Saccharibacteria (TM7) species, characterized by their abundant metabolic deficiencies. By embracing uncertainty, our approach can be broadly applied to understanding metabolic interactions in complex microbial ecosystems.The biosynthetic capabilities of microbes underlie their growth and interactions, playing a prominent role in microbial community structure. For large, diverse microbial communities, prediction of these capabilities is limited by uncertainty about metabolic functions and environmental conditions. To address this challenge, we propose a probabilistic method, inspired by percolation theory, to computationally quantify how robustly a genome-derived metabolic network produces a given set of metabolites under an ensemble of variable environments. We used this method to compile an atlas of predicted biosynthetic capabilities for 97 metabolites across 456 human oral microbes. This atlas captures taxonomically-related trends in biomass composition, and makes it possible to estimate inter-microbial metabolic distances that correlate with microbial co-occurrences. We also found a distinct cluster of fastidious/uncultivated taxa, including several  Metabolism, in addition to enabling growth and homeostasis for individual microbes, contributes to the organization of complex, dynamic microbial communities. Within these communities, different microbes have diverse metabolic capabilities that lead to interactions driving microbial community structure and dynamics at multiple spatial and temporal scales . For exaSaccharibacteria (TM7) phylum taxa: Saccharibacteria bacterium HMT-952 strain TM7x  strains. In addition to highlighting their biosynthetic deficiencies, we developed specific hypotheses for their metabolic exchange with growth-supporting partner microbes.Here we introduce a new method, which begins to address the above limitations, and provides a novel prediction of an organism’s biosynthetic capabilities. Our method applies a probabilistic approach to define and compute a metric that estimates which metabolites, such as biomass components, are robustly synthesized by a given metabolic network and which would likely need to be supplied from the environment/community. Discrepancies in these calculated estimates between organisms can be used to generate hypotheses regarding microbial auxotrophy and metabolic exchange in microbial communities. Importantly, our metric has the capacity to estimate biosynthetic capabilities in spite of uncertainty about environmental conditions by randomly sampling many different possible nutrient combinations. In this study, we first demonstrated our method on Our newly developed method quantifies the robustness with which a given metabolic network can produce a given metabolite from variable metabolic precursors. In essence, we quantify a metabolic network specific metric for metabolite producibility by probabilistically sampling sets of possible environments. While the probabilistic sampling can be adjusted to reflect a specific environment, its power lies largely in the capacity to explicitly incorporate in a statistical way the lack of knowledge about environmental composition.The inspiration for this method comes from the statistical physics concept of percolation. Percolation theory has been applied in a wide range of fields, including the study of cascading metabolic failure upon gene deletions in metabolism . In percinP). These probabilities could represent beliefs about the environment, chances of metabolites being available from a host organism, or any arbitrary prior assumption on metabolite inputs. Throughout the majority of our analyses we have assigned inP to be an identical value for all input metabolites. However, as illustrated in an example in our results section (Metabolite producibility in a protein vs. carbohydrate-enriched environment) this probabilistic framework can utilize inP values that vary across metabolites. Following the assignment of inP, the network structure is used to calculate the output probability (outP) of some specified target metabolite. In practice, random sampling of probabilistically drawn input metabolite sets is used to calculate the probability of producing the target metabolite. For each random sample, a modified version of FBA (feas).To implement our method, we first introduced a probabilistic framework for analyzing metabolic networks . In thisn of FBA  is used outP as a function of inP is generated for a given metabolic network and metabolite target. This curve can be estimated by sampling input metabolites for different values of inP (between 0 and 1), and calculating outP. Next, we calculated the inP value along the producibility curve at which outP is equal to 0.5 . Finally, PM is defined as PM = 1-in,0.5P, such that larger PM values correspond to increased robustness. Our method calculates PM efficiently by random sampling and a nonlinear fitting algorithm . In addition to calculating PM computationally for arbitrary metabolic networks and metabolites, we also derived a way to calculate PM analytically using combinatorial equations. The combinatorial equations are built up from simple scenarios to the most general in Using the above probabilistic framework, we defined a novel metric quantifying biosynthetic capabilities, the producibility metric (PM) . The PM https://github.com/segrelab/biosynthetic_network_robustness (https://github.com/elifesciences-publications/biosynthetic_network_robustness).The algorithms used to implement our method are written in MATLAB and designed as a set of modular functions that interface with the COBRA toolbox – a popular metabolic modeling software compendium . The metE. coli to illustrate the performance and interpretation of our method. We started with the E. coli core metabolic network, a simplified network consisting of central carbon metabolism and lacking peripheral metabolic pathways, such as amino acid or cofactor biosynthesis . For example, the metabolites H+ and pyruvate are both highly connected in the metabolic network and have high PM (PM = 0.968 and 0.952 respectively). However, the network also contains several metabolites that are well connected, but have lower PM values. These include, for example, the cofactors AMP/ADP/ATP and NAD+/NADH, which have PM values of ~0.7 and ~0.5 respectively, because they can be produced from each other, but not biosynthesized in this network. The network also includes several examples of metabolites that are poorly connected but have high PM values. One example is D-lactate, which is produced only via Lactate Dehydrogenase from the high PM metabolites Pyruvate and H+  has minimal influence on the PM value of D-lactate  calculations for a genome-scale metabolic networks with a given number of randomly removed reactions. In particular, we applied both FBA and our method to the E. coli auxotrophs to compensate for each other’s metabolic limitations. In particular, we compared experimental data from co-cultures of E. coli auxotrophs from E. coli iJO1366 metabolic network), we calculated the PM for all essential biomass components in each auxotroph and compared the PM values to the experimentally measured synergistic growth of auxotroph pairs  bacterium HMT-952 strain TM7x (Saccharibacteria (TM7) bacterium HMT-955 strain PM004 (Saccharibacteria (TM7) bacterium HMT-488 strain AC001 (Tannerella HMT-286 strain W11667 (Anaerolineae (Chloroflexi phylum) bacterium HMT-439 strain Chl2 (Absconditabacteria (SR1) bacterium HMT-874 strain MGEHA  format at https://github.com/segrelab/biosynthetic_network_robustness . Howeveg trends . These cNegativicutes. These organisms have relatively high PM values for phosphatidylethanolamine but PM values of 0 for cardiolipin and phosphatidylglycerol lipids. Consistent with this result, it has been previously observed that the Negativicutes organism Selenomonas ruminantium lacks cardiolipin and phosphatidylglycerol lipids in its inner and outer cell membranes, but does have phosphatidylethanolamine  is known to scavenge heme  and a saccharolytic organism (Streptococcus mutans) in a protein and a carbohydrate-enriched environment. The hypothesis was that the proteolytic organism would have a higher PM increase in the protein enriched environment as it is able to breakdown amino acids to synthesize other biomass components and likewise the saccharolytic organism would have a higher PM increase in the carbohydrate-enriched environment. We simulated a protein-enriched environment by fixing all amino acids to always be present (inP = 1) when calculating the PM, and simulated a carbohydrate-enriched environment by fixing D-glucose to always be present (inP = 1). Target metabolites were never fixed to be present; for example when calculating the PM of an amino acid in the protein-enriched environment we did not fix that amino acid to be present. We measured the increase in PM in the enriched environments relative to the originally calculated PM, for all 88 biomass metabolites and nine organic acids  showed the most consistent significant correlation with co-occurrence of any pairwise metabolic metric. The PM distance was consistently negatively correlated with the co-occurrence, indicating that organisms that are more similar in PM tend to co-occur. Several other pairwise metabolic metrics were found to be correlated with co-occurrence, although in a less consistent manner than the PM distance . AdditioWe next examined more closely the correlation between the pairwise metabolic metrics PM complementarity and Seed complementarity , Saccharibacteria (TM7), Proteobacteria (genus Desulfobulbus), and Chloroflexi (class Anaerolineae). Many of these organisms are thought to have reduced genomes and limited metabolic capabilities underlying their fastidious nature, much like Mycoplasma. Only one of the previously uncultivated organism we analyzed was found outside of this fastidious cluster, namely Tannerella HMT-286. Interestingly, this bacterium is hypothesized to rely on externally supplied siderophores to support its growth . To gain specific insight into the biosynthetic capabilities of these TM7 relative to other fastidious microorganisms, we further focused our analysis on identifying discrepancies between Mycoplasma and TM7. Our analysis included eight Mycoplasma genomes and three TM7 genomes. Mycoplasma are a relatively well characterized genus of intracellular parasites with reduced metabolic capabilities, and TM7 are a recently co-cultivated phylum of the candidate phyla radiation that display reduced metabolic capabilities and a parasitic lifestyle. There are several cell-wall components for which TM7 has relatively high PM values and Mycoplasma has PM values of zero  strains and their growth supporting partner microbes. Overall, our method provides preliminary insight into the metabolic capabilities of a large number of human oral microbiome organisms and helps further the understanding of the structure of this complex microbial ecosystem.Our method provides an estimate of the putative biosynthetic capabilities of a metabolic network from genomic information. We first implemented this method in Our method differs from other approaches in several key ways that we have demonstrated throughout our analysis. First, it is different from a pathway-based analysis where the percent completion of biosynthetic pathways is analyzed. Our method is based on the entire metabolic network and captures the multitude of different routes through which a metabolite could be synthesized. An additional advantage is that our method does not rely on previously defined biosynthetic pathway annotations and instead seeks to use the entire metabolic network structure to define biosynthetic capabilities. While prior knowledge of pathways can be quite useful in many contexts, specific biosynthetic routes can cross the boundaries of annotated pathways, making pathway completeness uninformative. A prior notable example of this effect is the discovery of an alternative pathway to bypass a TCA cycle gene impairment . This paIt is important to highlight the limitations of our approach. In particular, many of the issues that limit the accuracy of metabolic network analyses in general affect our method as well. The primary limitation is enzyme annotation. Aside from missing or incorrect annotations, subtle processes such as enzyme promiscuity and spontaneous reactions may have unquantified effects on metabolic network function. Reaction direction/reversibility is also difficult to predict as it requires detailed knowledge of reaction thermodynamics and metabolite concentrations. In particular, inaccurate or missing information about reaction direction/reversibility could lead to uncertainty about whether a high PM from our method should be interpreted as reflecting biosynthetic or degradative capabilities (or both). Throughout our analysis we have utilized default reversibility constraints provided by the KBase build metabolic models app , but morSaccharibacteria (TM7) phylum organisms that were recently successfully co-cultivated with growth supporting bacterial host organisms. These TM7 species are the first successfully cultured organisms from the candidate phyla radiation, a large branch of the tree of life consisting mainly of uncultivated organisms  for a specified metabolic network model and metabolite using an efficient nonlinear fitting technique. The nonlinear fitting algorithm estimates the PM by randomly sampling points on the producibility curve that fall near PM. The algorithm starts by sampling a point in the middle of the producibility curve (inP = 0.5) and then using the MATLAB function lsqnonlin to fit a sigmoidal curve to the sampled points of the producibility curve. The fit sigmoidal curve is then used to estimate a value for the PM. Next, a new sample point is obtained which is offset from the estimated PM value with some noise introduced with the specified noise parameter. In this way the algorithm converges on the PM value and samples points around PM, thus increasing the accuracy of its estimate with each iteration. The estimate converges when a specified n estimates of the PM value are all within a specified threshold. The default parameters associated with this function, used for the bulk of our analysis, were: noise = 0.3, n = 7, thresh = 0.01. The parameters chosen were selected by hand to provide reasonable performance.prep_mod– This function is used to prepare the metabolic network model for analysis with our method. The input for this function is a COBRA model, which is saved as a MATLAB structure variable. This code has been developed and optimized to work with KBase generated metabolic networks and is not guaranteed to work with networks from other sources that have different naming conventions. The first modification to the networks is to find and turn off all exchange and maintenance reactions to standardize the network models. Second, the extracellular and intracellular metabolites are identified based on naming conventions and output from the function. Third, exchange reactions are added for each metabolite (producing 1 unit of that metabolite), and a vector indicating the mapping from metabolites to these exchange reactions is output from the function. This vector is used by our method to control the presence and absence of input metabolites in the network model as well as to adjust the inequality mass balance constraints. The final output is a new network model which has been standardized for our method and in which the presence and absence of metabolites can be easily manipulated.find_PM_mods_mets– This function is designed to facilitate the parallelization of the PM calculation. The function takes as inputs a directory of metabolic network models, a directory to store results, a list of target metabolite names, the index of the current network model and metabolite being analyzed and all of the specifications necessary for running calc_PM_fit_nonlin. The metabolite and model being analyzed can be changed dynamically to allow for parallelization. In addition to these inputs, this function has several inputs that allow for standard modifications to the PM calculation procedure. It allows for certain metabolites to be fixed on or off. It allows for several choices of metabolites to be added during the PM calculation process, including adding all intracellular or extracellular metabolites and including the target metabolite or not. It also allows for specification of the inequality mass balance constraint as either all metabolites set to inequality mass balance or all metabolites set to equality mass balance. Furthermore, it has a parameter for the number of runs to calculate the PM to obtain statistics regarding the variability of calc_PM_fit_nonlin. For the analysis done in this work: calculation of PM for single metabolites was done by adding all intracellular metabolites (excluding targets), the mass balance constraint was set to use inequality constraints for all metabolites, the number of runs was set to 10.We used the Boston University shared computing cluster to run our analysis for a large number of metabolic networks and metabolites. The calculation of the PM for each individual network model and metabolite can be run in parallel, vastly increasing the number of possible computations. The average runtime for computing the PM for an individual network and metabolite for 10 repeated runs was ~9 min and the maximum run time was ~45 min, given the default parameters used in this study: a = 0, s = 1, samp = 50, noise = 0.3, n = 7, thresh = 0.01, runs = 10. We note that these parameters were chosen by hand to provide adequate performance for our algorithm, and future implementations could possibly alter these parameters to provide improved run-time and/or accuracy.E. coli core metabolic network. We used the network provided by the BiGG database . For our analysis of the histidine pathway across all 456 oral microbiome metabolic networks, the histidine pathway sum was the total number of reactions in the histidine pathway and the pathway length was the total number of reactions starting at histidine and counting until the first missing reaction. Both values were compared to the PM values of each organism for histidine by Spearman’s rank correlation.We analyzed the PM for the histidine biosynthetic pathway with auxotrophic metabolic networks generated by knocking out different reactions along the pathway in the E. coli iJO1366 metabolic network by randomly removing reactions and observing the results of flux balance analysis (FBA) and our producibility metric (PM). The iJO1366 metabolic network consists of 2583 reactions, and was perturbed by removing n random reactions . The biomass reactions (full and core) and the maintenance reaction were not candidates to be randomly removed. For each value of n, 50 different randomly perturbed metabolic networks were generated . For each of these networks, the core biomass reaction flux was optimized using FBA in a complete medium and a minimal glucose medium and the biomass flux was recorded. Next, the PM for all core biomass metabolites, excluding those with consistent PM of 0 , were calculated using our method. The accuracy of each method was calculated using a quantitative difference measure and a biomass production measure. For FBA the quantitative difference measure was calculated as the absolute value of the difference between the original biomass flux and the perturbed biomass flux. For the PM the quantitative difference measure was calculated as the sum of the absolute value of the differences between the PM value of each metabolite in the original model and the perturbed models. Note that for both FBA and the PM this measure is equivalent to the L1 norm of the difference between the original network metric and the perturbed network metric. The accuracy was measured as one minus the normalized difference measure. Means and standard errors across the 50 different randomly perturbed metabolic networks were calculated and reported. The biomass production measure was calculated in FBA as the fraction of perturbed metabolic networks that could produce biomass flux greater than 1% of the original optimal biomass flux. The biomass production measure was calculated for the PM as the fraction of perturbed metabolic networks that had PM for all biomass components analyzed above a specified threshold. Thresholds of 0.1 and 0.6 were analyzed and reported.We demonstrate the performance of our method on a network with missing reactions on perturbed E. coli auxotrophs using our PM metric. Experimental data were taken from the supplementary growth data of E. coli auxotrophs were modeled using the iJO1366 metabolic network. All reactions related to a gene, including those involving isoenzymes, were knocked out from the model by setting the upper and lower bound of the reaction to zero. Isoenzyme related reactions were included based on prior evidence that this improves performance of metabolic modeling of auxotrophs . The biomass components were chosen to be the union of the set of default KBase Gram-positive and Gram-negative biomass compositions , phylum (belonging to 1 of 12 phyla or not) and class (belonging to 1 of 22 classes or not) were used. We calculated the log likelihood ratio by taking difference between the log likelihood of the base quadratic model of genome size and the model including a specific taxonomic parameter. We identified highly significant relationships using an alpha value of 10Organic acid production was assessed by calculating the PM for nine different organic acids for each human oral microbiome organism. The organic acids analyzed were: acetate, formate, L-lactate, succinate, propionate, D-lactate, butyrate, isobutyrate, and isovalerate. The organic acids were chosen by searching through the literature for those that were found to be relevant for oral health . While tStreptococcus mutans UA 159) and a proteolytic organism . These organisms were chosen because they are known to be associated with oral diseases involving either saccharolytic or proteolytic activity, namely dental carries and periodontitis (inP = 1), by adding them to the fixon parameter, and then adding all other metabolites randomly. As in the other PM calculations, the target metabolite is never added or fixed to be on. The carbohydrate-enriched environment was simulated in a similar manner by fixing D-glucose to always be present.The production of metabolites in variable environments was implemented in our method by re-calculating the PM for all metabolites in a protein-enriched and carbohydrate-enriched environment for two organisms: a saccharolytic organism  than the original and N is the number of permutations.Partial Mantel tests were calculated in a similar manner, but using partial correlations between the first and second matrix while controlling for a third matrix. For the partial correlation permutations, only the first matrix is permuted and the partial correlation is recalculated.Actinomyces odontolyticus XH001, Pseudopropionibacterium propionicum F0700, and Pseudopropionibacterium propionicum F0230a) were re-clustered and analyzed. Metabolites were ranked and analyzed based on the difference between the average PM value of separate groups. Three different rankings were used throughout this analysis: (1) average fastidious cluster organisms PM subtracted from average oral microbiome organisms PM, (2) average Mycoplasma PM subtracted from average TM7 PM (3), average TM7 host PM subtracted from TM7 PM. Correlations between amino acid biosynthetic cost and difference in PM were calculated using Spearman’s rank correlation between the amino acid cost  and several host strains for the uncultivated TM7  in a manner that is better/more insightful than previous methods; or provide new experimental data to substantiate your claims.Reviewer #1:outP) scales with the probability of the presence of input metabolites (inP). This robustness can be summarized as PM – the higher PM, the more likely a metabolite can be synthesized. If one is worried about parameter overfitting , this seems like a good thing to try. Applying the metric PM to E. coli central metabolism, they found that PM is not correlated with connectivity. Some metabolites have high connectivity but low PM, and some low connectivity and high PM. They then quantified PM of 88 biomass metabolites for 456 oral microbes, and found that fastidious (difficult to culture) microbes have low PM values for several metabolites, consistent with them being fastidious. Genome size and taxonomy both contained information about PM. They found that cell wall metabolites have variable PM. They also found that a number of amino acids have high PM in Proteobacteria and low PM in Bacteroidetes. They also analyzed metabolic complementarity of several TM7 strains (fastidious microbes) and their symbiotic bacteria strains. The paper is of bioinformatics nature, and is in general clearly written."Quantifying biosynthetic network robustness across the human oral microbiome" from Segre lab was motivated by a desire to overcome the gap-filling limitation of standard flux balance analysis and the need to make assumptions on environments in metabolic network topology analysis. They quantified "biosynthetic network robustness", essentially how the probability of a product being made (1) What is the difference between PM and% completion of biosynthetic pathway?inP among all inputs. This seems similar to assuming constant concentration among all inputs for FBA, which is never shown.2) It's also not entirely clear to what extent their method improves upon the state of the art. In their Introduction, they say that two downsides that limit FBA (but not their method) are assumptions on environmental conditions and reconciling with stoichiometry-based constraints. I don't really understand their second limitation, but they sidestep the first limitation by assuming a constant Reviewer #2:The manuscript by Bernstein et al. presents a computational method to estimate metabolites that are likely to be exchanged in a microbial community. The essence of the novelty of the method, especially in comparison with the previous methods, is that it provides a probabilistic view accounting for multiple possible variations in substrate uptake combinations (e.g. different combinations of C/N sources etc.). The method is illustrated with the analysis of oral microbial community and the results suggest potential metabolic dependencies in the community. I find the method to be elegant but yet only of theoretical interest.1) The method assumes a uniform distribution of possible substrate uptake combinations – which is not necessarily biologically observed. There are hierarchies – e.g. preference of glucose over other C-sources in most organisms.2) The finding that metabolic dependencies may exist in oral microbiome is not that surprising per se given that a large body of literature  already suggest that metabolic dependencies are likely widespread in microbial communities. Thus, it is not clear whether only the proposed method would be able to identify these.3) Lack of experimental validation makes it difficult to assess whether the identified exchanges are happening in the system. At the least, a detailed analysis of systems with known metabolite exchanges (and how the proposed method there differs from the previous ones) should be provided.In summary, I do find the proposed method elegant and appealing but miss substantiation of the biological relevance.Reviewer #3:This manuscript introduces a new robustness metric that attempts to quantify the probability that an organism can produce a given metabolite directly from the genome. This probability is calculated as an average over possible environments defined by the presence or absence of the other metabolites in the network with production determined through the application of an FBA model. I found the metric itself intuitively appealing and easy to understand. In addition, the manuscript was clear and well written. The application to the oral microbiome and the novel CPR organisms in particular was also well motivated and interesting.E. coli strains and phenotypes defined in terms of growth conditions . If such datasets are not available then I feel the authors need to be more circumspect in their conclusions and concede that the metric may say something about the production of metabolites but without any certainty about how a given PM value translates into an actual probability of production.Given the rate of generation of microbial genomes it would be very useful to have a better method to even approximately predict metabolic products of organisms. However, what the study lacks in my opinion, is quantitative evidence that the metric actually does translate into a prediction that the organism produces a given metabolite. They provide some anecdotal examples where it appears to work but without a more thorough analysis of what the metric means then it will only be useful in a qualitative sense i.e. a higher PM indicating that one organism is more likely to produce a metabolite than another. Metabolic modelling is admittedly not my field, but datasets capable of testing the metric, must exist. A possible example might be this collection of Other than the above caveat, I thought this was a good study but it was sparse on the practical details of the methodology. The GitHub repository consists of a selection of Matlab scripts without a clear description of how to apply them. What would be really useful is a complete walkthrough of the methodology from genome to PM values including for example ggkbase commands used to build the models. This is necessary if this work is to be properly reproducible. One final comment was that some evaluation of the impact of sample number on the calculated PM values would be a worthwhile addition. The authors mention that 50 samples of input metabolite combinations were used but no analysis of the impact of this choice on the PM values was given.Thank you for submitting a revision plan for your article entitled "Quantifying biosynthetic network robustness across the human oral microbiome". The editors and reviewers have considered your plan and invite you to proceed with your revisions. Please also consider the following comments when preparing your revised manuscript.The Reviewing Editor stated:"I think that I know how authors can fix their problems from a theoretical aspect. They can start with a complete model as the "ground truth" model, but hide or mis-annotate various% links to mimic our incomplete knowledge of the system, and compare their method with existing methods. This way, they will always have a "ground truth" curve for any metric of interest to biologists. Of course, the task of assigning missing links will need to be repeated many times and in double-blind fashion to gain statistical power. I suspect that different methods might show tradeoff. For example, in their Figure 1, it is not clear whether the extra info provided by PM is useful to a biologist if all mutants are auxotrophic. Any tradeoff between methods is also valuable to know. Authors can also use this ground truth model to illustrate problems of gap filling etc."Another reviewer said:E. coli phenotypes to test their metric and the improved GitHub repository. ""I agree this is a very comprehensive plan and they do seem to have taken our comments to heart and developed a proposal to address them. I was pleased with their suggestions regarding an alternate dataset of The last reviewer said:E. coli is one organism and by no means representative of natural diversity and community complexity. E. coli auxotroph complementation experiments are also unique in some sense as I haven't seen many other studies showing similar data in other organisms. So, overall, I think recommending to focus on oral microbiome and reducing the general claims would put the paper on more solid foundation I believe.""I agree that the proposal is comprehensive and I like the Reviewing Editor's simulation idea. This also reminds me that the authors' should comment on the ensembleFBA approach which does address the main criticisms of the gap-filling. Furthermore, I think that a clear focus on oral microbiome would benefit the study much more rather than claiming general validity that is very difficult to substantiate based on their proposed plan – after all,  [Editors’ note: what follows is the authors’ plan to address the revisions.]Thank you very much for evaluating our manuscript, and for your valuable and constructive comments. In the summary letter, the reviewers and reviewing editor have asked us to further investigate and clarify the novelty and biological relevance of our method, especially in relation to previously developed approaches. In particular, they have asked us to “either show that the method is in agreement with previously published data (where a lot of direct evidence exist) in a manner that is better/more insightful than previous methods; or provide new experimental data to substantiate [our] claims”.We agree that a better description of the biological relevance of our method and additional analyses directly addressing how our method can provide novel insight relative to existing approaches will greatly strengthen our results and clarify the importance of our work. We propose several new analyses that will address the reviewers’ concerns. Based on revisiting the literature, and implementing some preliminary analyses (shown below), we believe that sufficient published data is available to clarify the biological relevance and distinct capabilities of our method.The current document outlines our plan for addressing the reviewers’ comments, and is structured as follows:In Part 1, we present an overview of how we will address each of the major issues raised across all reviewers. In Part 2, we have specifically addressed all reviewer’s comments in more detail. In Part 3, we have included preliminary and prospective figures that will be added to our manuscript to address the reviewer’s comments.We obviously cannot guarantee that all comparisons with available data will confirm the validity of our approach. However, some preliminary analyses we have performed so far, displayed below in the form of tentative figures, support and clarify the relevance of our method. Would any of the prospective analyses we have suggested yield uninformative or negative results, we would still be committed to including them in a revised manuscript as an opportunity to highlight the limitations of our approach, and possible directions for future improvement.Part 1 – Summary of how we address major issuesA) It is not clear how our method is different from and better/more insightful than previous methods .We appreciate this criticism and see it as an opportunity to clarify the novelty of our method and point out where it may be better/more insightful than other similar methods. We will address this criticism by describing how our method differs from several different methods:E. coli L-histidine biosynthesis pathway. In particular, the PM provides information on the structure of the pathway and on how the proximity of the knockout to the final product affects its producibility. Thus, a high PM value would indicate that the target metabolite can be produced from multiple distinct sets of precursors. This analysis will be presented as a supplemental analysis in the Materials and methods section of our manuscript.How our method differs from pathway completeness: We will first analyze the relationship between pathway completeness (the fraction of genes or reactions from a given pathway found in a metabolic network) and our Producibility Metric (PM) in depth for a single pathway. Figure 1 displays a preliminary analysis, showing how our metric provides a much more informative outcome than pathway completeness for the analysis of mutations in the To show the validity of this argument beyond a simple linear pathway and perform a more comprehensive analysis, we will also compare the relationship between pathway completeness and our PM for additional metabolites with known biosynthetic pathways and interesting distributions of PM across our set of oral microbiome organisms. This analysis will be presented in the results section of our manuscript. See also response to reviewer #1 comment 1 for additional details on these analyses.How our method differs from flux balance analysis (FBA): We will clarify how our method differs from classical FBA, in three major ways. First, in our approach we assess the producibility of individual biomass components, rather than optimizing the overall biomass production flux. This allows us to analyze incomplete networks that would be simply infeasible with FBA optimization of the biomass production flux. Second, we define environmental availability of precursors in a probabilistic way, and thus compute metabolite producibility based on random sampling. Third, we provide a novel measure of robustness (the Producibility Metric) that cannot be computed with standard FBA, which describes how well an organism can produce a metabolite across a statistical ensemble of possible environments.E. coli grown on minimal glucose and rich media . In the discussion of a revised manuscript we would also better explain that having to perform gap-filling in order to use FBA for any microbiome study is becoming an increasingly important and debated issue. While previous work has shown the utility of gapfilled models for predicting inter-species interactions , more recent papers have raised concerns about existing gap-filling pipelines . In general, we feel that exploring alternative strategies that can estimate metabolic properties of microbes and communities without gap-filling is going to be a crucial component of future genome-scale microbial modeling efforts.In the revised manuscript, in addition to describing in detail these differences and their implications, we will add a new figure supplement to our method section . To perform a comparison with this method, we will use our method to compute a complementarity score  and compare this metric to an analogous metric derived from NetCooperate. We will compare the two approaches for all pairs of oral microbiome organisms in our collection. A tentative new figure .B) The assumption of a constant inP  and of PM (the Producibility Metric), we could have done a better job at providing a biological intuition for our definitions. We will update our manuscript to include an improved description of PM, inP, and their relationship to FBA, which we outline tentatively in what follows.We wish to start by acknowledging that, while in our manuscript we described in detail the mathematical definitions of inP slides between 0 and 1. In this sense, in our current calculations, inP is uniform , but not constant (it changes between 0 and 1). Note also that while the PM of a given metabolite is the outcome of many FBA calculations, it is a number that could not easily be related to any individual FBA calculation. In summary, PM quantifies the overall propensity for an organism  to be able to produce a given metabolite. Therefore, our method is particularly useful for assessing the biosynthetic capabilities of a large number of organisms without having to make any arbitrary assumption beyond the metabolic information present in the organisms’ genomes.One way of briefly re-stating the interpretation of the Producibility Metric (PM) for a given metabolite is that it is an estimate of the fraction of distinct environmental compounds that one would have to add in the medium in order to expect, on average, a high chance (above 0.5) of being able to produce a given metabolite. We should clarify that the computation of PM is effectively the outcome of thousands of FBA calculations in which the production of a target metabolite is estimated under many sets of input metabolites randomly sampled as inP, which can be different for different metabolites. In fact, our algorithm was designed in a modular fashion such that it could accommodate such alternative implementations. An extreme, but illustrative, scenario is the one of inP = either 0 or 1 for all metabolites. We will show that this scenario would effectively be equivalent to estimating the producibility of biomass components with standard FBA, under a specific environmental condition, in which the available metabolites are the ones with inP = 1. We will further show how these extreme choices of inP differ from using intermediate inP values and PM by showing how the results of metabolite producibility in a minimal and rich medium are related to the PM. This analysis is described in further detail in response to reviewer #1 comment 2.That being said, nothing in our algorithm prevents one from making alternative choices for the values of inP values to probe nutrient preferences across different organisms, we will test the ability of our approach to distinguish between saccharolytic vs. proteolytic organisms in the human oral microbiome. These two classes of organisms have very different metabolic strategies and important implications in oral health . For this analysis, we will use variable inP values to define a sugar rich and an amino acid rich environment. Then we will calculate the producibility metric for different biomass components for a set of saccharolytic and proteolytic organisms from our collection of oral microbiome organisms and assess our ability to distinguish their environmental preferences. This analysis will be added to the results section of our manuscript in a new section addressing variable inP values. For additional details see prospective Figure 4 legend below.In order to address the specific suggestion to use non-uniform C) There is a lack of experimental validation about producible metabolites and exchange among microbial organisms .In general, experiments that directly confirm the exchange of a specific metabolites between two microbes are quite challenging, let alone experiments that could uncover the entire possible network of metabolic exchanges in a microbial community. However, a few published examples contain enough information to enable a direct comparison between computational and empirical outcomes. We propose to analyze different sources of existing data in order to validate the predictions of our algorithm. Whenever possible, during these analyses, we will also include analysis based on the methods mentioned in part A such that we can compare the performance of our method relative to these alternative methods. The specific sets of case studies we plan to focus on are described below:Streptococcus and consumed by Veillonella species ; and the exchange of succinate from T. denticola to P. gingivalis and isobutyric acid from P. gingivalis to T. denticola .Additionally, following the analysis of these specific experimentally validated systems, we will extend our analysis to all of our oral microbiome organisms to generate hypotheses regarding exchange of organic acids between previously undiscovered pairs of organisms. This analysis will be presented in the manuscript as a supplemental result that expands on our current matrix of biomass producibility. See the response to reviewer #2 comment 3 for further details.We will analyze organic acid exchange in the oral microbiome: We will test our method’s ability to predict the exchange of organic acids between oral microbes in two known examples. To do this we will extend our method to predict the producibility of metabolites beyond biomass components such as organic acids. The specific interactions we will focus on are the exchange of lactic acid, produced by E. coli auxotrophs: As a slightly more complex example of a microbial community with metabolic exchange we propose to analyze a dataset on putative exchange among amino acid auxotrophs . We will calculate the producibility metric for all amino acids across pairs and triplets of E. coli auxotrophs that are known to support each other through syntrophic exchange of amino acids. We will determine if indeed the production of the necessary amino acids to support partner growth is predicted by our method. This analysis will be added to the manuscript method section as an additional validation. See prospective Figure 5 legend and the response to reviewer #2 comment 3 for further details.We will analyze the exchange of amino acids in While the above analyses are focused on specific interactions for which molecular mechanistic details can be addressed with our methods, it will be also interesting to assess the performance of our method on microbial co-occurrence data from the human oral microbiome. It is important to note that co-occurrences are not necessarily indicative of metabolic interactions, but they are often related to metabolic trends, as shown before . We will utilize two different sources of microbial cooccurrence data for this analysis. The first will be high-throughput sequencing data from the human microbiome project, which contains co-occurrence data for microbes associated with several different human oral microbiome sites . The second source we will aim at utilizing is a set of CLASI-FISH experiments of dental plaque where physical interactions between different taxa have been imaged through fluorescence microscopy . This analysis will be added to the results section of our manuscript. See response to reviewer #2 comment 3 and prospective Figure 6 legend for further details.E. coli knockout mutants tested on different environments containing variable nutrients . We have contacted the authors of this paper in the hope that they will share the raw data of their study with us, in which case we would pursue an analysis wherein we analyze this data to provide a more-high throughput and quantitative clarification of our PM calculations. This point is further elaborated in our specific response to reviewer #3 comment 1.An additional analysis that we will pursue, as inspired by reviewer #3 comment 1, is the assessment of our methods performance on predicting high-throughput phenotype data. As pointed out by the reviewer, analyzing high-throughput phenotype data could allow us to more quantitatively benchmark the ability of our method to predict specific metabolic auxotrophies (or inabilities to produce certain metabolites). We have identified a promising dataset that contains a large number of Part 2 – Point by point response to reviewersReviewer #1:[…]1) What is the difference between PM and% completion of biosynthetic pathway?E. coli. In a preliminary analysis  biosynthetic pathway, biosynthesis of the amino acid L-histidine in The second analysis that we propose goes beyond a simple linear pathway, and constitutes a more general assessment of the relationship between PM and biosynthetic pathway% completeness. For this analysis we will utilize our large set of oral microbiome organisms. For several metabolites with well described biosynthetic pathways, such as amino acids, we will determine the% completion across these strains and make a direct comparison with the PM value. We do expect to see some correlation between the% completion of a pathway and the PM value. However, as demonstrated with the above analysis, we do not expect them to be redundant.We would also like to emphasize that we believe it is an advantage of our method that it does not rely on previously defined biosynthetic pathway annotations and instead seeks to use the entire metabolic network structure to define biosynthetic capabilities. While this prior knowledge can be quite useful in many contexts, specific biosynthetic routes can cross the boundaries of annotated pathways, making pathway completeness uninformative. A prior notable example of this effect is the discovery of an alternative pathway to bypass a TCA cycle gene impairment . This pathway connects in an unexpected way two distinct pathways, generating a new crucially important and experimentally validated type of connectivity that would be missed from regular pathway-based analysis. Another such example, in our current data, is the case of the arginine deiminase pathway and the urea cycle, which contain several overlapping metabolites and reactions. In fact, we have noticed that KEGG mappings of TM7x metabolism often highlight the urea cycle as a result of TM7x containing the complete arginine deiminase pathway. In the revised manuscript we will describe this advantage of the Producibility Metric relative to pathway completeness, and point to the specific examples mentioned.in among all inputs. This seems similar to assuming constant concentration among all inputs for FBA, which is never shown.2) It's also not entirely clear to what extent their method improves upon the state of the art. In their Introduction, they say that two downsides that limit FBA (but not their method) are assumptions on environmental conditions and reconciling with stoichiometry-based constraints. I don't really understand their second limitation, but they sidestep the first limitation by assuming a constant PinP and how they are related to FBA.We agree with the reviewer that the current description of how our method differs from FBA is not articulated clearly enough, and can be significantly improved. We have described in detail how we plan to address this issue in Part 1 Point B above, and will add further details to our manuscript to describe our method, and in particular the PM, inP). Indeed, in the current version of the manuscript, we focused on a uniform inP across all metabolites, essentially mimicking a uniformly distributed ensemble of environments. However, in general, each metabolite j can have a different value in(j)P. An extreme case is the one of all inP = 1, which would be comparable to running FBA with all environmental metabolites available. In a revised version of the manuscript, we propose to show some specific examples to clarify how our method chooses statistical ensembles of input metabolites based on inP and how this choice differs from, but is related to, setting constant inputs for FBA. We will calculate the set of producible metabolites in the E. coli core model by using FBA under two different conditions, one where we include all input metabolites, as in a rich medium, and one where we include only input metabolites expected to be found in a glucose minimal medium. We note that these two scenarios correspond respectively to: (a) Rich Medium – setting inP values equal to 1 for all metabolites; (b) Minimal Glucose Medium – setting inP values equal to 1 for all metabolites found in glucose minimal medium and 0 for all others. We will then compare the metabolites that are producible in those two scenarios to the PM values obtained from varying inP between 0 and 1. We expect that metabolites that are producible in the minimal medium will have higher PM values than those that are producible only in the rich medium.The first of the two “downsides” mentioned in the reviewer’s comment is related to a specific choice on how our approach can be employed for obtaining biological insight about an organism in the absence of specific information about the molecular composition of its environment. In a given FBA calculation, one necessarily needs to decide on a specific set of initial conditions, in the form of upper bounds to the fluxes associated with import of extracellular metabolites. Our method is instead statistical in nature, and computes the producibility of different metabolites as a function of the probability of availability of any given environmental metabolite . We will describe how our results differ from this method in terms of sensitivity and specificity. More specifically, we expect our method to be more specific in its predictions of exchanged metabolites and ability to discriminate different types of interactions than the NetCooperate method. Some results supporting this point are shown in preliminary Figure 3  below.Reviewer #2:[…]1) The method assumes a uniform distribution of possible substrate uptake combinations – which is not necessarily biologically observed. There are hierarchies – e.g. preference of glucose over other C-sources in most organisms.inP for our analysis was chosen specifically in order to assess environmental robustness across a uniformly sampled ensemble . Our method, however, can easily be implemented using variable inP values that represent any assumed prior distribution on input metabolites. We propose an analysis that will utilize variable inP values in order to further demonstrate the utility of our method for a specific biological example where variable assumptions about the environments may be of interest. We will analyze saccharolytic vs. proteolytic organisms from our set of oral microbiome organisms, which have key differing metabolic capabilities and implications in oral health and disease . Using variable inP values, we will define a sugar rich and an amino acid rich environment, and we will calculate the PM of all biomass components for both saccharolytic and proteolytic organisms in both. The sugar-rich environment will have sugars with fixed inP = 1  and the amino acid rich environment will have inP = 1 for amino acids. By fixing inP for these metabolites the PM will then become a measure of how many metabolites, beyond those that are fixed on, need to be added to the environment to produce a given target metabolite. These results will allow us to determine whether our method can capture the environmental preference and metabolic processes of these two classes of organisms from the human oral microbiome. This analysis is further described in prospective Figure 4, which has yet to be generated.This is a very interesting point. We first would like to clarify that the assumption of uniform 2) The finding that metabolic dependencies may exist in oral microbiome is not that surprising per se given that a large body of literature  already suggest that metabolic dependencies are likely widespread in microbial communities. Thus, it is not clear whether only the proposed method would be able to identify these.Indeed, as expressed by the reviewer, a lot of literature exists about computational and empirical reports of inter-species dependencies in microbial communities. However, we believe that the reviewer will agree that what has been done uncovers with limited fidelity a minuscule fraction of the interactions likely present in nature. The challenge that remains is in characterizing and describing the mechanisms of these dependencies/interactions. We will add a statement emphasizing this point. Beyond this clarification, we will be happy to address more specifically the reviewer’s concern, i.e. show that our method can provide insight that is substantially different from the type of insight provided by other methods. We will compare our method to results obtained from three different alternative methods: (1) Pathway completeness, (2) Flux balance analysis, and (3) NetCooperate. These comparisons are, in part, addressed in the responses to other reviewer comments, and are described in detail in Part 1 point A, which outlines this major issue. We also note that, to our knowledge, ours is the first large-scale metabolic analysis of this type in the human oral microbiome. In this sense it provides valuable new insight into this microbial community and can further serve as a blueprint for analyzing other complex microbial communities.3) Lack of experimental validation makes it difficult to assess whether the identified exchanges are happening in the system. At the least, a detailed analysis of systems with known metabolite exchanges (and how the proposed method there differs from the previous ones) should be provided.Streptococcus and consumed by Veillonella species . Another example is the exchange of succinate from T. denticola to P. gingivalis and isobutyric acid from P. gingivalis to T. denticola . To analyze these examples, we will extend our method to not only calculate PM values for essential biomass components but also to include possible secreted metabolites such as organic acids. We will then utilize our method to calculate the PM for these different organisms and identify metabolic complements. Through this analysis we will confirm whether or not our method is able to capture these well-known microbial interactions. Furthermore, we will extend this analysis to calculate the PM of a set of possibly exchanged organic acids for all oral microbiome organisms in our catalog in order to gain broad insight into organic acid producibility and potentially predict new metabolic exchanges.This is a good point and we will attempt to address it as best we can. Unfortunately, there are limited systems where microbial metabolic dependencies and interactions have been unraveled experimentally. One example where there is some experimental knowledge that we will analyze is the exchange of organic acids in the oral microbiome. One such example is the exchange of lactic acid produced by E. coli amino acid auxotrophs . In this work all pairs of E. coli single amino acid auxotrophs and all triplets of double auxotrophs where grown in co-culture to identify pairs and triplets that enabled syntrophic growth. We will re-analyze these E. coli auxotrophs and calculate their PM for all amino acids to determine if our method can predict the increased ability of growth-supporting auxotrophs to produce the amino acids that their syntrophic partners are lacking. We anticipate that certain amino acid auxotrophs, on top of being unable to produce a single specific amino acid, will have decreased robustness in their production of other amino acids that have similar biosynthetic pathways. This will lead to decreased syntrophic growth between auxotrophs that cannot robustly synthesize each other’s essential amino acids, and can be predicted by our PM calculations. For example, upon first inspection of the data from Mee et al. in Figure 1C we can see this pattern with regards to the L-methionine and L-cysteine auxotrophs (L-methionine and L-cysteine are the two sulfur containing amino acids and have similar biosynthetic pathways). While the L-methionine auxotroph has improved syntrophic growth with a number of other auxotrophs it has notably little syntrophic growth with the L-cysteine auxotroph. A further analysis of this data and comparison to our PM calculations will be presented in prospective Figure 5 (see legend below), to be included in the methods section of our manuscript as an additional validation of our method.Another analysis we propose to perform is the study of a slightly more complicated microbial ecosystem, consisting of We will also analyze the performance of our metric in describing microbial co-occurrence patterns across the human oral microbiome. Although co-occurrence does not necessarily imply interactions, and mechanisms of interaction are not known for these cases, previous methods have been shown to be capable of identifying metabolic trends associated with microbial co-occurrence . We will use our method to analyze two different type of co-occurrence data and attempt to similarly identify metabolic trends. The first set of co-occurrence data is from sequencing data from the human microbiome project . The human microbiome project included 9 different oral sites from which we will collect microbial co-occurrence data that can be compared to the oral microbiome strains that we have analyzed. The second form of co-occurrence data is from physical associations which have been observed through fluorescence microscopy . In this work the authors identified structure in supragingival plaque microbial communities from the oral microbiome. These structured communities suggest interactions that can similarly be compared with our PM metric to identify metabolic trends associated with microbial co-occurrence. The results of this analysis will be presented in prospective Figure 6 and included in a supplementary results section of our revised manuscript.Reviewer #3:[…]Given the rate of generation of microbial genomes it would be very useful to have a better method to even approximately predict metabolic products of organisms. However, what the study lacks in my opinion, is quantitative evidence that the metric actually does translate into a prediction that the organism produces a given metabolite. They provide some anecdotal examples where it appears to work but without a more thorough analysis of what the metric means then it will only be useful in a qualitative sense i.e. a higher PM indicating that one organism is more likely to produce a metabolite than another. Metabolic modelling is admittedly not my field, but datasets capable of testing the metric, must exist. A possible example might be this collection of E coli strains and phenotypes defined in terms of growth conditions . If such datasets are not available, then I feel the authors need to be more circumspect in their conclusions and concede that the metric may say something about the production of metabolites but without any certainty about how a given PM value translates into an actual probability of production.We appreciate the reviewer’s comment, which made us realize that a number of subtle but important aspects of our analysis were not clearly explained in the manuscript. First of all, we recognize that we can do a better job at providing an intuition for the meaning of the PM metric, including a clarification that it is not meant to quantitatively capture rates of reactions (fluxes) (as done by FBA) but rather the fraction of environmental metabolites that an organism is expected to need in order to produce with high probability a given metabolite. Additional details of the intuition behind our definition are provided in Part 1, point B. We will further emphasize, in our revised manuscript, the nature of PM as a measure of robustness rather than a probability of production.The most important concern expressed by the reviewer, however, seems to be the insufficient comparison with experimental data, which can lead one to legitimately wonder how accurate and valuable our predictions are. Irrespective of the outcome of the additional analyses we propose to perform for validating our predictions , we will certainly take to heart the reviewer’s suggestion to more explicitly describe the possible limitations of our inferences. At the same time, this will also give us an opportunity to emphasize that, relative to existing methods, our approach provides a very unbiased estimate of the metabolic capabilities of a given organisms given its genome, avoiding some of the issues of gap-filling algorithms used for flux balance models.E. coli auxotrophs. Both datasets are described in some more detail in response to reviewer #2 comment 3.In considering the reviewer’s recommendation of additional comparisons with experimental data, we have identified a few datasets whose analysis would enable a more substantial validation of our approach. These include a number of specific interactions between oral microbes, mediated by the exchange of organic acids, and a fairly rich dataset on amino acid exchange between E. coli mutant phenotyping study that we identified . This dataset includes phenotype data from 300 E. coli K12 mutants from the Keio collection grown on 1920 different conditions using Biolog Phenotypic Microarrays. Many of these conditions are metabolic in nature consisting of minimal media supplemented with different carbon, nitrogen, phosphorus, or sulfur sources. We have contacted the authors of this paper in the hope that they will share the raw data of their study with us, in which case we would pursue an analysis wherein we analyze this data to provide a more-high throughput clarification of PM and how exactly it relates to environmental robustness. In particular, we anticipate that E. coli knockouts with high PM for all essential biomass components will survive on a large number of variable nutrient environments, whereas knockouts with low PM for all essential biomass components will survive on a very small number of variable nutrient environments. Furthermore, analysis of the specific knockout/environment pairs could give us insight into the ability of our method to predict specific auxotrophies and metabolic requirements.We also appreciate the reviewer’s suggestion of a high-throughput dataset that could be used to additionally assess our method, and we thank the reviewer for suggesting the interesting paper included. Unfortunately, the majority of the conditions tested in this paper are undefined or non-metabolic (mainly consisting of antibiotics or other stressors), and it is therefore not the best dataset for evaluating our method. In the spirit of the reviewer’s comments, we would like to suggest a similar high-throughput analysis using data from a different Other than the above caveat, I thought this was a good study but it was sparse on the practical details of the methodology. The GitHub repository consists of a selection of Matlab scripts without a clear description of how to apply them. What would be really useful is a complete walkthrough of the methodology from genome to PM values including for example ggkbase commands used to build the models. This is necessary if this work is to be properly reproducible. One final comment was that some evaluation of the impact of sample number on the calculated PM values would be a worthwhile addition. The authors mention that 50 samples of input metabolite combinations were used but no analysis of the impact of this choice on the PM values was given.This is a good point and we appreciate the reviewer’s effort to help us make our method more reproducible. We will add to the GitHub repository example scripts that walk the readers through how to implement our algorithm and obtain our results. In addition to these example scripts, we will add a supplementary methods section that contains a procedural walk through on how to go from a genome to metabolic predictions using KBase (http://kbase.us) to reconstruct a model and our method to analyze it. Regarding the parameter choice for the algorithm, we note that those numbers were chosen by hand to improve algorithm performance. We will further describe the process of choosing these parameters and the impact on PM calculations including means and standard deviations of results.PART 3 – Preliminary and prospective figuresThese results will be further elaborated and included in a new figure in a supplementary methods section of our revised manuscript.E. coli iJO1366 metabolic network to produce biomass under different conditions and constraints was analyzed for networks impacted by an increasing number of random perturbations that remove reactions in the network. Reactions were removed sequentially from the metabolic network. The resulting biosynthetic capabilities (on a rich medium) are plotted for the average of 10 different random runs, with error bars indicating standard error across runs. Flux balance analysis (FBA) calculations of the biomass flux become infeasible fairly quickly, whereas our metabolite producibility metric extends far beyond the FBA infeasibility regionThe ability of the An updated version of this figure will be included in a supplementary methods section of our revised manuscript.Complementarity metrics were calculated to summarize the potential for any one organism to provide metabolic products to another. The “advantage metric” was calculated using our PM metric that describes the metabolic advantage one organism can provide to another. This metric was plotted against an analogous complementarity metric calculated using NetCooperate for all directed pairs of 456 oral microbiome organisms. Log-scale histograms display the distribution of complementarities for each method. The histograms show that the advantage metric has a bi-modality that distinguishes between interactions involving fastidious/uncultivated organisms from those that do not, while the NetCooperate complementarity does not display a similar distribution.The formula for the advantage metric is described below for organism A to B. The metric is calculated by summing over i = 1 to N metabolites.A→B=maxPMiA,PMiB-PMiB∑i=1NPMiAA subsequent version of this figure will be added to a supplementary results section of our revised manuscript as Figure 4—figure supplement 7.inP values for saccharolytic and proteolytic oral microbiome organisms.Proposed Figure 4. To be generated. Analysis of variable inP values to provide biological insight into a set of organisms that may prefer a specific environment. An analysis of the PM values calculated for a set of saccharolytic and another set of proteolytic oral microbiome organisms in either a sugar or amino acid rich environment that has been altered by changing inP values will be presented.This figure will display the ability of our method to utilize variable This figure will be added to a supplementary results section of our revised manuscript.E. coli amino acid auxotrophs.Proposed Figure 5. To be generated. Analysis of E. coli amino acid auxotrophs will be compared to data showing syntrophic growth among pairs and triplets of auxotrophs.This figure will display the ability of our method to predict metabolic interactions in a system with known metabolic dependencies. PM calculations for This figure will be added to a supplementary methods section of our revised manuscript as additional validation.Proposed Figure 6. To be generated. Analysis of co-occurrence in the oral microbiome.This figure will display the ability of our method to identify metabolic trends in microbial co-occurrence networks. Co-occurrence networks will be taken from two distinct sources. The first data source will be cooccurrence from sequencing data from the human microbiome project. The second will be physical associations from fluorescence microscopy data. We will further display how our metric, describing metabolic properties, can be used to describe metabolic trends in these co-occurrence networks.This figure will be added to a supplementary results section of our revised manuscript.[Editors' note: the authors’ plan for revisions was approved and the authors made a formal revised submission.]Section 1 The Reviewing Editor stated:"I think that I know how authors can fix their problems from a theoretical aspect. They can start with a complete model as the "ground truth" model, but hide or mis-annotate various% links to mimic our incomplete knowledge of the system, and compare their method with existing methods. This way, they will always have a "ground truth" curve for any metric of interest to biologists. Of course, the task of assigning missing links will need to be repeated many times and in double-blind fashion to gain statistical power. I suspect that different methods might show tradeoff. For example, in their Figure 1, it is not clear whether the extra info provided by PM is useful to a biologist if all mutants are auxotrophic. Any tradeoff between methods is also valuable to know. Authors can also use this ground truth model to illustrate problems of gap filling etc."E. coli iJO1366 metabolic network as our ground truth model, which we perturbed to different degrees by randomly removing reactions. This was repeated 50 times for 5 different levels of random reaction removal generating 250 different degraded metabolic networks. We analyzed these networks with FBA and with our producibility metric. This allowed us to show that the producibility metric is more tolerant of removed reactions in its predictions than FBA. Thus, this analysis illustrates that the producibility metric provides useful information on growth capabilities for draft metabolic networks that would need to be gap-filled in order to be analyzed with FBA.We thank the Reviewing Editor for this suggestion, which we addressed by analyzing a well curated metabolic network (“ground truth”) that has been degraded to different degrees (“miss-annotated”). This new analysis is presented in the main text, in a new section of the Results titled “Producibility analysis shows improved tolerance to missing reactions compared to flux balance analysis”. This section is accompanied by a newly added main figure . For this analysis, we used the well-curated Another reviewer said:"I agree this is a very comprehensive plan and they do seem to have taken our comments to heart and developed a proposal to address them. I was pleased with their suggestions regarding an alternate dataset of E. coli phenotypes to test their metric and the improved GitHub repository."E. coli (Results section “Metabolite producibility points to putative metabolic mechanisms for E. coli auxotroph co-cultures”) and in the human oral microbiome . Additionally, we have improved the GitHub repository by adding a detailed example of how to run our code.As described in Section 2, in response to reviewer #3’s comments 1 and 2, we have addressed in detail the comments made in the original review letter, expanding on our initial plan for a revision. This includes a number of new analyses including several that relate our method to experimental phenotypic data, both in The last reviewer said:"I agree that the proposal is comprehensive and I like the Reviewing Editor's simulation idea. This also reminds me that the authors' should comment on the ensembleFBA approach which does address the main criticisms of the gap-filling. Furthermore, I think that a clear focus on oral microbiome would benefit the study much more rather than claiming general validity that is very difficult to substantiate based on their proposed plan – after all, E. coli is one organism and by no means representative of natural diversity and community complexity. E. coli auxotroph complementation experiments are also unique in some sense as I haven't seen many other studies showing similar data in other organisms. So, overall, I think recommending to focus on oral microbiome and reducing the general claims would put the paper on more solid foundation I believe."We appreciated this comment and recommendation from the reviewer. We gladly included reference to the ensembleFBA approach , as well as to the newly published CarveMe method that is also capable of ensemble model reconstruction . We agree that these approaches constitute promising methods for addressing the gap-filling problem, and we are happy to mention them in the Introduction of the paper.E. coli, including an analysis of E. coli auxotroph co-cultures and the Reviewing Editor's simulation idea in E. coli; however, we have focused most other new analyses on oral microbiome organisms. New analyses focused on the oral microbiome include: (i) observing the relationship between the completeness of the histidine biosynthetic pathway and our metric , (ii) investigating organic acid production , (iii) implementing our method in an environment specific manner with the analysis of a saccharolytic and a proteolytic organism (Results section “Metabolite producibility in a protein vs. carbohydrate enriched environment”), and (iv) associating our metric with co-occurrence from 16S rRNA sequencing data from the human oral microbiome . In all of these analyses we have sought to relate our findings with phenotypes that are relevant for the human oral microbiome whenever possible, trying to candidly illustrate what works well and what doesn’t. Additionally, we feel that the revised manuscript provides a better explanation for why and how our approach is particularly useful for addressing microbial community questions in cases where the specific metabolic composition of the environment is highly uncertain, such as in the study of natural human-associated microbiomes. This clarifies our motivation for focusing on the human oral microbiome in this study and provides insight into which scenarios our method is best suited for in the future.Regarding the more general comment on remaining focused on the oral microbiome and reducing our general claims, we greatly appreciate this advice. In balancing other reviewers’ comments with this suggestion, we have implemented some illustrative examples in Section 2 Reviewer #1:[…]1) What is the difference between PM and% completion of biosynthetic pathway?This is an important question, which we have addressed through new analyses added to the Results section “Producibility of metabolites differs from pathway completeness and captures minimal precursor set structure” and Figure 2—figure supplement 2. We have additionally introduced a new paragraph in the Discussion addressing the difference between our method and alternative methods including biosynthetic pathway-based analysis. The specific changes are described in detail below:E. coli. We focused on this pathway because it is overall linear, and thus more easily interpretable. We used the well curated E. coli iJO1366 metabolic network and we examined this biosynthetic pathway by “knocking-out” different metabolic reactions along the pathway and calculating our Producibility Metric (PM). We observed that the PM was able to capture the impact of the specific location of the knockout and the topology of the metabolic pathway. In contrast, looking at the% completion of the biosynthetic pathway would not provide this information.The first analysis we performed was focused on looking in detail at the biosynthetic pathway for the amino acid histidine in E. coli.A second analysis extended this concept to all 456 oral microbiome metabolic networks. Specifically, we calculated both the% completion of the histidine biosynthetic pathway  and the length (distance from histidine before a reaction is missing). We found that both of these metrics are correlated with the PM for histidine. However, the length of the intact portion of the biosynthetic pathway is more strongly correlated with the PM than with the% completion, corroborating, across a large set of metabolically diverse organisms, the result obtained for A deeper, and theoretically motivated portion was additionally introduced in the end of this newly added Results section, to further clarify how the PM differs from% completion of a biosynthetic pathway. We found that the PM for histidine of different knock-outs matched closely with our theoretical predictions based on combinatorics. In this new section, we point out that the combinatorial equations establish an intimate connection between the PM and the minimal precursor set structure of a particular target metabolite, and thus captures a complex measure of the multiplicity of biosynthetic routes through which the target metabolite can be produced. This theoretical analysis points out a profound meaning of the PM, which could be further explored in future work.Finally, we added a section to the Discussion, to emphasize that our method has another important advantage over% completion: it does not rely on previously defined biosynthetic pathway annotations. While this prior knowledge can be quite useful in many contexts, specific biosynthetic routes can cross the boundaries of annotated pathways, making pathway completeness uninformative. We have highlighted a few scenarios from the literature and in our own analysis where this is the case, and where less biased network based approaches have an advantage.in among all inputs. This seems similar to assuming constant concentration among all inputs for FBA, which is never shown.2) It's also not entirely clear to what extent their method improves upon the state of the art. In their Introduction, they say that two downsides that limit FBA (but not their method) are assumptions on environmental conditions and reconciling with stoichiometry-based constraints. I don't really understand their second limitation, but they sidestep the first limitation by assuming a constant PWe agree with the reviewer’s comment that our original version of the manuscript did not clearly articulate how our method improves upon the state of the art. In the revised manuscript we have made changes to the Introduction and Discussion that clarify the novelty of our method, and we have added a number of analyses to the Results section where our method is directly compared with alternative methods.inP was chosen as the most naïve choice by which we could statistically sample the environment. This approach is different than providing all nutrients with uniform uptake rate in regular FBA, because it samples an ensemble of environments, rather than assuming a single uniformly rich one. Additionally, for reviewer #2 comment 1, we have implemented an analysis where we use non-uniform inP to demonstrate the capacity of our method to incorporate environmental assumptions (Results section “Metabolite producibility in a protein vs. carbohydrate enriched environment”). Regarding the second limitation mentioned by the reviewer, about stoichiometry-based constraints, we discuss this in more detail in a modified portion of the Discussion, where we highlight the difference between networks defined by reaction stoichiometry vs. connectivity.The main novelty of our method, i.e. the statistical nature of the percolation approach, is now reflected in a modified Title and Abstract, and better explained in a revised, more straightforward version of Figure 1 . Furthermore, we updated Figure 2B to more clearly demonstrate the features of the PM; specifically, that it is independent from node degree and that recycled co-factors have minimal impact on PM. To better explain in general terms how our method improves upon the state of the art, we significantly altered the text of our Introduction. In this revised Introduction, we revisit the first limitation mentioned by the reviewer, by clarifying the rationale of assumptions on environmental conditions, i.e. the ability of our method to provide predictions in scenarios where the chemical environment of the microbes is unknown. We also note that our choice of constant The reviewer’s concern about improving upon the state of the art was further addressed in detail by adding to the Results section several new analyses in which we compare our method with alternative ones. In addition to the comparison of our method with percent pathway completion, discussed in detail in the previous comment, we implemented the following new comparative analyses:i) As described also in Summary Comment 1, a comparison with FBA, including an analysis of how FBA and the PM cope with a gradually increasing number of perturbations of a genome-scale metabolic network (mimicking the situation of non-gap-filled draft reconstructions), was addressed in the new section “Producibility analysis shows improved tolerance to missing reactions compared to flux balance analysis” of the Results and Figure 3.ii) We also compared our method to several different metabolic network analysis methods in the context of microbial co-occurrence data in the new Results section “Metabolic similarity correlates with microbial co-occurrence in the human oral microbiome” and the newly added Figure 4—figure supplement 6. We showed that an inter-organism distance based on our PM score explains co-occurrences better than scores based on alternative methods we tested (as shown in the newly added Supplementary file 4). We further show that our approach more precisely separates fastidious/uncultivated microbes than an alternative approach in Figure 4—figure supplement 7. Further comments on how our method differs from and improves upon other potential approaches, as well as an extended discussion of limitations, have been added to two paragraphs in the Discussion.Reviewer #2:[…]1) The method assumes a uniform distribution of possible substrate uptake combinations – which is not necessarily biologically observed. There are hierarchies – e.g. preference of glucose over other C-sources in most organisms.inP for our analysis was chosen specifically in order to assess biosynthetic capabilities across a uniformly sampled ensemble of environments, i.e. under the assumption of minimal knowledge about the chemical composition of the growth medium. We have emphasized this point in the revised Abstract, mentioned it in the Introduction, and clarified it in the revised “Analysis Method” section and the newly added Figure 1.We thank the reviewer for raising this point, which gave us the opportunity to better clarify two important aspects of our analysis. First, the assumption of uniform inP, we were glad to clarify and exemplify in the revised manuscript the feasibility of arbitrarily chosen, metabolite specific set of inP values, which encode assumptions about the environmental composition. In particular, to demonstrate this capability, we have recalculated the producibility metric (PM) for one saccharolytic and one proteolytic organism in a protein enriched environment and carbohydrate enriched environment. While we found only modest increases in the PM in both of the enriched environments, we did find that the producibility metric was further increased for the proteolytic organism in the protein enriched environment than it was for the saccharolytic organism. This analysis demonstrates how we can tailor our method to use variable inP values to ask interesting questions about an organism’s environmental dependencies. The analysis is presented as newly added Results section “Metabolite producibility in a protein vs. carbohydrate enriched environment” and Figure 4—figure supplement 5.Second, while in the previous version of our manuscript we indeed only focused on the case of a uniform 2) The finding that metabolic dependencies may exist in oral microbiome is not that surprising per se given that a large body of literature  already suggest that metabolic dependencies are likely widespread in microbial communities. Thus, it is not clear whether only the proposed method would be able to identify these.Indeed, as expressed by the reviewer, the novelty of our work is not so much in pointing out the general possibility of inter-species metabolic exchanges, but rather in (i) the capacity of our method to produce predictions in a way that is specific to the underlying genome and molecular products, but at the same time robust to uncertainty in environmental composition and to missing gene annotations; and (ii) the production of a detailed atlas of biosynthetic capabilities and complementarities for a specific ecosystem of high interest for multiple health-related studies, namely the human oral microbiome. To our knowledge, ours is the first large-scale metabolic analysis of this type in the human oral microbiome. In this sense, it provides valuable new insight into this microbial community and can further serve as a blueprint for analyzing other complex microbial communities.In the revised manuscript, however, in line with the reviewer’s comment, we made sure to better present our results in the context of previous analyses. In particular, in addition to more clearly stating the objectives of our work in the Introduction, we reference and describe in more detail prior literature on computational and empirical analyses of inter-species dependencies in microbial communities. Beyond this clarification, we have also added a number of analyses that compare our method to different alternative methods including: pathway completeness , flux balance analysis , and alternative metabolic network analysis methods, such as NetCooperate used in a similar analysis , through an analysis of microbial co-occurrence data from the human oral microbiome .3) Lack of experimental validation makes it difficult to assess whether the identified exchanges are happening in the system. At the least, a detailed analysis of systems with known metabolite exchanges (and how the proposed method there differs from the previous ones) should be provided.This is an excellent point. We are grateful to the reviewer for the suggestion, which prompted us to perform a number of analyses to assess the capacity of our method to relate to experimental measurements, and to compare our approach with previously published ones. We believe that this process ended up strengthening our manuscript significantly.E. coli auxotroph co-culture data from Wintermute and Silver (2010). This dataset has the advantage of using genetically well-defined E. coli strains with specific known auxotrophies, such that corresponding genome scale models can be appropriately constructed, and metabolic exchanges can be inferred with reasonable confidence. We analyzed this system in detail to provide insight into the predictive capacity of our method. The comparison of model predictions with experimental data led to a number of observations, reported in the manuscript, and summarized briefly as follows: (i) we found that for several auxotrophs in the tryptophan pathway, the PM value for tryptophan was correlated with the auxotrophs’ ability to be supplemented by other auxotrophs; (ii) we observed that metabolically similar organisms  tend not to supplement each other’s growth; (iii) in the new section we also point out some exceptions to the trends mentioned above, including increased synergistic growth for at least one set of auxotrophs with knockouts in the same biosynthetic pathway, which highlights the complexity of this experimental data and the limitations of our method.First, we examined an experimental dataset on microbial co-culture growth. This new analysis is described in a new section of the Results titled “Metabolite producibility points to putative metabolic mechanisms for E. coli auxotroph co-cultures”, Figure 3—figure supplement 1. For this new analysis, we used In a second newly added analysis, we utilized our metric, as well as previously published metrics, to describe microbial co-occurrence patterns across the human oral microbiome. The results of these analyses are presented in a new Results section titled “Metabolic similarity correlates with microbial co-occurrence in the human oral microbiome”, accompanied by a newly added Supplementary file 4. Although co-occurrence does not necessarily imply interactions, and mechanisms of interaction are generally unknown, previous methods have been shown to be capable of identifying metabolic trends associated with microbial co-occurrence in the human microbiome  We used our method to analyze co-occurrence from metagenomics data from 7 different oral sites in the human microbiome project. Co-occurrence data calculated using both the SparCC method and Pearson’s correlation were taken from Friedman and Alm (2012). We compared our method with a number of different metabolic network analysis methods, including NetSeed, NetCooperate, and NetCmpt used in Levy and Borenstein, as well as simple metrics based on metabolic reaction distance and Jaccard’s distance. We found that our metabolic network metric, based on the difference in PM between two organisms for all biomass components, was the most consistently anticorrelated with co-occurrence data (irrespective of co-occurrence estimate method), showing that similar organisms tend to co-occur. This result corroborates the habitat filtering hypothesis previously proposed by Levy and Borenstein. We also found that our method, and other methods, correlated more consistently with co-occurrence inferred from the SparCC method than those inferred from Pearson’s correlation, which further corroborates the claims of Friedman and Alm that Pearson’s correlations can fail to capture true co-occurrence in compositional data. Additionally, we found that our PM based metric maintained correlation with co-occurrence when controlling for other metrics through partial correlations while the inverse was not always true. This analysis highlights our metric’s ability to capture metabolic similarities between organisms, that correlate with co-occurrence, beyond what is captured by existing metabolic network analysis methods.Fusobacteria genera had increased PM for butyrate, a result with important implications in oral health, and which is supported by independent transcriptomic data from the literature . Additionally, we found that some species of the Porphyromonas and Prevotella genera, which have been implicated in periodontal disease due to production of organic acids , had increased PM for butyrate as well. These results, while not directly proving exchange of a given metabolite across a specific organism pair, provide valuable information about putative secretions that could mediate these interactions.Finally, we extended our calculation of PM to include organic acid production. This analysis is presented in a new Results section titled “Organic acid production predicted for human oral microbiome organisms”, Figure 4—figure supplement 4. Through this analysis, we used our approach to determine whether it could predict organic acid production in human oral microbiome organisms. In particular, we were able to identify trends in organic acid production by different genera of oral microbiome organisms. We found that the Reviewer #3:[…]Given the rate of generation of microbial genomes it would be very useful to have a better method to even approximately predict metabolic products of organisms. However, what the study lacks in my opinion, is quantitative evidence that the metric actually does translate into a prediction that the organism produces a given metabolite. They provide some anecdotal examples where it appears to work but without a more thorough analysis of what the metric means then it will only be useful in a qualitative sense i.e. a higher PM indicating that one organism is more likely to produce a metabolite than another. Metabolic modelling is admittedly not my field, but datasets capable of testing the metric, must exist. A possible example might be this collection of E. coli strains and phenotypes defined in terms of growth conditions . If such datasets are not available then I feel the authors need to be more circumspect in their conclusions and concede that the metric may say something about the production of metabolites but without any certainty about how a given PM value translates into an actual probability of production.We appreciate the reviewer’s comment, which raises a very good point. The most important concern expressed by the reviewer seems to be the insufficient comparison with experimental data, which can lead one to legitimately wonder how accurate and valuable our predictions are. Throughout our response to all reviewer comments, we have taken to heart this concern, by implementing a number of new analyses that compare our predictions with different kinds of experimental data, as well as with previously published approaches. In presenting these new analyses, we have shown the strengths of our approach, but we have also explicitly described the possible limitations of our inferences. We believe that these additional analyses will provide the readers with a clearer perspective of the type of microbial ecology questions for which our method can provide valuable insight.E. coli in detail, calculating both the Producibility Metric (PM) and the% completion of the biosynthetic pathway for different knockouts along the linear pathway. Through this analysis we were able to illustrate the difference between the PM and a simpler pathway based analysis, giving additional insight into the meaning of the PM.The first analysis we performed to illustrate the value of our method was a comparison with the simpler approach of quantifying the percent completion of a pathway as a measure of biosynthetic capability. This analysis was also described in further detail for reviewer #1 comment 1, and is presented in the Results section “Producibility of metabolites differs from pathway completeness and captures minimal precursor set structure”, Figure 2—figure supplement 2. For this analysis, we analyzed the histidine biosynthetic pathway in Next, we compared our method with flux balance analysis (FBA) for a genome-scale metabolic network with varying degrees of perturbations generated by randomly removing reactions from the network. This analysis is described in further detail in the Reviewing Editor’s summary comment and is presented in the Results section “Producibility analysis shows improved tolerance to missing reactions compared to flux balance analysis” and newly added main text Figure 3. Through this analysis we demonstrated that the PM is more robust to missing reactions than traditional FBA and can therefore provide additional insight into draft metabolic networks with gaps. Again, this analysis provided additional context to the meaning of the PM and its applicability for analyzing metabolic networks.E. coli auxotroph co-cultures presented in Results section “Metabolite producibility points to putative metabolic mechanisms for E. coli auxotroph co-cultures”, Figure 3—figure supplement 1. In this section, we use the PM to analyze co-culture synergistic growth data of different E. coli auxotrophs from Wintermute and Silver (2010). The comparison of PM predictions with experimental data led to a number of observations, reported in the manuscript, and summarized briefly as follows: (i) we found that for several auxotrophs in the tryptophan pathway, the PM value for tryptophan was correlated with the auxotrophs’ ability to be supplemented by other auxotrophs; (ii) we observed that metabolically similar organisms  tend not to supplement each other’s growth; (iii) in the new section we also point out some exceptions to the trends mentioned above, including increased synergistic growth for at least one set of auxotrophs with knockouts in the same biosynthetic pathway, which highlights the complexity of this experimental data and the limitations of our method.Next, we introduced several new analyses that compare our PM predictions to experimental data. These analyses provide insight into how the PM can be used to analyze and interpret biological data. The first of these was an analysis of Fusobacteria genera had increased PM for butyrate, a result with important implications in oral health, and which is supported by independent transcriptomic data . Additionally, we found that some species of the Porphyromonas and Prevotella genera, which have been implicated in periodontal disease due to production of organic acids , had increased PM for butyrate as well.We next extended our analysis of the human oral microbiome to predict organic acid production. This analysis is presented in Results section “Organic acid production predicted for human oral microbiome organisms”, Figure 4—figure supplement 4. We were able to identify trends in organic acid production by different genera of oral microbiome organisms. We found that the Finally, we added a large analysis of microbial co-occurrence data from metagenomic sequencing data. This analysis is presented in the new Results section “Metabolic similarity correlates with microbial co-occurrence in the human oral microbiome”, Supplementary file 4. In this analysis, we analyzed co-occurrence data from Friedman and Alm (2012) and calculated the correlation of co-occurrence with various inter-organism metabolic metrics calculated using our PM and alternative methods. We showed that an inter-organism distance based on our PM score explains co-occurrences better than scores based on any alternative method that we tested. Furthermore, there was a strong negative correlation between PM based inter-organism distance and co-occurrence indicating that organisms with similar biosynthetic capabilities tend to co-occur. Our finding corroborates and strengthens previous similar analyses of co-occurrence data from the human microbiome , and demonstrates the ability of our method to provide insight into large-scale top down data such as microbial co-occurrence from metagenomic sequencing.We also appreciate the reviewer’s suggestion of a paper (and corresponding high-throughput dataset) that could be in principle used to additionally assess our method. Unfortunately, the majority of the conditions tested in this paper are undefined or non-metabolic (mainly consisting of antibiotics or other stressors), and it is therefore not the best dataset for evaluating our method. The alternative option we had considered, using a different dataset of similar type , ended up not being fruitful either, as we were unable to obtain this dataset. While this would have been a nice addition, we hope that the large number of new analyses we ended up performing to address this and other concerns will be deemed satisfactory.Other than the above caveat, I thought this was a good study but it was sparse on the practical details of the methodology. The GitHub repository consists of a selection of Matlab scripts without a clear description of how to apply them. What would be really useful is a complete walkthrough of the methodology from genome to PM values including for example ggkbase commands used to build the models. This is necessary if this work is to be properly reproducible. One final comment was that some evaluation of the impact of sample number on the calculated PM values would be a worthwhile addition. The authors mention that 50 samples of input metabolite combinations were used but no analysis of the impact of this choice on the PM values was given.This is a good point and we appreciate the reviewer’s effort to help us make our method more reproducible. We have added an example script to the GitHub page that can be run to calculate the producibility metric (PM) for a small subset of metabolic networks and metabolites. We also include code that could be used to calculate the PM for the 88 biomass metabolites and 456 oral microbiome metabolic networks analyzed throughout the paper. However, we note that this would take a long time and is best performed in parallel on a shared computing cluster, as described in the Materials and methods section.Regarding the parameter choices, we note that these parameters were chosen by hand to provide adequate performance for our algorithm, which we have further emphasized in the Materials and methods section of our manuscript.