Mutualistic cross-feeding in microbial systems generates bistability via an Allee effect.

In microbial ecosystems, species not only compete for common resources but may also display mutualistic interactions as a result from metabolic cross-feeding. Such mutualism can lead to bistability. Depending on the initial population sizes, species will either survive or go extinct. Various phenomenological models have been suggested to describe bistability in mutualistic systems. However, these models do not account for interaction mediators such as nutrients. In contrast, nutrient-explicit models do not provide an intuitive understanding of what causes bistability. Here, we reduce a theoretical nutrient-explicit model of two mutualistic cross-feeders in a chemostat, uncovering an explicit relation to a growth model with an Allee effect. We show that the dilution rate in the chemostat leads to bistability by turning a weak Allee effect into a strong Allee effect. This happens as long as there is more production than consumption of cross-fed nutrients. Thanks to the explicit relationship of the reduced model with the underlying experimental parameters, these results allow to predict the biological conditions that sustain or prevent the survival of mutualistic species.

Excitable dynamics through toxin-induced mRNA cleavage in bacteria.

Toxin-antitoxin (TA) systems in bacteria and archaea are small genetic elements consisting of the genes coding for an intracellular toxin and an antitoxin that can neutralize this toxin. In various cases, the toxins cleave the mRNA. In this theoretical work we use deterministic and stochastic modeling to explain how toxin-induced cleavage of mRNA in TA systems can lead to excitability, allowing large transient spikes in toxin levels to be triggered. By using a simplified network where secondary complex formation and transcriptional regulation are not included, we show that a two-dimensional, deterministic model captures the origin of such toxin excitations. Moreover, it allows to increase our understanding by examining the dynamics in the phase plane. By systematically comparing the deterministic results with Gillespie simulations we demonstrate that even though the real TA system is intrinsically stochastic, toxin excitations can be accurately described deterministically. A bifurcation analysis of the system shows that the excitable behavior is due to a nearby Hopf bifurcation in the parameter space, where the system becomes oscillatory. The influence of stress is modeled by varying the degradation rate of the antitoxin and the translation rate of the toxin. We find that stress increases the frequency of toxin excitations. The inclusion of secondary complex formation and transcriptional regulation does not fundamentally change the mechanism of toxin excitations. Finally, we show that including growth rate suppression and translational inhibition can lead to longer excitations, and even cause excitations in cases when the system would otherwise be non-excitable. To conclude, the deterministic model used in this work provides a simple and intuitive explanation of toxin excitations in TA systems.

Integrated culturing, modeling and transcriptomics uncovers complex interactions and emergent behavior in a three-species synthetic gut community.

The composition of the human gut microbiome is well resolved, but predictive understanding of its dynamics is still lacking. Here, we followed a bottom-up strategy to explore human gut community dynamics: we established a synthetic community composed of three representative human gut isolates (Roseburia intestinalis L1-82, Faecalibacterium prausnitzii A2-165 and Blautia hydrogenotrophica S5a33) and explored their interactions under well-controlled conditions in vitro. Systematic mono- and pair-wise fermentation experiments confirmed competition for fructose and cross-feeding of formate. We quantified with a mechanistic model how well tri-culture dynamics was predicted from mono-culture data. With the model as reference, we demonstrated that strains grown in co-culture behaved differently than those in mono-culture and confirmed their altered behavior at the transcriptional level. In addition, we showed with replicate tri-cultures and simulations that dominance in tri-culture sensitively depends on the initial conditions. Our work has important implications for gut microbial community modeling as well as for ecological interaction detection from batch cultures.

Bistability in a system of two species interacting through mutualism as well as competition: Chemostat vs. Lotka-Volterra equations.

We theoretically study the dynamics of two interacting microbial species in the chemostat. These species are competitors for a common resource, as well as mutualists due to cross-feeding. In line with previous studies (Assaneo, et al., 2013; Holland, et al., 2010; Iwata, et al., 2011), we demonstrate that this system has a rich repertoire of dynamical behavior, including bistability. Standard Lotka-Volterra equations are not capable to describe this particular system, as these account for only one type of interaction (mutualistic or competitive). We show here that the different steady state solutions can be well captured by an extended Lotka-Volterra model, which better describe the density-dependent interaction (mutualism at low density and competition at high density). This two-variable model provides a more intuitive description of the dynamical behavior than the chemostat equations.