Soil microbial activity is often concentrated in sparsely distributed hotspots that contribute disproportionally to macroscopic biogeochemical nutrient cycling and greenhouse gas emissions. The mechanistic representation of such dynamic hotspots requires new modeling approaches capable of representing the interplay between dynamic local conditions and the versatile microbial metabolic adaptations. We have developed IndiMeSH  as a spatially explicit model for the physical and chemical microenvironments of soil, combined with an individual-based representation of bacterial motility and growth using adaptive metabolic networks. The model uses angular pore networks and a physically based description of the aqueous phase as a backbone for nutrient diffusion and bacterial dispersal combined with dynamic flux balance analysis to calculate growth rates depending on local nutrient conditions. To maximize computational efficiency, reduced scale metabolic networks are used for the simulation scenarios and evaluated strategically to the genome scale model. IndiMeSH was compared to a well-established population-based spatiotemporal metabolic network model (COMETS) and to experimental data of bacterial spatial organization in pore networks mimicking soil aggregates. IndiMeSH was then used to strategically study dynamic response of a bacterial community to abrupt environmental perturbations and the influence of habitat geometry and hydration conditions. Results illustrate that IndiMeSH is capable of representing trophic interactions among bacterial species, predicting the spatial organization and segregation of bacterial populations due to oxygen and carbon gradients, and provides insights into dynamic community responses as a consequence of environmental changes. The modular design of IndiMeSH and its implementation are adaptable, allowing it to represent a wide variety of experimental and  in situ, we have developed a modeling platform, IndiMeSH , to enable systematic study of dense multispecies bacterial communities within a structured habitat resembling (but not limited) to soil. The model is capable of representing multispecies trophic interactions and spatial self-organization in response to nutrient gradients, as confirmed in comparison with published results. IndiMeSH offers new opportunities for quantifying bacterial hotspot formation and dynamics and observe their resilience and response to perturbations in hydration and nutrient conditions.Soil bacterial communities are key players in global biogeochemical cycles and drive other soil regulatory and provisional ecosystem functions. Despite the relatively high bacterial abundance found in fertile soil, bacteria occupy only a small fraction of the soil surfaces and often form hotspots with disproportionate contributions to observed biogenic fluxes. As soil opacity and complexity limit detailed observations of such hotspots  Nonet of soil ,5. This  of soil . These h of soil –9. ImproIn addition to its inherent complexity, soil opacity limits direct visualization of bacterial distribution within soil ,11. AlthNew approaches using spatiotemporal metabolic modeling with genome-scale metabolic networks enable quantification of cell growth rates, and the associated uptake of nutrients and excretion of intermediate (by-product) metabolites. Such approaches have been used to create biofilm models through an extension of Matlab with NetLogo named MatNet , a populIn this study, we developed and tested a new type of spatiotemporal metabolic model that assigns metabolic networks to individual agents capable of chemotactic motion within spatially resolved soil habitats. The physical domain is comprised of angular pore networks representing soil pores. The hydration conditions are imposed by a prescribed matric potential that interacts with the physical domain and results in aqueous phase configurations similar to those expected in soil . The matric potential is a component of the total soil water potential attributed to capillary and adsorptive forces between water and the soil solid matrix, with values ranging from 0 for saturated soil to large negative as the soil dries (often expressed as negative pressure). The physical domain including the water phase serve as a backbone for numerical diffusion of nutrients and intermediate metabolites, with explicit account of diffusive bottlenecks for oxygen when pores are saturated or for nutrient diffusion in unsaturated soil, whilst maintaining connectivity of the aqueous phase throughout the simulated domain. Finally, bacterial cells are represented as individual agents with the ability to autonomously move and disperse, intercept nutrients and grow at rates determined by local  nutrient conditions owing to the integration of metabolic networks. The model is compared to predictions obtained from a previously published population-based spatiotemporal metabolic network  and to bThe purpose of IndiMeSH is to quantify interactions among individual bacterial agents and their immediate environment within a realistic depiction of soil domains and unsaturated conditions. Specifically, we selected bacterial life in pseudo two-dimensional pore networks to mimic processes in cross-sections of soil aggregates and on other soil hydrated rough surfaces. We employ flux balance analysis (FBA)  to calcuA pseudo two-dimensional pore network composed of interlinked pores connected by nodes forming a lattice defines the spatial component of the model. The coordination number expresses the number of pores connected to each node within the lattice . Each pore has an angular cross-sectional area represented by either isosceles triangles  or rectaw is the water filled cross-sectional area (m2), At the total cross-section area of the pore (m2), Ψ the matric potential (Pa), σ the water surface tension (Nm-1) and γi the angle i within the corner of the angular pore.An important aspect of the model is its ability to represent different hydration conditions using the energy state of water or the matric potential. The matric potential determines the aqueous phase configuration (amount retained in the pores and connectivity), hence it also shapes the nutrient diffusional landscape and constrains bacterial dispersal ranges. The water-filled cross-sectional area in each pore is calculated from the matric potential and geometrical considerations  as shown-1) and γi the angle within the corner under consideration of the angular pore.Pores are considered unsaturated whenever an air phase is present, specifically, when a continuous connection of unsaturated pores is available from a liquid-air interface at the boundary to the pore under consideration. We note that the water-filled cross-sectional area of a pore defines available pathways for nutrient diffusion and for the calculation of total nutrient storage in each pore . An important parameter of the aqueous phase in each pore is the effective water film thickness defined as the diameter of the largest sphere fully inscribed between the liquid-air interface and the pore wall  and calcThe water film thickness affects the speed and range of bacterial motility, as further described below. Of particular importance is the fact that different angular pore geometries  may retain water films that are too thin to support bacterial flagellated motion, hence, disconnect this bond from other parts of the network in terms of cell dispersion . Despite2s-1), Aw the liquid cross-sectional area (m2), Vw the volume of water attributed to the node (m3), x the spatial coordinate along pores (m), and R a sink term (mols-1) attributed to the combined consumption of individual bacterial cells. The volume at each node is calculated using w the volume of water attributed to the node (m3), Aw the liquid cross-sectional area of connected pore j (m2), Lj the length of the connected pore j (m) and d the degree of the node.Diffusive fluxes of dissolved substrates within the aqueous phase are described by Fick’s law and are evaluated between nodes subject to mass balance at the nodes, as given by:Liquid films of pores sharing the same node are assumed to be continuous. Neglecting bacterial consumption, which is calculated separately using FBA, Bacteria are represented as individual agents capable of dispersing (by motility when the aqueous film thickness permits) within the pore network, intercepting nutrients and growing according to locally available nutrient conditions. Bacterial cells respond locally and independently with no knowledge of global system properties such as concentration fields or bacterial density even at the nearest pore. Thus, global phenomena such as exponential population growth, spatial organization of bacterial species or diffusion fields due to bacterial consumption are emergent properties based on the local interactions of individual agents with their immediate chemical and physical surroundings. Bacterial cells divide when they reach a prescribed mass at division; they may be removed from the simulation if they deplete internal energy and reach a critical biomass .t and mt+1 are the cell masses (kg) at time step t and t+dt, respectively, μ the growth rate (s-1) calculated using FBA, and dt the numerical time step (s). Finally, bacterial nutrient consumption is calculated from the substrate uptake rate per dry weight of cell predicted by dFBA and the local biomass.We employ dynamic Flux Balance Analysis (dFBA) to quantify growth of bacterial species depending on their physiological traits and local nutrient concentrations –23,31. I-1), V0 unrestricted bacterial swimming velocity, Fm the flagellar propulsion force (N), Fλ the cell-surface hydrodynamic interactions (N) and Fc the capillary pinning force (N). The derivation of this Equation has been previously published [Bacterial motility is an important aspect of local interactions and self-organization. Chemotactic motility is implemented as a series of a run-and-tumble steps  where ceublished  and relit is the tumbling probability with chemotaxis, p0 the tumbling probability in absence of any chemotactic behavior, X the chemotactic sensitivity (m2s-1), v the swimming velocity depending on hydrodynamic interactions (ms-1), umax the maximum growth rate (s-1) and Δμ the experienced growth rate gradient (m-1s-1).Chemotaxis enables to bias the resulting swimming direction towards favorable conditions (e.g. aerotaxis towards oxic conditions). This process is included in the mathematical model by calculating the tumbling probability based on the growth rate gradient of individual cells by comparing individual growth rates in time step t and t-1  and is cA binomial distribution based on the individual tumbling probabilities is used to determine whether a cell tumbles in the current time step. For tumbling within a pore, a cell has a 50% probability to change direction. When reaching a node, a new direction is selected at random from all connected pores. When entering a pore where the cell would be immobile due to thin water films, the cell has a 10% chance at each time step to detach back into the previous node. Mounting evidence suggests that motile cells can extract themselves from tight spots  but infoWe evaluated the proposed IndiMeSH framework by comparing it to a population-based metabolic model (COMETS)  and to eTo reduce the computational burden of the simulations and to focus on related parts of the metabolism, genome-scale metabolic networks (GEM) were systematically reduced using two previously published algorithms, redGEM  and lumpE. coli K-12 deficient in methionine production and S. enterica LT2. E. coli relies on the production of methionine by S. enterica, whereas S. enterica is dependent on the release of acetate by E. coli in microaerobic conditions due to its inability to directly metabolize lactose, thus engaging in a mutualistic relationship where neither species can grow in the absence of the other [We compared IndiMeSH with COMETS , a model designed primarily to investigate the growth and interrelation of bacterial communities in space using FBA and population-based approaches. In comparing IndiMeSH with COMETS predictions, we sought to verify the potential of IndiMeSH in simulating trophic dependencies of multispecies bacterial communities without making prior assumptions. For this reason, simulations were generated mimicking the two-member consortium investigated in the original publication . This cohe other . S. ente−10 m2s-1 is used for all simulations [−7 g bacterial biomass thus contains 3000 super agents  and was selected to maintain the functionality of bacterial motility as a pseudo run-and-tumble mechanism. To simulate colony growth and expansion on agar surfaces, bacterial cell velocity was reduced to 2.2*10−9 ms-1 to obtain good agreement between COMETS biomass diffusion and IndiMeSH run-and-tumble biomass dispersal  was created with the same topology as in the COMETS simulations (for details see ulations . Since t10−15 kg ). 100 raP. veronii 1YdBTEX2 as an obligate anaerobic species using simple Monod-type growth kinetics. In reality, P. veronii is capable of growing in both aerobic and anaerobic environments by adapting its metabolism. The lack of metabolic flexibility in the Monod-based application resulted in a certain discrepancy between experimental and simulation results, especially for the cases where facultative anaerobes were growing closer to the oxygen source [P. putida KT2440, a reduced core model of the genome-scale metabolic network iJN746 [P. veronii 1YdBTEX2, we have used a reduced-scale model of P. stutzeri A1501 (iPB890) [A similar core IBM (without the FBA component) has been used in previous studies to investigate an experimental system designed to visualize and quantify bacterial spatial organization in pore networks . The expn source . In thisk iJN746  was impl(iPB890)  due to tA main advantage of the IndiMeSH model is its capability to capture the aqueous phase configuration and related limitations to bacterial dispersal and nutrient diffusion landscape. Previously conducted experiments performed in 2mm soil aggregates investigated the effect of carbon perfusion by adding glucose after a 7 day incubation period as reported in . These eThe previous case studies included scenarios with saturated  and unsaturated (glucose perfusion) conditions. However, a strategic comparison of simulations under wet and dry conditions in the same pore network is missing. For this reason, a final case study containing three pore networks  and two hydration levels (-1 kPa for wet and -10 kPa for dry conditions) was created. The simulation domain comprised of a 4 mm diameter carbon hotspot representing a soil aggregate or rhizosphere cross-section. The pore lengths was adapted for each network to conserve porosity. Pore size distributions were taken from a lognormal distribution with mean radius of 5, 50 and 200 microns for the small, medium and large pore networks, respectively, with corresponding standard deviations of 5, 10 and 50 microns. Simulations included central glucose and nitrate sources with a peripheral oxygen source (0.27 mM). Glucose and nitrate concentrations were adapted for each network to represent constant flux boundary conditions. Acetate was included in the simulations as an intermediate metabolite without any physical sources. Pseudomonas stutzeri A1501 was used as a model organism (reduced metabolic network iPB890) due to its facultative anaerobic growth capability. The total simulated time was five days with a 10 s time step.E. coli metabolic networks. E. coli perform differently at the combination of high lactose, low methionine and medium to high oxygen uptakes.The performances of genome-scale metabolic networks (GEM) and their reduced-scale networks (rGEM) were compared using flux variability analysis in varying environmental conditions. E. coli and S. enterica after 48 h of simulated growth, including the experimental results and model simulations from the original COMETS publication [E.coli:S.enterica inoculated at 100 randomly chosen nodes) were included, demonstrating the metabolic interdependence of the two species and the convergence of the system to the same stable community composition. No significant difference was found between IndiMeSH simulations and both COMETS experimental and simulation results . Additional simulations were performed to ensure that the motility algorithm of IndiMeSH and changing to super agents resulted in similar biomass dispersion characteristics as in the diffusion algorithm used in COMETS. - The aim of comparing COMETS with IndiMeSH was to verify IndiMeSH ability to predict bacterial community trophic interactions in the absence of prior assumptions regarding nutrient uptake (in contrast with Monod kinetic models). lication . Both inP. putida (further termed aerobes) and P. veronii/P. stutzeri (further termed facultative anaerobes) along the shortest path from the central to the peripheral ports of the physical and simulated pore networks , we compared IndiMeSH predictions with previously published experimental data . Fig 3 dWe evaluated the capability of IndiMeSH to predict the shift in total bacterial population size due to perturbations in boundary conditions in the form of glucose perfusion into soil aggregates previously under certain steady ecological state. Simulations were set up to mimic experiments performed on 2 mm soil aggregates where the bacterial community was first grown into steady state for 7 days after which glucose was added at high concentrations to observe the short-term impact on the function and the spatial distribution of soil bacteria and fungi . Fig 4 dFinally, we created simulations with two contrasting hydration conditions in three different pore networks to highlight the capability of IndiMeSH to capture and predict the shift in metabolic activity due to the interplay of soil physics, aqueous configuration and bacterial metabolism. Pore size distributions resembling different soils are shown in E. coli, all reduced-scale models perform very similarly to their genome-scale counterparts. Reactions which have a net flux difference greater than 10 mmol/gDw/h are predominantly attributed to internal cycles within the genome-scale models or cycling of nutrients between compartments of the genome-scale model that are absent in the reduced-scale model, as has been previously reported [E. coli. This is due to overoptimistic predictions of the genome-scale model where the predicted high fluxes can only be achieved through net CO2 fixation, which is unlikely [The IndiMeSH model has been developed to capture the multifaceted bacterial metabolism of individual-based agents inhabiting a complex habitat such as soil. The use of adaptive metabolic networks enables a life-like transition between aerobic and anaerobic conditions compared to empirical and arbitrary kinetic models. Additionally, FBA predicts uptake and secretion rates depending on locally variable nutrient conditions and thus enables simulations of trophically interacting bacterial species within a complex medium such as, but not limited to, soil. The heavy computational burden related to the motility of individual bacterial cells and the numerous iterations of the FBA requires the reduction of genome-scale metabolic networks using the previously published redGEM  and lumpreported . There iunlikely .The main difference between a group of spatiotemporal metabolic models and the newly developed IndiMeSH lies in the ability of the latter to represent complex habitats such as soil, including pore spaces, aqueous phase configurations and related constraints to chemical diffusion and bacterial dispersion. The IndiMeSH model is designed for a different range of applications than the COMETS model; however, we obtained comparable simulation scenarios through simple adjustments to the physical and biological domain of the model. These include the representation of bacterial cells as super agents as well as a reduction in velocity to account for growth on agar. The use of super agents has been implemented in the past ,45 and iThe importance of emergent spatial patterns and bacterial spatial organization prompted us to examine how IndiMeSH reproduces previously published experimental data of bacterial distributions in micrometric pore networks dominated by carbon-oxygen counter gradients . The oriAbrupt perturbations are ubiquitous in all natural systems such as soil, either due to rapid changes in hydration conditions following rainfall or irrigation, or chemical alteration by the application of fertilizer or contaminants to the soil, or physical alterations such as tillage or rapid soil compaction. To test the capability of IndiMeSH to simulate such dynamic changes in environmental conditions, a simulation scenario was created where a change in electron donor availability alters the macroscopic conditions within a soil aggregate cross-section based on experimental results of glucose perfusion in soil aggregates . These eAn important aspect differentiating IndiMeSH from other current spatiotemporal metabolic network models is the accuracy with which the physical habitat of the bacterial cells is represented. Angular pore networks enable to link the aqueous phase configuration dictated by the pore geometry to the underlying chemical conditions and ultimately to the spatial landscape of bacterial metabolism. For the same matric potential, pore networks of different mean diameter expose bacteria to fundamentally different growth conditions as shown for instance in IndiMeSH offers a representation of metabolic versatility with an individual-based model of bacterial life in soil habitats. Metabolic networks enabled a natural transition between aerobic and anaerobic pathways and associated nutrient consumption patterns, inducing trophic interactions without prior assumptions, as required by mathematical models using simple growth kinetics. The detailed description of the physical habitat and aqueous phase and emergent nutrient diffusion fields give rise to complex metabolic landscapes with changes in metabolic activity at the millimeter scale. Due to the modular design of the IndiMeSH model, individual components can be modified to represent, for instance, a different physical habitat, method of motility or metabolic network optimization . Thus, the applicability of the model is endless, ranging from the quantification of bacterial metabolism in soil, or the growth of bacteria during food spoilage, to the proliferation of Pseudomonas aeruginosa in the lungs of cystic fibrosis patients.S1 Figw. If Aw is smaller than the total pore cross-sectional area and has a continuous unsaturated connection to an air interface, the pore is considered to be unsaturated. Finally, the water film thickness WFT, which dictates bacterial swimming velocity, is defined as the radius of an inscribed circle between the pore walls and the liquid-air interface.The geometry of each triangular pore in the pore network is defined by the inscribed circle radius r and central angle γ. Rectangular pore geometry is determined by the width W and height H for each pore. Interfacial curvature R  determines the total water filled cross-sectional area A(TIF)Click here for additional data file.S2 Fig(a) The COMETS habitat geometry contains a rectangular grid consisting of individual rectangular pores with homogeneous size . Constant concentration boundaries of 2.92 mM lactose and 0.10 mM oxygen are supplied homogeneously throughout the domain. Acetate and methionine are solely produced by bacterial metabolism. 100 randomly chosen nodes are inoculated with 3000 super agents each. (b) For the micromodel comparison, a hexagonal lattice of individual cuboid pores  is used with peripheral oxygen sources (0.27 mM) and central citrate and nitrate sources (each 10 mM). All bacterial cells are inoculated at the center. (c) For the glucose perfusion scenario, a hexagonal lattice with individual triangular pores  is used with peripheral oxygen source (0.27 mM) and central glucose and nitrate sources . After 7 days, an additional pulse of glucose was added, homogeneously distributing 333 mM of glucose in all pores. 1000 cells were inoculated randomly across the domain.(TIF)Click here for additional data file.S3 Fig-7g bacterial biomass at the center node. IndiMeSH predictions were produced both for individual bacterial cells and super agents with a scaling ratio of 100 . Predictions of the two models are congruent with a velocity of 8 microns per hour for bacterial swimming motility in the IndiMeSH model.Algorithms were compared in a one-dimensional pore (2000 microns length with 100 nodes) and inoculation of 3*10(TIF)Click here for additional data file.S4 FigE. coli genome-scale network Click here for additional data file.S1 TableIf sufficient nutrient is available, cells consume nutrients at the maximum rate. At low nutrient concentrations, the amount is divided equally between all cells residing within a node, resulting in uptake rates lower than the maximum uptake rate.(DOCX)Click here for additional data file.S2 TableThis table contains a list of all parameters that can be set by the user for simulations containing multiple substrates and species. The list is exhaustive excluding the actual topology of the pore network .(DOCX)Click here for additional data file.S1 Data(ZIP)Click here for additional data file.


Escherichia coli K-12 strain was transformed with genes enabling sucrose assimilation. It was observed that the combined deletion of the genes adhE, adhP, mhpF, ldhA, and pta abolished the anaerobic growth using sucrose. Therefore, the biomass-specific conversion rates were obtained using oxygen-limited continuous cultures. Strains performing the breakdown of the sucrose by hydrolysis (SUC-HYD) or phosphorolysis (SUC-PHOSP) were studied in such conditions. An experimentally validated in silico model, modified to account for plasmid and protein burdens, was employed to calculate carbon and electron consistent conversion rates. In both strains, the biomass yields were lower than expected and, strikingly, SUC-PHOSP showed a yield lower than SUC-HYD. Flux balance analyses indicated a significant increase in the non-growth-associated ATP expenses by comparison with the growth on glucose. The observed fructose-1,6-biphosphatase and phosphoglucomutase activities, as well as the concentrations of glycogen, suggest the operation of ATP futile cycles triggered by a combination of the oxygen limitation and the metabolites released during the sucrose breakdown.Biotechnological industry strives to develop anaerobic bioprocesses fueled by abundant and cheap carbon sources, like sucrose. However, oxygen-limiting conditions often lead to by-product formation and reduced ATP yields. While by-product formation is typically decreased by gene deletion, the breakdown of oligosaccharides with inorganic phosphate instead of water could increment the ATP yield. To observe the effect of oxygen limitation during sucrose consumption, a non-fermentative The online version of this article (10.1007/s00253-019-09909-6) contains supplementary material, which is available to authorized users. The design of efficient and sustainable biotechnological processes demands the maximization of product titer, production rate, and yield, and the reduction of fixed and variable costs , weak acids could be transported cyclically across the membrane, leading to ATP losses  to catalyze the breakdown of oligosaccharides , with a limited oxygen supply, and using genetically modified cells to diminish by-product generation. Having this objective, we expressed genes enabling the sucrose uptake and hydrolysis/phosphorolysis , adhP , ldhA (encoding for the lactate dehydrogenase), pta (encoding for the phosphotransacetylase), and mhpF . These deletions had already been performed, using the method described by Wanner and Datsenko SO4, 2 g KH2PO4, 0.5 g MgSO4·7H2O, 0.5 g NaCl, 2 g NH4Cl, 0.001 g of thiamine, and 2 mL of a trace-element solution prepared as previously described  was 5 g of 2 × 6 H2O to provide the metals required for the activity of the formate hydrogen lyase  .The growth medium employed for the continuous cultures was the same as that employed for the cultures in batch. The continuous cultures were performed at dilution rates of 0.05 h2 in the outgas were followed until non-stable fluctuations in CO2 in the outgas were observed. Once the oxygen-limited steady states were approached, samples of broth, biomass, and cell-free extracellular media (filtrates) were obtained at two different times during the same steady state. Continuous cultures were assumed to be in steady state when the signal corresponding to the CO2 in the outgas remained stable for at least two culture volume changes. Other details of the setup, operation, sampling, and sample analyses of the continuous cultures are explained in Supplementary Materials 3 and 4.The stirring rate was gradually decreased to achieve the oxygen limitation. The signals of dissolved oxygen tension and CO+. Thus, the production of NADPH, which was followed spectrophotometrically at 340 nm, was used to calculate the reaction rate. All the enzymatic assays were performed at 37 °C. The choice of the buffer used in each case was related to the stability of the substrates and the products, while the concentration of the substrates and the auxiliary enzymes was always high enough to ensure maximum activity of the studied enzymes under the conditions of the assays. In each case, the background activity observed when no substrate is added to the reaction mixture was subtracted from the total activity. Moreover, we checked that no changes in the signal were observed before addition of the cell-free extracts. The details of each enzymatic assay are described in Supplementary Material 5.Cells harvested from batch cultures during the exponential growth phase or from the continuous cultures were used for determination of the specific activities. Three different assays were performed: sucrose phosphorylase (SucP), phosphoglucomutase, and fructose-1,6-bisphosphatase. These three experiments were coupled assays leading to the production of NADPH from NADPData availabilityAll the relevant data and scripts are provided as supplementary material.E. coli K-12, we chose the episomal expression of the foreign genes cscB and cscK from E. coli W combined with the cscA gene from E. coli W or the sucP gene from B. adolescentis. The processes enabled by the proteins encoded by these genes are presented in Fig. cscA gene . These deletions were previously performed with the aim of minimizing the formation of by-products  under oxygen-limited conditions.The hosting cells were from an cscKB, no growth on sucrose was observed. This result confirms that, without the introduction of some gene encoding for an enzyme catalyzing the breakdown of the sucrose—either a hydrolase or a phosphorylase—growth of E. coli K-12 on sucrose is not possible.Batch cultures at 37 °C, in aerobic or anaerobic conditions, were monitored for up to seven days. The different outcomes are shown in Table adhE, adhP, ldhA, pta, and mhpF were sufficient to abolish growth under the tested conditions. Because we were interested in the study of the sucrose metabolism under oxygen limitation while maintaining low (or zero) by-product formation rates, our chosen approach was the study of the biomass-specific consumption and production rates in strains with the ΔadhE ΔadhP ΔldhA Δpta ΔmhpF deletions using oxygen-limited continuous cultures.Regarding the growth/no-growth pattern observed under anaerobiosis, it is possible to conclude that the deletions of the genes iKOGmaker.m, iKOG.mat, and Ecolicore.mat). This model was chosen because (i) it contains experimentally validated estimates for the energetic parameters P/O ratio , growth-dependent ATP expense , and ATP expense for growth-independent maintenance ; and (ii) it contains experimentally determined biomass composition data for the employed dilution rate. However, some modifications were implemented in the original model to represent the genetic modifications present in the constructed strains. For example, the fluxes through the reactions catalyzed by the ethanol dehydrogenase, acetaldehyde dehydrogenase, lactate dehydrogenase, and phosphotransacetylase were set to zero to represent the effect of the gene deletions ΔadhE, ΔadhP, ΔmhpF, ΔldhA, and Δpta. Moreover, the in silico model was further adapted to account for the plasmidial DNA and plasmid-encoded protein burdens in the mutant strains. For these corrections, the DNA and protein sequences, the contribution to the cellular weight of the plasmid-encoded beta-lactamase, and the observed specific sucP activities  were considered.For calculation of the biomass-specific conversion rates and possible flux distributions, the biomass composition and the network stoichiometry are very relevant . To estimate the actual metabolic fluxes, reconciled specific consumption and production rates were employed as constraints, and maximization of the ATP production was used as the objective function. Maximization of ATP production has been reported as a reliable objective function when cells are growing in continuous cultures  using the software Constraints Based Reconstruction and Analysis   formed the input used to estimate reconciled rates , consistent with the carbon and electron conservation principle. Results obtained by other groups while studying E. coli MG1655 and E. coli mutants with gene deletions similar to the employed in this study, using continuous cultures, are included in Table The experimentally determined specific consumption/production rates with their associated errors . Considering the extracellular concentrations measured for sucrose, formate, acetate, lactate, pyruvate, and succinate, it was possible to account for 90–95% of the total organic carbon (TOC) present in the filtrate (cell-free) samples obtained from the bioreactors . For this reason, it was assumed that no other metabolites, beyond the measured ones, were produced in meaningful amounts.E. coli W mutant strain where the cscK gene was knocked out  and electrons (9% and 11%) in SUC-HYD and SUC-PHOSP, respectively. However, some small differences in the by-product profiles were observed between the strains Table .pho regulon  and SUC-HYD (2.2 mM). These values are far above the critical concentration triggering the Strikingly, the biomass yield observed for SUC-PHOSP was lower than the observed for SUC-HYD (Table Biomass composition.xls), using the reconciled specific consumption/production rates as constraints, and setting the production of ATP as the objective to be maximized, the distributions of the metabolic fluxes were calculated using FBA (see supplementary files SucHYD_with_burden.m and SucPHOSP_with_burden.m). The upper and lower boundaries for the experimentally determined fluxes were constrained considering the reconciled errors. The calculated metabolic flux distributions are reported in the supplementary file metabolic fluxes distributions.xls.With the in silico model corrected to account for the plasmid and recombinant protein burdens  anaerobically growing on glucose  in SUC-HYD was 0.117 mol of ATP/C-molE. coli K-12–derived strains on sucrose under oxygen-limiting conditions, despite the kind of enzymatic mechanism for the breakdown of the disaccharide, implied a large increase in the ATP expenses generically named “maintenance”; and (ii) because biomass compositions, plasmid and protein burdens, P/O ratios, and growth-dependent ATP expenses in SUC-HYD and SUC-PHOSP are similar , with the available data it is not possible to unmistakably identify the biological process(es) responsible for the difference between the biomass yields observed in such strains. However, further analyses pointed to an increase in ATP futile cycles triggered by the use of sucrose under oxygen-limiting conditions, being these futile cycles higher in SUC-PHOSP.Two important conclusions can be obtained from these calculations: (i) the growth of E. coli K-12 MG1655 grown on 5 g/L of acetate and 5 g/L of glucose were included for comparison. The results showed that the activity of FBPase was approximately eight times higher in SUC-PHOSP than in SUC-HYD  and the phosphofructokinase (PFK). The specific FBPase activities in samples of SUC-HYD and SUC-PHOSP, obtained during the continuous cultures, were measured. The activities from aerobic batch cultures of YD Table . RemarkacsrA gene  leads to overexpression of phosphoglucomutase (PGM)  was also measured. The results showed that the PGM activity was much higher in the sample taken from SUC-PHOSP compared with that from SUC-HYD and TUD69 Table . This obE. coli MG1655 growing on glucose in an aerobic carbon-limited chemostat at a dilution rate of 0.05 h−1 is about 0.8%  after the introduction of a plasmid carrying the putative sucP gene from Bifidobacterium longum   reduced products such as ethanol, lactic acid, or polyhydroxyalkanoates, the decrease in the substrate-level production of ATP and by-product suppression is a frequent problem in anaerobic bioprocesses. Because the deletions of the + symport and the plasmid and protein burdens. Remarkably, the biomass yield of the strain SUC-PHOSP was unexpectedly smaller than that observed for the strain SUC-HYD, with a relatively larger fraction of the sucrose being fully catabolized to CO2.The observed biomass yields were lower than expected, even considering the cost of sucrose:Hin vivo FBPase activity is highly regulated by allosterism  the gene deletions, (ii) the oxygen limitation, (iii) the carbon source, (iv) the intracellular phosphate concentrations, and (v) the mechanism to break down the sucrose.Evidence was found consistent with the idea of ATP futile cycles as the reason behind the difference between the expected and the observed biomass yields. Although the FBPase activity in SUC-PHOSP was near eight times higher than that in SUC-HYD, it is known that the pflB  between E. coli MG1655 and its mutant lacking the genes ackA, pta, and poxB while growing anaerobically on glucose as the sole carbon source , it has been reported that the specific activities of both FBPase and PFK increase in comparison with fully aerobic conditions , an increased PEP to pyruvate ratio has previously been observed in None of the previous discussed factors, however, explains the unexpected lower biomass yield observed in SUC-PHOSP by comparison with SUC-HYD. One of the factors that could be indeed different between these strains, leading to different network operations, is the intracellular free phosphate concentrations (iv). Phosphate is a substrate for the reaction catalyzed by the SucP and, at the same time, it is one of the products of the reaction catalyzed by the FBPase. Thus, it is possible that in those cells with higher FBPase activity, the released phosphate had a positive impact on the rate of sucrose phosphorolysis, probably easing a metabolic bottleneck. Another source of phosphate could be the flow through the methylglyoxal pathway. In this pathway, one dihydroxyacetone-phosphate is converted into pyruvate and inorganic phosphate is realized, while no ATP is produced. In that case, although more phosphate is released, the ATP yield is affected. Moreover, methylglyoxal toxicity could have additional negative effects.+:ATP stoichiometries in the proton pumps  could result in different metabolomics profile. Because PTS has the capacity to phosphorylate both extracellular and intracellular glucose  and the FBPase. One theoretically possible way to eliminate this futile cycle is the deletion of the genes pfkA and pfkB, enforcing the glycolytic flow through reactions belonging to the Entner-Doudoroff pathway or the pentose-phosphate pathway  and pyruvate kinase (EC 2.7.1.40)  explaining the fall in the biomass yields are seldom discussed. Wang and co-workers proposed that ATP dissipation was probably a response to a relative excess of ATP respect to the amino acids and other building blocks in the mutant lacking Regarding the potential effect of oxygen limitation in the observed decrease of the ATP yields, it seems interesting to study the impact on the ATP yields of the introduction of production pathways capable to re-oxidize the NADH under anaerobic conditions. One possibility could be the introduction of a NADH-consuming polyhydroxybutyrate pathway


Metabolic exchange mediates interactions among microbes, helping explain diversity in microbial communities. As these interactions often involve a fitness cost, it is unclear how stable cooperation can emerge. Here we use genome-scale metabolic models to investigate whether the release of “costless” metabolites (i.e. those that cause no fitness cost to the producer), can be a prominent driver of intermicrobial interactions. By performing over 2 million pairwise growth simulations of 24 species in a combinatorial assortment of environments, we identify a large space of metabolites that can be secreted without cost, thus generating ample cross-feeding opportunities. In addition to providing an atlas of putative interactions, we show that anoxic conditions can promote mutualisms by providing more opportunities for exchange of costless metabolites, resulting in an overrepresentation of stable ecological network motifs. These results may help identify interaction patterns in natural communities and inform the design of synthetic microbial consortia. In considering cross-feeding among microbes within communities, it is typically assumed that metabolic secretions are costly to produce. However, Pacheco et al. use metabolic models to show that ‘costless’ secretions could be common in some environments and important for structuring interactions among microbes. A variety of explanations have been proposed as possible solutions to this discrepancy10, including metabolic cross-feeding13. This phenomenon, in which one species produces metabolites that are then consumed by another, has been shown to enhance the capacity of microbes to survive in resource-poor environments16. However, it is not clear how these cooperative phenotypes emerge, as they often involve the exchange of metabolites that are costly for the producer. This apparent altruism introduces the potential for the rise of cheating organisms that do not contribute common goods but still benefit metabolically from others, challenging community stability17. Previous studies have addressed this dilemma in different ways21, though some modes of exchange are not associated with a drop in fitness22. Given the evolutionary dilemmas associated with costly cooperation, we ask here whether the exchange of metabolic secretions that do not impose an effective fitness cost can in principle help account for the degrees of biodiversity observed in nature.The astonishing number of microbial species observed in natureEscherichia coli secreting acetate under limited oxygen) that can support other species15. This phenomenon may allow community benefits to emerge as a product of otherwise selfish acts by individual organisms. It is not obvious, however, whether such behavior extends beyond a few fermentation byproducts or how widely it varies across microbial species and environmental contexts23. Moreover, it is not clear whether these byproducts have the potential to enable or enhance growth of other species in complex communities.It is known that microbes often secrete waste products 29. In this study, we evaluate the impact of costless metabolic secretions by applying FBA to a large space of microbial species and environmental conditions. Moreover, we quantify the degree to which environmental variables, such as oxygen and carbon source, contribute to costless metabolic secretions, interspecies interactions, and community stability. Though the present work focuses on secretions and interactions predicted computationally, we restricted our analysis to microbes associated with high-quality and experimentally verified in silico models, which have allowed us to make predictions consistent with previously established empirical knowledge. However, the current analysis should be viewed as an exploration of a large space of stoichiometrically possible costless interactions , whose global patterns can motivate and inform future experimental and theoretical endeavors.Previous computational models of microbial community metabolism have yielded useful predictions on mutually beneficial and competitive behaviorsvs, and then ask whether this constraint is expected to cause the organism’s growth rate  to be less than its growth rate without this constraint . A small set of simulations of this kind for a single organism  forms the basis of our subsequent calculations. The above equation can thus be viewed as the defining characteristic of a costless metabolic secretion.Understanding whether the secretion of a metabolite by an organism is associated with a decrease in fitness (interpreted here as growth rate) is difficult to assess experimentally, but can be readily calculated using genome-scale models of metabolism (see Methods). For example, one can impose the secretion of a given compound at a given rate 30, signaling and gene regulation35, pH changes36, and explicit pathway-dependent cost of enzyme production37. Our definition of “costless” may therefore be interpreted as a heuristic that captures expected spontaneous metabolite secretions, in contrast to secretion that would be associated with a growth or fitness reduction.We note that while FBA provides mechanistic insight into the tradeoff between metabolic reaction costs and benefits, current predictions (including those on the costless nature of a metabolic secretion) may depend on factors not captured by our method, including temperatureHaving illustrated in an individual case how metabolite secretion costs can strongly depend on carbon sources, we sought to map the prevalence of costless secretions across a broad set of organisms and environments. As an initial core analysis, we carried out a total of 1,051,596 unique simulations, each with two organisms from a set of 14 genome-scale models of facultative anaerobes and two carbon sources from a set of 108 compounds . Upon running such simulations for all combinations of species and environments, we obtained distributions for the value of cs  simulations that substrate concentration had a negligible effect on the identity of secreted metabolites . Moreover, though empirical testing of every simulation we performed is inaccessible, we note that experimental data from previously published work supports key portions of our predictions , the majority of such relationships were unidirectional. One striking example of this phenomenon is that of cyanobacteria and heterotrophic organisms, with Synechocystis depending frequently on other organisms. We also observed that E. coli, Bacillus subtilis, and S. cerevisiae, three species commonly used as model microbial organisms, were more frequently the giving organisms in cases of obligate syntrophy. These pairings not only shed light on the mechanisms behind interspecies codependencies, but may also serve as a map for assembling co-dependent synthetic communities stabilized by costless metabolic exchange.After analyzing general growth outcomes across our entire simulation set, we sought to determine which specific organisms could not grow without the costless secretions of a partner. Our simulations identified a diverse space of such organisms, with most species exhibiting at least one case of obligate syntrophy with all others Fig. . Though 52, we defined the cooperativity index C of two carbon sources α and β as the difference between the number of simulations that resulted in growth from both carbon sources  and the product of the number of simulations that resulted from single carbon sources . These counts were normalized by the total number of simulations involving the specific pairing of carbon sources being analyzed , and mutualism , each with or without competition for a primary carbon source Fig. . We chosM. extorquens with B. subtilis, E. coli, and K. pneumoniae exhibited commensal interactions (chiefly with M. extorquens receiving). In contrast, the distribution of interactions shifted toward mutualism when oxygen was made unavailable. These patterns were also mirrored in a majority of individual species pairings. As with the positive shift observed in the distributions of secreted metabolites , we first enumerated all possible interaction network motifs Fig.  and calcμmax) of each species from 0 to 1 h-1, we simulated the growth of the pair under each motif type for 500 h. If both species survived at the end of the simulation, we marked the motif type as stable at that combination of specific growth rates. We mapped the space of stable species pairs under each motif type, observing that competitive interactions generally had a reduced parameter space for enabling stability , the potential for stability greatly increases across our parameter space, even in the presence of competition for carbon sources. These motifs, with their associated prevalence data and dynamical properties, can overall serve as an atlas for guiding the engineering of stable synthetic consortia built off of costless metabolic relationships.We have investigated the pairwise growth phenotypes and interactions of 24 diverse microbial species in over 2 million computational experiments. We found that resource-poor environments can provide the basis for the release of a wide variety of useful metabolic products secreted without cost by their producing organism; these costless metabolic products provide, in a manner chiefly dependent on oxygen availability and environmental composition, valuable environmental enrichment, nearly doubling the potential of minimal environments to sustain growth. We further found that exchange of costless metabolites established beneficial uni- and bidirectional interspecies interactions, associated with different chances of stability of the ensuing consortia.54, purely competitive phenotypes can lead to community collapse in homogenous environments, which can limit taxonomic diversity in nature55. By studying the prevalence of mutually beneficial interactions in the presence of competition, our study can help understand metabolic dynamics in resource-poor environments, such as the oligotrophic communities found in the open ocean. Costless secretions, some of which resemble the metabolic leakages that underlie the Black Queen Hypothesis may also contribute to the maintenance of small genomes in resource-poor environments, as the metabolic needs of some organisms can be fulfilled by others. Interestingly, the prediction that resource-poor environments can lead to diverse secretions and thus to the emergence and maintenance of beneficial interspecies interactions is consistent with prior suggestions that resource abundance or lack of stress may reduce the reliance of communities on metabolic exchange60.Our iterative medium expansion method allowed us to observe which metabolites were secreted in response to others in a mechanistic fashion, highlighting the capability of costless metabolites to enrich minimal environments and sustain biodiversity, even when organisms were competing for the same primary nutrients. Though spatial segregation of competing organisms can also allow for stable communities27 and that provides a window into metabolic relationships in environments harboring steep oxygen gradients, such as the human gut61. By carrying out a set of hybrid oxic–anoxic in silico experiments, we observed that the additional metabolites secreted anoxically by a facultative anaerobe could provide valuable nutrients for aerobically growing organisms. This phenomenon has been suggested to play an important role in maintaining equilibrium in communities at oxic–anoxic interfaces in the mammalian gut63 and could be the subject of further mechanistic studies.Our interaction analysis provides deeper mechanistic insight into the increased prevalence of mutualistic interactions without oxygen, a phenomenon that has been previously predicted computationally29, such as temperature30, signaling and regulatory-based decisions35, pH changes and metabolite toxicity36, and concentration-dependent thermodynamic gradients64. In addition, the cost of metabolite secretion and the cooperative or competitive nature of an interaction may change when interpreted across different timescales23, a quality that is not fully captured by the framework described here. In spite of these limitations, however, our analysis is able to demonstrate the plausibility of widespread costless cross-feeding in nature. Our results can also serve as a basis for prioritizing future specific experiments, for which model predictions could be thought of as a null hypothesis against which to compare empirical measurements. Dynamical modeling coupled with these metabolic analyses could then be used to obtain the parameter space most likely to yield desired stable partnerships in vivo. Because this approach relies on screening, in a scalable way, synergy-inducing environments, as opposed to engineering individual strains, it can simplify the process of assembling synthetic communities65 and enhance our understanding of microbiomes.Although our modeling method considered a wide space of mechanistic constraints in predicting costless metabolic exchange, we acknowledge that secretion patterns and exchange potential are also defined by a variety of other biological factors that fall outside the scope of our modeling framework69 and described procedurally70 by various groups, and generally comprises an automatic generation of a model based on pathway and genome data followed by manual curation by integrating phenotyping, metabolomic, or transcriptomic data71. We note that although an automatically generated draft metabolic model can be constructed for virtually any organism for which a genome annotation exists, the space of high-quality, experimentally verified metabolic models that have undergone the manual curation process summarized above is comparatively very small72. This is due to the time and resources needed to complete the curation process, which can span from 6 months70 to >10 years for the iteratively refined model of E. coli K-1273. We nonetheless consider this process to be essential in producing models that can generate the mechanistic cross-feeding predictions detailed here, which rely on verified metabolic capabilities in monoculture.A genome-scale metabolic reconstruction was obtained for each of the 14 facultative anaerobic organisms used in the analysis, as well as for the organisms used in our habitat-specific simulations , making the resulting costless cross-feeding predictions particularly useful for synthetic ecology experiments and microbial community assembly. Importantly, each metabolic model includes reactions that account for the energy requirements of organism growth, as well as those of metabolite production and secretion. These requirements are often incorporated as two key reactions: (1) NGAM, or non-growth-associated ATP maintenance, which comprises an ATP hydrolysis step that simulates ATP usage for processes that are not needed for growth; and (2) GAM, or growth-associated ATP maintenance, which accounts for energy usage in growth-associated processes such as macromolecule and protein synthesis. A minimum level of flux  must flow through each of these reactions in order for the models to grow in silico. In this way, energetic costs of growth and metabolite production and transport are accounted for in the models.The models used in this analysis span five taxonomic phyla, as well as a variety of primary metabolic strategies  using the constraint-based reconstruction and analysis (COBRA) Toolbox70. An FBA problem is framed in the context of several constraints, namely: (i) S, the stoichiometric matrix of dimensions m × n where m is the number of metabolites and n is the number of reactions in the model; (ii) v, the vector of all reaction fluxes; and (iii) vmin and vmax, flux constraints placed on v, defined by enzymatic capacity and experimentally measured uptake rates.Our computational method comprises a set of programs written in MATLAB that use FBA to mechanistically define the growth status and metabolic exchange of microbes through costlessly secreted byproducts. Briefly, FBA is a mathematical method that determines an optimal distribution of metabolic flux through a biochemical network that will maximize a given objective, usually biomassvg,0. To determine which metabolites are secreted costlessly, we set this growth rate as a minimum for the biomass flux and apply FBA again, recording any metabolites that were secreted and the new growth rate, vg,s. We also apply the additional constraint of minimizing all reaction fluxes across the network to more closely simulate efficient use of the proteome and minimize cycling of metabolites through the network75. Our linear program therefore becomes:We employ FBA to determine if an organism is able to grow on the in silico growth media conditions we define, in addition to which metabolites are taken up and costlessly secreted. We first apply FBA by maximizing for growth and obtaining an optimal growth rate for an organism, i and j, with biomass production set as the objective function while minimizing the sum of the absolute value of v. Because we focus on the emergence of potential metabolic exchange through the availability of costlessly secreted metabolites, our modeling framework purposefully keeps FBA optimizations separate for each model without accounting for spatial or temporal community structure. It is also for this reason that we establish the biomass fluxes of each in silico organism as the objective functions to be optimized, as we are concerned with secretion of potentially useful metabolic byproducts that arise out of “selfish” optimal growth. This assumption of maximum growth with proteome optimality is also key for translating these organisms and predictions to in vivo synthetic ecologies, where biomass optimization more closely describes the behavior of organisms in batch or continuous culture76. In simulations where we employed alternative objective functions, we optimized either minimization of biomass production, maximization of ATP production, or minimization of ATP production  to compare secretion profiles to those observed under biomass maximization. For ATP maximization and minimization functions, we set the ATP maintenance reaction in each of the models as the objective.This optimization aims to encompass any enzymatic cost incurred by the organism in synthesizing and exporting any metabolite we deem to be costless. During each step in which growth or metabolite absorption and secretion are computed, FBA optimizations are performed separately for each in silico organism NM of in silico organisms to be simulated together (for pairwise simulations NM = 2), (4) the number NCS of carbon sources to be provided to each simulation, (5) a Boolean variable Ω = {1,0} that specifies if oxygen will be made available to the in silico organisms, and (6) a list of metabolites that makes up a simulated base growth medium, Mmin. This base medium contains various nitrogen, sulfur, and phosphorus sources, as well as vitamins, ions, and metals needed for growth of the organisms  a data structure containing the genome-scale metabolic models to be used, 2) a list of carbon sources, (3) the number  a list oNM,NCS = 2). Although each genome-scale metabolic model we used has been manually curated to reflect in vivo metabolic capabilities, very few experiments have been performed to verify FBA-generated predictions for more than a single species77. We therefore limit the number of in silico species to two, in order to interpret the growth and cross-feeding predictions with greater confidence. This limit also constrains the combinatorial space of the simulations, which grows exponentially and becomes numerically intractable with more models and carbon sources. In addition, limiting simulations to NM = 2 allows for greater experimental accessibility for assembling synthetic ecologies based on costless metabolite exchange. Our algorithm can nonetheless be applied to any {NM, NCS >0}.We focused on pairwise species growth with two carbon sources  plate, which is used for phenotyping and curation of genome-scale metabolic modelsvmax for each exchange reaction pertaining to a medium metabolite was removed in each of the models i and j. This bound was fully removed (vmax = 1000 mmol × gDW−1 × h−1) for non-limiting medium components, and was set to (vmax = 10 mmol × gDW−1 × h−1) for the growth-limiting carbon sources α and β. This latter value is drawn from experimentally estimated uptake rates of sugars by E. coli in exponential growth conditions73, and is applied equally to all other species to simulate general availability of the carbon sources in the environment. In all aerobic simulations, the maximum uptake rate for oxygen was also unconstrained (vmax = 1000 mmol × gDW−1 × h−1), so as not to explicitly model conditions similar to those of overflow metabolism. All other exchange reaction vmax values are set to zero to block uptake of metabolites not in the medium.To permit uptake of the metabolites in the medium, the constraint on the uptake flux bound F that, given a medium condition M and organisms i and j, outputs the binary growth status g of the organisms, as well as the set of metabolites σ secreted costlessly by the organisms:We describe the FBA operations at the core of our algorithm as a function E for a given organism pair with a pair of carbon sources is made up of an initialization step, an expansion step consisting of series of applications of F, and a completion step  of both organisms and the set of any costlessly secreted metabolites, σc. To avoid recording metabolites reported to be secreted only as a result of numerical uncertainty in FBA, a minimal lower flux bound of 0.01 mmol × gDW−1 × h−1 was applied as a cutoff for determining secretion. If at least one organism in the pair grows, the medium is supplemented with σc:In the expansion step, the function As long as new metabolites continue to be secreted into the medium, that is,F continues to be applied. This stepwise expansion simulates the organisms responding to the costlessly secreted metabolites being secreted and generating a richer medium. The completion step occurs when no new metabolites are secreted,cS. Our algorithm therefore carries out individual in silico experiments cs applications of F given organisms i and j, carbon sources α and β, and the presence or absence Ω of oxygen:81 and are intended to simulate growth of species in a chemostat, with constant replenishment of medium components. The abundance of each organism si, in g/L, is modeled as follows:We designed a dynamical modeling method to simulate the long-term stability of each pairwise interaction type observed in our in silico experiments. We first established a graph theory framework to map each simulation to a specific interaction motif, each of which accounted for the general interaction type , the number of carbon sources consumed by the pair, and the competition status for the carbon sources  Fig. . We nextμimax, is the maximum specific growth rate of organism i in h−1, mα is the concentration of carbon source α in g × L−1, i reaches half its maximal growth rate in g × L−1, and D is the chemostat dilution rate in h−1. If two carbon sources are present and the organism is determined to take up both by the motif definition, the equation is modified to include a carbon source β as follows:where The concentrations of each carbon source are defined as follows:mα in g × L−1, and gnutrient × gcells−1. This equation is modified with an additional term (organism j) to simulate competition for mα.where −1 were defined as follows:i and consumed by organism j. −1, sj in gmetabolite × gcells−1, and sj to reach half of its maximum growth rate in g × L−1.To simulate metabolic exchange, equations for the abundances of costlessly produced metabolites  classifiers to quantify the degree to which oxygen availability, species identity, and carbon source type contribute to the variability in secretion profiles. SVMs were constructed using the MATLAB function “fitcsvm” for the two-class oxygen availability vector, and using the MATLAB function “fitcecoc” for the multi-class species and carbon source category vectors. Secretion profiles were represented as a binary matrix, with each row representing a simulation and each column denoting a metabolite. Cross-validation was performed by: (1) randomly partitioning the matrix of secreted metabolites into 10 sets of equal size, (2) training the classifier on nine of the sets and testing on the remaining sets, (3) repeating training and testing for the remaining nine partitions, and (4) combining accuracy statistics for each set.39, which uses dFBA38 to integrate metabolic fluxes over sequential time intervals. This method enables specification of substrate concentrations as well as measurement of biomass growth and byproduct concentrations. As dFBA is more time- and computationally intensive than our primary FBA-based algorithm, we limited the number of COMETS simulations to analyzing single organisms growing on one carbon source. For each organism–carbon source pair, we ran COMETS with three different carbon source concentrations  for a simulated 2 h to capture differences in secreted metabolites. These combinations yielded a total of 9072 distinct simulations.We carried out a set of simulations to determine the effect of substrate concentration on metabolite secretion patterns. For these simulations, we used the COMETS  software packagegithub.com/segrelab/CostlessExchange.Code for running pairwise cross-feeding simulations is available at Supplementary InformationPeer Review FileDescription of Additional Supplementary FilesSupplementary Data 1Supplementary Data 2Reporting Summary


We demonstrate several interesting applications of our algorithm, ranging from identifying amino acid biosynthesis pathways to identifying the most diverse pathways involved in degradation of complex molecules. We also illustrate the scalability of our algorithm, by studying large graphs such as those corresponding to microbial communities, and identify several metabolic interactions happening therein. MetQuest is available as a Python package, and the source codes can be found at https://github.com/RamanLab/metquest.Exhaustive identification of all possible alternate pathways that exist in metabolic networks can provide valuable insights into cellular metabolism. With the growing number of metabolic reconstructions, there is a need for an efficient method to enumerate pathways, which can also scale well to large metabolic networks, such as those corresponding to microbial communities. We developed MetQuest, an efficient graph-theoretic algorithm to enumerate all possible pathways of a particular size between a given set of source and target molecules. Our algorithm employs a  Typically, a genome-scale metabolic network consists of thousands of reactions and metabolites, which capture vital metabolic pathways such as the biosynthesis of amino acids and lipids, ATP synthesis, as well as transport of molecules inside the cells. Over the recent years, the construction of such networks has increased tremendously, in part also due to the growing number of genomes sequenced4. There are several well-established constraint-based methods to analyse metabolic networks5; however, these methods require well-curated genome-scale metabolic models for making reliable predictions. The number of such well-curated models are very few7, in comparison to the genome sequences available. Alternative approaches to analyse genome-scale models are based on network “topology”10 or Boolean rules12. In the former, the metabolic networks are abstracted as networks or graphs, and graph-theoretic algorithms are employed to predict or infer metabolic pathways. The latter set of methods are based on definitions of Boolean functions for identifying if particular reactions can proceed or not. Both methods generate qualitative predictions and do not entail the requirement of well-curated genome-scale models.Genome-scale metabolic networks are very useful to understand the complex network of metabolic reactions happening inside cells13, atom–atom mapping, subgraph matching or stoichiometry16 have been developed previously. These methods, regardless of the approach, aim to determine the route(s) of conversion between sets of source and target molecules. The algorithms based on network expansion traverse the graph depending on the availability of precursor compounds and determine different routes of conversions from the metabolic network. The input graph to these algorithms can be represented in different ways, such as a substrate graph17 or a hypergraph18, each of which captures information at different levels of complexity. Substrate graphs are one of the simplest forms of representation, where all metabolites participating in a reaction are connected to each other. Traversing these graphs using breadth-first or depth-first search to identify different routes of conversion often leads to erroneous paths such as a 2-step glycolysis, converting glucose to pyruvate (via ADP), since these could proceed using the connections between “side” metabolites. To avoid such spurious results, several tools, such as FMM (From Metabolite to Metabolite19); and Metabolic Tinker20 use substrate graphs after excluding the connections from (high degree) “currency metabolites”17 such as H+, Water and NADPH. However, the substrate graph representation fails to capture the fact that more than one reactant may be required for a reaction to occur.Several graph-based methods, using naïve network expansion22. These representations consider the participation of multiple compounds in a reaction to produce product(s), which is crucial while depicting metabolic networks. One such hypergraph-based algorithm, Rahnuma18, performs a depth-first search to identify pathways that lead to the target metabolite from the source. In a few other studies13, the metabolic networks are represented as bipartite graphs to first determine the scope of the starting seed metabolites. The synthesis pathways were then assembled by backtracking from the target to the source, which becomes computationally challenging due to the presence of branched and cyclic pathways in metabolic networks.To overcome these problems, algorithms were developed to operate on more informative bi-partite and hypergraph representations of metabolic networks23 BPAT-S (Branched Pathfinding using Atom Tracking and Seed pathways), seed pathways (linear) are first identified between the source and target compounds, based on the atom loss/gain. The branched pathways are then identified by finding the linear pathways between the metabolites contributing to this atom loss/gain. These pathways are then ranked based on the total number of reactions and the number of conserved atoms. ReTrace24, another algorithm to find branched pathways, tries to combine linear shortest paths based on the transfer of a high fraction of atoms from source to target, thereby finding only the k-shortest paths.The problem with determining branched-pathways has been addressed in a few studies, which seek to use atom tracing. In one such method9 defines a set of atom-mapping rules based on the possible chemical conversions and seeks to identify paths where the atom loss is minimum. The predictions of this algorithm are restricted to the first k-shortest paths. PathPred14, another tool to predict metabolic pathways, performs subgraph matching on the graph generated from the KEGG RPAIR database. Similarly, RouteSearch25, another algorithm based on branch-and-bound search, finds paths based on the mapped network generated from the atom mappings.Another class of methods use either information from atom-mapping, thermodynamics or structural transformation. For instance, the algorithm developed27. EFMs have been widely used to study metabolic networks31; there are many tools that have been developed to study and evaluate EFMs, in different contexts33. However, the methods to enumerate EFMs, not only entail the requirement of well-curated genome-scale metabolic networks but also identify only the pathways at steady state. Such steady-state identification of pathways can limit the scope of analyses to in vitro experiments34.Another set of methods to study alternate pathways in metabolic networks are based on Elementary Flux Modes (EFMs), which are minimal sets of enzymes, operating in the correct direction, and are required for a given system to carry a steady-state fluxDespite the availability of several types of methods to understand and analyse metabolic networks, a simple and efficient method with minimum input for performing large-scale analyses is still lacking. Also, the current methods to identify pathways between the source and target molecules are restricted to smaller networks and do not enumerate long pathways, thereby restricting the scope of analyses. Although a few of these algorithms handle cyclic and branched pathways, they require additional information such as atom transfer, which may not be readily available from the semi-curated metabolic networks. Further, we find that many of these tools are web-based, and do not lend easily to large-scale analyses; a large fraction of these tools are also currently inaccessible  requires only the topology of the reaction network (rather than stoichiometry and atom mapping), (b) is simple and scalable to metabolic networks , (c) efficiently handles cyclic and branched pathways, and (d) examines multiple alternate routes of conversion. An important application of identifying and understanding such multiple alternate pathways is in metabolic engineering, where organisms are routinely engineered to produce a given molecule. To this end, we developed MetQuest, an efficient and scalable graph-theoretic algorithm, which exhaustively identifies all the pathways, or “sub-networks” between a given set of source and target metabolites using the input reaction network. In contrast to constraint-based approaches, our algorithm requires only the reaction network topologies which are readily available from draft reconstructions and does not necessitate the requirement of well-curated genome-scale models. Due to the nature of the implementation, we are able to successfully identify branched and cyclic pathways. In comparison to other graph-based algorithms, we observe better results, in terms of the completeness of the output pathways. Since we perform exhaustive enumeration, we not only recover the well-known pathways such as glycolysis and amino acid biosynthesis but also identify several diverse pathways such as those involved in biodegradation of pollutants such as catechol. Further, because of the scalability of our algorithm to operate on large metabolic networks, we are also able to demonstrate several metabolic exchanges happening in known natural and synthetic microbial communities.guided breadth-first search (BFS) of the metabolic network, to identify all the metabolites that can be reached from a given set of “seed” metabolites. In the second phase, we design a dynamic programming algorithm, which solves the non-trivial problem of assembling reactions into pathways to produce the metabolite of interest.In this section, we present a detailed overview of our algorithm MetQuest, broadly divided into two phases. The first phase involves a 35. The non-common exchange reactions are connected only to the extracellular environment. Such a bipartite representation disallows invalid conversions as may be interpreted from substrate graphs and helps in generating valid paths with biologically meaningful conversions36. The input to MetQuest is a directed bipartite graph T of target metabolites and an integer size of any pathway generated by MetQuest. Note that the set We begin by describing the input representation of the metabolic network. Any given metabolic network can be represented as a directed bipartite graph Definition 1 (Reachable metabolite): A metabolite Definition 2 (Branched pathway producing): An Definition 3 (Cyclic pathway producing): A cyclic pathway Definition 4 (Size of a pathway): The size of a pathway The goal of MetQuest is to identify all pathways of size at most 38. We modify the standard BFS by guiding it, based on the availability of precursor metabolites. Starting with the set of seed metabolites breadth-first manner, incrementally adding triggerable reactions to the BFS queue. The expansion stops when there are no further reactions that can be visited. During the expansion, a reaction node is labelled as stuck, if it does not (yet) have the necessary precursors in visited.BFS is a classic graph traversal technique that visits all the nodes of a given graph, starting at a source node, in a breadth-first fashion. BFS employs a queue of vertices, where newly discovered vertices are enqueued, to be processed at a later stage. A complete description of the BFS algorithm can be found elsewhereAt the end of the traversal, we obtain the scope 8, and forward propagation39 reported earlier. The former method seeks to identify the synthesising capacity of the metabolic network using the input seed set of metabolites. The latter aims to identify the minimal precursor sets of seed metabolites that are required to produce a given set of target metabolites. This step in our algorithm also derives the information about the scope of metabolites from the given metabolic network; it, however, distinguishes itself by making a systematic note of the visited and stuck reaction nodes, which are exploited at a later stage for efficient and exhaustive enumeration of biosynthetic pathways.This process of graph traversal resembles the ideas of network expansionmemoising the precomputed values. The algorithm steps are listed below and the pseudo-code can be found in Algorithm 1 and Algorithm 2. Our algorithm maintains a table of size scope of seed metabolites and the maximum number of reactions we allow in a pathway (the “size cut-off”) respectively. We start filling the table entries by first considering the seed metabolite set MetQuest uses a recursive dynamic programming formulation for computation of sub-networks. However, it avoids repeated recursive calls by In the first iteration, we find all the reactions Our algorithm fills Let one pathway of size Now, assume that we have fixed a set of To address the above issue, our algorithm not only generates the sum The for loop from Line 13–21 (Algorithm 1) generates a set of partitions populateTable  for the reaction populateTable is to populate the entries of the form For every For a particular partition populateTable.Our algorithm iterates over every pathway or reaction sub-network all the input metabolites of a reaction. Due to this, any pathway generated by our algorithm is complete, i.e. the reactants required by the reactions constituting the pathway are all producible. Further, since for any metabolite, we perform a union of sets of reactions, we avoid repeated generation of the same reaction sets. Due to this, we automatically report only the first occurrence of cyclic pathways. The demonstration of our algorithm on a toy-network and a cyclic pathway can be found in Supplementary Methods https://github.com/RamanLab/MetQuest. Supplementary Methods 40 using the constituent reactions.We note that the output pathways for every metabolite are generated by considering the sub-networks of complete pathways. Further, we showcase the ability of MetQuest to identify diverse pathways involved in biodegradation of an important industrial pollutant. Finally, we show that MetQuest scales well to large networks, and is, therefore, a powerful tool to predict and understand metabolic exchanges in microbial communities.In this section, we show that our algorithm can recover sub-networks of different types, including the well-known glycolysis and amino acid synthesis pathways. We also compare our output sub-networks with those generated by other algorithms and demonstrate that MetQuest produces better results since it generates Genome-scale metabolic networks catalogue numerous metabolic pathways happening inside a cell. Identifying these pathways helps us to better understand the level of redundancy in the cells for producing key metabolites. To this end, we applied MetQuest on well-curated networks to identify and understand pathways between different reactants and products.E. coli iJO136641. We constructed the corresponding directed bipartite graph, consisting of 12,974 edges and 5,659 nodes, and specified pyruvate as the target node. We included glucose from extracellular environment (“glc-D_e”), co-factors, co-enzymes and the energy currencies in the seed metabolite set We identify well-known biochemical pathways such as glycolysis using the genome-scale metabolic model of We successfully recovered the well-known glycolysis pathway and, in addition, due to the exhaustive enumeration, we could also identify 4,787 paths from the seed set of metabolites These observations raise an important question: “Why should so many pathways potentially exist inside the cell in addition to glycolysis, which is the most preferred pathway?” To answer this question and understand the differences between each of these pathways, we studied the similarity between the obtained sub-networks, using the Jaccard index. Of 42. The latter set, with lower Jaccard values, point towards the existence of alternate pathways that produce identical precursor metabolites to synthesise pyruvate. These predominantly include the methylglyoxal pathway, the Entner-Doudoroff pathway and the pentose-phosphate pathway. The existence of many alternate pathways points towards the extent of redundancy in metabolic networks, which helps the organism salvage gene losses43. Further, some of these alternate pathways were also shown to outperform the canonical pathways under different sets of physiological conditions44. Identification of such alternate pathways by MetQuest through an exhaustive enumeration not only showcases its ability to correctly identify pathways on well-studied networks, but also renders MetQuest a viable tool to identify pathways from metabolic networks about which very little is known.The former set of sub-network pairs, with higher Jaccard values, can be understood in light of the presence of multiple transporters, which are either used to transport compounds from the environment or between different compartments of the cells. These transporters function under varied environmental conditions, where they employ different mechanisms to transport glucose inside the cellS. cerevisiae iMM90445. As there are additional transport reactions between the compartments, we used a higher cut-off We also determined sub-networks between different metabolites in a compartmentalised model of mentclass2pt{minimPseudomonas putida for bioremediation of such pollutants47. We sought to identify the pathways that render P. putida unique and tailored for this application. To this end, we investigated pathways involved in the metabolism of such compounds, which are otherwise harmful to many other micro-organisms. Further, we explored if the breakdown of catechols could directly lead to energy producing pathways. Hence, we identified all the pathways that start from catechols and lead to the intermediates of the tricarboxylic acid (TCA) cycle. Since catechols require complex mechanisms to be degraded to smaller intermediates, we used a higher cut-off P. putida to degrade catechols to the intermediates of the TCA cycle  of multiple organisms and identify sub-networks between different metabolites. Specifically, we construct the community bipartite graph of a microbial community by considering a common extracellular space through which metabolite exchanges can happen. Further, we analyse the sub-networks generated by MetQuest and show that it can correctly recover previously reported metabolic interactions.Beyond individual networks, it is also interesting to identify sub-networks in communities of organisms and understand their metabolic interactions, which are known to play a critical role in determining the stability of microbial communitiesEscherichia coli, computational analyses were performed on genetically modified E. coli strains55. Specifically, two different E. coli strains with knockouts of b2276 and b3708 genes were modelled together, and the metabolic interactions were predicted. We simulated these gene knockouts by removing the reactions catalysed by these genes from the genome-scale metabolic model2, after considering the Gene-Protein-Reaction relationships. We then constructed the community bipartite graph and applied MetQuest to predict the metabolic exchanges between these two strains. We assumed seed metabolites, including glycolate (as given55) and applied MetQuest to find all sets of sub-networks to every metabolite within the scope of glycolate, pyruvate and both these sources independently, with a size cut-off To study the metabolic interactions in From the sub-networks generated, we determined the metabolites that can be potentially exchanged between the strains. We were able to recover the reported acetate and formate exchanges happening between the two strains. In addition, we observe that acetate , Desulfovibrio vulgaris (dv), and Geobacter sulfurreducens (gs) from the Path2Models database57, which hosts metabolic networks generated through automatic pipelines. We constructed the three-member community bipartite graph by connecting the genome-scale metabolic models through their common exchange reactions. We defined the seed metabolite set tRNA molecules. We also added cellobiose to this set (as reported56) and chose to determine sub-networks with a size cut-off 56 predominantly led to the production of amino acids such as L-serine, L-leucine, L-aspartate and L-valine (in gs) and L-threonine and L-glycine (in dv) respectively, which contribute to the biomass, thereby enabling a stable microbial consortium.To illustrate the performance of MetQuest on a larger network, we computed multiple sub-networks in an experimentally demonstrated three-member microbial consortiumWith the increasing number of draft genome-scale metabolic reconstructions, there is a pressing need for efficient algorithms to analyse these metabolic networks and generate useful predictions. It is particularly important that these algorithms perform efficiently with minimum information such as the reaction topology, and also identify pathways in large (multi-)genome-scale metabolic networks.To this end, we propose MetQuest, a scalable and efficient graph-based algorithm for identifying all possible metabolic pathways in genome-scale metabolic models. Specifically, we focus on exhaustively determining all alternate pathways (of a particular size) between a set of seed and target metabolites. We also demonstrate the application of our algorithm by identifying multiple pathways involved in several important parts of metabolisms such as the central carbon metabolism and the amino acid metabolism. Further, we show its usefulness in determining several diverse pathways, which take part in catechol degradation. Besides its applications on the metabolic networks of individual organisms, MetQuest, due to its scalability, can be applied to study larger and more complex networks.13 tries to backtrace the pathway from the target to the source based on the information obtained from the scope calculation. Since the metabolic networks contain many branched pathways, identifying the routes of conversion by back tracing becomes computationally expensive, and can break down rapidly at higher cut-offs. Another method, Rahnuma18, tries to solve the problem of path prediction on genome-scale metabolic networks by abstracting these networks into hypergraphs. Rahnuma, based on depth-first search on hypergraphs, seeks to obtain pathways between two metabolites. However, the performance of Rahnuma on metabolic networks was demonstrated only for shorter path-lengths of 6, and it may not be applicable for identifying longer pathways, such as those involved in the biosynthesis of aromatic amino acids from simple sugars. Moreover, the pathways are computed based on a condition that the metabolite can be used only once in any pathway, which inherently fails to capture cyclic pathways. MetQuest, on the other hand, can identify branched and cyclic pathways, and can perform well on larger metabolic networks for much longer cut-offs, thereby extending its application to analysing microbial communities. Further, MetQuest does not entail the necessity of well-curated metabolic networks, as demanded by enumeration methods based on elementary modes. This renders MetQuest a useful tool to identify pathways and perform large-scale analyses using draft reconstructions. The identified pathways can be further analysed through elementary mode based techniques.A number of graph-based methods to find pathways in metabolic networks have been developed so far. These methods convert the metabolic networks either into substrate graphs, bipartite graphs or hypergraphs. However, these methods are well-suited only for smaller networks and lower cut-offs. For instance, MetaPathE. coli strains. Further, MetQuest also predicted novel interactions involving amino acids such as L-cysteine in the previously reported microbial community56.We have also demonstrated the major strengths of MetQuest: in multiple examples we considered, of individual metabolic networks and real-world microbial communities, MetQuest was able to identify multiple pathways and correctly predict the metabolic exchanges/interactions taking place. MetQuest was able to correctly predict the acetate exchange happening between the two genetically modified However, as with any modelling technique, MetQuest also has its limitations. Firstly, the predictions from MetQuest rely heavily on the quality of the underlying metabolic network. Specifically, a few of the metabolic interactions predicted by MetQuest could be due to model artefacts. There may be other metabolic interactions happening between microbes, which could be absent in the metabolic network (gaps in the metabolic network). Due to this reason, such interactions may not be predicted by MetQuest. Further, our algorithm does not assign any weights to metabolites/paths. Although there are other methods like cFBA and OptCom, which make more quantitative predictions, they also demand better curated metabolic networks. Moreover, as with any graph-based technique, MetQuest also generates a large number of pathways between a given set of seed and target metabolites. All these pathways may not be active at a given time or in a given environment. We primarily see the use of MetQuest as a first-line investigatory tool, to cull down from a very large set of possible communities to a more tractable set, which may be studied further using EFM analyses, constraint-based techniques or through wet lab experiments.In sum, we report a novel and efficient algorithm MetQuest, which (i) rapidly enumerates all possible biosynthetic pathways from a given metabolic network, (ii) efficiently handles branched and cyclic pathways, and most importantly, (iii) scales well to very large networks such as those representing microbial communities. Further, our algorithm requires only the genome-scale metabolic networks, a set of seed and target metabolites and a size cut-off, as against thermodynamic or atom-mapping information, thereby rendering it a very potent tool to perform large-scale analyses. Overall, we believe that MetQuest is a very useful tool for exploring and understanding metabolic pathways in large-scale networks, to generate testable hypotheses for further experiments.Supplementary Information