Mathematical modeling and experimental analytical description of a designed gut microbiota mixed culture, for the study of nonlinear dynamic interactions

Abstract

Gut microbiota is a complex community, its ecological interactions are studied to understand the relation between its composition and human health. It is known that these interactions are modified by external stimuli like the presence of drugs. In this thesis a new strategy of anaerobic batch culture with the use of microbioreactors was designed. It was tested with two members of the gut microbiota C. butyricum and L. lactis. They were cultured in monoculture and in mixed culture, as well as with and without a treatment of 10 mg/mL of acetaminophen, after determination of the minimum inhibitory concentration. The data of the growth kinetics was analyzed in terms of bacterial concentration [CFU/mL], with two mathematical approaches: regression analysis (logistic regression) and Sparse Identification of Nonlinear Dynamics (SINDy) considering Lotka-Volterra structure. Regression analysis showed that the mixed culture reached a 27% faster peak growth rate [CFU/mL] than the fastest monoculture (L. Lactis). Under the acetaminophen effect, all cultures showed a decrease in peak growth rates [CFU/(mL*h)], however, in terms of maximum growth [CFU/mL] C. butyricum had a 24% increase, while L. lactis and mixed culture had a decrease of 25% and 5% respectively. These findings lead us to believe that mutualism or commensalism is present between the species during mixed culture. Parametric identification of Lotka- Volterra models with SINDy showed that the growth rate [CFU/(mL*h)] depends mainly in the linear relation with the current concentration for both species, while the intraspecies interaction parameter defined the maximum concentration that culture would reach. The coupling of the microbioreactor strategy with the mathematical analysis allowed us to describe the ecological interactions of the complex dynamics of this designed gut microbiota cultures.