Mathematical modeling of primary succession of murine intestinal microbiota

Abstract

Understanding the nature of interpopulation interactions in host-associated microbial communities is critical to understanding gut colonization, responses to perturbations, and transitions between health and disease. Characterizing these interactions is complicated by the complexity of these communities and the observation that even if populations can be cultured, their in vitro and in vivo phenotypes differ significantly. Dynamic models are the cornerstone of computational systems biology and a key objective of computational systems biologists is the reconstruction of biological networks (i.e., network inference) from high-throughput data. When such computational models reflect biology, they provide an opportunity to generate testable hypotheses as well as to perform experiments that are impractical or not feasible in vivo or in vitro. We modeled time-series data for murine microbial communities using statistical approaches and systems of ordinary differential equations. To obtain the dense time-series data, we sequenced the 16S ribosomal RNA (rRNA) gene from DNA isolated from the fecal material of germfree mice colonized with cecal contents of conventionally raised animals. The modeling results suggested a lack of mutualistic interactions within the community. Among the members of the Bacteroidetes, there was evidence for closely related pairs of populations to exhibit parasitic interactions. Among the Firmicutes, the interactions were all competitive. These results suggest future animal and in silico experiments. Our modeling approach can be applied to other systems to provide a greater understanding of the dynamics of communities associated with health and disease.

Keywords: 454 sequencing; culture independent; dynamical systems; microbial ecology; microbiome.

Fig. 1.

Average distance between the gut community structure from the present day and the previous day (A) and to the other mice on the same day (B) during the 21 d after colonization. Error bars represent 95% confidence intervals.

Fig. 2.

Average relative abundance for the most abundant OTUs that classified within the phyla Bacteroidetes, Firmicutes, Proteobacteria, and Verrucomicrobia during the 21 d after colonization. Error bars represent 95% confidence interval for the OTU across the five mice.

Fig. 3.

Association network describing the co-occurrence patterns between OTUs that had a correlation value less than −0.25 or larger than 0.25. OTUs 8, 22, 36, and 38 had an average relative abundance of at least 0.5% in individual mice but were not included in the correlation analysis because they did not meet the threshold abundance in all mice.

Fig. 4.

Heat map of the modeled parameters that describe the interactions between OTUs (β_ij). Each value represents the effect of the OTU in the row on the OTU represented by the column. Because the relationships are asymmetrical, so is the matrix. The rows and columns are sorted together according to the neighbor joining phylogenetic tree that was calculated using a representative sequence from each OTU.