Metagenomics has revealed hundreds of species in almost all microbiota. In a few well-studied cases, microbial communities have been observed to coordinate their metabolic fluxes. In principle, microbes can divide tasks to reap the benefits of specialization, as in human economies. However, the benefits and stability of an economy of microbial specialists are far from obvious. Here, we physically model the population dynamics of microbes that compete for steadily supplied resources. Importantly, we explicitly model the metabolic fluxes yielding cellular biomass production under the constraint of a limited enzyme budget. We find that population dynamics generally leads to the coexistence of different metabolic types. We establish that these microbial consortia act as cartels, whereby population dynamics pins down resource concentrations at values for which no other strategy can invade. Finally, we propose that at steady supply, cartels of competing strategies automatically yield maximum biomass, thereby achieving a collective optimum.DOI:http://dx.doi.org/10.7554/eLife.22644.001 Microbes are found in virtually every environment on Earth. Like other organisms, microbes grow by using enzymes to convert nutrients into proteins, DNA and other molecules that make up their cells. Together, these chemical transformations define the “metabolism” of a microbe.In any given environment, there is almost always a diverse variety of microbes living together. Different microbes in these communities will use different combinations of enzymes to exploit the available nutrients, and members of well-studied communities have been found to work together to make the most of the nutrient source. This is remarkable because one might expect competition between microbes to select for a single “best” microbe, rather than diverse communities.The economic concept of “division of labor” suggests that if microbes divide chemical tasks between each other, they will use the available resources more efficiently. The concept provides a possible explanation for metabolic diversity amongst microbes, yet it remains to be shown whether microbial communities actually benefit from a division of labor.Here, Taillefumier et al. used mathematical models to reveal that even in a uniform environment, metabolic competition generally leads to the steady coexistence of distinct microbes, collectively called a “consortium”. In a consortium, distinct microbes organize themselves to create a community-level metabolism that best exploits the nutrients present. The models showed that while growing, a consortium depletes the available pool of nutrients to such low levels that only members of the consortium can survive. The findings suggest that the benefit of metabolic diversity stems from the ability of a consortium to automatically deplete nutrients to levels at which no other microbes can invade.Taillefumier et al. propose that consortia that arise naturally under conditions where there is a steady supply of nutrients produce the maximum mass of microbes. Future experiments that analyze the impact of fluctuating nutrient supply may help us to understand the benefit of metabolic diversity in real-world microbial communities.DOI:http://dx.doi.org/10.7554/eLife.22644.002 Microbial diversity is ubiquitous. Every gram of soil or liter of seawater contains hundreds or more microbial species . In huma species . These d species . Shotgun species , and rec species . However species .There are also serious conceptual challenges to understanding diversity in metabolically competing microbial communities. For instance, the emergence of diversity in ‘consumer-resource’ models is limited by the competitive exclusion principle: at stationary state, the number of coexisting species cannot exceed the number of available resources . This prThe above conceptual challenges call for a physically-based model for competing metabolic strategies. However, classical consumer-resource models generally prescribe the rate of biomass production via phenomenological functions of the abundances of essential resources without explicit conservation of fluxes . Here, wConsidering that biomass (primarily protein ) resultsIn human economies, consortia that avoid competition by controlling prices are called ‘cartels’. At fixed building-block supply, we find that metabolic competition between microbes similarly leads to the emergence of a kind of cartel that controls resource availability via population dynamics. Specifically, cartels avoid competition by pinning down resource concentrations at values for which no other strategy can outcompete the cartel’s members. We employ optimization principles from transport-network theory to elucidate the structure of these cartels, relating the metabolic strategies of their constituent cell types to the hierarchy of external building-block availabilities. This analysis illustrates how division of labor among distinct metabolic types can be predicted from optimization principles. Finally, we propose that cartels also yield maximum biomass, constituting a microbial example of Adam Smith’s ‘invisible hand’ leading to collective optimal usage of resources. In this regard, microbial cartels improve on human cartels insofar as price-fixing by the latter generally leads to non-optimal use of resources.In this section, we present a model for the population dynamics of cell types metabolically competing for external resources see . ImportaAs cellular growth is primarily due to protein biosynthesis, we consider biomass production to result from the incorporation of building blocks (amino acids or amino acid precursors) into biologically functional units (proteins). Specifically, we assume that biomass production requires where In order to accumulate block iffusion . For simwhere Note that for given external building-block concentrations, a cell type is ‘optimal’, i.e. achieves the fastest growth rate, if no other cell type can achieve the same growth rate with a lower enzyme budget. If such a cell type existed, allocating the saved enzyme budget to importing more building blocks would yield a new cell type with higher internal building-block concentrations, and thereby faster growth.Our model considers a very simplified coarse-grained description of metabolic pathways. In reality, the details of biochemistry play an important role in determining metabolic efficiency. While our modeling framework can be easily generalized to realistic metabolic networks, capturing the complexity of real metabolic pathways is not the purpose of the present analysis, which aims at general principles. Indeed, because our model is anchored in flux conservation, we expect our results concerning the emergence and benefit of division of labor in microbial communities to hold independent of specific pathway biochemistry.We consider various cell types where the only nonlinearity is due to the growth function ll death . Conservwith cell-type-specific fluxeswhere The inverse of the cellular death rate which are coupled via the external concentrations. Note that the population dynamics is driven and dissipative: building blocks are constantly both supplied to and lost from the external media, while cell death leads to loss of building blocks because only a fraction of biomass is recycled rinciple .The population dynamics prescribed above can be simulated by standard numerical methods. If the number of distinct strategies initially introduced exceeds the number of resources, then over time some cell types will become ‘extinct’, i.e. In the following, we characterize the enzyme distributions In this section, we demonstrate the possibility of stable coexistence at steady supply rates by simulating competitive population dynamics subject to continual invasion by new metabolic variants. We consider that coexistence is stable when a population of distinct cell types can resist invasion by any other metabolic variants. In our simulations, cell types have distinct metabolic strategies defined by randomly chosen enzyme distributions First, we show that competitive population dynamics with the continual introduction of new cell types leads to a stationary state with fixed building-block availability and with fixed populations of distinct cell types. Second, we show that these final cell types achieve optimal growth given the fixed building-block supply rates. Third, we show that final, optimal populations generally consist of consortia of distinct cell types and that a consortium of identical cell types can emerge for different building-block supplies.We simulated the population dynamics To begin each simulation, the As external building-block concentrations approach their stationary values, virtually all newly introduced metabolic variants quickly become extinct because randomly chosen cell types are unable to compete with those already present. As a result, new cell types are continually introduced, for a total of more than Our numerical simulations indicate that competitive population dynamics subjected to continual invasion leads to the emergence of stationary states. To show that these stationary states emerge independently of how metabolic variants are introduced, we developed an iterative optimization algorithm that yields stationary states without relying on random sampling of cell types. Specifically, the algorithm iterates two optimization steps: First, given distinct cell types lgorithm  to compuCrucially, for fixed supply rates, this optimization algorithm yields steady-state cell types that are virtually identical to the final cell types obtained via simulations. Moreover, additional simulations show that when present among the initial types, optimal steady-state cell types resist invasion by the more than At steady supply, our numerical simulations together with numerical optimization reveal that competitive population dynamics leads to the stable emergence of optimal cell types. The metabolic strategies of these optimal cell types exhibit network structures that are directly related to external building-block availability. In fact, the building-block supply determines whether many distinct cell types can be jointly optimal, i.e. whether a consortium emerges. For instance, as shown in Can the same metabolic consortia emerge for different building block supplies? To answer this question, observe in In this section, we mathematically elucidate the emergence of microbial consortia at steady state and characterize the benefit of the division of labor in these consortia. Our analysis exploits the demonstrated convergence of competitive population dynamics toward a stationary state, which allows us to analytically derive the metabolic strategies of optimal cell types. The benefit of division of labor among these optimal cell types follows geometrical considerations in the space of stationary states.First, we exploit arguments from transport-network theory to systematically identify the metabolic classes of optimal cell types at steady state. Second, we elucidate the structure of microbial consortia by establishing which metabolic classes can be jointly optimal within a consortium. Third, we characterize the benefit of division of labor showing that consortia can act as cartels, whereby population dynamics pins down resource concentrations at values for which no other strategy can invade.A metabolic class is defined as the set of strategies that utilize the same enzymes, i.e. for which a particular subset of enzymes satisfies Can we specify the network structures of optimal metabolic classes using rigorous optimization principles? Exploiting the linearity of metabolic fluxes, we adapt arguments from transport-network theory  to achieUsing the above approach, we show that optimal metabolic networks process building blocks via non-overlapping trees of conversions , each trTo find the composition of consortia, we must identify the enzyme distributions At competitive stationary state, the maximum growth rate must equal the death rate Obtaining analytical expressions for optimal enzyme distributions proves intractable for a nonlinear growth-rate function such as cf. the intersection points in Can competitive population dynamics lead to these cartels for generic supply conditions? To answer this question, we compute the set of supply conditions compatible with the emergence of a cartel. We label a microbial cartel Microbial cartels only exist for specific external building-block concentrations  with respect to building-block concentrations, microbes must utilize their enzymes in the linear regime to be metabolically optimal: Because resources are depleted by competitive growth between metabolic classes, fluxes mediated by saturated enzymes do not limit growth. Cells can improve their growth rate by reallocating their enzyme budget from saturated enzymes to the unsaturated enzymes mediating growth-limiting linear fluxes. Moreover, independent of rates, production costs, and stoichiometries, optimal metabolic types must consist of non-overlapping trees of conversions. Indeed, the optimality of such metabolic networks, obtained from transport-network theory, only requires the linearity of metabolic fluxes with respect to enzyme concentrations. As a result, optimal metabolic types, as well as cartels, can still be enumerated. Interestingly, we discovered that distinct cartels can arise for very similar external building-block availabilities, and cartels can even merge under special conditions. In an extended model that includes fluctuations, e.g. in enzyme expression , we expeWhat relevance might our results have for real metabolic networks? Microbes regulate metabolic processes via complex networks with, e.g., multistep reaction chains and metabolic branch points . HoweverAbiotic and biotic processes controlling resource turnover in nutrient reservoirs, such as the ocean or soil sediments, operate on many different temporal and spatial scales . In our The spatial structure of microbial communities may also reflect the extracellular division of labor. Extracellular division of labor involves metabolic pathways with obligatory external reactions, i.e. with enzymes that are public goods. In a homogeneous environment, ‘cheating’ cell types that do not produce the public good are always at an advantage and their introduction causes the collapse of the entire population. In our framework, we expect producer cartels to spatially segregate from neighboring non-producer cartels .Temporally varying supply can also be addressed within our framework. For supply fluctuations on long timescales l cycles , while fl cycles . The efftuations . CharactMicrobes also adjust to fluctuating conditions by switching their metabolic type via gene regulation instead of relying on population dynamics. Within our framework, to consistently implement the optimal mix of metabolic strategies, the role of sensing and regulation is then primarily to determine the relevant ‘supply sector’ by assessing the relative abundance of various resources. Thus, in principle, division of labor within a single species can lead to cartels with distinct metabolic strategies associated with distinct phenotypic states. However, the persistence of cartels requires the coexistence of all cartel strategies, which within a single species could be facilitated by cell-to-cell communication (quorum sensing). We therefore anticipate that extension of our analysis to fluctuating supply conditions may provide insight into the design principles underlying regulation and signaling in microbial communities. In the interests of transparency, eLife includes the editorial decision letter and accompanying author responses. A lightly edited version of the letter sent to the authors after peer review is shown, indicating the most substantive concerns; minor comments are not usually included.Editors’ note: a previous version of this study was rejected after peer review, but the authors submitted for reconsideration. The first decision letter after peer review is shown below.]eLife. Your article has been reviewed by two peer reviewers, and the evaluation has been overseen by a Reviewing Editor and Arup Chakraborty as the Senior Editor. The following individual involved in review of your submission has agreed to reveal his identity: Eric D Kelsic (Reviewer #1).Thank you for submitting your work entitled "Bacterial cartels at steady supply" for consideration by eLife.Our decision has been reached after consultation between the reviewers. As you will see, one of the reviewers raised a number of significant concerns, many of which the other reviewer acknowledged to be important during subsequent discussion. Based on these discussions and the individual reviews below, we regret to inform you that your work will not be considered further for publication in Reviewer #1:The manuscript by Taillefumier et al. is well written and comprehensive, and I found the theory of bacterial cartels to be quite elegant and thought-provoking. The authors set out to understand microbial diversity by modeling communities of organisms that require a number of essential building blocks for growth. If the building blocks are present in the environment they may be imported into cells, or cells may choose to obtain the building block by enzymatically converting from one type to another. The authors model the growth potential of different strategies under the constraint of a fixed enzyme budget. Through a number of simplifying assumptions and linearizations the authors identify optimal metabolic classes and finally show that sets of organisms, termed "cartels", can optimally consume resources and prevent other species from invading. While such communities only coexist at fixed points within the space of external resource concentrations, the authors beautifully show that these points are attractors for regions within the space of supply rates, and thus cartels will frequently emerge when communities are continually challenged with organisms exhibiting various metabolic strategies.eLife.The cartel theory makes significant progress toward understanding the diversity of microbial communities. Importantly, the work shifts the emphasis away from the number of (rather abstract) environmental resources and focuses instead on the building blocks that are essential for growth and the various strategies by which to obtain these building blocks. I find this setup more conceptually appealing. I believe that the manuscript will be of broad general interest and it would be great to see it published in I have no major concerns. The manuscript is already highly polished and could be published without significant revisions.Reviewer #2:The manuscript by Wingreen and co-workers examines the structure of bacterial communities that consist of different metabolic types, under a non-trivial model that involves feedbacks from external metabolite concentrations and internal metabolic conversions and fluxes, subject to specific enzyme availability, onto the growth rates. Overall, this is an important subject for which general theoretical results could be useful for guiding experiments as well as introducing new ideas for analysis of bacterial communities.extremely poor job of explaining the main conclusions. One can follow the main assumptions of the model, but once the notions of consortia and cartels are introduced, it requires a good deal of work to follow which features of the model have been preserved and which ones have been conveniently thrown out the window under some new assumption that enables analysis. Over the course of the manuscript, several such assumptions are made, which effectively change the underlying model, while the key notions of consortia and cartels are defined non-rigorously and in a model-dependent manner.Unfortunately, the text does an The section entitled Model is the clearest section of the paper. The authors make many modeling assumptions here, some of which are questionable (see below), but these are all explained clearly.The Results section begins with Numerical Simulations, which motivates the rest of the manuscript. The authors give too few details on how extensive their simulations are. How reproducible are they? How long have they run them? How complex a space of strategies was explored?A) A key point at this stage of the manuscript (i.e. Results) and at the end of the Model Section is the statement that the authors are interested only in the structure of the equilibrium attained, not in the dynamics. They state: "Eventually, at long times, the surviving population will consist entirely of optimal cell types and will no longer change. It is this final population that concerns us; we only simulate metabolic competition to gain insight into the final optimized population, which is independent of the specific dynamics of the simulation."This statement appears to be some kind of hope since it is neither (a) proven nor (b) demonstrated by extensive numerical simulations. The simulations assume that new types are only added once other types have gone extinct , which is a pretty big assumption regarding "specific dynamics of the simulation" and which, in fact, guarantees that once a community consists of types that are not going extinct it won't have to worry about new types coming in. Indeed, the structures that are later called "cartels" in this manuscript are automatically stable under the given dynamics, due to the fact that avoidance of extinction necessarily excludes competition by new types; such dynamics are intrinsically 'cartel-friendly'. Under different dynamics, for example where new types appear at random times, or are formed by mutation from existing types, there would be no such guarantee, and it is therefore not at all clear that the final population structure  would not depend on the specific dynamics.In fact, B) The entire analytical treatment of the manuscript is predicated on the assumption that the external concentrations Thus, at this point in the text, the authors have subtly shifted our attention away from the dynamics they initially presented, to some new scenario, in which they search for a certain type of optimum . They motivated this problem in the context of a dynamical system, but they have failed to demonstrate that the dynamics converge to their optimum; or more precisely, to give a characterization of conditions  under which their optimum is achieved. Therefore, I recommend that they submit this paper elsewhere, e.g. to a graph theory or combinatorial optimization journal, where their more rigorous results will be properly assessed by mathematicians. Biologists who read Other concerns:ib variables that were introduced initially. This is another example of the authors presenting a much more general model than the one they ultimately analyze. For the poor reader who has made it through the Model section, but is not technically proficient to follow the derivations where the extra assumptions are buried (such as in the last paragraph of the subsection “Structure of consortia”), this can end up being misleading.C) The assumption to study the "minimum model" in the last paragraph of the subsection “Structure of consortia” is quite strong. For example, the growth rate no longer depends on the ib is important, since different bacteria may have different composition, at least with regard to a subset of key building blocks, and one would like to know if this impacts the metabolic specialization across the community to any extent. Another place where this seems to be relevant is in igb at the end of the equation corresponds to the assumption, stated earlier, that building blocks are consumed at a rate proportional to their concentration in biomass, i.e. ib. This is necessary for the steady-state growth, and will be achieved automatically at the level of the bulk population, but at the level of enzymatic activity inside cells, one expects something like -igc. This point should be discussed, and the relevant extra assumptions that are being made here need to be pointed out.D) On the technical level, the question of the E) In the Discussion, the authors state "In particular, cartels maintain fixed external resource concentrations by adjusting their populations to compensate for changes in supply." This is a question of dynamics, again, but dynamics have not been addressed in the analysis. Critically, the statement here is that if the external resource changes , the subpopulation sizes that contribute to the cartel will adjust such that the external resource concentrations will be maintained. Since the change of subpopulation size is what appears to be controlling the resource concentrations in such cases, the authors appear to be violating their own "separation of timescales" assumption which they made: "since the lifetime of a cell is much larger than the timescales associated with metabolic processes… separation of timescales justifies steady-state approximation for the fast variables: F) Consortia and Cartels are never rigorously defined before they are used. The terms are typically used first and defined later. For example, Cartels are actually defined only in Even after reading these sections multiple times, it seems that the authors are missing something in their verbal definitions. There is no mention of "co-optimality" in their final definition: "Cartels are defined as consortia of at least as many distinct optimal cell types – each with a fixed metabolic strategy – as there are shared resources". The definition really should include the fact that all of these types contribute to the same optimum.It is striking that the authors neglected to give a rigorous mathematical definition of either Cartel or Consortia, for example in terms of a big set C = {σ: condition is true}.Additional points:parallel pathways.G) The derivation of the growth rate function, ij, could in reality involve multiple reactants, for example any metabolic reaction of the form A + B <-> C, and these would introduce non-linearities that are not captured by the equations.H) Interconversion reactions, represented by ΚI) Taking the death rate to be independent of the phenotype and the external conditions seems to be a very strong assumption J) One could not tell in the last paragraph of the subsection “Competitive population dynamics” whether the simulation captures finite population size effects or not, i.e. demographic fluctuations of size 1 / N.K) The numerical simulations do not involve mutation, in that new types are introduced randomly rather than as mutated version of existing types. One expects that mutational dynamics could have different stability criteria. Also, if a random type is introduced, presumably it arrives from outside the community, and therefore why should it be introduced in small numbers? Is that a reasonable assumption for bacteria? It doesn't seem intuitive.L) What happens to a cartel if one member is removed? Does it matter which member is removed?M) The word cartel has strong negative associations (i.e. drug cartels), and even at a more basic level the use of this word in the manuscript is fundamentally inaccurate, since the economic definition of a cartel is based on an agreement to control prices, instead of an optimization principle. I am not sure why the authors want to go in this direction.[Editors’ note: what now follows is the decision letter after the authors submitted for further consideration.]eLife. Your revised article has been favorably evaluated by Arup Chakraborty as the Senior Editor, Carl Bergstrom as the Reviewing Editor (Carl Bergstrom) and two reviewers.Thank you for resubmitting your work entitled "Microbial consortia at steady supply" for further consideration at The manuscript has been greatly improved and both referees enthusiastically recommend publication.Reviewer #1:In "Microbial consortia at steady supply", the authors consider a population model in which microorganisms exposed to a flux of metabolites follow different strategies concerning which metabolites to import and which to produce through conversion. They show that populations evolve to form cartels, which prevent invasion from other strategies and keep external resources fixed. Overall, I think the authors do a good and extensive job of demonstrating their results. I recommend this paper for publication.Reviewer #2:Taillefumier et al. present an elegant and compelling theory of microbial coexistence driven by diverse strategies for import and synthesis of essential metabolic building blocks. I found the revised manuscript to be improved over the original submission, making several changes that facilitated communication of the main results. In particular, the elaborated explanation of the dynamics of the simulation better clarifies that communities are converging toward optimal consortia (rather than being mistaken for oscillatory dynamics). Additionally, I found it reassuring that the new results using gradient-based optimization of communities arrived at similar results as the simulations that were continuously challenged with randomly sampled species types. This resolves one of my main concerns from the original manuscript, and shows that the authors' theory of optimal cartels captures essential aspects of the simulations despite extensive simplifications. Finally, the earlier definition of cartels in the Introduction aided understanding, and multiple revisions in the Discussion helped for putting the theory in context.eLife where it can reach a broad biological audience.This is a high-quality work in theoretical ecology that makes significant progress toward the major problem of understanding microbial diversity, and I support its publication in  [Editors’ note: the author responses to the first round of peer review follow.]Reviewer #2:The manuscript by Wingreen and co-workers examines the structure of bacterial communities that consist of different metabolic types, under a non-trivial model that involves feedbacks from external metabolite concentrations and internal metabolic conversions and fluxes, subject to specific enzyme availability, onto the growth rates. Overall, this is an important subject for which general theoretical results could be useful for guiding experiments as well as introducing new ideas for analysis of bacterial communities.Unfortunately, the text does an extremely poor job of explaining the main conclusions. One can follow the main assumptions of the model, but once the notions of consortia and cartels are introduced, it requires a good deal of work to follow which features of the model have been preserved and which ones have been conveniently thrown out the window under some new assumption that enables analysis. Over the course of the manuscript, several such assumptions are made, which effectively change the underlying model, while the key notions of consortia and cartels are defined non-rigorously and in a model-dependent manner.The section entitled Model is the clearest section of the paper. The authors make many modeling assumptions here, some of which are questionable (see below), but these are all explained clearly.The Results section begins with Numerical Simulations, which motivates the rest of the manuscript. The authors give too few details on how extensive their simulations are. How reproducible are they? How long have they run them? How complex a space of strategies was explored?We regret the lack of clarity in our presentation. As we understand it, at the root of virtually all the reviewer’s objections is a concern that metabolic competition between different metabolic types may not lead to stable stationary states. This concern is the consequence of a miscommunication about the methodology and results of our simulations of competitive bacterial dynamics. This miscommunication led the reviewer to think that the population dynamics of metabolic types can exhibit “oscillations”. However, population oscillations never happen in our simulations: there are only new strategies sweeping existing ones. We hope to dispel the concern about the stability of the dynamics by offering detailed responses to the reviewer’s objections (A) and (B). We also have substantially revised our manuscript for greater clarity and to avoid any other unfortunate miscommunications. In particular, we added two new figures and revised the original figure at the root of the confusion.A) A key point at this stage of the manuscript (i.e. Results) and at the end of the Model Section is the statement that the authors are interested only in the structure of the equilibrium attained, not in the dynamics. They state: "Eventually, at long times, the surviving population will consist entirely of optimal cell types and will no longer change. It is this final population that concerns us; we only simulate metabolic competition to gain insight into the final optimized population, which is independent of the specific dynamics of the simulation."This statement appears to be some kind of hope since it is neither (a) proven nor (b) demonstrated by extensive numerical simulations. The simulations assume that new types are only added once other types have gone extinct , which is a pretty big assumption regarding "specific dynamics of the simulation" and which, in fact, guarantees that once a community consists of types that are not going extinct it won't have to worry about new types coming in. Indeed, the structures that are later called "cartels" in this manuscript are automatically stable under the given dynamics, due to the fact that avoidance of extinction necessarily excludes competition by new types; such dynamics are intrinsically 'cartel-friendly'. Under different dynamics, for example where new types appear at random times, or are formed by mutation from existing types, there would be no such guarantee, and it is therefore not at all clear that the final population structure  would not depend on the specific dynamics.In fact, 1 = 11, s2 = 9 > s3 = 0, starting from 24 different initial conditions for each run (i.e. different metabolic strategies). The volume of the colony Ω is chosen so that the carrying capacity is ≈ V/v = 100, 000 cells. Each simulation is run for 108 time steps, which represents on the order of 105 generations. In each case, the population of bacteria quickly reaches carrying capacity, at which point the availability of building blocks plumets to low values, and metabolic competition begins in earnest. At each time step, we simulate 24 different strategies. The simulation of Although we did not include an extensive account of our simulations in the original submission, we did perform exhaustive simulations, and indeed had thoroughly tested all these important points raised by the reviewer. In the revised manuscript, we show that the simulations of metabolic competition between microbes consistently lead to stationary states populated by the same metabolic types. In 1) The external building-block concentrations converge toward cartel-specific values.In 2) Competition between metabolic types leads to stable selection of metabolic types.After metabolic competition begins in earnest, building-block concentrations approach their theoretically optimal values and virtually all newly introduced variants quickly be- come extinct. Only metabolic strategies that improve on the already present, nearly optimal strategies can persist. When a newly introduced type does successfully invade the population, it always belongs to an optimal class and replaces the existing population of that same class. For instance, in the top panel of 3) Existing types are constantly competing with newly introduced variants.σn < 0.9999. Upon extinction, a new type is introduced at σn = 1. The overwhelming majority of these new types do not invade the already present types and quickly become extinct, leading to the introduction of new variants. As a result of this scheme, new metabolic strategies are constantly introduced, representing a total of more than 109 different introduced strategies during each run.While three types may coexist for extended periods according to the competitive exclusion principle, the 21 other types have populations nσ that decay exponentially until extinction, i.e. until 4) The space of metabolic strategies is extensively sampled.E. This sampling scheme revealed that competition consistently selected for types for which certain enzymes were negligible, approximating the theoretically predicted metabolic types (belonging to “metabolic classes” for which the abundance of certain enzymes is zero). Therefore, in subsequent simulations, including the ones presented here, new strategies were sampled according to a new scheme: four strategies were still uniformly sampled from the simplex Ʃ α + Ʃ κ = E, but two strategies were sampled from each of the 10 possible optimal metabolic classes. Whenever a strategy goes extinct, we replace it with a strategy sampled from the same metabolic class. We use this scheme because drawing a type from an optimal class has probability zero when one uses the naive uniform sampling of the simplex Ʃ α + Ʃ κ = E. The observed persistence of the expected optimal types confirmed our theoretical analysis.In a first set of simulations we performed, new strategies were uniformly sampled from the simplex Ʃ α + Ʃ κ = We hope that the above points will dispel the reviewer’s concerns about our methodology used to simulate competitive bacterial dynamics.B) The entire analytical treatment of the manuscript is predicated on the assumption that the external concentrations Thus, at this point in the text, the authors have subtly shifted our attention away from the dynamics they initially presented, to some new scenario, in which they search for a certain type of optimum . They motivated this problem in the context of a dynamical system, but they have failed to demonstrate that the dynamics converge to their optimum; or more precisely, to give a characterization of conditions  under which their optimum is achieved. Therefore, I recommend that they submit this paper elsewhere, e.g. to a graph theory or combinatorial optimization journal, where their more rigorous results will be properly assessed by mathematicians. Biologists who read eLife will not understand the range of applicability, or lack thereof, of these results. I certainly do not.We addressed the reviewer’s concern about the stability of the population dynamics in response to point (A). We believe that the reviewer’s concern was due to a miscommunication and apologize for the confusion. In all of our extensive simulations, competitive dynamics converge to a final state where both the resource external concentrations and the cell-type populations are constant. To further address the reviewer’s concern, we numerically confirmed that the final cell types obtained via competitive dynamics achieve the optimal cell growth given resource availabilities. As explained in the expanded section “Numerical results”, we designed an iterative optimization algorithm that yields steady-state optimal cell types with high accuracy. The thus-obtained cell types are guaranteed to achieve optimal growth for the given external resource concentrations by design of the algorithm and are virtually identical to the final cell types obtained via competitive population dynamics. We illustrate the convergence of surviving cell types toward the optimal types in Other concerns:i variables that were introduced initially. This is another example of the authors presenting a much more general model than the one they ultimately analyze. For the poor reader who has made it through the Model section, but is not technically proficient to follow the derivations where the extra assumptions are buried (such as in the last paragraph of the subsection 2Structure of consortia”), this can end up being misleading.C) The assumption to study the "minimum model" in the last paragraph of the subsection 2Structure of consortia” is quite strong. For example, the growth rate no longer depends on the bib. While we presented the simple case of ib= 1 in the main text, the optimization has been carried out for arbitrary ib in the Supporting Information. Changing the values of ib shifts the hypersurfaces of steady-state external concentrations, but cartels always emerge and are always made of the optimal types identified in our analysis. We show in Supporting Information that the results derived for the minimum model rigorously hold for any growth functions with reasonable properties, i.e. functions that are increasing with internal resources and that are limited by the relatively least abundant resource. Thus, our main conclusions are not dependent on the details of the model.The main conclusions of our paper concern the generic emergence of cartels and the benefit that division of labor provides to cartels’ members. This conclusion is independent of the growth model considered or the values of the i is important, since different bacteria may have different composition, at least with regard to a subset of key building blocks, and one would like to know if this impacts the metabolic specialization across the community to any extent. Another place where this seems to be relevant is in i at the end of the equation corresponds to the assumption, stated earlier, that building blocks are consumed at a rate proportional to their concentration in biomass, i.e. bi. This is necessary for the steady-state growth, and will be achieved automatically at the level of the bulk population, but at the level of enzymatic activity inside cells, one expects something like -gci. This point should be discussed, and the relevant extra assumptions that are being made here need to be pointed out.D) On the technical level, the question of the bi−gcin our model. In Supporting Information, we justify why these terms are negligible compared with the production/consumption fluxes within the cells. Moreover, we check that neglecting such dilution terms is compatible with overall building-block conservation.As the reviewer suggests, we have considered dilution terms E) In the Discussion, the authors state "In particular, cartels maintain fixed external resource concentrations by adjusting their populations to compensate for changes in supply." This is a question of dynamics, again, but dynamics have not been addressed in the analysis. Critically, the statement here is that if the external resource changes , the subpopulation sizes that contribute to the cartel will adjust such that the external resource concentrations will be maintained. Since the change of subpopulation size is what appears to be controlling the resource concentrations in such cases, the authors appear to be violating their own "separation of timescales" assumption which they made: "since the lifetime of a cell is much larger than the timescales associated with metabolic processes… separation of timescales justifies steady-state approximation for the fast variables:In microbial communities, metabolic processes generally have a much faster kinetic rate than the rate of cellular growth (≍δ). As a result, metabolic fluxes quickly equilibrate, which means that internal and external building-block concentrations are stationary on the slow timescale 1/δ, i.e. F) Consortia and Cartels are never rigorously defined before they are used. The terms are typically used first and defined later. For example, Cartels are actually defined only in Even after reading these sections multiple times, it seems that the authors are missing something in their verbal definitions. There is no mention of "co-optimality" in their final definition: "Cartels are defined as consortia of at least as many distinct optimal cell types – each with a fixed metabolic strategy – as there are shared resources". The definition really should include the fact that all of these types contribute to the same optimum.It is striking that the authors neglected to give a rigorous mathematical definition of either Cartel or Consortia, for example in terms of a big set C = {σ: condition is true}.We apologize for the lack of clarity in the definition of “consortia” and “cartels”. We have added a paragraph at the end of the Model section where “consortia” and “cartels” are both clearly defined and where the co-optimality of the final cell types is mentioned.Additional points:G) The derivation of the growth rate function, We agree that other biomass constituents such as RNA can be formed along different parallel pathways. However, proteins represents ∼ 60 − 70% of the dry biomass of prokaryotes  and ∼ 50% of the dry biomass of eukaryotes . Moreover, metabolic pathways are universally mediated by protein enzymes. Accordingly, our model primarily equates the rate of biomass production with the rate of protein biosynthesis.ij, could in reality involve multiple reactants, for example any metabolic reaction of the form A + B <-> C, and these would introduce non-linearities that are not captured by the equations.H) Interconversion reactions, represented by ΚWe agree that considering reactions involving multiple reactants is an important question. In particular, a central issue to address is whether the nonlinearities of the corresponding reaction fluxes can impact the stability of the population dynamics. Unfortunately, studying the general effect of such nonlinearities is a very difficult problem which is beyond the scope of the present paper.I) Taking the death rate to be independent of the phenotype and the external conditions seems to be a very strong assumption In our study, we assume the death rate δ to be a “failure rate” that is independent of the phenotype or the external conditions. Such an assumption would of course be very accurate in a chemostat environment, where cells are lost at a fixed dilution rate. However, we argue more generally that taking δ as an independent constant is not necessarily a strong assumption . Changing the values of δ for each cell type only shifts the hypersurface of steady-state concentrations J) One could not tell in the last paragraph of the subsection “Competitive population dynamics” whether the simulation captures finite population size effects or not, i.e. demographic fluctuations of size 1 / N.Our simulations do not capture finite population size effects. Our analysis is primarily concerned with the emergence of division of labor in metabolically competing species. We are considering resource supplies for which relatively large population of cells emerge.K) The numerical simulations do not involve mutation, in that new types are introduced randomly rather than as mutated version of existing types. One expects that mutational dynamics could have different stability criteria. Also, if a random type is introduced, presumably it arrives from outside the community, and therefore why should it be introduced in small numbers? Is that a reasonable assumption for bacteria? It doesn't seem intuitive.Considering mutated versions rather than random variants does not change the results of our analysis as long as the set of possible cell types remains the same. Extensive simulations  show that mutational population dynamics are also unconditionally stable.Introducing random variants or mutated versions in larger numbers does not change the results of our analysis either. When a new strategy is introduced in larger numbers, the change in consumption and leakage by the population may temporarily perturb the external concentrations of building blocks. However, the ensuing population dynamics ultimately converges to the same population steady state as when a new strategy is introduced in small numbers.L) What happens to a cartel if one member is removed? Does it matter which member is removed?The complete removal of a member of a cartel clearly modifies the steady state of the population dynamics. Suppose we consider a cartel emerging for three building blocks with well-ordered supply rates. Removing the pure-converter strategy causes the external concentrations of the two least abundant building blocks to decrease, yielding a decrease of both remaining cell-type populations, and potentially their extinction. Removing the mixed strategy causes the most abundant external concentrations to increase but the least abundant building block to decrease, yielding an increase of the pure-converter population and a decrease of the pure-importer population, and potentially its extinction. Removing the pure-importer strategy causes the external concentrations of the two least abundant building blocks to increase, yielding an increase of both remaining strategies. However, in all cases, the overall cell population will decrease.Although interesting, we believe that the study of such removal effects is beyond the scope of our analysis. Moreover, it is hard to justify the meaning of such removals from a biological standpoint, since even after a catastrophic event that eliminated a species (e.g. phage infection), new species would likely quickly establish in the available niche.M) The word cartel has strong negative associations (i.e. drug cartels), and even at a more basic level the use of this word in the manuscript is fundamentally inaccurate, since the economic definition of a cartel is based on an agreement to control prices, instead of an optimization principle. I am not sure why the authors want to go in this direction.We note the reviewer’s comment and agree that the concept of microbial cartel is not a literal transposition of the economics concept. In fact, we only use the word “cartel” as a helpful analogy because we believe that this concept captures the idea that the benefit of diversity stems from the ability to collectively control resource availabilities. We followed the reviewer’s recommendation and now clarify that we use the word “cartel” only by analogy and specify to which extent this analogy applies. We also changed the title of the manuscript to “Microbial consortia at steady supply”. Finally, we made sure that the concept of cartel is not negatively connoted in the main text, stressing that microbial cartels achieve a collective optimum in term of biomass yield.[Editors’ note: the author responses to the re-review follow.]The manuscript has been greatly improved and both referees enthusiastically recommend publication.Reviewer #1:In "Microbial consortia at steady supply", the authors consider a population model in which microorganisms exposed to a flux of metabolites follow different strategies concerning which metabolites to import and which to produce through conversion. They show that populations evolve to form cartels, which prevent invasion from other strategies and keep external resources fixed. Overall, I think the authors do a good and extensive job of demonstrating their results. I recommend this paper for publication.Reviewer #2:Taillefumier et al. present an elegant and compelling theory of microbial coexistence driven by diverse strategies for import and synthesis of essential metabolic building blocks. I found the revised manuscript to be improved over the original submission, making several changes that facilitated communication of the main results. In particular, the elaborated explanation of the dynamics of the simulation better clarifies that communities are converging toward optimal consortia (rather than being mistaken for oscillatory dynamics). Additionally, I found it reassuring that the new results using gradient-based optimization of communities arrived at similar results as the simulations that were continuously challenged with randomly sampled species types. This resolves one of my main concerns from the original manuscript, and shows that the authors' theory of optimal cartels captures essential aspects of the simulations despite extensive simplifications. Finally, the earlier definition of cartels in the Introduction aided understanding, and multiple revisions in the Discussion helped for putting the theory in context.This is a high-quality work in theoretical ecology that makes significant progress toward the major problem of understanding microbial diversity, and I support its publication in eLife where it can reach a broad biological audience.We made two minor modifications to the manuscript in order to address the reviewers’ minor points: i) We added a sentence in the Model section stating that our growth model is inspired from protein elongation whereby building blocks (amino acids) are sequentially incorporated into biomass (protein). ii) We corrected the erroneously labeled time axes in panels B and C of


Bacillus subtilis has already been proven to possess significant importance for the food industry and have become one of the most widely used riboflavin-producing strains. In the practical fermentation processes, a sharp decrease in riboflavin production is encountered along with a decrease in the dissolved oxygen (DO) tension. Influence of this oxygen availability on riboflavin biosynthesis through carbon central metabolic pathways in B. subtilis is unknown so far. Therefore the unveiled effective metabolic pathways were still an unaccomplished task till present research work.Riboflavin, an intermediate of primary metabolism, is one kind of important food additive with high economic value. The microbial cell factory B. subtilis grown under different dissolved oxygen tensions were studied by integrating 13C metabolic flux analysis, metabolomics and transcriptomics. It was revealed that the glucose metabolic flux through pentose phosphate (PP) pathway was lower as being confirmed by smaller pool sizes of metabolites in PP pathway and lower expression amount of ykgB at transcriptional level. The latter encodes 6-phosphogluconolactonase (6-PGL) under low DO tension. In response to low DO tension in broth, the glucose metabolic flux through Embden–Meyerhof–Parnas (EMP) pathway was higher and the gene, alsS, encoding for acetolactate synthase was significantly activated that may result due to lower ATP concentration and higher NADH/NAD+ ratio. Moreover, ResE, a membrane-anchored protein that is capable of oxygen regulated phosphorylase activity, and ResD, a regulatory protein that can be phosphorylated and dephosphorylated by ResE, were considered as DO tension sensor and transcriptional regulator respectively.In this paper, the microscopic regulation mechanisms of 13C metabolic flux analysis and metabolomics analysis provides a comprehensive understanding of biosynthesized riboflavin’s regulatory mechanisms in B. subtilis grown under different dissolved oxygen tension conditions. The two-component system, ResD–ResE, was considered as the signal receiver of DO tension and gene regulator that led to differences between biomass and riboflavin production after triggering the shifts in gene expression, metabolic flux distributions and metabolite pool sizes.This study shows that integration of transcriptomics, The online version of this article (doi:10.1186/s12934-017-0764-z) contains supplementary material, which is available to authorized users. It is a precursor of flavin adenine dinucleotide (FAD) and flavin mononucleotide (FMN), which are cofactors involved in several important metabolic reactions. Nutritional deficiency of riboflavin can cause a variety of fundamental and clinical abnormalities from mitochondrial dysfunction and hemolytic anemia to growth retardation and neurological disorders -glucose and 50% [U-13C]-glucose. The labeling experiments were performed in two independent cultivation bioreactors.13C-labeling experiments for analysis of mass isotopomer distributions (MID) of intracellular free amino acids and rapidly mixed with 15 mL pre-cooled quenching reagent . The cells were washed twice with deionized water after 5 min centrifugation at 4 °C, 7500 rpm. Then the intracellular free amino acids were extracted with 75% (v/v) ethanol solution at 95 °C for 4 min. The supernatant was evaporated through a rotary evaporator at −101 kPa (relative pressure) before determination by gas chromatography–mass spectrometry (GC–MS).5 mL broth was taken during the B. subtilis with compartments and reversible reactions was constructed based on the models as previously described [13C-metabolic flux analysis (MFA) fitting results were subjected to a χ2-statistical test. The estimated fluxes were considered acceptable only when the obtained minimal weighted residual was below the χ2 at a 95% confidence level. At convergence, accurate 68 and 95% confidence intervals were computed for all estimated fluxes by evaluating the sensitivity of the minimized SSR to flux variations.A stoichiometric model of escribed . To deteTo study the gene expressing distinctions between the high DO level mode and the low DO level mode, during whole fermentation process, three sampling points were set in each culture mode. The supernatant was removed after centrifugation at 4 °C, 4000 rpm for 5 min. Then the cell pellets were stored at −80 °C till analysis. The extraction of mRNA, reverse transcription and sequencing were done by Shanghai Majorbio Bio-Pharm Technology Co., Ltd .A 5 mL broth was taken and the supernatant was removed by centrifugation at 4000 rpm for 5 min at 4 °C. Then cDNA samples were prepared by RNA extraction and reverse transcription according to RNAiso Plus  and PrimeScript™RT reagent Kit , separately. For real-time PCR, 2 μL cDNA sample, 0.6 μL forward primer, 0.6 μL reverse primer, 6.8 μL sterile deionized water and 10 μL SYBR premix dimer eraser (2×) were mixed for one reaction and the reaction was performed in a CFX96 Touch™ Real-Time PCR Detection System . Primers for each gene were listed in Table B. subtilis cells cultivated under two different DO tension conditions was characterized. At first 24 h, it showed a similar performance in both batches because of the controlled DO levels above 30%. After 24 h, the DO tension was adjusted and phenotypical performance of these two bioprocesses became diverged  in Batch H  software package v1.5) was used to determine metabolic fluxes based on kinetic parameters Table , the iso.5 was usons Fig. .Table 3CObvious differences were found in the central carbon fluxes between two batches. The relative flux  through PP pathway was higher in Batch H (64.85%) than that in Batch L (50.79%). PP pathway offered precursors for nucleotide and amino acid biosynthesis which are essential for the cell growth . FurtherBased on the metabolic flux distribution, the generation rate of NAD(P)H from different pathways and ATP production by substrate level phosphorylation can be calculated Fig. . By settIt can be speculated based on MFA that in Batch L, lower flux through PP pathway led to lower specific growth rate and riboflavin production rate. Higher flux through EMP pathway and TCA cycle may cause higher NADH generating rate but lower ATP producing rate because of deficiency of electron receptors like oxygen. These results can be explained by following metabolomics and transcriptomics analysis.B. subtilis showed obvious differences between two batches  were highlighted as they encoded enzymes that catalyze pathways for riboflavin generation but were inhibited in the later phase of fermentation process. These genes may be potential genetically modified targets to improve the riboflavin biosynthesis.In the clustering of all genes, it is obvious that all genes were divided into 4 main clusters Fig. . The genB. subtilis grown under low dissolved oxygen tension stress, the differential expression analysis of genes between the same phases under two conditions was performed. It was found that there were 224 and 169 differential expression between two conditions in the second and third phase respectively; and 53 genes were overlapped. Interactive pathways explorer 2 (http://pathways.embl.de/iPath2.cgi#) was used to show the results of the analysis  was up-regulated under low oxygen availability. This can be explained that this reaction was proved to be propitious to stabilize the ratio of NAD+/NADH and maintain the redox balance [B. subtilis [To study the regulatory mechanism of  balance . In addisubtilis , 20, wasmdh, sdhA, ykgB and sucD) were picked because obvious differences lied between the two batches. To verify these differences showed by RNA-seq, qRT-PCR was performed and a consistent result was gained  may be responsible for lower flux through PP pathway in Batch L than that in Batch H.To explain the results gotten from MFA and metabolomics, the genes involved in central carbon metabolism were further studied. Four genes  were highly up regulated. This agreed with Vetter and Schlievert [B. subtilis used nitrogen as a final electron acceptor while growing anaerobically. Besides, the expression of two-component system regulator ResD–ResE that can regulate nitrate reductases was also up-regulated significantly in Batch L, indicating that some of the response reactions were regulated by this system. This two-component system has been proved to be implicated in the global regulation of aerobic and anaerobic respiration of B. subtilis and can sense the extracellular oxygen concentration and regulate genes like narK, J, I, H, G and fnr [fnr encodes a global transcriptional regulator FNR which can trigger several transcriptional responses to adapt low oxygen tension. In some studies, FNR showed ability to regulate the central carbon metabolism [ykgB, alsS, sucC, sdhA and mdh while B. subtilis grew under low DO concentration. ResE is a sensor kinase which has histidine kinase activity and phosphatase activity. ResE can phosphorylate ResD as a histidine kinase and dephosphorylate ResD only when the oxygen tension was low. In summary, ResE receive the signal of oxygen tension then deliver to ResD, making it phosphorylated or dephosphorylated. These different status of ResD subsequently lead to different gene expression pattern and metabolic flux distribution  of intracellular free amino acids.Additional file 2. Results of iPath analysis.


Cinara cedri. Using in-silico computed physicochemical properties of metabolites of this and other biosynthetic pathways, we verified that the splitting point of the pathway corresponds to the most permeable intermediate.Bacterial communities may display metabolic complementation, in which different members of the association partially contribute to the same biosynthetic pathway. In this way, the end product of the pathway is synthesized by the community as a whole. However, the emergence and the benefits of such complementation are poorly understood. Herein, we present a simple model to analyze the metabolic interactions among bacteria, including the host in the case of endosymbiotic bacteria. The model considers two cell populations, with both cell types encoding for the same linear biosynthetic pathway. We have found that, for metabolic complementation to emerge as an optimal strategy, both product inhibition and large permeabilities are needed. In the light of these results, we then consider the patterns found in the case of tryptophan biosynthesis in the endosymbiont consortium hosted by the aphid  Species that coexists on time and space form complex networks of interactions which are shaped by abiotic and biotic factors , coexist  of identical cells, so that in practice it is sufficient to consider two different compartments, modeling a single cell of each bacterial strain, enclosed in a larger compartment, which allows for exchanges of metabolites between cells and the host. Both endosymbionts code for the same hypothetical biosynthetic pathway, which allows the conversion of a precursor S (produced by the bacteria), to an end product P, which is essential for any of the three members of the consortium. The biosynthetic pathway is a linear chain composed by two reactions , a term representing such effect was introduced in the kinetic equation of the first reaction  is analogous to Equation (1) but without the inhibition term ([P]/Ki).The two reactions in the biosynthetic pathway, X and P are allowed to be exchanged with the surrounding environment. Endosymbiotic bacteria usually lack transport systems  are constrained to be larger than some fixed flux JP, i. The extracellular product is instead consumed by the host. It is useful to normalize this rate to the size of the bacterial populations N = N1 + N2, so that the consumption rate equals d[P]out/dt = −NJP, 0. The three parameters JP, 0 and JP, i thus set the demand of the metabolite P from the bacteria or the host.The fluxes n1 = N1/N and n2 = N2/N, with N1 + N2 = N. We will therefore first show results obtained by fixing the cell relative populations to be n1 = n2 = 1/2, and then exploring the case in which the two population fractions differ. When the whole model is considered, the balance equations for all the metabolites of the system can be written as follows:N corresponds to the total number of cells in both populations. Is worth to note that the equations for intracellular metabolites are symmetric for the two species, while the balance equations of the extracellular metabolites depend on the size of each symbiont population and, in the case of P0, on the host demand flux JP, 0. The substrate S is a precursor produced by each of the two cell types, and its concentration is assumed to be fixed . Accordingly, each solution will consist of a set of metabolites and enzymes concentrations, from which one can compute the optimal fluxes using the kinetic laws. A complementary formulation of the optimization problem is possible, i.e., maximization of the flux subject to a constraint on the maximum amount of total enzyme concentration. This other approach can be shown to be completely equivalent to the “enzyme” minimization approach, as shown in Supplementary Note Herein, we will adopt the second formulation, i.e., enzyme minimization subject to a certain demand flux of the product Aα, defined for each enzyme α as follows:In order to highlight the patterns of proteome allocation between the cell populations, we introduce the measure of enzyme asymmetries Aα will be zero if the enzyme concentrations in the two cells are the same, while it will equal either 1 or −1 if one cell type completely lacks the corresponding enzyme. In particular, if the two type of cells have the same sets of kinetic parameters, one would expect that the protein asymmetries would be equal to 0, unless some metabolic interaction emerges.This quantity reflects the relative difference in the concentration of each enzyme between the two different endosymbiont. Thus, fmincon function in Matlab 2015a forLinux. Due to the non-linear formulation of the optimization problem, the cost function exhibits multiple local minimums. Therefore, local optimization strategies such that gradient descent are not always able to find the correct minimum. However, if the parameters of the model are varied smoothly, such as in the case of the permeabilities DX and DP in Figure Optimizations were solved using the x*}, and the corresponding optimal ES protein asymmetry, AS =  / , where the asterisk indicates the optimal solution. Then, for each parameter ki, we compute the following correlation:N samples. In order to ensure that the optimal concentration corresponded to real absolute minima of the cost function, an iterative approach was developed, which is described in detail in Supplementary Text In the sensitivity analysis, we chose a point in the parameter space, roughly corresponding to the border between the symmetric and asymmetric region Then, we randomized by various amounts the kinetic parameters, and for each set of parameters we computed the optimal concentrations, {1, S] − E, S) / ( =  = 0.Then, we probed the effect of different demand fluxes, both to the host (n1 ≠ n2. As n1 is moved away from ½(with n2 = 1 − n1), the protein asymmetry is generally enhanced, with larger asymmetries AX , the concentration of the S metabolite, and the diffusion constant DX of the X metabolite . We see that the parameters which promote the enzyme asymmetry most are, as expected, the inverse inhibition constant 1/X1, …, X5, along with five enzymes EX1, …, EX5. Each enzyme EXi, with the index i ranging between 1 and 5, catalyses the reversible conversion of Xi into Xi+1 or, in the case of EX5, the product metabolite P. This extended model allows us to study how a long biosynthetic pathway is differently partitioned within the two cells for different permeabilities of the intermediate metabolites.In the previous section, we gave an in depth characterization of a model in which the biosynthetic pathway is composed by two reactions. However, real biosynthetic pathways are usually composed by a larger number of reactions. In order to study how the permeability affects the emergence of a complementation, an extended version of the model was developed, which keeps the fundamental features of its simplest version, while adding more intermediates in the pathway. The extended version of the model was obtained by introducing five intermediate metabolite, S into the intermediate metabolite with large permeability, which in turn is (mostly) shuttled to the other cell and converted into the product P, which is then shared between the two bacteria. A wide range of behaviors are obtained when different, more complex, scenarios are considered . As shown in Figure B. aphidicola and S. symbiotica SCc hosted by the cedar aphid , which allows the conversion of chorismate to tryptophan  are encoded by the genome of the co-primary S. symbiotica SCc, which in turn, lacks the trpEG genes , including the molecular weights and the solubility of the compounds. Using these parameters, we identify plausible candidate metabolites for becoming breaking points in the tryptophan biosynthetic pathway. As seen in Table C. cedri, C. tujafilina, and T. salignus) harbor B. aphidicola and S. symbiotica in their bacteriocytes, and the biotin pathway is fragmented in two parts  whereas Serratia genomes code for the enzymes required for biotin biosynthesis from KAPA. Since all the precursors of this intermediate are covalently bounded to an acyl carrier protein, KAPA is the first metabolite in the pathway showing an adequate permeability to cross membranes and paving the way for a metabolic complementation, in agreement with our model  metabolite. Thus, metabolite permeability is a plausible predictor of the splitting point of complementation events.The emergence of metabolic complementation in endosymbiotic consortia is a complex phenomenon-poorly understood from a theoretical point of view. For this reason, we have developed a simple model to analyzed the possible advantages (or disadvantages) of metabolic complementation, as well as the necessary conditions that may drive its emergence. Under the model assumptions, we have found that for metabolic complementation to emerge, two necessary conditions should be fulfilled: first, the pathway must exhibit product inhibition, and the inhibition constant should be strong enough so that the over-production requires a high increase in the enzyme concentration. Second, some of the intermediate metabolites of the pathway should be permeable enough to diffuse across cell membrane so that it can reach the other cell type. Thus, an “indifferent,” or “neutralist” strategy, with both cell populations allocating the same enzymes, is favored if the metabolites cannot easily permeate through the cell membranes, and/or if there is no substantial product inhibition on the first step of the pathway. On the other hand, if the intermediate metabolites can permeate easily through the membrane, and if product inhibition is present, metabolic complementation strategies allow to reduce the global enzyme burden. Moreover, when analyzing the case of tryptophan biosynthesis in the endosymbiotic consortium of The evolution of metabolic complementation in bacterial communities is most likely shaped by different forces, many of them may acting simultaneously . Therefore, hosts whose endosymbionts are able to sustain a given demand of certain product while reducing the protein cost will exhibit an improvement in their fitness . According to the BQH, whenever a metabolic function is redundant among the member of a microbial community, and the final product of the process leaks or escape from the producer cells, becoming a public good, the rest of the members can take advantage of this “common good”  were found to grow efficiently, even faster than the growth of the wild-type strain (Pande et al., E. coli (Mori et al., In perspective, understanding the evolutionary and mechanistic properties of natural microbial communities might allow the design of synthetic ones of potential industrial interest (Hosoda and Yomo, MP, FM, and JP conceived the work. MM and MP developed the model. MM performed the simulations and analyzed the data. MP analyzed the membrane permeability data and the trpE sequences. All authors discussed the results wrote and the manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Together, these microbial species form a complex food web that can break down nutrient sources that our own digestive enzymes cannot handle, including complex polysaccharides, producing short chain fatty acids and additional metabolites, e.g., vitamin K. Microbial diversity is important for colonic health: Changes in the composition of the microbiota have been associated with inflammatory bowel disease, diabetes, obesity and Crohn’s disease, and make the microbiota more vulnerable to infestation by harmful species, e.g., Clostridium difficile. To get a grip on the controlling factors of microbial diversity in the gut, we here propose a multi-scale, spatiotemporal dynamic flux-balance analysis model to study the emergence of metabolic diversity in a spatial gut-like, tubular environment. The model features genome-scale metabolic models (GEM) of microbial populations, resource sharing via extracellular metabolites, and spatial population dynamics and evolution.The human gut contains approximately 10In this model, cross-feeding interactions emerge readily, despite the species’ ability to metabolize sugars autonomously. Interestingly, the community requires cross-feeding for producing a realistic set of short-chain fatty acids from an input of glucose, If we let the composition of the microbial subpopulations change during invasion of adjacent space, a complex and stratified microbiota evolves, with subspecies specializing on cross-feeding interactions via a mechanism of compensated trait loss. The microbial diversity and stratification collapse if the flux through the gut is enhanced to mimic diarrhea.In conclusion, this in silico model is a helpful tool in systems biology to predict and explain the controlling factors of microbial diversity in the gut. It can be extended to include, e.g., complex nutrient sources, and host-microbiota interactions via the intestinal wall.The online version of this article (doi:10.1186/s12918-017-0430-4) contains supplementary material, which is available to authorized users. The human colon is a dense and diverse microbial habitat, that contains hundreds of microbial species . These sThe most important source of bacterial diversity in the colon is probably due to metabolic interactions between bacteria . The maiE. coli reproducibly evolve acetate cross-feeding within about 100 generations  found in the gut have been shown to sustain diverse microbial communities , 7. Intesee Ref.  and refeMathematical modeling can help understand under what conditions such cross-feeding and diversification can emerge in homogeneous environments. In their isologous diversification model, Kaneko and Yomo , 14 studThese initial mathematical models included simplified or conceptual models of metabolism. More recently, it has become feasible to construct models of microbial communities based on genome-scale metabolic network models (reviewed in Ref. ). In theE. coli, the framework could reproduce experimentally observed succession of an ancestral monoculture of E. coli by a cross-feeding pair of specialists. Because these models assume direct metabolic coupling of all species in the model via the culture medium, the model best applies to well-mixed batch culture systems or chemostats. The more recent coupled dynamic multi-species dFBA and mass transfer models [To also capture the emergent population dynamics of bacterial communities due to secretion and uptake of metabolites by the bacteria, (static optimization-based) dynamic flux-balance analysis (dFBA) has been introduced . These cr models , 25–27, In order to explore whether and under which circumstances a diverse microbial community can arise from a single nutrient source in the gut, here we extended the sdFBA approach to develop a multiscale model of collective, colonic carbohydrate metabolism and bacterial population dynamics and evolution in a gut-like geometry. To this end, we combined spatial models of population dynamics with genome-scale metabolic models (GEMs) for individual bacterial species and a spatial mass transport model. In addition to the sdFBA approaches, we extended the model with an “evolutionary” component, in order to allow for unsupervised diversification of the microbial communities. We inoculate the metabolic system with a meta-population of bacteria containing a set of available metabolic pathways. When, depending on the local availability of nutrients, the bacterial population expands into its local neighborhood the metapopulation gains or looses metabolic pathways at random. We find that spatially structured, microbial diversity emerges spontaneously in our model starting from a single resource. This diversity depends on interspecies cross-feeding interactions.14 individual bacteria belonging to hundreds of bacterial species, for which in many cases curated GEMs are unavailable. We thus necessarily resorted to a more coarse-grained approach, while maintaining some level of biological realism by constructing the model based on a validated, genome-scale metabolic network model of Lactobacillus plantarum [A full multiscale model of the metabolism of the human gut would need to include around 10lantarum . Figure lantarum , 23, 29,lantarum , 30. To Lactobacillus plantarum [We first constructed a hypothetical, but biologically-realistic “supra-organism” model , 31, callantarum , a residlantarum , 33. ForE. coli, Saccharomyces cerevisiae [L.plantarum [Vmax. For each reaction, FBAwMC requires a crowding coefficient, defined as the enzymatic volume needed to reach unit flux through that reaction. Each reaction is assigned a “crowding coefficient”, a measure of the protein cost of a reaction: Enzymes with low crowding coefficients have small molecular volume or catalyse fast reactions. Given a set of maximum input fluxes, FBAwMC predicts the optimal uptake and excretion fluxes as a function of the extracellular metabolite concentrations.The uptake and excretion rates of genome-scale metabolic networks can be calculated using constraint-based modeling. To represent diauxic growth, i.e., by-product secretion as a function of extracellular metabolite concentrations, we used an extension of FBA called Flux Balance Analysis with Molecular Crowding (FBAwMC) . FBAwMC revisiae , and L.plantarum . As an arate, not growth yield as in standard FBA, it predicts a switch to glycolytic metabolism at high glucose concentrations at which faster metabolism is obtained with suboptimal yield. Its accurate prediction of diauxic growth together with by-product secretion as a function of extracellular metabolite concentrations make FBAwMC a suitable method for a microbial community model.As FBAwMC optimizes growth Escherichia coli [L. plantarum. The simulation was initiated with pure glucose and was ran under anaerobic conditions. We then performed FBAwMC on all 1000 metapopulations, optimizing for ATP production rate as a proxy for growth rate. This yielded 1000 sets of metabolic input and output fluxes, Fi, and growth rates, μi for all 1000 metapopulations. These were used to update the extracellular concentrations, Xi, by performing a single finite-difference step of [To study the extent of cross-feeding emerging already from a non-evolving metabolic community of “metabacteria”, we first set up a simulation of 1000 interacting metapopulations, where each subpopulation was initiated with a set of crowding coefficients selected at random from an experimentally determined distribution of crowding coefficients of hia coli , 36, for step of , 29 1\dand Δt=0.1 h. After updating the environment in this way, we performed a next time simulation step.with a timestep O2 is also increasing due to the turnover of pyruvate into acetyl co-A via pathway 5 (pyruvate dehydrogenase). After about two hours of simulated time, proprionate and CO2 levels drop again due to the production of butyrate (blue): proprionate is consumed reversing reaction 3 and 4; CO2 is consumed in pathway 9 that produces acetate from formate. The conversion of acetate back to acetyl-coA then drives the production of butyrate; a surplus of acetyl-coA is turned over into acetaldehyde and ethanol in pathway 10. Interestingly, formate and CO2 are produced at the same time; this rarely occurs in any single organism but does occur in this microbial consortium.Figure To test to what extent these results depend on the ability of the individual FBAwMC models to represent metabolic switching and overflow metabolism , 36, we C(i), with i a species identifier. Let Most of the metabolites were only transiently present in the medium, j that species i consumes and excretes during the simulation. B here equals the biomass of species i at time t. The amount of carbon species i gets via cross-feeding then equals, be the total amount of metabolite cC(j) is the molar amount of carbon atoms per mol metabolite j =6). If species i during the fermentation consumes more of metabolite j than it has produced, species i has cross-fed on metabolite j. We subtract the amount of glucose from the sum, because glucose is the primary nutrient source that is present at the start of the simulation. Now we can calculate the total amount of carbon the population acquires via cross-feeding, relative to the total amount of carbon taken up by the population Here, Crel=0, there is no cross-feeding. In that case, every species only consumes glucose as carbon source or only consumes as much carbon from other metabolites as it has secreted itself. Conversely, if Crel=1 all carbon the species has consumed during the simulation is from non-glucose carbon sources the species has excreted itself. For the whole simulation Crel=0.39±0.02, indicating that 39% of all carbon consumed by the bacteria comes from cross-feeding. Cross-feeding was largest on lactate, CO2, acetate, ethanol, formate and propionate. Many of these metabolites are known to be involved in bacterial cross-feeding in the colon or cecum . In the E. coli , these sThe well-mixed simulations showed that cross-feeding appears in populations of interacting metabacterial metabolic networks. However, this does not necessarily imply microbial diversity, because it is possible that the same metabacterium secretes and reabsorbs the same metabolites into the substrate, in which case there would be no true cross-feeding. Furthermore, the previous section did not make clear whether cross-feeding will be ecologically stable under conditions where subpopulations of the supra-organisms are lost. In a spatially explicit model, cross-feeding possibly arises more easily and is more easy to detect, as different metabolic functions can be performed at different locations . We therm2, each containing a uniform concentration of metabolites, and potentially a metapopulation of gut bacteria   Fig. a. Each ate Fig. c, yieldD is a diffusion coefficient and L=1 cm the interface length between two adjacent patches. The local density of metabacteria, where in vitro models of the gut microbiota ; later  in Ref. .When the local biomass in a patch, int Fig. h. To miint Fig. i and 4.Vmax of the enzyme and enzyme volume [Vmax. Because the Vmax of a reaction can differ orders of magnitudes between species  method that we used for this model, give the minimum cellular volume filled with enzymes required to generate a unit metabolic flux; they are given by the e volume . Equivale BRENDA ), the eve BRENDA , 48: MicAs an initial condition, we distribute metabacteria over the grid, each containing all available metabolic reactions, i.e., each metabacterium initially contains all bacterial “species” that the complete metabacterium represents. To reflect variability in the relative abundances of the bacterial species in each metabacterium the crowding coefficients are drawn at random from an experimental distribution as described above Fig. a.t=0 all metabacteria still have all 674 reactions, but over time the number of available reactions gradually drops to below 200. This reduction of the number of metabolic genes could indicate a homogeneous population that is specialized, e.g., on fermentation of glucose where most of the metabolic network is not used. An alternative explanation is that each of the metapopulation retains a subset of the full network, an indication of cross-feeding. The amount of cross-feeding will likely change over the tube: The metabacteria in the front have direct access to glucose, whereas the metabacteria further down in the tube may rely on the waste-products of those in front. We therefore determined a temporal average of the cross-feeding factors, Crel . The cross-feeding factor for individual cells (C(i), Eq. To evaluate the behavior of our model, we performed ten independent simulations. These show largely similar phenomenology; therefore we will first describe the progression of one representative simulation in detail, and then discuss differences with the other simulations. Figure rel Eq. , at eachWe next investigated the mechanism by which such cross-feeding emerges in the simulation. Additional file O2, showing that the metabacteria convert the glucose into secondary metabolites. Among these secondary metabolites, the levels of acetate  in six, homogeneous metabolic environments, containing uniform concentrations of pure (1) glucose, (2) acetate, (3) formate, (4) lactate, and (5) propionate, and (6) a mixture of of CO2 and H2. Figure O2, because of the presence of hydrogen gas, that allows growth on CO2 via the Wood-Ljungdahl pathway [These results demonstrate that the metabacteria spatially structure their metabolic environment, generating a stratified structure of metabolic “niches” along the tube, each offering a separate set of metabolites. Therefore, we next asked if this environmental structuring gives rise to metapopulations uniquely adopted to the microenvironment. We took computational samples of all metabacteria found in the tube between 3500 h and 4000 h, to average out the variations at the short timescale. We tested the growth rate of these samples  have lower diversity .Of course our model is a simplification as it lacks many key features of the gut microbiota and of the gut itself. The metabacterium only contain a minimal subset of the metabolic pathways that are found in the gut microbiota. Future versions of our model could extend the current metabacterium model with additional metabolic pathways, e.g., methanogenesis or sulfate reduction. Adding multiple pathways would increase the number of potential cross-feeding interactions and improve the biological realism of the model. An alternative route that we are currently taking is to include multiple, alternative metabacteria, each representing a functional group in the human gut microbiota . This wiA further simplification of this first study of our model, is that we have focused exclusively on glucose metabolism. Future versions of the model will also consider lipid and amino acid metabolism, allowing us to compare the effect of alternative “diets” and consider the break-down of complex polysaccharides present in plant-derived food fibers. Further extensions include more complex interactions with the gut wall, which is currently impenetrable as in some in vitro models of the gut microbiota , 62. AddL. plantarum [S. Reversible reactions were replaced by a forward and a backward irreversible reactions. Next, we added four metabolic pathways that are crucial in carbohydrate fermentation in the colon, but are not present in the network: propionate fermentation, butyrate fermentation, the acrylate pathway and the Wood-Ljungdahl pathway. We used the Kegg database (http://www.genome.jp/kegg) [L. plantarum.We converted the GEM of lantarum  to a stojp/kegg)  to add tjp/kegg) . AdditioTo calculate the fluxes through the metabolic network as a function of the extracellular environment, we used flux-balance analysis with molecular crowding (FBAwMC) , 35. FBAS is the stoichiometric matrix. FBAwMC attempts to find a solution where M the cell mass, V the cell volume, vi the molar volume of the enzyme catalysing reaction i and bi is a parameter describing the proportionality between enzyme concentration and flux. For a derivation of Eq. Vprot is a constant (0≤Vprot≤1) representing the volume fraction of macromolecules devoted to metabolic enzymes. We use a value of Vprot=0.2, equal to the value used in [where  used in  for otheE. coli based on published molar volumes  and tur(Metacyc ). Both i(Metacyc  and it aum model .E. coli (see Section B) of 0.01 gram dry weight/liter (gDW/l), divided equally over all 1000 metabacteria =10−5 gr DW/l). At time t=0 we initiate the environment with a glucose concentration of 1.0 mM. At every time-step, the maximal uptake rate for each metabolite j is a function of its concentration, cj(t), as, Simulations of the well-mixed model are performed in Matlab, using the COBRA Toolbox . We use We then perform FBAwMC for all 1000 supra-bacteria and update the concentrations of all metabolites that are excreted or taken up, as, μi for each supra-bacterium i, which is used to update the biomass as, FBAwMC yields a growth rate This procedure is continued until the supra-bacteria have stopped growing.http://www.gnu.org/software/glpk/) as linear programming tool. The multiscale, computational model of the gut microbiota was also developed in C++. It describes individual metabacteria, or “cells” living on a grid, each with its own, unique GEM. Nutriets enter the grid at one end, flows through the grid, diffuses over the grid and is consumed by the cells. Uptake and excretion of metabolites is calculated using the GEM in each cell. The cells divide proportional to the calculated ATP production rate and mutate upon division. We simulate a total time of 4000 h . A model description in pseudocode is given in Fig. For the spatially explicit simulations, we developed a C++ package to perform constraint-based modeling using the GNU Linear Programming Kit , each cell should be viewed as a metapopulation of bacteria that is representative for the local composition of the intestinal microbiota: i.e, a metabacterium.We assumed that nutrients enter the colon every eight hours. In this study we consider glucose as the primary resource, because we want to focus on the bacterial diversity that can result from a single resource. Thus we assume that polysaccharides are already broken down to glucose. To allow for variability, we pick the amount of glucose from a normal distribution with mean of 42 mmol and a relative standard deviation of 20%. This mean value is chosen such that one the one hand all nutrients are consumed during passage through the gut and on the other hand it allows for a sufficiently large population size (≈1000 metabacteria).The glucose is consumed by the metabacteria, according to the metabolic networks. These network take into account 115 extracellular metabolites, whose dynamics are all modeled explicitly in the model. The majority of these metabolites are never produced. Production and consumption for each metabolite is modeled using ci(t) of each metabolite i is updated each timestep Δt according to the calculated influx/efflux, Fi,n, and cell volume, Vn, of the cells on the grid point . Fluxes in the metabolic network have unit mmol·g DW−1·h−1, where external metabolite concentrations are in mmol·l−1. To convert the fluxes to extracellular concentration changes, we therefore multiply with DENS_MAX; it is the maximum bacterial density in g DW·l−1, which is estimated as explained in Table 14 cells/l, an estimated bacterial cell size of 10−16 l/cell and a cellular density of 100 g DW/l, i.e., Δt is capped at Thus, the concentration ·lcell−1 , 69. To 3μm2/s for all metabolites. This dispersion coefficient is an order of magnitude higher than the diffusion constant of glucose in water, and provides a good balance between local mixing while maintaining sufficient differentiation in our simulations.Each metabolite flows through the colon: Every 15 min, all metabolites are shifted one grid point to the right. This results in a passage time of 37.5 h, similar to observed colonic transit times . Every μ, for each metabacterium i using an empirical, auxiliary reaction [FBAwMC yields growth rate, reaction . The volCell death is taken into account in a density dependent way. This stabilizes the population, making sure that the population does not grow too fast if too much nutrients are given or dies out if too little nutrients are given. The death rate of a cell is calculated as follows where TOTAL_NEIGHBOURS is the total amount of neighbours and MAX_NEIGHBOURS the maximum amount of neighbours .the complete deletion of a reaction, i.e., extinction of the species responsible for this reaction, with probability μ_DEL;the reintroduction of metabolic pathways, corresponding to the invasion of the bacterium previously responsible for this pathway, with probability μ_BIRTH;the strengthening or weakening of one of the pathways, corresponding to the relative growth or suppression of a bacterial species in the metapopulation, with probability μ_POINT.Next the metabacteria expand into the empty patch on the same grid point when their volume exceeds a value of 2. The volume of the parent metabacterium is then equally distributed over the two daughter metabacteria. During this expansion, three types of “mutations” can occur: ai in Eq. To delete reaction (a) the maximal flux through that reaction is set to 0. To reintroduce a reaction (b), we release the constraint by setting it to a practically infinite value (999999 mmol/gr DW hr). A point mutation (c) corresponds to a change of the crowding coefficient . Metabolite dynamics over time. The simulation is initialized with a pulse of glucose. Note that with standard FBA all 1000 cells behave identically, because the crowding coefficients are not used. (PDF 93 kb)Additional file 2Figure S2. Simulation of the non-spatial, standard L. plantarum model using flux-balance analysis with molecular crowding (FBAwMC). Metabolite dynamics over time. The simulation is initialized with a pulse of glucose. (PDF 105 kb)Additional file 3Figure S3. Population average and standard deviation of the cross-feeding factor Ci as a function of the position in the colon for all n=10 runs. The averages and standard deviation are over the vertical dimension and are calculated over the final part of the simulation, from 3500 h until 4000 h. (PDF 259 kb)Additional file 4Figure S4. Population averages of the metabolite concentrations over evolutionary time of the simulation in Fig. Additional file 5Figure S5. Average metabolite concentraties along the tube for all n=10 simulations. The averages are taken over the second half of the simulations, from 2000 h to 4000 h. (PDF 462 kb)Additional file 6Lactobacillus plantarum [Microsoft Excel File with all reactions and metabolites of the genome scale model of lantarum , extende