  Social interaction between microbes can be described at many levels of
details, ranging from the biochemistry of cell-cell interactions to the
ecological dynamics of populations. Choosing the best level to model microbial
communities without losing generality remains a challenge. Here we propose to
model cross-feeding interactions at an intermediate level between genome-scale
metabolic models of individual species and consumer-resource models of
ecosystems, which is suitable to empirical data. We applied our method to three
published examples of multi-strain Escherichia coli communities with increasing
complexity consisting of uni-, bi-, and multi-directional cross-feeding of
either substitutable metabolic byproducts or essential nutrients. The
intermediate-scale model accurately described empirical data and could quantify
exchange rates elusive by other means, such as the byproduct secretions, even
for a complex community of 14 amino acid auxotrophs. We used the three models
to study each community's limits of robustness to perturbations such as
variations in resource supply, antibiotic treatments and invasion by other
"cheaters" species. Our analysis provides a foundation to quantify
cross-feeding interactions from experimental data, and highlights the
importance of metabolic exchanges in the dynamics and stability of microbial
communities.
