Counteraction of antibiotic production and degradation stabilizes microbial communities

Abstract

A major challenge in theoretical ecology is understanding how natural microbial communities support species diversity, and in particular how antibiotic-producing, -sensitive and -resistant species coexist. While cyclic ‘rock–paper–scissors’ interactions can stabilize communities in spatial environments, coexistence in unstructured environments remains unexplained. Here, using simulations and analytical models, we show that the opposing actions of antibiotic production and degradation enable coexistence even in well-mixed environments. Coexistence depends on three-way interactions in which an antibiotic-degrading species attenuates the inhibitory interactions between two other species. These interactions enable coexistence that is robust to substantial differences in inherent species growth rates and to invasion by ‘cheating’ species that cease to produce or degrade antibiotics. At least two antibiotics are required for stability, with greater numbers of antibiotics enabling more complex communities and diverse dynamic behaviours ranging from stable fixed points to limit cycles and chaos. Together, these results show how multi-species antibiotic interactions can generate ecological stability in both spatially structured and mixed microbial communities, suggesting strategies for engineering synthetic ecosystems and highlighting the importance of toxin production and degradation for microbial biodiversity.

Extended Data Figure 1. Antibiotic attenuation is widespread among natural antibiotic producing species isolated from soil

a, Diagram of 3-species assays: measuring the antibiotic inhibition-zone of E. coli around a producer strain enables quantification of 3-species interactions caused by a modulator strain. b, Attenuating interactions dominate among a set of 54 Streptomyces producer-modulator combinations. Triangle and square markers show scoring from example images in Figure 1b, left and right respectively. c, Antibiotic modulation assays: attenuating interactions dominate among combinations of soil species with a panel of 10 pure antibiotics. Combinations are colored by modulation index as in panel b and marked with a dot where the modulation index is significantly different from zero (N=3, Methods). Strains 1 and 2 are the strongest modulators from the 3-species assays, strain 3 is Streptomyces coelicolor, strains 4-18 are additional soil isolates (Extended Data Table 1). Antibiotics: doxycycline=DOX, chloramphenicol=CMP, tobramycin=TOB, ciprofloxacin=CPR, cefoxitin=FOX, piperacillin=PIP, penicillin=PEN, nitrofurantoin=NIT, rifampicin=RIF, trimethoprim=TMP. d, Scatter plots of average modulation index M for 12 species from panel c, with and without β-lactamase inhibitors. Points occur off the diagonal for the β-lactams piperacillin and penicillin but near the diagonal for the structurally unrelated antibiotics rifampin and nitrofurantoin, consistent with attenuation of the β-lactams through a mechanism of antibiotic degradation. Error bars are standard error of the mean for technical replicas with inhibitor (N=3) or without inhibitor (control, N=6). Control is addition of H₂O instead of inhibitor. Clav=clavulanic acid, tazB=tazobactum, sulB=sulbactam.

Extended Data Figure 2. Example images from 3-species interaction assays and antibiotic assays

a, Images and scoring for 3-species interaction assays from Extended Data Figure 1b. b, Example images and scoring from the antibiotic modulation assays from Extended Data Figure 1c. Each plate shows tests for modulation of antibiotic inhibition for 3 different species against a different antibiotic. Color lines show the size of the inhibition-zone at the location of the radially positioned modulator species; the white circle show the radius of the zone of inhibition as inferred from the left side of the plate that contains no modulators. c, Example images from an antibiotic modulation assay with β-lactamase inhibitors and the β-lactam antibiotic cefoxitin. Left and right side of each plate is inoculated with a line of species 4 from Extended Data Figure 1c. Attenuation is significantly reduced by the β-lactamase inhibitors (especially clavulanic acid and tazobactam) when compared to controls (H₂O).

Extended Data Figure 3. Illustration of the spatial inhibition-zone model

The simulation is performed on a grid of size LxL. A single individual occupies each grid location. During each generation: 1) Individuals from species of type P produce antibiotics within a circle of radius r_production. 2) Individuals of type R_D remove antibiotics within a circle of radius r_degradation. This process is repeated for each of the different antibiotics. 3) All sensitive individuals (type S) are killed at any locations that still contain the corresponding antibiotics (crossed out S; antibiotic values at each location are calculated at center positions). 4) Empty locations of a new grid are filled by randomly choosing from any surviving individuals within a radius r_dispersal. If there are no surviving individuals within r_dispersal then an empty location remains empty.

Extended Data Figure 4. Dependence of coexistence on degradation in the mixed inhibition-zone model

a, Stability analysis of the full parameter space in the mixed inhibition-zone model. Using simulations, we tested the stability of cyclic 3-species 3-antibiotic communities with dense sampling of all possible parameters for the inhibition-zone model, varying strengths of K_P and K_D, initial abundances of species 1-3 and growth ratios g₂/g₁ and g₃/g₁. As in Figure 2b, each grid shows a 100 fold range of growth rate ratios from 0.1 to 10. Large basins of attraction exist across a wide range of parameter values, with maximal stability at high levels of antibiotic production and intermediate levels of degradation. b-d, Intuition for why coexistence depends on degradation. b, the inhibition-zone model calculates the probability of a given sensitive species being inhibited by an antibiotic producer (blue), or being protected by a degrading species (red), given the relative strengths of production (K_P) and degradation (K_D). The expected area covered by the overlapping circles (left) is used to calculate the corresponding inhibition and attenuation probabilities (percentage area of filled boxes, right; Methods). c, Focusing on one antibiotic in a stable 3-species community: increasing the abundance of the yellow species creates negative feedback by decreasing the abundance of blue and red, which results in more inhibition of yellow. d, Communities are not stable at low levels of degradation due to positive feedback, whereby increasing the abundance of the yellow species results in a decrease of inhibition.

Extended Data Figure 5. Coexistence of antibiotic degrading communities in a well-mixed chemostat model with three antibiotics

a, Stability of the 3-species 3-antibiotic community in a single resource chemostat model in which species and antibiotics are completely homogeneous. Communities in the chemostat model may coexist through fixed points or limit cycles. For parameter sets in which the fixed point of the chemostat model was unstable, we started simulations close to the fixed point to determine if the community coexists through a limit cycle. Limit cycles occur in the areas between the dashed and solid black lines. Chemostat parameters: g₁ = 3, g₂ = 6, g₂ = 9, k_s = 0.5, p = 1. b, Communities coexist in the chemostat for a wide range of assumptions regarding antibiotic mechanisms. We simulated the chemostat model while changing how the action of the antibiotics is modeled and observed robust coexistence across all models. For each simulation we started all species at equal concentration (X_i = 0.2), ran the simulation until t = 100 and calculated the Shannon diversity of the final species levels. The default chemostat model assumes exponential inhibition of species by antibiotics, but similar coexistence is observed for Monod-like inhibition, species killing instead of inhibition, when species are only partially inhibited or when each species is sensitive at some level to all antibiotics. G₁ is the growth rate of species 1 under inhibition, while g₁ is its maximal rate of growth; R(x) captures resource dependence on current species levels; C₁, C₂ and C₃ are the concentrations of antibiotics produced by species 1-3 respectively (Methods). Equations for the growth of species 2 and 3 have the same form as G₁. All other parameters are the same as for panel a.

Extended Data Figure 6. Coexistence of communities with three species and two antibiotics

a, Comparing community diversity in the mixed inhibition-zone model and the chemostat model. For each simulation we started all species at equal concentration (X_i = 1/3 for the inhibition-zone model, X_i = 0.2 for the chemostat model), ran the simulation for time 100 and calculated the Shannon diversity of the final species levels. Other parameters are the same as in Figure 2 for the inhibition-zone model or Extended Data Figure 5 for the chemostat model. b, Three species communities require two antibiotics for stability. When only one antibiotic is degraded the community either lacks stability (first panel), or is stable only for a small number of growth rates and initial conditions (second panel). When two antibiotics are degraded the community is robustly stable to differences in species growth rates and initial conditions (third panel), provided that the antibiotics inhibit the faster growing species (species 2 and 3). Basin colors as in Figure 2b; gray shows parameters for which no initial conditions were stable; K_P = 40, K_D = 4.

Extended Data Figure 7. Robustness of three species communities to invasion by cheaters in the mixed inhibition-zone model

Analysis of production cheaters (P→R_I, left) and degradation cheaters (R_D→S, right). As in Figure 3, we plot the final abundance of each cheater as a function of its growth advantage ε over its parent species. a, Cheaters cannot invade the 3-species 3-antibiotic network when their growth advantage is small, except for the production cheater of the species with the fastest inherent growth rate (species 3, green line), which replaces its parent generating a new stable community of 3 species interacting through 2 antibiotics. b, This resulting 3-species 2-antibiotic community is resilient to invasion by all cheaters; cheaters must have a substantial growth advantage to invade and take over. Parameters for both networks are the same as Figure 3. Shaded areas indicate the maximum and minimum abundance when the community reaches stable oscillations. Note: The analysis above is for networks with g₁ < g₂ < g₃. The alternative network of g₁ > g₂ > g₃, is less robust to cheater invasion. Two cheaters can invade this community even with small ε: the production cheater for species 2, which gives rise to a stable 3-species 2-antibiotic community, and the production cheater of species 1, which takes over the community.

Extended Data Figure 8. Complex network topologies support coexistence of larger numbers of species in the mixed inhibition-zone model

For given initial numbers of species and antibiotics, sets of up to 10⁶ communities with random networks were simulated and the final number of surviving species recorded. The number inside each square shows how many networks resulted in the specified number of final species (after removing networks that did not use all of the initial antibiotics, Methods). Colors show the frequency of each outcome within all simulated networks, with gray where no stable networks were found. We sparsely sampled parameters for species growth rates and antibiotic production and degradation levels (Methods). The sparse sampling means that a given network topology may exhibit stability for parameter combinations that were not tested.

Extended Data Figure 9. A community with chaotic dynamics

Plotting the abundance of species 1-3 for the network from Figure 4b. We show the last 30,000 steps of a length 40,000 time-series, colored with a slowly changing gradient. The trajectories form a strange attractor.

Figure 1. Replacing intrinsic antibiotic resistance with degradation-based resistance generates community robustness to species dispersal

a, Pairwise interactions among antibiotic producing (P), sensitive (S) and intrinsically resistant (R_I) species are compared to 3-way interactions where the sensitive species can be protected by an antibiotic degrading species (R_D). b, Images of a YFP-labeled probe Escherichia coli strain (S, yellow-green) growing in the presence of two Streptomyces colonies. The inhibition of the probe strain by a producer (dark area around P) is unaffected by an intrinsically resistant species (R_I, left), but is strongly attenuated around an antibiotic degrading species (right, yellow-green halo around R_D colony). Images are representative of cases without and with 3-way interactions among 54 Streptomyces pairs tested (1 replica, Extended Data Fig. 1-2). c, Spatial inhibition-zone model: a producer (P) kills nearby species that are sensitive to its antibiotic (crossed out S), but does not affect resistant species (R_I, R_D). Sensitive species are protected by degrader species (right, S within dashed circle around R_D). Surviving species then replicate and disperse over distance r_dispersal. d, Snapshots of spatial simulations for cyclical 3-species 3-antibiotic interaction networks (labels indicate species phenotypes for each antibiotic). e, Intrinsically resistant communities collapse with increased dispersal (left), while communities with antibiotic degradation are robust to any level of dispersal (right). Insets show typical subregion snapshots. Number of species is based on average Shannon diversity of subregions (Methods).

Figure 2. Strong antibiotic production with intermediate levels of degradation leads to stable communities robust to initial conditions and substantial differences in species growth rates

a, Communities with intrinsic resistance diverge from an unstable fixed point (green dot, left), while communities with antibiotic degradation converge toward a stable fixed point within a large basin of attraction (green area, right). Shown in trilinear coordinates are abundance changes per generation (white arrows) and example trajectories (black) for species with inherent growth rates: g₁ < g₂ < g₃. b, Communities with degradation remain stable even for large differences in inherent species growth rates (right), while communities with intrinsic resistance are always unstable (left). c, Maximal community stability occurs at high levels of antibiotic production (K_P) and intermediate levels of degradation (K_D). Shading shows rate of exponential convergence (green) or escape (grey) from the fixed point. Black lines in panels b-c show the stability region boundary based on linear stability analysis (Methods).

Figure 3. Communities are robust to invasion by cheaters that cease antibiotic production or degradation

a, Production or degradation cheaters (open circles with solid or dashed lines, respectively) are introduced at low abundance into a stable 3-species community (filled colored circles). b, When cheater growth advantage ε is small, only the production cheater of the fastest growing species can invade (species 3, green). This cheater replaces its parent, forming a new stable community, which is in turn robust to further invasions. The other two production cheaters can invade only when ε is large enough, taking over the community (yellow) or replacing their parent in a stable community (red). c, Degradation cheaters cannot invade the community at low ε, whereas at high enough ε they invade but do not replace their parents, rather generating a stable 4-species community. A 4-species interaction network is shown for the species 2 degradation cheater: gray interactions are inherited from the parent species; yellow interactions are specific to the cheater. Shaded areas span lower/upper bounds when the community exhibits sustained oscillations.

Figure 4. Complex interaction networks support coexistence through diverse dynamical behaviors

An example of a stable network with 4 species interacting through production and degradation of three antibiotics. Depending on the strengths of antibiotic production and degradation, this community can coexist through stable equilibrium, limit cycles or chaos (Methods). Line colors indicate species identity.