A model of a syntrophic relationship between two microbial species in a chemostat including maintenance

Sari, Tewfik; Harmand, Jérôme

doi:10.1016/j.mbs.2016.02.008

Cited by 34 publications

(67 citation statements)

References 27 publications

(80 reference statements)

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“…The total biomass B tot [gDW L −1 ] decays at a rate k deg B tot , with degradation rate constant k deg [h −1 ]. In other words, non-growth-related maintenance of the biomass requires an expenditure of resources equal to k deg B tot [44].…”

Section: Resultsmentioning

confidence: 99%

Enhanced production of heterologous proteins by a synthetic microbial community: Conditions and trade-offs

Mauri

Gouzé

Jong

et al. 2020

Preprint

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AbstractSynthetic microbial consortia have been increasingly utilized in biotechnology and experimental evidence shows that suitably engineered consortia can outperform individual species in the synthesis of valuable products. Despite significant achievements, though, a quantitative understanding of the conditions that make this possible, and of the trade-offs due to the concurrent growth of multiple species, is still limited. In this work, we contribute to filling this gap by the investigation of a known prototypical synthetic consortium. A first E. coli strain, producing a heterologous protein, is sided by a second E. coli strain engineered to scavenge toxic byproducts, thus favoring the growth of the producer at the expense of diverting part of the resources to the growth of the cleaner. The simplicity of the consortium is ideal to perform an in depth-analysis and draw conclusions of more general interest. We develop a coarse-grained mathematical model that quantitatively accounts for literature data from different key growth phenotypes. Based on this, assuming growth in chemostat, we first investigate the conditions enabling stable coexistence of both strains and the effect of the metabolic load due to heterologous protein production. In these conditions, we establish when and to what extent the consortium outperforms the producer alone in terms of productivity. Finally, we show in chemostat as well as in a fed-batch scenario that gain in productivity comes at the price of a reduced yield, reflecting at the level of the consortium resource allocation trade-offs that are well-known for individual species.

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Section: Resultsmentioning

confidence: 99%

Enhanced production of heterologous proteins by a synthetic microbial community: Conditions and trade-offs

Mauri

Gouzé

Jong

et al. 2020

Preprint

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show abstract

“…R 5 + , the closed non-negative cone in R 5 , is positively invariant by the system (2.6) [22,23,24,25,26,27,28,29,30,31,32,33]. More precisely, let m = min(mS, mV , mE, mI , mR), then I get Proposition 1.…”

Section: Generalitiesmentioning

confidence: 97%

Analysis of a Fractional-order “SVEIR” Epidemic Mo del with a General Nonlinear Saturated Incidence Rate in a Continuous Reactor

Hajji¹,

Sayari²

2019

ARJOM

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In this paper, I propose a fractional-order mathematical five-dimensional dynamical system modeling a SVEIR model of infectious disease transmission in a chemostat. A profound qualitative analysis is given. The analysis of the local and global stability of equilibrium points is carried out. It is proved that if R > 1, then the disease-persistence (endemic) equilibrium is globally asymptotically stable. However, if R ≤ 1, then the disease-free equilibrium is globally asymptotically stable in R 5. Finally, some numerical tests are done using the ”PECE” method in order to validate the obtained results.

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“…+ , the closed non-negative cone in R 3 , is positively invariant [22,23,24,25,4,26,27,28,29,30,31,32,33] for the system (2.6). More precisely, Proposition 1.…”

Section: Mathematical Model and Propertiesmentioning

confidence: 99%

“…Now, if R = 1, then D α V2 = 0 if and only if S = Sin and the largest compact invariant set in {(S, I) ∈ Ω : D α V2 = 0} is the singleton {Ē}. Therefore, by the LaSalle's invariance principle (see, for instance, [34]), {Ē} is globally asymptotically stable (for other applications, see [26,27,28,31,33]).…”

Section: Theoremmentioning

confidence: 99%

Mathematical Analysis of a Fractional-order "SIR" Epidemic Model with a General Nonlinear Saturated Incidence Rate in a Chemostat

Hajji

2019

ARJOM

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In the present work, a fractional-order differential equation based on the Susceptible-Infected- Recovered (SIR) model with nonlinear incidence rate in a continuous reactor is proposed. A profound qualitative analysis is given. The analysis of the local and global stability of equilibrium points is carried out. It is proved that if the basic reproduction number R > 1 then the disease-persistence (endemic) equilibrium is globally asymptotically stable. However, if R ≤ 1, then the disease-free equilibrium is globally asymptotically stable. Finally, some numerical tests are done in order to validate the obtained results.

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A model of a syntrophic relationship between two microbial species in a chemostat including maintenance

Cited by 34 publications

References 27 publications

Enhanced production of heterologous proteins by a synthetic microbial community: Conditions and trade-offs

Enhanced production of heterologous proteins by a synthetic microbial community: Conditions and trade-offs

Analysis of a Fractional-order “SVEIR” Epidemic Mo del with a General Nonlinear Saturated Incidence Rate in a Continuous Reactor

Mathematical Analysis of a Fractional-order "SIR" Epidemic Model with a General Nonlinear Saturated Incidence Rate in a Chemostat

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