Costless metabolic secretions as drivers of interspecies interactions in microbial ecosystems

Bioinformatics

Metabolite secretion cost depends on environmental context

Understanding whether the secretion of a metabolite by an organism is associated with a decrease in fitness (interpreted here as growth rate) is difficult to assess experimentally, but can be readily calculated using genome-scale models of metabolism (see Methods). For example, one can impose the secretion of a given compound at a given rate vs, and then ask whether this constraint is expected to cause the organism’s growth rate (vg,s) to be less than its growth rate without this constraint (vg,0). A small set of simulations of this kind for a single organism (Supplementary Fig. 1) exemplifies the spectrum of possible outcomes: depending on the carbon sources provided, different metabolites can be produced either (i) at the expense of growth capacity, (ii) with no apparent effect, or (iii) even to its benefit. For cases (ii) and (iii), since fitness is not reduced by the metabolite secretion, vg,s ≥ vg,0. The existence of solutions that satisfy this equation (i.e., flux states that have higher growth in presence of a metabolic secretion) forms the basis of our subsequent calculations. The above equation can thus be viewed as the defining characteristic of a costless metabolic secretion.

We note that while FBA provides mechanistic insight into the tradeoff between metabolic reaction costs and benefits, current predictions (including those on the costless nature of a metabolic secretion) may depend on factors not captured by our method, including temperature30, signaling and gene regulation31,32,33,34,35, pH changes36, and explicit pathway-dependent cost of enzyme production37. Our definition of “costless” may therefore be interpreted as a heuristic that captures expected spontaneous metabolite secretions, in contrast to secretion that would be associated with a growth or fitness reduction.

Costless secretions promote environmental enrichment

Having illustrated in an individual case how metabolite secretion costs can strongly depend on carbon sources, we sought to map the prevalence of costless secretions across a broad set of organisms and environments. As an initial core analysis, we carried out a total of 1,051,596 unique simulations, each with two organisms from a set of 14 genome-scale models of facultative anaerobes and two carbon sources from a set of 108 compounds (Fig. 1, Supplementary Data 1, Supplementary Table 1). We chose facultative anaerobes in order to enable a direct comparison of secretion profiles in oxic vs. anoxic conditions. Each simulation was conducted as an iterative process that emulates a coculture experiment, uniquely defined by the organisms involved, the carbon sources provided, and the availability of oxygen. At each iteration, we used FBA to determine the ability of each organism to grow on the provided medium, in addition to the set of metabolites predicted to be spontaneously (i.e., costlessly) secreted by each microbe. We incorporated several measures into these simulations to minimize false-positive reporting of secreted metabolites (see Methods).

Fig. 1

Simplified schematic illustrating the in silico experiments. A growth medium (Mc) containing two carbon sources (α, β) with or without oxygen (Ω) is provided to genome-scale metabolic models of two microbial organisms (i, j). If at least one organism grows, any costlessly secreted metabolites (σc) are added to the medium, which is fed back to the organisms. This process is repeated for a series of iterations c, and terminates at iteration cs, defined as the last iteration in which any new metabolites were secreted into the medium

If at the first iteration (c = 1, Fig. 1) at least one organism was able to grow on the carbon sources provided, all newly secreted costless metabolites were added to the medium for the next iteration. This process was repeated until no new metabolites were produced (defining a final iteration c = cs). Upon running such simulations for all combinations of species and environments, we obtained distributions for the value of cs (Fig. 2a). A majority of cases reached a steady state after only one iteration, possibly due to organisms secreting multiple byproducts that only contributed weakly to subsequent secretions.

Fig. 2
Fig. 2

Analysis of costlessly secreted metabolites in pairwise simulations. Only simulations that led to growth of at least one organism are shown. a Distribution of number of expansions until final medium expansion iteration. Ninety-two percent of simulations reached a steady medium composition after only one iteration with oxygen, compared to 82% of simulations without oxygen. b Distribution of the number of metabolites secreted into the medium by one or both organisms in a pair after one iteration of FBA (c = 1). These distributions were unimodal for both conditions, centered between two and three metabolites with oxygen and around five metabolites without oxygen. After this first iteration, the maximum number of secreted metabolites was 11 with oxygen and 16 without oxygen. In the anoxic simulations, the central carbon metabolites most commonly secreted after the first iteration were fermentation byproducts such as acetate, formate, succinate, and ethanol. These metabolites were secreted in 87.5%, 74.5%, 25.7%, and 20.2% of growth-yielding simulations respectively. With oxygen, the most commonly secreted central carbon metabolites after the first iteration were formate and acetate, secreted in 46.8% and 18.3% of growth-yielding simulations, respectively. c Distribution of the number of metabolites secreted by one or both organisms after the last iteration of FBA (c = cS). The last iteration is defined as the iteration in which no additional metabolites were released into the medium. The total number of secreted metabolites followed similar distributions with a maximum at 18 and 21 metabolites for oxic and anoxic conditions, respectively. Despite the large variability in number of expansions and number of secreted metabolites, we observe a poor correlation between these distributions, indicating that a simulation resulting in a high number of expansions does not necessarily result in a high number of metabolites being secreted (Supplementary Fig. 3)

In aggregate, our simulations showed a rightward shift in the diversity of metabolites secreted under anoxic conditions when compared to the number secreted when oxygen was available (Fig. 2b), as well as a shift in the quantity of metabolites secreted between the first and last iteration of each simulation (Fig. 2c). This latter effect reflects organisms taking up metabolites secreted by themselves or their partner, and secreting different metabolites as a response. Based on these results, we hypothesized that oxygen availability would be among the best indicators of the metabolites secreted in a simulation. To quantify this effect, we applied a machine learning approach to a modified simulation set consisting of all 14 organisms individually feeding on a single carbon source (see Methods). Using this method, we found that sets of secreted metabolites could be used to yield varying degrees of information on simulation starting conditions. Specifically, oxygen availability, species identity, and carbon source type could be predicted with cross-validation accuracies of 93.4%, 58.0%, and 85.3%, respectively. Notably, organism identity appeared to be not strongly associated with specific costless secretions compared to carbon source and oxygen. This may be due to the fact that, while an organism may have a pathway to secrete a particular byproduct, utilization of that pathway would be strongly contingent on the presence of the necessary substrates. The observed associations of secretions with the carbon source mirrored previous experimental observations, which identified carbon sources as the main drivers of community composition through metabolic cross-feeding13. While the specific concentration of environmental substrates could in principle affect predicted secretions, we found through dynamic FBA38,39 (dFBA) simulations that substrate concentration had a negligible effect on the identity of secreted metabolites (see Methods and Supplementary Data 2). Nonetheless, one should consider the possibility that this result may be due to limitations of constraint-based modeling, which may be overcome in future studies.

Useful costlessly secreted byproducts are abundant

Our analysis revealed that most organisms secreted a broad distribution of metabolically useful compounds without cost in a variety of environmental conditions (Fig. 3, Supplementary Fig. 4a). Though inorganic compounds such as water and carbon dioxide were, as expected, the most commonly secreted molecules across all simulations, nitrogen-containing compounds such as nitrite, ammonium, and urea were secreted in 73.5% of the analyzed cases, suggesting maintenance of an appropriate carbon-to-nitrogen ratio in the cell. We note specifically that nitrite is secreted in fewer than 100 simulations with oxygen, but its secretion is prevalent in anoxic simulations—a phenomenon previously observed in anaerobic enteric bacteria40. Moreover, ~10% of anoxic simulations resulted in at least one organism fully reducing nitrate into nitrogen gas, suggesting that anaerobic respiration was a preferred strategy in some environments. Organic acids made up the second most abundant category of costless secretions, followed by nucleotides, peptides, and carbohydrates. Altogether, this space of secreted metabolites points to a large variety of molecules that can be freely produced in resource-poor environments.

Fig. 3
Fig. 3

Categorization of metabolites secreted costlessly in all simulations. a, b Categorization for all simulations with oxygen (a) and without oxygen (b). Though inorganic waste products (e.g., water, CO2) make up the majority of unique metabolites secreted with and without oxygen, release of potentially valuable metabolites such as organic acids, carbohydrates, and peptides is observed in a major subset of simulations. In anoxic simulations in which at least one organism fully reduced nitrate into nitrogen gas, we observed a modest reduction in the number of fermentation byproducts secreted (2.81 ± 1.11 metabolites for non-nitrate respirers vs 2.38 ± 0.54 metabolites for nitrate respirers)

Despite our careful design of the simulation process, it remains difficult to quantify the degree to which these secretions will be observed experimentally. For this reason, we have relied exclusively on genome-scale metabolic models that have undergone experimental validation under conditions that in many cases mirror those that we have simulated, in addition to imposing our own set of constraints (see Methods). Moreover, though empirical testing of every simulation we performed is inaccessible, we note that experimental data from previously published work supports key portions of our predictions (Supplementary Table 4). In an additional effort to ensure the accuracy of the set of secreted metabolites, we also carried out all simulations using alternative objective functions. In particular, though optimization of growth reflects the possibility of organisms “selfishly” growing as rapidly as possible and “unintentionally” secreting useful metabolites, alternative objective functions may best capture metabolic regimes relevant across different conditions. We therefore compared metabolite secretion profiles inferred by maximizing growth to those obtained through minimization of biomass production, as well as maximization and minimization of ATP production. All objectives gave rise to secretion profiles highly similar to each other, with an increase of only 0.18% of all predicted metabolic secretions in the growth maximization condition relative to the others (see details and results in Supplementary Fig. 5, and Supplementary Table 5).

Given the abundance of secretions from different organisms, we asked whether specific metabolite secretions were highly correlated. We thus used a Spearman correlation analysis to identify secretion patterns that appeared with high frequency (Supplementary Fig. 6). In the presence of oxygen, we observed a strong co-occurrence of glycerol, lactate, succinate, malate, and acetate, which may reflect the high frequency of secretion of these carbon-containing compounds. We also observed positive, but weaker correlations between these metabolites and other central carbon compounds such as fumarate, citrate, and 2-oxoglutarate. Our analysis also pointed to the simultaneous release of multiple nitrogen-containing compounds, chiefly urea, ammonium, and nitrate. Without oxygen, we observed stronger correlations between secretion of nitrogen-containing compounds and fermentation byproducts. Amino acids also co-occurred with high frequency without oxygen in patterns consistent with examples of previously studied exometabolomic profiles, including those showing co-secretion of central carbon intermediates in E. coli and of amino acids in yeast41,42, as well as time-dependent patterns of metabolites released simultaneously in soil communities43. These co-secretion profiles suggest that environments modified by metabolic activities of existing organisms may be simultaneously enriched by specific combinations of molecules.

Having mapped the space of metabolites secreted at no fitness cost to the producer, we sought to understand which metabolites could be subsequently taken up by other organisms. We found that the organic metabolites most commonly exchanged across species were central carbon intermediates, secreted mainly in anoxic conditions (Supplementary Fig. 4b). These secretion patterns mirrored those of anoxic gut bacteria, which divide the task of digesting complex polysaccharides by exchanging intermediate organic acids11,44. Importantly, we observed that amino acids, secreted chiefly by Saccharomyces cerevisiae, but also in a substantial number of simulations by Salmonella enterica, Klebsiella pneumoniae, and E. coli, were among the most frequently exchanged costless metabolites. This phenomenon has been previously documented in relation to overflow metabolism in S. cerevisiae45 and E. coli46,47, as well as in yeast–bacteria symbioses48,49. This high prevalence of exchange underscores the metabolic utility of these secreted byproducts.

Costless metabolite exchange enhances growth capabilities

We next assessed how often the exchange of costlessly produced molecules could directly enable growth of other organisms that would otherwise not grow on the initial environmental nutrients. Before taking into account the costless secretions, 18.2% and 11.9% of simulations predicted growth of both organisms with and without oxygen, respectively (Fig. 4a). After the organism pairs were allowed to exchange costlessly secreted metabolites, our algorithm predicted a substantial increase in growth-supporting environments (72.7% with oxygen and 82.5% without oxygen relative to minimal medium), suggesting that exchange of costlessly secreted metabolites can enable growth of additional organisms in resource-poor environments.

Fig. 4
Fig. 4

Growth outcomes of pairwise cross-feeding simulations. a Growth outcomes of all in silico experiments with and without oxygen, grouped by pairwise growth phenotype. b Organism-specific growth outcomes. Size of circles represent the relative number of environments in which an organism was able to grow out of 5774 in silico experiments with each partner. c, d Frequency of obligate pairwise growth by species in single carbon source simulations for oxic (N = 69,420, c) and anoxic (N = 52,897, d) conditions. Each color ribbon is unique to an individual species pair. Width of ribbons is proportional to the number of experiments in which obligate syntrophy was predicted for each species pair. Radial axis colors represent directionality of exchange: blue: organism provided essential metabolites to partner organism in over 75% of simulations; red: organism received essential metabolites in over 75% of simulations; gray: both organisms gave and received essential nutrients in most simulations. Most pairings of organisms were imbalanced, with one organism more frequently providing essential nutrients to another. For example, with oxygen, Synechocystis relied on metabolites from nine different organisms across the vast majority of simulations in which it grew with a partner. As all organisms were grown heterotrophically, carbon dioxide and ammonium were the main byproducts that enabled growth of Synechocystis in these simulations. BS: B. subtilis, EC: E. coli, KP: K. pneumoniae, LL: L. lactis, ME: M. extorquens, PA: P. aeruginosa, PG: P. gingivalis, RS: R. sphaeroides, SB: S. boydii, SC: S. cerevisiae, SE: S. enterica, SO: S. oneidensis, SS: Synechocystis, ZM: Z. mobilis

In addition to a global increase in growth capabilities due to costless metabolite secretion, we observed species-specific growth patterns that varied widely across our dataset (Fig. 4b). Lactococcus lactis and Porphyromonas gingivalis, for example, are host-associated microbes that are auxotrophic for a wide range of metabolites and that often depend on metabolic products from the host or other commensal microbes50,51. In our study, these organisms failed to grow in all simulations even after costless metabolites were made available by a partner. This failure to sustain growth of highly dependent organisms suggests that there is an upper limit to the degree to which costless metabolite production can enable species growth, especially in the minimal environments that were tested. Nonetheless, most of the metabolites that these organisms require to grow were producible separately by multiple species, suggesting a possible important role of multi-partner cross-feeding interactions in complex communities. Aside from these extreme cases, our analysis shed light on the performance of generalist organisms, such as E. coli, K. pneumoniae, S. cerevisiae, and S. enterica. These organisms grew in at least half of all tested environmental conditions, in contrast with organisms such as Methylobacterium extorquens or Zymomonas mobilis, which exhibited much more limited pairwise growth capabilities. The growth patterns of these latter organisms suggest a greater dependence on the metabolic byproducts of their partners, particularly in anoxic conditions.

As our study relied on a limited set of curated metabolic models, we wondered how sensitive these results were to the organisms being assessed. In order to explore possible bias, we conducted additional simulations in which we binned organisms by environmental habitat. These simulations were separated into three sets: the first with 13 aquatic microbes grown aerobically, the second with 12 soil microbes grown aerobically, and the third with 12 human gut-associated microbes grown anaerobically. These simulations employed additional genome-scale models (including obligate aerobes or obligate anaerobes, see Supplementary Data 1) that were not used in our core analysis of 14 facultative anaerobes. By analyzing the expanded set of organisms in a habitat-specific manner, we found that exchange of costless metabolites substantially improved the ability of minimal environments to support pairwise growth in all three habitats (Supplementary Fig. 7a). Notably, metabolite secretion and exchange for aquatic and soil microbes resembled the profiles found for the core organisms grown with oxygen (Supplementary Fig. 7b, c, Supplementary Table 6). Conversely, the distribution of secreted metabolites for gut-associated microbes featured widespread secretion and exchange of organic acids that were similar to those found across core organisms grown anoxically (Supplementary Fig. 7d, Supplementary Table 6).

Costless metabolic exchange yields specific partnerships

After analyzing general growth outcomes across our entire simulation set, we sought to determine which specific organisms could not grow without the costless secretions of a partner. Our simulations identified a diverse space of such organisms, with most species exhibiting at least one case of obligate syntrophy with all others (Fig. 4c, d). Though many organisms had balanced distributions of dependence (i.e., organism i enabled the growth of organism j in some cases, and organism j enabled the growth of i in others), the majority of such relationships were unidirectional. One striking example of this phenomenon is that of cyanobacteria and heterotrophic organisms, with Synechocystis depending frequently on other organisms. We also observed that E. coli, Bacillus subtilis, and S. cerevisiae, three species commonly used as model microbial organisms, were more frequently the giving organisms in cases of obligate syntrophy. These pairings not only shed light on the mechanisms behind interspecies codependencies, but may also serve as a map for assembling co-dependent synthetic communities stabilized by costless metabolic exchange.

Carbon sources exhibit cooperativity in promoting growth

In addition to characterizing the global space of in silico growth phenotypes, we examined how cooperativity of carbon sources could enhance growth capabilities in organism pairs. Drawing from techniques used to quantify epistasic interactions52, we defined the cooperativity index C of two carbon sources α and β as the difference between the number of simulations that resulted in growth from both carbon sources (gα,β) and the product of the number of simulations that resulted from single carbon sources (gα,gβ). These counts were normalized by the total number of simulations involving the specific pairing of carbon sources being analyzed (represented here by the combinatorial formula (( {begin{array}{*{20}{c}} N \ 2 end{array}} ))), as follows:

$$C^{upalpha ,upbeta } = frac{{g_{upalpha ,upbeta }}}{{left( {begin{array}{*{20}{c}} {N_{upalpha ,upbeta }} \ 2 end{array}} right)}} – left( {frac{{g_upalpha }}{{left( {begin{array}{*{20}{c}} {N_upalpha } \ 2 end{array}} right)}} times frac{{g_upbeta }}{{left( {begin{array}{*{20}{c}} {N_upbeta } \ 2 end{array}} right)}}} right).$$

(1)

This metric reflects the cooperative potential of each carbon source pair relative to that of each carbon source in isolation. Upon averaging a single carbon source over its cooperativity index, we obtain a relative degree to which a carbon source “depends” on another to sustain growth. By framing cooperativity in this context, we observed that simple sugars such as glucose and sucrose had relatively low cooperativity indices, that is, they were able to sustain growth efficiently on their own. In contrast, more complex molecules and dipeptides had higher average cooperativity indices, indicating they performed better in the presence of another carbon source. We grouped these average cooperativity indices through hierarchical clustering (Supplementary Fig. 8, Supplementary Table 7) and observed general clustering by carbon source type—especially with sugars and amino acids appearing in distinct groups. This analysis illustrates the nonlinear effects of adding additional nutrients to a minimal medium, underscoring the observed complex metabolite usage patterns in organism pairs.

Costless cross-feeding can offset competition for nutrients

Our analysis so far has examined the contexts in which a metabolite can be secreted costlessly, as well as the potential for these metabolites to promote growth. Additional insight about the relevance of these interactions can be obtained by comparing them to ecological expectations of cooperation and competition. Towards this goal, we defined six types of possible interactions: non-interaction, commensalism (unidirectional exchange), and mutualism (bidirectional exchange), each with or without competition for a primary carbon source (Fig. 5a). We chose to decouple competition for nutrients from exchange of secreted metabolites in order to more fully understand the degree to which the latter can promote organism coexistence despite resource scarcity. When analyzing our dataset under this framework, we found that competition for one or both carbon sources constituted the majority of all interactions (Fig. 5b), as previously observed experimentally53. However, these predicted competitive phenotypes were observed to frequently occur simultaneously with potentially beneficial interactions mediated by metabolic byproducts.

Fig. 5
Fig. 5

Distribution of metabolic interaction types. a Schematic representation of interaction types arising from costlessly secreted metabolites. Competition is defined as both organisms consuming the same carbon source. Commensalism is defined as a unidirectional exchange of one or more costlessly secreted metabolites, and mutualism is defined as a bidirectional exchange of one or more costlessly secreted metabolites. b Overall distributions of competitive and non-competitive interactions for oxic (out of 164,939 simulations that yielded pairwise growth) and anoxic conditions (out of 115,463 simulations that yielded pairwise growth). c Overall distributions of general interactions mediated by costless metabolites for oxic and anoxic conditions. These interactions at the level of secreted metabolites exist simultaneously with competition or no competition for a primary carbon source. d Organism-specific growth outcomes and interaction type distributions. Size of circles represent the relative number of environments in which an organism was able to grow out of 5774 in silico experiments with each partner. BS: B. subtilis, EC: E. coli, KP: K. pneumoniae, LL: L. lactis, ME: M. extorquens, PA: P. aeruginosa, PG: P. gingivalis, RS: R. sphaeroides, SB: S. boydii, SC: S. cerevisiae, SE: S. enterica, SO: S. oneidensis, SS: Synechocystis, ZM: Z. mobilis

Our modeling predicted bidirectional interactions to be far more common without oxygen than with oxygen (Fig. 5c). We obtained a more fine-grained perspective on costless metabolic interactions by considering the distributions of interaction types by species pairs (Fig. 5d). For example, the majority of pairings of M. extorquens with B. subtilis, E. coli, and K. pneumoniae exhibited commensal interactions (chiefly with M. extorquens receiving). In contrast, the distribution of interactions shifted toward mutualism when oxygen was made unavailable. These patterns were also mirrored in a majority of individual species pairings. As with the positive shift observed in the distributions of secreted metabolites (Fig. 2b, c), we attributed the increased prevalence of mutualistic interactions without oxygen to a greater availability of metabolic byproducts that contributed to reciprocity. To test this hypothesis, we performed a small subset of “hybrid” in silico experiments, where we analyzed the interactions that arose from one species being grown with oxygen and the other without oxygen. We studied the examples of E. coli with B. subtilis and S. enterica, whose pairwise simulations showed greater amounts of mutualistic interactions without oxygen (Fig. 6). These hybrid simulations demonstrated how an organism grown anoxically can provide a higher number of useful byproducts to its aerobic partner, leading to bidirectional interactions when both are grown without oxygen.

Fig. 6
Fig. 6

Interaction type distributions from hybrid oxic–anoxic simulations for two organism pairs. a E. coli with B. subtilis. b E. coli with S. enterica. Both hybrid simulations demonstrate that regardless of organism, availability of oxygen is a strong determiner of the potential for bidirectional exchange. When oxygen is not provided to an organism in these simulations, it tends to provide metabolites to its partner, resulting in an abundance of commensal interactions. These scenarios may act as a “stepping stone” toward fully anoxic environments, in which mutualistic interactions become more prevalent

We also analyzed the interaction type distributions of our habitat-specific simulation sets. Though direct comparison between oxic and anoxic conditions was not possible with these organisms, we found their interaction patterns to be largely comparable to those in our core set. This was particularly evident when comparing competition and exchange patterns between our core set grown with oxygen and the aerobic aquatic and soil organisms (Supplementary Fig. 7e, f, h, i). We nonetheless noticed a substantial difference between the interactions predicted in the gut-associated microbes and our 14 core organisms grown anoxically. In simulations of gut-associated organisms, we predicted a lower frequency of competition and mutualism (Supplementary Fig. 7g, j). We suspect that the widespread costless secretion of amino acids by Bifidobacterium adolescentis and Faecalibacterium prausnitzii may be skewing these distributions, as an abundance of valuable secreted byproducts may preclude their partner organism from competing for primary carbon sources and equally contributing to an exchange.

Costless secretions can produce stable interaction motifs

Lastly, we combined data generated by our algorithm with ecological network simulations to understand how the simultaneous competition for common nutrients and cooperation through costless metabolite exchange could jointly affect the stability of pairwise consortia. Using the general interaction types outlined previously (non-interaction, commensalism, and mutualism with and without competition), we first enumerated all possible interaction network motifs (Fig. 7a) and calculated the frequency with which each motif was observed in our simulation set (Fig. 7b). For non-interacting motifs, our simulations predicted an almost exclusive representation of relationships involving competition for a primary carbon source. The distribution between competitive and non-competitive motifs was more balanced for commensal and mutualistic interactions, showing a slight preference for interactions involving competition.

Fig. 7
Fig. 7

Interaction motif analysis and dynamical modeling of motif stability. a Schematic representation of specific motif types. Motifs are named according to three features: the interaction type (non-interacting, N; commensal, C; mutualistic, M), the number of carbon sources consumed by the pair (1–2), and competition for a primary carbon source (no competition, a; competition, b). Orange circles denote organisms, black dots denote primary carbon sources, and violet dots indicate any arbitrary number of costlessly shared metabolites. Arrows indicate direction of metabolite flow. b Frequency of specific motif types. Height of empty white bars indicate the total number of simulations that exhibited the general motif type (non-interacting, commensal, mutualistic). Colored bars within indicate the number of the specific motif type (N1a, N1b, and so on). c Stability space of motifs from dynamical chemostat modeling, as a function of the specific growth rates of the two organisms involved (GR1, GR2). Red indicates area of stable coculture

In order to simulate how these interactions could contribute to stable symbioses, we created a dynamical chemostat model of two arbitrary species consuming carbon sources and exchanging costless metabolites according to each motif type (see Methods, Supplementary Fig. 9). By varying the maximum specific growth rates (μmax) of each species from 0 to 1 h-1, we simulated the growth of the pair under each motif type for 500 h. If both species survived at the end of the simulation, we marked the motif type as stable at that combination of specific growth rates. We mapped the space of stable species pairs under each motif type, observing that competitive interactions generally had a reduced parameter space for enabling stability (Fig. 7c). Notably, though motif N1b was highly prevalent in the costless FBA simulation set, this motif represents competitive exclusion and cannot result in long-term stability. In contrast, though complete nutrient–organism orthogonality can yield stability over the whole space of parameters (N2a), this motif was not predicted to occur in the FBA simulations. An intermediate case between these two extremes (N2b) represents a balance between competition and independence with respect to external carbon source utilization: in this case, which frequently occurs in our dataset, stability is achievable only for a narrow set of specific growth rates.

Our models predicted a marked increase in stability when costless metabolite exchange was enabled. In motif C1a, for example, the rate of costless metabolite secretion from organism 1 is enough to sustain organism 2, even when the specific growth rate of organism 2 is greater. This nonintuitive space of stable solutions is the result of the effective growth rate of organism 2 being reduced such that its rate of byproduct consumption does not exceed the rate of secretion by organism 1. Nonetheless, competition for primary carbon sources leads to decreases in the space of possible stable solutions, as observed in motifs C1b and C2b. In motif C2b, both organisms are competing for a carbon source and organism 1 is providing one or more costless metabolites to organism 2. Our dynamical modeling showed that the specific growth rate of organism 1 must usually be greater than that of organism 2 in order for both species to be stable. When feedback is allowed to occur (mutualism), the potential for stability greatly increases across our parameter space, even in the presence of competition for carbon sources. These motifs, with their associated prevalence data and dynamical properties, can overall serve as an atlas for guiding the engineering of stable synthetic consortia built off of costless metabolic relationships.

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