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Martínez C, Cinquemani E, Jong HD, Gouzé JL. Optimal protein production by a synthetic microbial consortium: coexistence, distribution of labor, and syntrophy. J Math Biol 2023; 87:23. [PMID: 37395814 DOI: 10.1007/s00285-023-01935-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2021] [Revised: 12/22/2022] [Accepted: 05/17/2023] [Indexed: 07/04/2023]
Abstract
The bacterium E. coli is widely used to produce recombinant proteins such as growth hormone and insulin. One inconvenience with E. coli cultures is the secretion of acetate through overflow metabolism. Acetate inhibits cell growth and represents a carbon diversion, which results in several negative effects on protein production. One way to overcome this problem is the use of a synthetic consortium of two different E. coli strains, one producing recombinant proteins and one reducing the acetate concentration. In this paper, we study a mathematical model of such a synthetic community in a chemostat where both strains are allowed to produce recombinant proteins. We give necessary and sufficient conditions for the existence of a coexistence equilibrium and show that it is unique. Based on this equilibrium, we define a multi-objective optimization problem for the maximization of two important bioprocess performance metrics, process yield and productivity. Solving numerically this problem, we find the best available trade-offs between the metrics. Under optimal operation of the mixed community, both strains must produce the protein of interest, and not only one (distribution instead of division of labor). Moreover, in this regime acetate secretion by one strain is necessary for the survival of the other (syntrophy). The results thus illustrate how complex multi-level dynamics shape the optimal production of recombinant proteins by synthetic microbial consortia.
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Affiliation(s)
- Carlos Martínez
- Université Côte d' Azur, Inria, INRAE, CNRS, Sorbonne Université, Biocore Team, Sophia Antipolis, France.
- Biology Centre of the Czech Academy of Sciences, Institute of Hydrobiology, Na Sádkách 7, 370 05, České Budějovice, Czech Republic.
| | | | - Hidde de Jong
- Univ. Grenoble Alpes, Inria, 38000, Grenoble, France
| | - Jean-Luc Gouzé
- Université Côte d' Azur, Inria, INRAE, CNRS, Sorbonne Université, Biocore Team, Sophia Antipolis, France
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Abgrall R. A Combination of Residual Distribution and the Active Flux Formulations or a New Class of Schemes That Can Combine Several Writings of the Same Hyperbolic Problem: Application to the 1D Euler Equations. Commun Appl Math Comput 2022; 5:370-402. [PMID: 36816474 PMCID: PMC9925591 DOI: 10.1007/s42967-021-00175-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/24/2020] [Revised: 10/23/2021] [Accepted: 10/25/2021] [Indexed: 06/18/2023]
Abstract
We show how to combine in a natural way (i.e., without any test nor switch) the conservative and non-conservative formulations of an hyperbolic system that has a conservative form. This is inspired from two different classes of schemes: the residual distribution one (Abgrall in Commun Appl Math Comput 2(3): 341-368, 2020), and the active flux formulations (Eyman and Roe in 49th AIAA Aerospace Science Meeting, 2011; Eyman in active flux. PhD thesis, University of Michigan, 2013; Helzel et al. in J Sci Comput 80(3): 35-61, 2019; Barsukow in J Sci Comput 86(1): paper No. 3, 34, 2021; Roe in J Sci Comput 73: 1094-1114, 2017). The solution is globally continuous, and as in the active flux method, described by a combination of point values and average values. Unlike the "classical" active flux methods, the meaning of the point-wise and cell average degrees of freedom is different, and hence follow different forms of PDEs; it is a conservative version of the cell average, and a possibly non-conservative one for the points. This new class of scheme is proved to satisfy a Lax-Wendroff-like theorem. We also develop a method to perform non-linear stability. We illustrate the behaviour on several benchmarks, some quite challenging.
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Affiliation(s)
- R. Abgrall
- Institute of Mathematics, University of Zürich, Winterthurerstrasse 190, CH 8057 Zurich, Switzerland
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Laso-Jadart R, Ambroise C, Peterlongo P, Madoui MA. metaVaR: Introducing metavariant species models for reference-free metagenomic-based population genomics. PLoS One 2020; 15:e0244637. [PMID: 33378381 PMCID: PMC7773188 DOI: 10.1371/journal.pone.0244637] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2020] [Accepted: 12/14/2020] [Indexed: 11/18/2022] Open
Abstract
The availability of large metagenomic data offers great opportunities for the population genomic analysis of uncultured organisms, which represent a large part of the unexplored biosphere and play a key ecological role. However, the majority of these organisms lack a reference genome or transcriptome, which constitutes a technical obstacle for classical population genomic analyses. We introduce the metavariant species (MVS) model, in which a species is represented only by intra-species nucleotide polymorphism. We designed a method combining reference-free variant calling, multiple density-based clustering and maximum-weighted independent set algorithms to cluster intra-species variants into MVSs directly from multisample metagenomic raw reads without a reference genome or read assembly. The frequencies of the MVS variants are then used to compute population genomic statistics such as FST, in order to estimate genomic differentiation between populations and to identify loci under natural selection. The MVS construction was tested on simulated and real metagenomic data. MVSs showed the required quality for robust population genomics and allowed an accurate estimation of genomic differentiation (ΔFST < 0.0001 and <0.03 on simulated and real data respectively). Loci predicted under natural selection on real data were all detected by MVSs. MVSs represent a new paradigm that may simplify and enhance holistic approaches for population genomics and the evolution of microorganisms.
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Affiliation(s)
- Romuald Laso-Jadart
- Institut François Jacob, CEA, CNRS, Génomique Métabolique - UMR 8030, Univ Evry, Université Paris-Saclay, Evry, France
| | | | | | - Mohammed-Amin Madoui
- Institut François Jacob, CEA, CNRS, Génomique Métabolique - UMR 8030, Univ Evry, Université Paris-Saclay, Evry, France
- * E-mail:
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Morales M, Hélias A, Bernard O. Optimal integration of microalgae production with photovoltaic panels: environmental impacts and energy balance. Biotechnol Biofuels 2019; 12:239. [PMID: 31624501 PMCID: PMC6781331 DOI: 10.1186/s13068-019-1579-4] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/09/2019] [Accepted: 09/24/2019] [Indexed: 06/10/2023]
Abstract
BACKGROUND Microalgae are 10 to 20 times more productive than the current agricultural biodiesel producing oleaginous crops. However, they require larger energy supplies, so that their environmental impacts remain uncertain, as illustrated by the contradictory results in the literature. Besides, solar radiation is often too high relative to the photosynthetic capacity of microalgae. This leads to photosaturation, photoinhibition, overheating and eventually induces mortality. Shadowing microalgae with solar panels would, therefore, be a promising solution for both increasing productivity during hotter periods and producing local electricity for the process. The main objective of this study is to measure, via LCA framework, the energy performance and environmental impact of microalgae biodiesel produced in a solar greenhouse, alternating optimal microalgae species and photovoltaic panel (PV) coverage. A mathematical model is simulated to investigate the microalgae productivity in raceways under meteorological conditions in Sophia Antipolis (south of France) at variable coverture percentages (0% to 90%) of CIGS solar panels on greenhouses constructed with low-emissivity (low-E) glass. RESULTS A trade-off must be met between electricity and biomass production, as a larger photovoltaic coverture would limit microalgae production. From an energetic point of view, the optimal configuration lies between 10 and 20% of PV coverage. Nevertheless, from an environmental point of view, the best option is 50% PV coverage. However, the difference between impact assessments obtained for 20% and 50% PV is negligible, while the NER is 48% higher for 20% PV than for 50% PV coverage. Hence, a 20% coverture of photovoltaic panels is the best scenario from an energetic and environmental point of view. CONCLUSIONS In comparison with the cultivation of microalgae without PV, the use of photovoltaic panels triggers a synergetic effect, sourcing local electricity and reducing climate change impacts. Considering an economic approach, low photovoltaic panel coverage would probably be more attractive. However, even with a 10% area of photovoltaic panels, the environmental footprint would already significantly decrease. It is expected that significant improvements in microalgae productivity or more advanced production processes should rapidly enhance these performances.
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Affiliation(s)
| | - Arnaud Hélias
- Laboratoire de Biotechnologie de l’Environnement, Montpellier SupAgro, INRA, Univ Montpellier, 2 Place Pierre Viala, 34060 Montpellier Cedex 1, France
- Elsa, Research Group for Environmental Life Cycle Sustainability Assessment, Montpellier, France
| | - Olivier Bernard
- INRIA BIOCORE, BP 93, 06902 Sophia Antipolis Cedex, France
- Department of Energy and Process Engineering, Faculty of Engineering, Norwegian University of Science and Technology (NTNU), 7491 Trondheim, Norway
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Rousseau E, Moury B, Mailleret L, Senoussi R, Palloix A, Simon V, Valière S, Grognard F, Fabre F. Estimating virus effective population size and selection without neutral markers. PLoS Pathog 2017; 13:e1006702. [PMID: 29155894 PMCID: PMC5720836 DOI: 10.1371/journal.ppat.1006702] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2017] [Revised: 12/07/2017] [Accepted: 10/19/2017] [Indexed: 12/04/2022] Open
Abstract
By combining high-throughput sequencing (HTS) with experimental evolution, we can observe the within-host dynamics of pathogen variants of biomedical or ecological interest. We studied the evolutionary dynamics of five variants of Potato virus Y (PVY) in 15 doubled-haploid lines of pepper. All plants were inoculated with the same mixture of virus variants and variant frequencies were determined by HTS in eight plants of each pepper line at each of six sampling dates. We developed a method for estimating the intensities of selection and genetic drift in a multi-allelic Wright-Fisher model, applicable whether these forces are strong or weak, and in the absence of neutral markers. This method requires variant frequency determination at several time points, in independent hosts. The parameters are the selection coefficients for each PVY variant and four effective population sizes Ne at different time-points of the experiment. Numerical simulations of asexual haploid Wright-Fisher populations subjected to contrasting genetic drift (Ne ∈ [10, 2000]) and selection (|s| ∈ [0, 0.15]) regimes were used to validate the method proposed. The experiment in closely related pepper host genotypes revealed that viruses experienced a considerable diversity of selection and genetic drift regimes. The resulting variant dynamics were accurately described by Wright-Fisher models. The fitness ranks of the variants were almost identical between host genotypes. By contrast, the dynamics of Ne were highly variable, although a bottleneck was often identified during the systemic movement of the virus. We demonstrated that, for a fixed initial PVY population, virus effective population size is a heritable trait in plants. These findings pave the way for the breeding of plant varieties exposing viruses to stronger genetic drift, thereby slowing virus adaptation. A growing number of experimental evolution studies are using an “evolve-and-resequence” approach to observe the within-host dynamics of pathogen variants of biomedical or ecological interest. The resulting data are particularly appropriate for studying the effects of evolutionary forces, such as selection and genetic drift, on the emergence of new pathogen variants. However, it remains challenging to unravel the effects of selection and genetic drift in the absence of neutral markers, a situation frequently encountered for microbes, such as viruses, due to their small constrained genomes. Using such an approach on a plant virus, we observed that the same set of virus variants displayed highly diverse dynamics in closely related plant genotypes. We developed and validated a method that does not require neutral markers, for estimating selection coefficients and effective population sizes from these experimental evolution data. We found that the viruses experienced considerable diversity in genetic drift regimes, depending on host genotype. Importantly, genetic drift experienced by virus populations was shown to be a heritable plant trait. These findings pave the way for the breeding of plant varieties exposing viruses to strong genetic drift, thereby slowing virus adaptation.
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Affiliation(s)
- Elsa Rousseau
- Université Côte d’Azur, Inria, INRA, CNRS, UPMC Univ Paris 06, Biocore team, Sophia Antipolis, France
- Université Côte d’Azur, INRA, CNRS, ISA, Sophia Antipolis, France
- Pathologie Végétale, INRA, 84140 Montfavet, France
- * E-mail: (ER); (FF)
| | - Benoît Moury
- Pathologie Végétale, INRA, 84140 Montfavet, France
| | - Ludovic Mailleret
- Université Côte d’Azur, Inria, INRA, CNRS, UPMC Univ Paris 06, Biocore team, Sophia Antipolis, France
- Université Côte d’Azur, INRA, CNRS, ISA, Sophia Antipolis, France
| | | | | | - Vincent Simon
- Pathologie Végétale, INRA, 84140 Montfavet, France
- UMR BFP, INRA, Villenave d’Ornon, France
| | - Sophie Valière
- GeT-PlaGe, INRA, Genotoul, Castanet-tolosan, France
- UAR DEPT GA, INRA, Castanet-Tolosan, France
| | - Frédéric Grognard
- Université Côte d’Azur, Inria, INRA, CNRS, UPMC Univ Paris 06, Biocore team, Sophia Antipolis, France
| | - Frédéric Fabre
- UMR SAVE, INRA, Villenave d’Ornon, France
- * E-mail: (ER); (FF)
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