A Mathematical Model Explains Why Microbes That Depend on Each Other Are Surprisingly Stable

Depending on others for something you need feels risky. In biology, that dependence turns out to be one of the most common and stable arrangements in the microbial world. Bacteria routinely form communities in which individual strains cannot synthesize essential nutrients on their own and must obtain them from neighbors. These auxotrophic microbes - missing the biochemical machinery to make one or several amino acids - appear throughout natural environments, from soil to the human gut, where they make up a substantial fraction of microbial diversity.

Why mutual dependence is so prevalent and how it produces stable communities has been difficult to explain with existing models. A new study published in Cell Systems by researchers from the University of Illinois Urbana-Champaign, the Broad Institute, and Purdue University builds a mathematical framework that answers both questions - and tests it against experimental data from a living microbial system.

The Modeling Approach

The research was led by bioengineering professor Sergei Maslov at Illinois, computational scientist Ashish George (now at the Broad Institute), and biology professor Tong Wang (now at Purdue). Their collaboration began during overlapping appointments at the Carl R. Woese Institute for Genomic Biology at Illinois.

The model is built around two core principles. The first is flux balance: everything that is produced within the community must be consumed by someone in the community. No nutrient accumulates indefinitely and none is systematically wasted. "Let's make sure that everything that is being generated, all the amino acids being generated by the community, is consumed by somebody in the community, so nothing is left," Maslov said.

The second principle is that every species in a stable community must have a limiting resource - something that constrains its growth. Without such a constraint, a species grows exponentially until it dominates and eliminates competitors. A diverse, stable community requires each species to be limited by something different, so that no single organism can outcompete all others simultaneously. "Let's make sure that, for every species, there is actually something that limits its growth... so we explored in this model how we can simultaneously balance fluxes, and make sure that all the species have their unique limiting resource and they can all coexist because they are fighting for different things," Maslov explained.

Testing Against Real Data

To validate the model, the researchers applied it to a previously published experiment in which 14 laboratory-created auxotrophic strains of Escherichia coli were combined and allowed to compete. In that experiment, four strains survived to form a stable community. The Illinois team's model correctly predicted the identity of three of those four strains - a substantially better result than previous modeling approaches had achieved.

The fourth strain the model did not predict correctly represents an important limitation: no model of this complexity will achieve perfect predictive accuracy, and the discrepancy points toward biological factors the current model does not yet capture, such as strain-specific growth rates under particular conditions.

Why Cooperative Dependence Is Stable

The model's results explain a pattern that has puzzled ecologists: communities with more auxotrophic species tend to be more stable, not less. The mechanism is collective self-sufficiency. When multiple species depend on each other for different nutrients, the community as a whole becomes more robust to fluctuations in external nutrient supply - the internal trading network buffers the system against external variation.

The model also explains why established communities resist invasion by outsiders. A new microbe can only join the community if its specific nutrient requirements fit into the established trading network - if there is something it needs that others are producing, and something it produces that others need. Most potential invaders do not fit neatly into an established network, giving stable communities a kind of immunological resistance to colonization.

Applications to Human Health

The research team's next targets include applying the modeling approach to real-world microbial communities, particularly the human gut microbiome. "We would like to study community assembly and try to explain some of the patterns of the human gut microbiome, why some species tend to sort of coexist together," Wang said. Understanding which species are complementary in their nutrient production and consumption could eventually inform strategies for manipulating gut communities to improve health outcomes. The National Science Foundation, the Simons Foundation, and the National Institute for Theory and Mathematics in Biology supported the research.