# A mechanistic model of disjunctive metabolic symbioses in microbes

## TL;DR

This paper develops a detailed mathematical model of microbial symbiosis based on nutrient exchange, analyzing how biological traits and external conditions influence system stability and interaction types.

## Contribution

It introduces a mechanistic differential equation model for microbial symbioses, linking biological traits to system dynamics and interaction spectra.

## Key findings

- Model captures stability conditions of microbial symbiosis
- External metabolite manipulation shifts interaction types
- Biological traits influence equilibrium states

## Abstract

Lately, experimental research on microbial symbioses based on nutrient exchange and interdependence has yielded a number of interesting findings, however an in-depth mathematical description of the exact underlying dynamics of such symbiotic associations is still missing. Here, we derive and analyse a mechanistic mathematical model of such a relationship in a continuous chemostat culture based on five coupled differential equations. The influence of the biological traits of the involved organisms on the position and stability of the equilibrium states of the system is examined. We also demonstrate how manipulating the external metabolite concentrations of the system can shift the species interaction on a continuous spectrum ranging from mutualism over commensalism to parasitism.