Microbial Competition in Reactors with Wall Attachment: A Mathematical Comparison of Chemostat and Plug Flow Models

Competition for nutrient and the ability of bacteria to colonize the gut wall are factors believed to play a role in the observed stability of the indigenous microbiota of the mammalian large intestine. These factors were incorporated into the two-strain continuous-stirred tank reactor (CSTR) model formulated and numerically investigated by Freter et al. In their model simulations, the reactor is parameterized using data for the mouse intestine. An invading bacterial strain is introduced into a CSTR that has already been colonized by a resident strain. The two strains compete for a single growth-limiting nutrient and for limited adhesion sites on the wall of the reactor. The mathematical model described in this paper is motivated in part by the CSTR model, but is based on the plug flow reactor (PFR). Parameter values and initial conditions are chosen so that the numerical performance of the PFR can be compared to that of the CSTR. In simulations bearing a remarkable qualitative and quantitative resemblance to those of the CSTR it is found that the invader is virtually eliminated, despite the fact that it has uptake rate and affinity for the wall identical to those of the resident. The PFR model is then parametrized using data for the human large intestine, and the two-strain simulations are repeated. Though obvious quantitative differences are noted, the more important qualitative outcome is preserved. It is also found that when three strains compete for a single nutrient and for adhesion sites there exists a steady-state solution characterized by the segregation of the bacterial strains into separate nonoverlapping segments along the wall of the reactor.