Practical coexistence of two species in the chemostat – A slow–fast characterization

Hajji, Miled El; Rapaport, Alain

doi:10.1016/j.mbs.2008.12.003

Cited by 27 publications

(27 citation statements)

References 17 publications

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“…After 35 days a “quasi steady state” was obtained between the wildtype and mutant, a phenomenon which has been described previously in chemostat cultures [40]. The reasons for the maintenance of competing strains in the chemostat remains controversial and is subject to continuing mathematical investigation [41], [42]. When the dilution rate was then switched to a fast growth rate the selective advantage was lost, the wild type recovered and both strains returned to approximately equivalent amounts (Figure 5).…”

Section: Resultsmentioning

confidence: 52%

The Genetic Requirements for Fast and Slow Growth in Mycobacteria

et al. 2009

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Mycobacterium tuberculosis infects a third of the world's population. Primary tuberculosis involving active fast bacterial replication is often followed by asymptomatic latent tuberculosis, which is characterised by slow or non-replicating bacteria. Reactivation of the latent infection involving a switch back to active bacterial replication can lead to post-primary transmissible tuberculosis. Mycobacterial mechanisms involved in slow growth or switching growth rate provide rational targets for the development of new drugs against persistent mycobacterial infection. Using chemostat culture to control growth rate, we screened a transposon mutant library by Transposon site hybridization (TraSH) selection to define the genetic requirements for slow and fast growth of Mycobacterium bovis (BCG) and for the requirements of switching growth rate. We identified 84 genes that are exclusively required for slow growth (69 hours doubling time) and 256 genes required for switching from slow to fast growth. To validate these findings we performed experiments using individual M. tuberculosis and M. bovis BCG knock out mutants. We have demonstrated that growth rate control is a carefully orchestrated process which requires a distinct set of genes encoding several virulence determinants, gene regulators, and metabolic enzymes. The mce1 locus appears to be a component of the switch to slow growth rate, which is consistent with the proposed role in virulence of M. tuberculosis. These results suggest novel perspectives for unravelling the mechanisms involved in the switch between acute and persistent TB infections and provide a means to study aspects of this important phenomenon in vitro.

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Section: Resultsmentioning

confidence: 52%

The Genetic Requirements for Fast and Slow Growth in Mycobacteria

et al. 2009

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“…The classical model of competition for a nonreproducing substrate in a well-stirred chemostat operated under constant input concentration and dilution predicts competitive exclusion. That is, it predicts that at most one competitor population avoids extinction [6,21,25,26]. However, the coexistence of competing populations is ubiquitous in nature.…”

Section: Introductionmentioning

confidence: 99%

Association between competition and obligate mutualism in a chemostat

Hajji

Harmand

Chaker

et al. 2009

Journal of Biological Dynamics

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In this paper, we consider a simple chemostat model involving two obligate mutualistic species feeding on a limiting substrate. Systems of differential equations are proposed as models of this association. A detailed qualitative analysis is carried out. We show the existence of a domain of coexistence, which is a set of initial conditions in which both species survive. We demonstrate, under certain supplementary assumptions, the uniqueness of the stable equilibrium point which corresponds to the coexistence of the two species.

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“…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: 98%

“…Since arithmetical mean of nonnegative real numbers is greater than the geometrical one, we have the following inequalities [30] for other application). Define…”

Section: Proof Consider the Following Lyapunov Functionmentioning

confidence: 99%

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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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Practical coexistence of two species in the chemostat – A slow–fast characterization

Cited by 27 publications

References 17 publications

The Genetic Requirements for Fast and Slow Growth in Mycobacteria

The Genetic Requirements for Fast and Slow Growth in Mycobacteria

Association between competition and obligate mutualism in a chemostat

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

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