Enzymatic Hydrolysis of Complex Carbohydrates and the Mucus in a Mathematical Model of a Gut Reactor

Abstract

The human gut microbiota rely on complex carbohydrates for energy and growth, particularly dietary fiber and host-produced mucins. These complex carbohydrates must first be hydrolysed by certain microbial groups to enable cross-feeding by the gut microbial community. We consider a mathematical model of the enzymatic hydrolysis of complex carbohydrates into monomers by a microbial species. The resulting monomers are subsequently digested by the microbial species for growth. We first consider the microbial species in a single compartment continuous stirred-tank reactor where dietary fiber is the only available substrate. A two compartment configuration in which a side compartment connected by diffusion is also studied. The side compartment is taken to be the mucus layer of the human colon, providing refuge from washout and an additional source of complex carbohydrate in the form of mucins. The two models are studied using stability analysis, numerical exploration, and sensitivity analysis. The delay in substrate availability due to hydrolysis results in bistability and the unconditional asymptotic stability of the trivial equilibrium. The addition of the mucus compartment allows the microbial species to survive under conditions that would otherwise result in washout in a comparable single compartment reactor. This would suggest that depending on the features of the gut microbiota being studied, extracellular hydrolysis and a representation of the mucus layer should be included in mathematical and lab reactor models of the human gut microbiota.