Ecological modeling from time-series inference: insight into dynamics and stability of intestinal microbiota

Abstract

The intestinal microbiota is a microbial ecosystem of crucial importance to human health. Understanding how the microbiota confers resistance against enteric pathogens and how antibiotics disrupt that resistance is key to the prevention and cure of intestinal infections. We present a novel method to infer microbial community ecology directly from time-resolved metagenomics. This method extends generalized Lotka-Volterra dynamics to account for external perturbations. Data from recent experiments on antibiotic-mediated Clostridium difficile infection is analyzed to quantify microbial interactions, commensal-pathogen interactions, and the effect of the antibiotic on the community. Stability analysis reveals that the microbiota is intrinsically stable, explaining how antibiotic perturbations and C. difficile inoculation can produce catastrophic shifts that persist even after removal of the perturbations. Importantly, the analysis suggests a subnetwork of bacterial groups implicated in protection against C. difficile. Due to its generality, our method can be applied to any high-resolution ecological time-series data to infer community structure and response to external stimuli.

Figure 1. Conceptual figure highlighting the difference between our approach and the currently available methods for microbiota analysis.

Used input data are the temporal records of microbial total abundances (colored bars on left) and the temporal signal of external perturbations (e.g. presence/absence or concentration). (A) Example and list of current computational approaches used to analyze community data for microbiota studies. (B) Our approach uses ecological modeling to infer a network of microbial interactions, susceptibilities to external perturbations and growth rates. The inferred parameters are used in an ecological community model which can then be used to predict ecosystem dynamics and to identify steady states.

Figure 2. Growth and interaction rates and susceptibilities to clindamycin application from cecal mouse data.

All growth rates are found to be positive (A). Interaction parameters in row i and column j represent the effect of genus j on i where red stands for activation and blue for repression (B). Blue bars in the susceptibility panel refer to an inhibiting effect of clindamycin, while red ones refer to activation (C). The optimal regularization parameters obtained in a 3-fold cross-validation are , , .

Figure 3. Comparison between observation and predicted microbial composition in the cecum.

(A) refers to replicate 2 of population #1 (C. difficile inoculation at day 0), (B) to clindamycin administration at day 1 (replicate 2 of population #2) and (C) to clindamycin and C. difficile administration at day 1 and 2 respectively (replicate 2 of population #3). The composition bar is linearly scaled. Note, the total abundance of the intestinal microbiota does not decrease with antibiotic treatment. This may indicate the specific function of the bacteria that are present after the perturbation. (D) Rank correlation of measured with predicted data points. Colors indicate elapsed time. 75% confidence ellipses are drawn for the first (blue) and last (red) predicted time points.

Figure 4. Steady state microbial composition for the cases described in Figure 3A–C.

(A) predicted composition of the second replicates of the three different populations. These states are asymptotically stable as depicted in (B) where the corresponding largest eigenvalues of the Jacobian matrix evaluated at each steady state is compared (red dot) against the histogram of largest eigenvalues of all attainable and biologically meaningful steady states.

Figure 5. Colonization mechanism.

(A) Mechanism of C. difficile colonization in mice. (B) Schematics of step-by-step dynamics leading to C. difficile establishment following clindamycin treatment.