobioreactor; Optical depth; Photoinhibition; Light limitation; Turbidity; Modelling.
Ano: 2018 URL: https://archimer.ifremer.fr/doc/00450/56133/57675.pdf
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Optimal proteome allocation and the temperature dependence of microbial growth laws ArchiMer
Mairet, Francis; Gouzé, Jean-luc; De Jong, Hidde.
Although the effect of temperature on microbial growth has been widely studied, the role of proteome allocation in bringing about temperature-induced changes remains elusive. To tackle this problem, we propose a coarse-grained model of microbial growth, including the processes of temperature-sensitive protein unfolding and chaperone-assisted (re)folding. We determine the proteome sector allocation that maximizes balanced growth rate as a function of nutrient limitation and temperature. Calibrated with quantitative proteomic data for Escherichia coli, the model allows us to clarify general principles of temperature-dependent proteome allocation and formulate generalized growth laws. The same activation energy for metabolic enzymes and ribosomes leads to an...
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Ano: 2021 URL: https://archimer.ifremer.fr/doc/00686/79829/82633.pdf
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Getting the most out of it: Optimal experiments for parameter estimation of microalgae growth models ArchiMer
Munoz-tamayo, Rafael; Martinon, Pierre; Bougaran, Gael; Mairet, Francis; Bernard, Olivier.
Mathematical models are expected to play a pivotal role for driving microalgal production towards a profitable process of renewable energy generation. To render models of microalgae growth useful tools for prediction and process optimization, reliable parameters need to be provided. This reliability implies a careful design of experiments that can be exploited for parameter estimation. In this paper, we provide guidelines for the design of experiments with high informative content based on optimal experiment techniques to attain an accurate parameter estimation. We study a real experimental device devoted to evaluate the effect of temperature and light on microalgae growth. On the basis of a mathematical model of the experimental system, the optimal...
Tipo: Text Palavras-chave: Biofuel; Biological processes; Modelling; Parameter identification; Optimal experiment design.
Ano: 2014 URL: http://archimer.ifremer.fr/doc/00191/30252/28684.pdf
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Parameter Estimation for Dynamic Resource Allocation in Microorganisms: A Bi-level Optimization Problem ArchiMer
Mairet, Francis; Bayen, Térence.
Given their key roles in almost all ecosystems and in several industries, understanding and predicting microorganism growth is of utmost importance. In compliance with evolutionary principles, coarse-grained or genome-scale models of microbial growth can be used to determine optimal resource allocation scheme under dynamic environmental conditions. Resource allocation approaches have given important qualitative results, but it still remains a gap towards quantitiative predictions. The first step in this direction is parameter calibration with experimental data. But fitting these models results in a bi-level optimization problem, whose numerical resolution involves complex optimization issues. As a case study, we present here a coarse-grained model...
Tipo: Text Palavras-chave: Bi-level optimization; Optimal control; Pontryagin’s principle; Chattering; Microbial growth; Microalgae.
Ano: 2020 URL: https://archimer.ifremer.fr/doc/00690/80163/83228.pdf
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How do microalgae perceive light in a high-rate pond? Towards more realistic Lagrangian experiments ArchiMer
Demory, David; Combe, Charlotte; Hartmann, Philipp; Talec, Amelle; Pruvost, Eric; Hamouda, Raouf; Souille, Fabien; Lamarea, Pierre-olivier; Bristeau, Marie-odile; Sainte-marie, Jacques; Rabouille, Sophie; Mairet, Francis; Sciandra, Antoine; Bernard, Olivier.
Hydrodynamics in a high-rate production reactor for microalgae cultivation affects the light history perceived by cells. The interplay between cell movement and medium turbidity leads to a complex light pattern, whose forcing effects on photosynthesis and photoacclimation dynamics are nontrivial. Hydrodynamics of high density algal ponds mixed by a paddle wheel has been studied recently, although the focus has never been on describing its impact on photosynthetic growth efficiency. In this multidisciplinary downscaling study, we first reconstructed single cell trajectories in an open raceway using an original hydrodynamical model offering a powerful discretization of the Navier-Stokes equations tailored to systems with free surfaces. The trajectory of a...
Tipo: Text Palavras-chave: Photosynthesis; Hydrodynamics; Modelling; Photoacclimation; Dunaliella salina; Non-photochemical quenching.
Ano: 2018 URL: https://archimer.ifremer.fr/doc/00445/55692/57352.pdf
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Quantifying the potential of microalgae to remove nutrients from wastewater ArchiMer
Martinez, Carlos; Mairet, Francis; Plaza, Luis; Sciandra, Antoine; Bernard, Olivier.
The main resources limiting microalgae growth are typically phosphorus, nitrogen, and light. Based on the theory of the light limited chemostat, the variable cell quota approach, and photoacclimation models, we build a mathematical model for describing microalgae growth under limitation by these resources. The model is calibrated with a data set from the literature. Then, by numerical simulations, we find that under constant operation of the culture and constant environmental conditions (illumination, temperature, pH, etc.), solutions of the model approach towards either a positive or an extinction steady state. Based on the positive steady state, and in the context of wastewater treatment, we evaluate the capacity of microalgae to remove contaminants. We...
Tipo: Text Palavras-chave: Control; Biotechnology; Wastewater treatment; Microalgae; Cell quota model.
Ano: 2019 URL: https://archimer.ifremer.fr/doc/00600/71188/69541.pdf
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Twelve quick tips for designing sound dynamical models for bioprocesses ArchiMer
Mairet, Francis; Bernard, Olivier.
Because of the inherent complexity of bioprocesses, mathematical models are more and more used for process design, control, optimization, etc. These models are generally based on a set of biochemical reactions. Model equations are then derived from mass balance, coupled with empirical kinetics. Biological models are nonlinear and represent processes, which by essence are dynamic and adaptive. The temptation to embed most of the biology is high, with the risk that calibration would not be significant anymore. The most important task for a modeler is thus to ensure a balance between model complexity and ease of use. Since a model should be tailored to the objectives, which will depend on applications and environment, a universal model representing any...
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Ano: 2019 URL: https://archimer.ifremer.fr/doc/00512/62336/66596.pdf
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Dynamics of the periodically forced light-limited Droop model ArchiMer
Martinez, Carlos; Mairet, Francis; Bernard, Olivier.
The periodically forced light-limited Droop model represents microalgae growth under co-limitation by light and a single substrate, accounting for periodic fluctuations of factors such as light and temperature. In this paper, we describe the global dynamics of this model, considering general monotone growth and uptake rate functions. Our main result gives necessary and sufficient conditions for the existence of a positive periodic solution (i.e. a periodic solution characterized by the presence of microalgae) which is globally attractive. In our approach, we reduce the model to a cooperative planar periodic system. Using results on periodic Kolmogorov equations and on monotone sub-homogeneous dynamical systems, we describe the global dynamics of the...
Tipo: Text Palavras-chave: Variable quota model; Positive periodic solution; Global stability; Microalgae; Cooperative system.
Ano: 2020 URL: https://archimer.ifremer.fr/doc/00599/71140/69455.pdf
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Cobalamin Scarcity Modifies Carbon Allocation and Impairs DMSP Production Through Methionine Metabolism in the Haptophyte Microalgae Tisochrysis lutea ArchiMer
Nef, Charlotte; Henry, Céline; Nicolau, Elodie; Bérard, Jean-baptiste; Hervé, Fabienne; Caruana, Amandine; Kaas, Raymond; Mairet, Francis; Garnier, Matthieu.
Cobalamin (vitamin B12) is a cobalt-containing enzymatic cofactor involved in methionine synthesis. Provided only by select bacteria and archaea in marine systems, this vitamin is known to limit primary production in different oceanic areas. Understanding the consequences of cobalamin limitation on phytoplankton physiology is of great interest, notably for cobalamin-dependent haptophytes that significantly contribute to oceanic carbon fixation and sulfur cycle through dimethyl sulfonio propionate (DMSP) synthesis. Here, the effect of cobalamin limitation was compared to nitrogen limitation on the model haptophyte Tisochrysis lutea grown in chemostats, combining comparative proteomics with the analysis of major macromolecules and specific osmolytes. Our...
Tipo: Text Palavras-chave: Cobalamin; Vitamin B-12; Haptophyte microalgae; Tisochrysis lutea; DMSP; Chemostat; Comparative proteomics; Metabolism.
Ano: 2020 URL: https://archimer.ifremer.fr/doc/00654/76575/77711.pdf
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Optimal feedback strategies for bacterial growth with degradation, recycling, and effect of temperature ArchiMer
Yegorov, Ivan; Mairet, Francis; Gouze, Jean-luc.
Mechanisms of bacterial adaptation to environmental changes are of great interest for both fundamental biology and engineering applications. In this work, we consider a continuous-time dynamic problem of resource allocation between metabolic and gene expression machineries for a self-replicating prokaryotic cell population. In compliance with evolutionary principles, the criterion is to maximize the accumulated structural biomass. In the model, we include both the degradation of proteins into amino acids and the recycling of the latter (ie, using as precursors again). On the basis of the analytical investigation of our problem by Pontryagin's maximum principle, we develop a numerical method to approximate the switching curve of the optimal feedback control...
Tipo: Text Palavras-chave: Bacterial growth; Chattering regime; Effect of temperature; Feedback strategy; Optimal control; Pontryagin's maximum principle; Protein degradation; Recycling; Resource allocation; Singular regime; Switching curve.
Ano: 2018 URL: https://archimer.ifremer.fr/doc/00434/54592/56057.pdf
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Optimal control of bacterial growth for the maximization of metabolite production ArchiMer
Yegorov, Ivan; Mairet, Francis; De Jong, Hidde; Gouze, Jean-luc.
Microorganisms have evolved complex strategies for controlling the distribution of available resources over cellular functions. Biotechnology aims at interfering with these strategies, so as to optimize the production of metabolites and other compounds of interest, by (re)engineering the underlying regulatory networks of the cell. The resulting reallocation of resources can be described by simple so-called self-replicator models and the maximization of the synthesis of a product of interest formulated as a dynamic optimal control problem. Motivated by recent experimental work, we are specifically interested in the maximization of metabolite production in cases where growth can be switched off through an external control signal. We study various optimal...
Tipo: Text Palavras-chave: Optimal control; Nonlinear dynamical systems; Mathematical modelling; Bacterial growth; Biotechnology.
Ano: 2019 URL: https://archimer.ifremer.fr/doc/00486/59791/63028.pdf
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Dynamics and control of a periodically forced microalgae culture ArchiMer
Martínez, Carlos; Mairet, Francis; Martinon, Pierre; Bernard, Olivier.
Microalgae cultivation with wastewater is a promising way of reducing the energetic needs for wastewater treatment and the costs of biofuel production. However, the very turbid medium is not favorable for the development of microalgae. Indeed, light, the key element for photosynthesis, rapidly vanishes along depth due to absorption and scattering. Therefore it is crucial to understand the effects of the depth on turbid cultures. In this work, we study theoretically the long-term behavior of a continuous culture of microalgae exposed to a periodic source of light. By allowing periodic variations of the depth and the hydraulic retention time, we show that the microalgae population is forced to a periodic regime. Finally, we address numerically the problem of...
Tipo: Text Palavras-chave: Dynamics and control; Industrial biotechnology; Wastewater; Biomass productivity; Microalgae.
Ano: 2019 URL: https://archimer.ifremer.fr/doc/00505/61623/65654.pdf
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