Practical coexistence of two species in the chemostat - a slow-fast characterization

How can inter-specific interferences explain coexistence or confirm the competitive exclusion principle in a chemostat?

In this paper, I consider two species feeding on limiting substrate in a chemostat taking into account some possible effects of each species on the other one. System of differential equations is proposed as model of these effects with general inter-specific density-dependent growth rates. Three cases were considered. The first one for a mutual inhibitory relationship where it is proved that at most one species can survive which confirms the competitive exclusion principle. Initial concentrations of species have great importance in determination of which species is the winner. The second one for a food web relationship where it is proved that under general assumptions on the dilution rate, both species persist for any initial conditions. Finally, a third case dealing with an obligate mutualistic relationship was discussed. It is proved that initial condition has a great importance in determination of persistence or extinction of both species.

The operating diagram of a model of two competitors in a chemostat with an external inhibitor

Understanding and exploiting the inhibition phenomenon, which promotes the stable coexistence of species, is a major challenge in the mathematical theory of the chemostat. Here, we study a model of two microbial species in a chemostat competing for a single resource in the presence of an external inhibitor. The model is a four-dimensional system of ordinary differential equations. Using general monotonic growth rate functions of the species and absorption rate of the inhibitor, we give a complete analysis for the existence and local stability of all steady states. We focus on the behavior of the system with respect of the three operating parameters represented by the dilution rate and the input concentrations of the substrate and the inhibitor. The operating diagram has the operating parameters as its coordinates and the various regions defined in it correspond to qualitatively different asymptotic behavior: washout, competitive exclusion of one species, coexistence of the species around a stable steady state and coexistence around a stable cycle. This bifurcation diagram which determines the effect of the operating parameters, is very useful to understand the model from both the mathematical and biological points of view, and is often constructed in the mathematical and biological literature.

Multiscale analysis of biological systems

It is argued that multiscale approaches are necessary for an explanatory modeling of biological systems. A first step, besides common to the multiscale modeling of physical and living systems, is a bottom-up integration based on the notions of effective parameters and minimal models. Top-down effects can be accounted for in terms of effective constraints and inputs. Biological systems are essentially characterized by an entanglement of bottom-up and top-down influences following from their evolutionary history. A self-consistent multiscale scheme is proposed to capture the ensuing circular causality. Its differences with standard mean-field self-consistent equations and slow-fast decompositions are discussed. As such, this scheme offers a way to unravel the multilevel architecture of living systems and their regulation. Two examples, genome functions and biofilms, are detailed.

The mathematical analysis of a syntrophic relationship between two microbial species in a chemostat

A mathematical model involving a syntrophic relationship between two populations of bacteria in a continuous culture is proposed. A detailed qualitative analysis is carried out as well as the analysis of the local and global stability of the equilibria. We demonstrate, under general assumptions of monotonicity which are relevant from an applied point of view, the asymptotic stability of the positive equilibrium point which corresponds to the coexistence of the two bacteria. A syntrophic relationship in the anaerobic digestion process is proposed as a real candidate for this model.

Association between competition and obligate mutualism in a chemostat

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.

The genetic requirements for fast and slow growth in mycobacteria

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.