Understanding how the metabolic rates of prokaryotes respond to temperature is fundamental to our understanding of how ecosystem functioning will be altered by climate change, as these micro-organisms are major contributors to global carbon efflux. Ecological metabolic theory suggests that species living at higher temperatures evolve higher growth rates than those in cooler niches due to thermodynamic constraints. Here, using a global prokaryotic dataset, we find that maximal growth rate at thermal optimum increases with temperature for mesophiles (temperature optima  Warmer temperatures could increase the growth and metabolic rates of microbes. Here, the authors assemble a dataset of thermal performance curves for over 400 bacteria and archaea, showing that metabolic rates are likely to increase under warming, with implications for global carbon cycling. Because fundamental physiological rates of ectotherms are directly affected by environmental temperature6, climatic warming may be expected to lead to ectotherm communities with higher metabolic rates on average7. How environmental temperature drives metabolic rates of prokaryotes (bacteria and archaea) is of particular importance because they are globally ubiquitous, estimated to comprise up to half of the planet’s global biomass8, and are the end users of the majority of net primary production10. Therefore, climate-driven changes in prokaryotic metabolic rates are expected to significantly alter ecosystem productivity, nutrient cycling and carbon flux14. Indeed, increased carbon efflux  thermal responses of prokaryotes can be compensated by acclimation  or longer-term  evolutionary adaptation20 is currently unclear. The most recent study to investigate this idea concluded that both short- and long-term responses of ecosystem-level heterotrophic respiration were similar21. However, this study quantified short-term responses by aggregating day-level carbon fluxes across sites, and did not have data on the direct respiratory contributions of prokaryotyes per se.A general understanding of how individual organisms respond to changing environmental temperature is necessary for predicting how populations, communities and ecosystems will respond to a changing climate22  hypothesis posits that trait performance at 24. Thus this hypothesis essentially links the short-term TPC of trait performance to the longer-term performance mediated by evolution. The HiB hypothesis is also implicit in the universal temperature-dependence concept of the Metabolic Theory of Ecology (MTE)25. However, whether the HiB hypothesis holds across organisms and environments is a question that is still debated28. Deviations from a HiB pattern would indicate that either thermodynamic constraints do not exist, or are compensated for by other mechanisms. In particular, an alternative hypothesis is that natural selection acts to override thermodynamic constraints, allowing peak trait performance and fitness to be, on average, equalised across different adaptation temperatures  responses of prokaryotic populations has neither been made nor the potential effects of responses at different timescales on ecosystem fluxes studied.The short term, or instantaneous response of metabolic traits of individual organisms to changing temperature  is typically unimodal, with the thermal performance curve (TPC) of the trait increasing with temperature up to a peak value  thermal sensitivity around which species are expected to evolve, which we term 2. However, these values are derived from data sets which have largely or entirely excluded prokaryotes. Previous work on sub-groups of prokaryotes—cyanobacteria32 and methanogenic archaea17—has indicated comparatively high thermal sensitivities which deviate from the eukaryote-derived MTE expectations. Whether this deviation from MTE is a property of prokaryotes in general has never been thoroughly tested. Given the ubiquity of prokaryotes, this is a matter of particular importance for theories applying MTE to whole ecosystems33.Under MTE, the global thermodynamic constraint is expected to centre n ~0.65 eV for heterotrophsmentclass2pt{minim24, covering practically the entire range of habitable global temperature niches  and the majority of the phylogenetic diversity of prokaryotes . In total, we compare 542 growth rate TPCs and an additional 54 metabolic flux TPCs, spanning 482 unique prokaryotic strains. In order to test the generalisations around global thermodynamic constraints, we also assemble a data set of 381 eukaryote TPCs spanning aquatic and terrestrial autotrophs, for direct comparison with our prokaryote TPCs. We find that HiB holds for mesophilic bacteria, but not thermophiles, and that mesophilic archaea also show long-term increases in rate with temperature, although the coupling of short- and long-term responses is less clear for these prokaryotes. We also show that prokaryotes tend to have generally higher thermal sensitivities than eukaryotes and conclude that as global temperatures increase, carbon efflux from the prokaryotic components of ecosystems is likely to increase at a greater rate than carbon efflux from eukaryotes.Here, we build and analyse a global data set of TPCs in bacteria and archaea to quantify general patterns in both the short-term (intra-specific) response, and to test whether the HiB hypothesis holds  within and across taxonomic and functional groups adapted to different temperatures Fig. . These dp n = 165; archaea slope = 0.92, 95% CI n = 58) because First, we compared each strain’s thermal optimum  across mesophilic bacteria  and long-term (inter-specific) thermal responses see Fig. ; Methodsmentclass2pt{minimmentclass2pt{minim6 and previously observed mean intra-specific values 2. The data are right-skewed , but even after accounting for this skew by taking the median, activation energy still falls significantly >0.65 eV  of population growth rate. However, to understand the implications of the short- and long-term thermal responses of prokaryotes for ecosystem functioning, it is necessary to test whether these reflect the activation energies of underlying metabolic flux rates. To investigate this, we assembled another thermal response data set (Methods) for metabolic fluxes recorded in prokaryotes  and asked whether, on average, thermal sensitivity is equivalent for growth rate and metabolic fluxes. We find that average intra-specific mentclass2pt{minimlts Fig. d further35. The results , using the actual difference in sensitivity that we have found (39). When we consider the effects of longer-term warming  on the prokaryotic sub-community using the inter-specific (evolutionary) thermal sensitivity, 42. In our model, each percentage point increase in prokaryotic biomass within the heterotrophic component causes a flux increase of Our results suggest that higher sensitivity of both short- (higher intra-specific activation energies) and long-term (higher inter-specific activation energies—a HiB constraint) thermal responses in mesophilic prokaryotes may have profound implications for responses of ecosystem fluxes to climatic warming. To illustrate this, we built a simple mathematical model to calculate the potential change in the relative contribution of heterotrophs to ecosystem carbon efflux . Using our new estimates of mentclass2pt{minim17 and cyanobacteria32, but have never been demonstrated across all major lineages of prokaryotes. In particular, Yvon-Durocher et al.17 have argued that the high Our results demonstrate that mean thermal sensitivities for both bacteria and archaea fall significantly >0.65 eV  HiB curve , the thermal performance of these organisms has been generally less well-characterised. More work is necessary in order to fully understand the coupling of short- and long-term thermal responses in archaea.While in general, we see a tendency towards high thermal sensitivity . Ultimately, despite all this variation, we find that both, the short-term (intra-specific) and long-term (HiB hypothesis) amplification of metabolic rate holds true for the mesophiles (≲45 °C), temperatures which encompass most of the biomass on the planet.We also note that while the majority of heterotrophic bacteria in our data set respire aerobically, there are a number of anaerobic strains, the majority of which were grown under various fermentation conditions. However, when we consider these groups of bacteria separately, we see no significant difference between their mean intra-specific thermal sensitivities , within which the Boltzmann-Arrhenius model is appropriate57. If these fluctuations were frequent enough to have strong effects on the community, using the Sharpe–Schoolfield model as an alternative to Boltzmann–Arrhenius may be an interesting approach to predicting the effects of extreme warming events at the ecosystem level. However, parameterising this would again require the data on the specific species present in a given ecosystem and their individual TPCs, which is outside of the scope of our current study.Following previous approaches applying MTE to ecosystem functioning, such as Enquist et al.59. Also, our comparisons for growth rate and metabolic flux We have focused on the ecosystem consequences in the face of global change, but our results also have implications for understanding prokaryotic physiology. We are not aware of any previous work showing that prokaryotes differ systematically in their thermal sensitivity from eukaryotes. Therefore, further studies are needed to explore the mechanistic basis of this difference, and may reveal a major physiological transition mediated by an increase in cellular complexity as well as multi-cellularity in eukaryotes60 and thus adaptation to such niches may incur a fitness cost to thermophiles as seen in our results. This result is in concurrence with an investigation of the maximum growth rates of life on Earth, which found increases in microbial growth up to a peak before an attenuation of growth rates in warmer adapted organisms31. Our results also suggest a limit to thermal adaptation as we find that strains cultured at very high temperature tend to display lower than expected thermal optima  and inter (long-term)-specific thermal responses are similarly conserved across other groups of organisms that are important for ecosystem function, such as fungi and insects in terrestrial, and phytoplankton and zooplankton in marine ecosystems.61 was used to extract data points, including error bounds when reported. The ‘Taxize’ R package62 was used to standardise taxonomy of extracted data to the NCBI database. The papers were also manually searched to collect data on growth conditions as well as other metadata where possible . In instances where doubling rates or doubling times were reported, we used Doubling time We compiled a data set of published prokaryotic thermal performance curves (TPCs) by searching the literature for papers with these data and using digitisation software to collect the thermal performance point estimates. Candidate TPC data were identified via manual searches of google scholar and pubmed databases. Search terms, such as ‘bacteria’, ‘bacterium’, ‘archaea’, ‘archaeon’, ’temperature’, ‘temperature response’, ‘thermal response’, ‘growth’, ‘adaptation’, were used to find papers with response data particularly for growth rates. Later searches included terms such as ‘characterisation’, ‘isolation’, ‘nov.’, ‘novel’, ‘gen.’, ‘sp.’, as it became clear that thermal responses were often tested in publications describing newly isolated species/strains. When presented as a response curve figure, ‘Plot Digitizer’ softwareAlthough we primarily collected growth rate data as a measure of fitness in order to test HiB, we additionally collected 54 TPCs covering various metabolic fluxes for comparison to growth rate TPCs. Our complete prokaryote data set comprises 596 TPCs from 482 unique prokaryote strains across 239 published studies.Finally, we compiled thermal response data for respiration rates in autotrophs from the literature using the same methods for digitisation and data collation as for the prokaryote data set. In total, this autotroph data set comprises 381 respiration rate TPCs from 140 unique autotroph species .We use prokaryotic ‘strains' to designate separate prokaryotic taxonomic entities with potentially differing TPCs. If a single study provided multiple TPCs from the same prokaryotic strain under the same conditions, these were considered pseudoreplicates. In these cases, all data were collected and a single Sharpe–Schoolfield fit (see Model fitting) was computed for the combined set of points, yielding a single set of TPC parameters. Where multiple TPCs were provided for the same strain under different growth conditions, these were considered as separate biological replicates, however in practice this is only the case for two replicates in each of two different strains in our data set. Where TPCs were obtained from prokaryotes identified only to the species level (or higher), these were considered biological replicates as likely representing different strains of those species.The eukaryotic autotroph data set did contain organisms identified as the same species grown under similar conditions. Given the slower generation times of eukaryotes and thus slower species divergence, we do not consider these as representative of different strains, as we do for prokaryotes, and thus consider them pseudoreplicates. To remove pseudoreplicates, we compared Sharpe–Schoolfield model fits (see Model fitting) from each replicate and chose the one with the best fit as most representative of thermal performance for that species, discarding data with worse fits.63, Eq. , 64.Here, Each strain’s TPC has a potentially different mentclass2pt{minimmentclass2pt{minimAll Boltzmann–Arrhenius and Sharpe–Schoolfield model fitting were performed in Python with the NumPy package, using the Levenberg–Marquardt ordinary non-linear least-squares regression method.We determined whether HiB by testing whether the activation energies from intra- (short-term) and inter-specific (long-term) TPCs were  significantly different. In order to provide a comparison between intra-  followed by an attenuation of maximum growth rates until a second peak at ~67 °C (thermophile peak), suggesting a biological transition between mesophiles and thermophiles.Psychrophiles and mesophiles inhabit low to medium temperature ranges, while thermophiles and hyperthermophiles grow at much higher temperatures66. Segmented is not compatible with non-linear least-squares (nls) fitting, so this was performed with a linearised version of Boltzmann–Arrhenius, i.e., 30 and were thus used as cut-off points for defining mesophiles and thermophiles in our analysis. For this work, we provide no lower limit for mesophiles, essentially grouping psychrophiles and mesophiles together. Were psychrophiles to display a pattern different to mesophiles, we would expect this to have shown up in the break-point analysis, but only one break point (separating mesophiles and thermophiles) was found for both bacteria and archaea.In order to determine whether it was appropriate to consider mesophiles and thermophiles separately, we performed a break-point analysis on our data set using the ‘Segmented’ R package52. A major physiological difference between these taxa lies in their fundamentally divergent membrane structures. This affects these organisms’ abilities to maintain proton gradients and thus drive metabolism under different conditions52, a difference that may be particularly important for thermal performance. As such, we separate bacteria and archaea in our analysis as disparate organisms with divergent evolutionary histories.In addition, archaea are typified by their adaptations to energetically demanding niches, while in contrast bacteria perform better in more ambient environments67 before manually checking the culture conditions in each study for the metabolites required for certain metabolic processes.In order to classify prokaryotes by the energy generating metabolic processes that they use, we took note of the growth conditions used when initially digitising the TPC data. For the majority of heterotrophic bacteria and archaea, this was simply whether they were grown under aerobic or anaerobic (fermentative) conditions. However, there are also a number of strains utilising more exotic metabolic processes such, as methanogenesis, sulfur reduction, etc. In these cases, we matched taxa against those able to utilise certain metabolic reactions according to Amend and Shock68 to understand whether each strain was potentially pathogenic, and what taxa they were known to infect.We also categorised taxa by their status as potential pathogens. We matched taxon names against the database of host-pathogen interactions provided in Wardeh et al.To quantify the effect of differences in activation energy of respiration between prokaryotes and eukaryotes on carbon flux, one can calculate the fold increase in flux , as these are not expected to provide a significant flux contribution to a typical terrestrial ecosystem. Alternative models and parameterisations for ecosystems which include cyanobacteria  are described in the Supplementary Methods and further discussed in the Supplementary Discussion.Here, each compartment’s total flux contribution  is modelled as a Boltzmann–Arrhenius equation, with mentclass2pt{minim38. For We then use Eq.  to calcue in Eq.  = 0.65 ementclass2pt{minimWe calculated the emergent 69:We also calculated the emergent x = 10 °C for short-term responses because this at the upper end  of the range of daily (over 24 h) fluctuations that organisms experience39. For long-term warming scenarios, we used 70.We chose a warming magnitude 40. This heterotrophic component would be comprised largely of prokaryotes and soil fungi biomass, the ratios of which have shown to vary widely depending on soil type and the experimental methodology used13. Here, we vary the percentage of heterotrophs within an ecosystem (35, this model does not include changes in the relative biomass of ecosystem components with warming.The biomass proportions Further information on research design is available in the Supplementary InformationPeer Review FileReporting SummarySource Data


Biomass Objective Function from experimental data. BOFdat has a modular implementation that divides the BOF definition process into three independent modules defined here as steps: 1) the coefficients for major macromolecules are calculated, 2) coenzymes and inorganic ions are identified and their stoichiometric coefficients estimated, 3) the remaining species-specific metabolic biomass precursors are algorithmically extracted in an unbiased way from experimental data. We used BOFdat to reconstruct the BOF of the Escherichia coli model iML1515, a gold standard in the field. The BOF generated by BOFdat resulted in the most concordant biomass composition, growth rate, and gene essentiality prediction accuracy when compared to other methods. Installation instructions for BOFdat are available in the documentation and the source code is available on GitHub (https://github.com/jclachance/BOFdat).Genome-scale metabolic models (GEMs) are mathematically structured knowledge bases of metabolism that provide phenotypic predictions from genomic information. GEM-guided predictions of growth phenotypes rely on the accurate definition of a biomass objective function (BOF) that is designed to include key cellular biomass components such as the major macromolecules , lipids, coenzymes, inorganic ions and species-specific components. Despite its importance, no standardized computational platform is currently available to generate species-specific biomass objective functions in a data-driven, unbiased fashion. To fill this gap in the metabolic modeling software ecosystem, we implemented BOFdat, a Python package for the definition of a  The formulation of phenotypic predictions by genome-scale models (GEMs) is dependent on the specified objective. The idea of a biomass objective function (BOF) is to represent all metabolites necessary for cells to double so that optimizing the BOF is equivalent to optimizing growth. Knowledge of the qualitative and quantitative organism’s composition (i.e. which metabolites are necessary for growth and in what proportion) is critical for accurate predictions. We implemented BOFdat with the idea that experimental data should drive the definition of the biomass composition. As omic datasets become more available, the possibility of integrating them to obtain a condition-specific biomass composition is in reach and therefore one of the main features of BOFdat. While major macromolecules, coenzymes, and inorganic ions are ubiquitous components across species, several species-specific components exist in the cell that should be accounted for in the BOF. To identify these, we implemented an approach that minimizes the error between experimental essentiality data and GEM-driven prediction. Hence BOFdat provides an unbiased, data-driven approach to defining BOF that has the potential to improve the quality of new genome-scale models and greatly decrease the time required to generate a new reconstruction. PLOS Computational Biology Software paper.This is a et al. studied the importance of the quantitative definition of the BOF and showed its impact on model behavior and predictions [et al. attempted to organize the content of the BOF of existing genome-scale models to understand the phylogenetic relationship of cellular compositions in prokaryotes [Genome-scale metabolic models (GEMs) are widely used to generate phenotypic predictions from genomic information, with wide-ranging applications from discovery to metabolic engineering . To compdictions . Xavier karyotes . While tet al. recently reviewed and provided a state of the art method of determining experimental macromolecular composition, and showed that the macromolecular composition varies considerably from one species to another [Experimental measurements of biomass composition have been developed, and it is already known that the cellular composition varies upon different growth conditions. Ratios between DNA, RNA and proteins have been shown to vary depending on growth rate and nutrient availability . The gro another . While tBOFdat, a Python software package for the complete definition of organism-specific BOF from experimental data. This package embeds a systematic 3-step procedure, where each step can be performed independently, that generates both qualitative and quantitative definitions of the BOF. BOFdat takes advantage of nowadays routinely generated multiple omic datasets  as well as the increasingly available gene essentiality data [Previously developed tools provide modelers with either a biased or unbiased approach to define the BOF for a metabolic reconstruction. Biased approaches have the benefit of being based on current biological knowledge but are hampered by potential fluctuations in metabolic objectives over specific conditions or across species and strains. For example, the SEED platform  automateity data  to generStep 1 aims at calculating the stoichiometric coefficients of the major macromolecules mentioned above, thereby providing a computational tool compatible with the experimental methods for the measurement of macromolecular cell composition reviewed by Beck et al. [Step 2 aims at refining the BOF by adding coenzymes and inorganic ions. The stoichiometric coefficients for suitable metabolites are calculated using the MWF of the soluble pool. This MWF may vary from an organism to another and can be generated experimentally or obtained from the literature. Step 3 aims at finding condition and species-specific metabolic end goals. To do so, an unbiased approach based on experimental gene essentiality data uses the power of the metaheuristic genetic algorithm (GA) and spatial clustering to identify groups of metabolites that represent cellular objectives under the condition of interest.In a GEM, the BOF is represented as a reaction in the stoichiometric matrix, where metabolites are consumed or produced in a proportion given by each stoichiometric coefficient to represent the net requirements for generation of cell biomass at steady state . Feist ak et al. . As menthttps://bofdat.readthedocs.io/). The characterization of the MWF of the major macromolecules is the most important factor to determine the stoichiometric coefficients and should be prioritized in experimental design. The use of genomic, transcriptomic, proteomic and lipidomic data refines the stoichiometric coefficient under a given condition . Implementation and calculation details are provided in In most cells, major macromolecules  occupy a significant fraction of the total mass  Fig 2A)Fig 2A). The DNA coefficients are calculated using the genome sequence, which is used to determine the relative abundance of each nucleotide . The MWF of DNA is provided by the user as a fraction between 0 and 1. The molar weight of each nucleotide is extracted from the model formula weight. Together this information is sufficient to calculate the stoichiometric coefficient (expressed in mmol/gDW/hr) of each metabolite  Fig 2C)Fig 2C).The coefficients of the monomers that compose RNA and proteins are obtained by weighting each metabolite frequency within a sequence (RNA transcript or translated protein) by the relative abundance of this transcript/protein in the corresponding omic dataset. This allows the user to calculate the relative abundance of each ribonucleotide and amino acid (AA) metabolites in the entire cell. To calculate stoichiometric coefficients, BOFdat thus uses the sequence of each RNA and protein along with the relative abundance of each transcript or translated protein. To ensure proper calculation of the stoichiometric coefficients, modelers must provide true relative abundances . The whole-cell relative abundances calculated using these input files are then converted into stoichiometric coefficients using the same calculation method as for the DNA metabolites .The lipidic constituents of the cell can also be incorporated into the BOF with BOFdat. To do so, modelers require access to a lipidomic dataset. The first input to provide is a conversion between BiGG identifier and the lipid generic name. This conversion step is intended to encourage a lipid network definition that matches experimental data. The second input file contains the relative abundances of each lipid species identified. Once provided with these two elements along with the lipidic MWF, BOFdat applies the conversion to BiGG and finds the molar weight of each lipid to compute their stoichiometric coefficients . Lipid set al. [http://bofdat.readthedocs.io). Briefly, growth-associated maintenance is represented as the slope of the curve obtained by linear regression, and the non-growth associated maintenance is the y-intercept of that curve  are obtained from growth rate, substrate uptake rate and secretion rate on different media conditions as performed by Monk et al.  Fig 2D)et al. [Fat curve .bona fide coenzymes . The COBRApy toolbox [in vivo [in silico evolution, referred to simply as evolution throughout the text; and 3) the results are interpreted through spatial clustering to form metabolic end goals.The GA supposes that the addition of a metabolite to the objective function may change and improve the gene essentiality prediction of a model. As illustrated in a simplified network composed of two linear pathways , the add toolbox  allows u toolbox  and othe[in vivo . For com[in vivo . Using tAn initial population is generated, on which the evolution will be performed. Conceptually, each individual in the population may contain any combination of all metabolites in the model. In order to reduce the search space of the algorithm, BOFdat utilizes a series of feature selection operations. The metabolites from the output of BOFdat Step 2 are removed from the complete set of metabolites. Metabolites that cannot be produced individually by the model are also removed. Lastly, the impact on gene essentiality prediction for remaining metabolites is assessed by optimizing for the production of each individual metabolite and calculating the MCC score as described above . MetabolAn individual is represented by a binary list referring to the presence (1) or absence (0) of the metabolites subset . Individin silico mating event, crossovers can arise between two individuals. In such case, a position in the list of two individuals is chosen and their elements are exchanged. An individual is an index of metabolites associated with an indicator of presence (1) or absence (0). This format allows to apply mutations which revert a 0 into a 1 and vice-versa. Selection is key to the GA since it ensures that a trait, referred to as fitness, is optimized throughout the evolution. In BOFdat Step 3, the fitness of each individual is measured by the MCC score, where a higher MCC score increases the chances of an individual being a member of the next generation. The process of applying the genetic operators on a population of individuals is called a generation.An evolution is performed by iteratively applying genetic operators to the initial population. The three genetic operators used in the GA are mutation, mating, and selection. Mating and mutation operators generate diversity within the population, allowing the GA to screen more combinations of BOFs. During an https://deap.readthedocs.io), the output of the GA can be presented in the form of a logbook or hall of fame (HOF). The logbook records the statistics of the population fitness at each generation , allowing the user to follow the increase of fitness over generations. The HOF records the best individuals generated throughout an entire evolution and can be used to assess the metabolite content of optimal solutions.The GA implementation also ensures that a limited number of metabolites is contained within individuals. To do so, the number of metabolites that a single individual can contain is restrained by applying a second objective to the fitness function used to select individuals. This maximizes the MCC score while minimizing the number of selected metabolites . As mentThe results of multiple evolutions are interpreted through the clustering of significant metabolites identified by the GA based on their network distance . The stoEscherichia coli K-12 MG1655. We compared our obtained biomass compositions and phenotypic predictions with the recently updated E.coli model iML1515 [a priori knowledge to determine the BOF composition and thus can be categorized as a biased method, BOSS uses a mixed-integer linear programming (MILP) optimization to extract biomass precursors and components from experimental data and is considered unbiased. In order to provide a valid point of comparison with the unbiased third step of BOFdat, we used an expanded version of the original BOSS that performs the optimization at the genome-scale   . This reiML1515 wild-type BOF . Naming the clusters creates a link from identified metabolites to knowledge, where the name of a cluster represents a metabolic objective.To evaluate the approach we generated 150 different initial populations and evolved each of them for 500 generations. The optimal solutions from those 150 evolutions were filtered and clustered as described above  and 15 cE. coli that maintains bacterial shape and allows resistance to intracellular osmotic pressure [iML1515 identified the production of quinone as biomass objective E. coli td before ,13.iML1515, 12 with SEED, 16 with BOFdat and 7 with BOSS. These raw results revealed that SEED is the closest method to iML1515 with 11 shared clusters, while BOFdat shares 7 and BOSS shares 1. The naming of the clusters found for each method was executed in the same way as for BOFdat alone  than BOSS (1). The number of non-shared clusters is also lower for BOFdat (2) than for BOSS (6). The underperformance of BOSS to identify biomass precursors is likely to be attributed to the coverage of the data used to generate the predictions. While state-of-the-art MFA data was used for the prediction [We compared the metabolites found with BOFdat by applying spatial clustering to the complete list of metabolites found in each method . In totaat alone  and clusat alone . While Sediction   where a link to the full documentation and API is available. We are confident that its use will contribute to more reliable BOF and GEMs. By providing an unbiased, data-driven approach to defining biomass objective functions, BOFdat has the potential to improve the quality of new genome-scale models and also greatly decrease the time required to generate a new reconstruction. With the increasing number of omic datasets being generated and the realization of community models, we expect BOFdat to be leveraged for the generation of condition- and strain-specific BOF definitions, hereby increasing the quality of GEMs phenotypic predictions. While using experimental essentiality data provides metabolic end goals, other unbiased methods using different data types could be developed and added to the package, hence revealing more precisely the metabolic end goals of the cells.BOFdat is a systematic computational framework for the definition of biomass objective functions for genome-scale models from experimental data. BOFdat is implemented in Python and is conceived to be a part of the COBRApy ecosystem , an enviS1 FigAs established in the literature, the degree is the number of metabolites to which a given metabolite is linked in the network. The red dashed line represents the threshold to identify a coenzyme, set as the mean (5.63) + one standard deviation (33.26) of 1877 metabolites of the network.(TIF)Click here for additional data file.S2 FigiML1515 model contains 1877 metabolites, 63 metabolites were removed because they were present in BOFdat Step 2 and 766 were removed because the model could not solve when they were set as an objective. The MCC was determined for the 1048 remaining metabolites. The threshold is set at the mean of the distribution + one standard deviation (MCC = 0.20) allowing to select 186 metabolites with the highest potential and referred to as the metabolites subset.The pre-feature selection for the generation of initial populations of BOFdat Step 3 includes the evaluation of the MCC value of each remaining metabolites (dark blue bars). The (TIF)Click here for additional data file.S3 FigiML1515 BOF (0.775). The orange dashed line represents the percentage of evolutions in which the best individual exceeds the baseline (right Y-axis). The vertical green line shows the number of generations necessary to obtain 50% of evolutions exceeding the baseline, in this case 166.At each generation, the highest MCC value of the population was plotted for each evolution (left Y-axis). The solid horizontal red line represents the baseline established by the MCC value of the original (TIF)Click here for additional data file.S4 FigNumber of metabolites contained in each individual (Y-axis) present in every generation over a typical evolution. The size constraint is a second weight applied on the fitness function. Here a weight of 1.0 is applied to maximize the MCC while a weight of 0.0 (A) and -0.25 (B) is applied to evolutions performed for 200 generations. In both cases, the individuals are initialized with a number of metabolites randomly varying from 60 to 100. Without applying a size constraint (A) the size of the individuals is ever increasing through the evolution. The application of a weight of -0.25 penalizes the individuals for the addition of metabolites and the individual size is stabilized (B).(TIF)Click here for additional data file.S5 FigMCA is used to compare feature similarity between 35 individuals selected from HOFs from different evolutions. The fitness value is represented from the minimum value recorded  to the maximum . The percent variability explained by the first two factors is 19.54% for factor 1 and 13.92% for factor 2. This analysis shows that similar fitness values can be obtained from diverse sets of metabolites.(TIF)Click here for additional data file.S6 FigEach evolution generates a Hall of Fame (HOF) that, by default, stores the 1000 best individuals generated in the course of that evolution. The individuals produced by all the evolutions are pooled together and, arbitrarily, the 20% best individuals are selected based on their fitness value. The metabolites that compose these individuals are then ranked based on their frequency of apparition in those individuals. The metabolites with a frequency of apparition above average are selected. The Dijkstra algorithm is then used to calculate the distance in the metabolic network between the selected metabolites, assuming that a single reaction is one unit of distance. The distance matrix is then clustered using DBSCAN to identify clusters of metabolic end goals. The removal of highly connected metabolites may break the connection of certain metabolites to the rest of the network. For visualization purposes, the maximum distance is attributed to such metabolites.(TIF)Click here for additional data file.S7 FigA high-quality quantitative proteomic dataset was used to generate stoichiometric coefficients for 18 different growth conditions . Each bo(TIF)Click here for additional data file.S8 FigiML1515 for 20 evolutions pooled together and reaches a maximum of 0.779 after 40 evolutions. (B) The selected metabolites are compared against the original biomass of iML1515. New clusters are formed and the distribution of percentage of shared clusters is shown (y-axis). The use of more evolution yields an increase in the percentage of shared clusters with the original BOF from 26.61% for 10 evolutions to 31.19% at 150 evolutions.HOFs from the 150 evolutions over 500 generations are sampled, such that 20 samples are formed per number of evolutions pooled together (x-axis). The number of evolutions is the number of HOF pooled together to form clusters and select metabolites. (A) The MCC value of the automatic selection of metabolites following the clustering in BOFdat Step 3 for an increasing number of HOF from different evolutions. The median MCC value exceeds the baseline set by (TIF)Click here for additional data file.S9 FigSelected metabolites from the 20% best individuals generated over 150 generations were clustered using the DBSCAN algorithm while varying the hyperparameters (eps and min_sample). As shown in the legend, two different values of min_sample were used . For these two min_sample values, the eps was varied from 1 to 50 and the number of clusters generated for these hyperparameters recorded (y-axis). Varying the “min_sample” for values 0 to 1 generated a single curve, while using a min_sample above 1 generated another. Hence only two values were represented. In this study, we systematically used a min_sample value inferior or equal to 1 (blue curve) and eps values that yielded a number of clusters around half of the number of metabolites provided.(TIF)Click here for additional data file.S1 File(CSV)Click here for additional data file.S2 File(CSV)Click here for additional data file.S1 Text(PDF)Click here for additional data file.


The application of instationary metabolic flux analysis (INST-MFA) to photosynthetic microorganisms has allowed researchers to quantify fluxes and identify bottlenecks and metabolic inefficiencies to improve strain performance or gain insight into cellular physiology. Additionally, flux measurements can also highlight deviations between measured and predicted fluxes, revealing weaknesses in metabolic models and highlighting areas where a lack of understanding still exists. In this review, we outline the experimental steps necessary to successfully perform photosynthetic flux experiments and analysis. We also discuss the challenges unique to photosynthetic microorganisms and how to account for them, including: light supply, quenching, concentration, extraction, analysis, and flux calculation. We hope that this will enable a larger number of researchers to successfully apply isotope assisted metabolic flux analysis ( Escherichia coli. The latter example actually had a relatively fast design to production phase, approximately 27 months (www.genomatica.com), due in part, to the use of metabolic modeling and isotope assisted flux analysis. Isotope assisted metabolic flux analysis, or 13C-MFA  as the building block for all carbon in the cell, and the light harvesting apparatus uses photons to regenerate reducing equivalents and ATP. The decoupling of carbon and energy metabolism introduces many complications in the design and implementation of experiments to measure fluxes; the discussion below will focus on how these are overcome.Experimental design for photoautotrophic cells differs significantly from heterotrophic cells due in a large part to the uncoupling of carbon and energy substrates. Heterotrophic organisms use the same substrate for both carbon and energy; for example, when grown on glucose, microbes break down and build up molecules from the carbon backbone of glucose and oxidize carbon (from the same substrate) in the TCA cycle to provide reducing power and energy in the form of ATP. In contrast, photoautotrophs utilize a one-carbon substrate . Light intensity plays an important role in growth rate for photoautotrophs; increasing light intensity increases growth rate up to a saturation point, after which the cells suffer from photoinhibition  and chromatography coupled to mass spectrometry (MS). Each has its own distinct advantages and disadvantages. NMR has the advantage of being non-selective and non-destructive, meaning it is capable of detecting all metabolites in the sample simultaneously without altering the viability of the sample. NMR is also useful for determining the position of labeled carbon atoms and the structure of metabolites, which is useful for identifying unknowns. The main disadvantage of NMR is the low sensitivity and signal overlap among individual metabolites. While there have been some studies which use NMR, the majority of 13C-MFA experiments have utilized either gas-chromatography MS (GC/MS) or liquid chromatography MS (LC/MS or LC/MS/MS). Heterotrophic steady state 13C-MFA studies tend to favor GC/MS because they analyze mainly amino acids, carbohydrates and lipids. For isotopic nonstationary MFA (INST-MFA), LC/MS/MS is the method of choice. The type of data that is required from these experiments are the metabolite pool size (concentration), parent ion mass and fragment masses. Metabolite pool size measurements verify the assumption of metabolic steady state for INST-MFA; however they are not always directly required for flux determination and may instead be evaluated as adjustable parameters  (Arrivault et al. Finally, photoautotrophic cells do not reach a metabolic steady state under diel light patterns. As the cell transitions between light and dark, different transcripts and enzymes activate and deactivate (Wagner et al. It is worth noting that computational applications within metabolomics are not just limited to converting mass fractions into fluxes. Three areas of particular focus come to the fore. First, confidence and error calculations are quite important when assessing flux. Generally, error estimations are extracted from confidence values, and various methods exist to do so (Antoniewicz et al. Experimental techniques and computational methods act in concert, and are matched in importance. Photoautotrophic flux measurement requires rapid and accurate sampling techniques, followed by powerful analysis. In order to produce high-quality, repeatable data, collection and analysis must be well practiced and documented. However, the effort required for generating this data is wasted without a thorough grounding in the computational complexities involved. An accurate picture of photoautotrophic metabolic fluxes can only be reached by combining both aspects.13C-MFA to measure phototrophic fluxes in 2011, there have been a handful of studies on other organisms (Table 13C-MFA experiment and the major stumbling blocks in applying this technology to photosynthetic microorganisms. While challenges still exist within the field, there are promising avenues of research for each. For example, optimization of quenching and extraction protocols for specific species will reduce metabolite leakage and perhaps aide in the development of a predictive model based on cell wall structure/composition. Improvements in computational approaches will allow more complex analyses and result in better models of photosynthetic metabolism. Finally, improved models will allow for better experimental design, as research simulations will indicate where data collection will have the largest impact. The field of photosynthetic flux measurement is rapidly developing and will continue to grow in importance as usage of photosynthetic organisms increases.Since the first report of the use of instationary


Synechocystis sp. PCC 6803 assimilates carbon dioxide as the sole carbon source, and a major portion of the assimilated carbon is metabolically consumed by the tricarboxylic acid (TCA) cycle. Effects of partial interference of TCA cycle metabolic activity on other carbon metabolism have yet to be examined. Here, the γ-aminobutyric acid (GABA) shunt, one of the metabolic pathways for completing TCA cycle in Synechocystis, was disrupted via inactivating the glutamate decarboxylase gene (gdc). Under normal photoautotrophic condition, cell growth and the level of the TCA cycle metabolites succinate, malate and citrate were decreased by 25%, 35%, 19% and 28%, respectively, in Δgdc mutant relative to those in the wild type (WT). The cellular levels of glycogen and total lipids of the Δgdc mutant were comparable to those of the WT, but the intracellular levels of pyruvate and bioplastic poly(3-hydroxybutyrate) (PHB) were 1.23- and 2.50-fold higher, respectively, in Δgdc mutant. Thus, disruption of the GABA shunt pathway reduced the TCA cycle metabolites levels, but positively enhanced the bioaccumulation of pyruvate and PHB. The PHB production rate in Δgdc mutant was 2.0-fold higher than in the WT under normal photoautotrophy.The photoautotrophic cyanobacterium  Synechocystis sp. PCC 6803  assimilates carbon dioxide (CO2) as the sole carbon source. Two thirds (66% mole) of the assimilated carbon is metabolically consumed by glycolysis and the tricarboxylic acid (TCA) cycle, while the rest (34% mole) of the fixed carbon fluxes to other metabolism, including biosynthesis of the carbon reserve products: glycogen, total lipids and poly(3-hydroxybutyrate) (PHB)1. These carbon reserve products are of interest since glycogen and lipids, particularly fatty acids and hydrocarbons, are efficient substrates for the production of bioethanol3 and biodiesel6, respectively, while PHB can be utilized as a biodegradable plastic9. Thus, metabolic inhibition targeted on the TCA cycle would reduce the TCA cycle metabolic consumption, and so potentially could increase the cellular metabolic carbon flux towards other biochemical pathways, such as biosynthesis of the carbon reserve products. However, inhibition of the TCA cycle metabolic activity reduced the cell growth of Synechocystis10. Thus, a partial inhibition of the TCA cycle that does not cause deleterious effects to cell growth, but is capable of redirecting the carbon metabolic flux towards carbon reserve biosynthesis is a desirable strategy for the bioproduction of carbon reserve products.The well-studied photoautotrophic cyanobacterium Synechocystis TCA cycle is distinct from the traditional TCA cycle in that it lacks the two steps for the conversion of 2-oxoglutarate to succinyl-CoA and then to succinate12. Recent experiments have shown that Synechocystis completes the TCA cycle using the (i) Oxo/Sucsem/Suc metabolic route  and (ii) γ-aminobutyric acid (GABA) shunt metabolic route 13. Thus, disrupting one of these two routes may partially reduce the TCA cycle metabolic activity in Synechocystis.The Synechocystis GABA shunt route was disrupted with the aim to negatively interfere with the TCA-cycle metabolic activity via inactivating the glutamate decarboxylase (the enzyme in GABA shunt route for converting glutamate to GABA) gene (gdc). We asked whether gdc inactivation affects the (i) TCA cycle metabolic activity and (ii) has effects on the nearby metabolic pathways (PHB synthesis and glycolysis), and the more distal carbon reserve metabolisms of lipid and glycogen synthesis. We found that gdc inactivation reduced the metabolites levels in the TCA cycle, but increased the accumulation levels of PHB and pyruvate. Since, gdc inactivation has also been shown to significantly increase the glutamate (Glu) level in Synechocystis14, we next asked whether the increased PHB level mediated by gdc inactivation was a consequence from the increased Glu level or from the affected TCA cycle. To address this, a section of the metabolic network that links Glu metabolism, the TCA cycle and PHB synthesis was examined by analyzing relevant metabolites and enzymatic activities. In addition, the effects of an external Glu supply on the PHB level were investigated.Here, the Synechocystis sp. PCC 6803 was obtained from the Pasteur culture collection. The Δgdc mutant was constructed previously14 by deleting the gdc gene (sll1641) in the WT Synechocystis. Approximately 5% (v/v) of a 14-d-old cell culture was inoculated into BG-11 medium15 without citrate but supplemented with 20 mM HEPES-NaOH (pH 7.5). Cells were supplied by atmospheric CO2 and cultured at 30 °C under continuous white light at 50 µmol/m2/s. Culture in nitrogen-deprived (-N) or phosphorus-deprived (-P) condition was performed as previously described16. Sodium glutamate was supplied as Glu source when required.Wild type (WT) 17. Essentially, dry cells were boiled in 18 M sulphuric acid to convert PHB into crotonic acid, which was then quantified by HPLC analysis. Commercial PHB was examined in parallel, where a PHB conversion level to crotonic acid was obtained at 82 ± 5% (w/w). Glycogen was purified, enzymatically digested to glucose and the glucose levels were quantified using the glucose oxidase assay  as previously described16. Total lipids were extracted and quantified using the acidic dichromate methods as previously described16.Approximately 10 mg dry cells were used for the analyses, where PHB levels were determined as previously described18, but with a slight modification in the HPLC analysis section (see below). Wet cells were frozen in liquid nitrogen, resuspended in methanol, sonicated and centrifuged. The supernatant was freeze-dried and reconstituted in methanol. Then, the organic acid metabolites were quantified using a Shimadzu (Japan) HPLC system according to the manufacturer’s protocol. The HPLC was equipped with an InertSustain Carbon-18 column and eluted in a 1:49 (v/v) of methanol: 0.1% (v/v) H3PO4 mobile phase with UV detection at 210 nm. Adipic acid was used as the HPLC internal standard.From a total of 250 mL of homogeneously-suspended cell culture, 50 mL was used for the dry cell mass determination and 200 mL was used for wet cell harvest. The organic acid metabolites  in the wet cells were extracted and quantified essentially as described before19. In brief, Glu was extracted from wet cells and subsequently derivatized with o-phthaldehyde and analyzed by HPLC using 338-nm detection. Acetyl-CoA levels were determined using the acetyl-CoA assay kit MAK039 , where the acetyl-CoA is extracted and specifically catabolized by a coupled-enzymatic assay which resulted in a product that was quantified by its fluorescent intensity (535-nm excitation and 587-nm emission). Cellular NADPH levels were determined using an NADPH quantification kit MAK038 . Briefly, total NADP+ and NADPH were extracted from wet cells. Samples were then heated at 60 °C to decompose NADP+ and the obtained NADPH samples were quantified using a colorimetric assay, determined by the absorbance at 450 nm.Cellular glutamate (Glu) contents were quantified as previously described20. The reaction was performed in Tris-glycerol buffer (5% v/v glycerol in 25 mM Tris-HCl pH 7.5) that contained 0.5 mM 5,5-dithiobis(2-nitrobenzoic acid), 1.5 mM 3-hydroxybutyryl-CoA and 0.2 mg/mL crude cell protein extract. The assay was incubated at 30 °C for 10 min and the thiobenzoate anion product was quantified spectrophotometrically at 412 nm. The crude protein concentration was determined using the Lowry method.The PHA synthase activity was determined as described before21. The reaction was performed in 50 mM Tris-HCl pH 8.0 buffer containing 50 mM Glu, 2 mM NADP+ and 0.2 mg/mL crude protein extract. The assay was incubated at 30 °C for 10 min, and the product was determined by the absorbance at 340 nm.The NADP-dependent glutamate dehydrogenase activity was determined as described before22 and then analyzed by 1Hydrogen- and 13Carbon-nuclear magnetic resonance (NMR) at 25 °C using a Bruker Advance 400 MHz spectrometer (Germany). Physical properties were examined using a material analyzing machine . Thermal properties and polymer molecular weight was determined as described23.The PHB was purified from dry cells as previously describedSynechocystis was disrupted by inactivating the gdc gene encoding glutamate decarboxylase, to yield the Δgdc mutant of Synechocystis, as previously reported14. Here, the effect of gdc inactivation on PHB accumulation was examined.The GABA shunt metabolic route of Synechocystis had a maximal PHB level of only 2.2% w/w dry weight (DW) at late-growth phase (after 21 d of culture), whereas the Δgdc mutant had a 2.5-fold higher PHB level at 5.5% w/w DW , the wild type (WT) gdc mutant was found to have a higher intracellular level of glutamate (Glu) than the WT  , which converts Glu to 2-oxoglutarate and releases NADPH (the reducing co-factor for PHB synthesis) was found to be comparable in the Δgdc mutant and the WT cells , NADPH (the reducing co-factor for PHB synthesis) and cellular polyhydroxyalkanoate synthase activity (the last enzyme in PHB synthetic pathway) of the Δels Fig. , suggestgdc inactivation directly disrupted the GABA shunt, one of the main metabolic routes for completing the TCA cycle in Synechocystis10. In the present study, gdc inactivation increased the level of 2-oxoglutarate (an upstream TCA cycle metabolite) by 1.41-fold, but significantly decreased the levels of the subsequent TCA cycle metabolites, i.e., succinate, malate and citrate by 0.35-, 0.19- and 0.28-fold, respectively , thus making it difficult to accurately determine these metabolites levels by this technique.With respect to the TCA cycle, gdc mutant  and PHB, respectively  Oxo/Sucsem/Suc route  and (ii) GABA shunt route10  reduced the levels of succinate and malate in the TCA cycle by 0.8- and 0.5-fold, respectively, but increased 2-oxoglutarate accumulation by 2.3-fold31. Likewise, disrupting the Synechocystis GABA shunt route  also reduced the TCA cycle metabolites succinate, malate and citrate, but increased the bioaccumulation of PHB and pyruvate  and an elevated PHB accumulation of 5.5% w/w DW, a 2.5-fold higher than that of the WT  and a 14% lower polydispersity relative to the commercial PHB  in Synechocystis.Disruption of the GABA shunt via Disruption of cyanobacterial γ-aminobutyric acid shunt pathway reduces metabolites levels in tricarboxylic acid cycle, but enhances pyruvate and poly(3-hydroxybutyrate) accumulation


Chlorophytes, Bryophytes, Lycophytes and Angiosperms. The plant metabolic networks were built using the substrate-product network modeling based on the metabolic reactions available on the PlantCyc database (version 9.5), from which their local topological properties such as degree, in-degree, out-degree, clustering coefficient, hub-score, authority-score, local efficiency, betweenness and eigencentrality were measured. The topological measurements corresponding to each metabolite within the networks were considered as a set of metabolic characters to compound a feature vector representing each plant. Our results revealed that some local topological characters are able to discern among plant kinships, since similar phylogenies were found when comparing dendrograms obtained by topological metrics to the one obtained by DNA sequences of chloroplast genes. Furthermore, we also found that even a smaller number of metabolic characters is able to separate among major clades with high bootstrap support (BS > 95), while for some suborders a bigger content has been required.Evolutionary information was inferred from the topology of metabolic networks corresponding to 17 plant species belonging to major plant lineages  The molecular biology and recombinant DNA technology enabled the evaluation of the evolutionary relationships by comparison of highly conserved DNA primary sequence of plastid genes, such as the successfully established phylogenetic relationships between plants by correctly discerning the ancestry relations2.Phylogenetic studies of plants were initiated by morphological observations related to their reproductive organs14. Early approaches to construct phylogenetic trees were applied using, for instances, graph matching comparison algorithm4, graph kernel method5 and graph-based decomposition algorithm6 to organisms such as archaea, eukaryota, and bacteria. Other authors have traced phylogenetic distances between metabolic networks using network’s global properties, for instances, Zhu & Qin7 used higher-level topological properties , while others works have explored the spectral distribution (Laplacian spectrum) in different approaches10. Further attempts have used alternative models such as NIPs (network of interacting pathways)11, from which several network-descriptors are extracted in order to predict phylogenetic distances within these three living beings groups. Besides that, protein-protein interaction networks were explored as well based on the identification of modular network components from each network12, and graph alignment for the cross-species analysis applied on Homo sapiens and Mus musculus species13.Many works have used the metabolic network content and its topology as an alternative tool to assess the phylogenetic relationshipset al.14 have shown phylogenetic similarities based on the comparison of the content of reactions among plant species. However, less attention has been put to the local topological properties of metabolic networks. It could be applied to explore the separation of organisms belonging to a specific kingdom such as Viridiplantae in their respective phyla, classes, orders and so on.Other efforts have brought progress to better understand the evolution of plants by means of their molecular networks. In that regard, Chae 17, has brought great advances. In general, the existence of hubs is one of the most evident characteristics of scale-free networks, which is corroborated by the correlation between the average shortest path length and the average clustering coefficient17. The existence of hubs is a direct consequence of the fact that many links tend to be established on nodes with high connectivity. This scale-free property on metabolic networks indicates that the probability of finding a highly connected node is conserved among living beings18. Therefore, the analysis of local topological properties from metabolic networks based on most representative measures such as the degree distribution, clustering coefficient, hub score and many other18, may allow finding evolutionary information that is hidden within their complex connections.Indeed, exploring the scale-free properties of metabolic networks, similarly to how non-biological networks are studiedBrachypodium distachyon (BD), Hordeum vulgare (HV), Oryza sativa japonica (OSJ), Panicum virgatum (PV), Setaria italica (SI), Sorghum bicolor (SB), Zea mays (ZM); Arabidopsis thaliana (AT), Brassica rapa pekinensis (BRP), Carica papaya (CP), Glycine max (GM), Manihot esculenta (ME), Populus trichocarpa (PT), Vitis vinifera (VV); Selaginella moellendorffii (SM); Physcomitrella patens (PP) and Chlamydomonas reinhardtii (CR); whose metabolic pathways, catalytic enzymes and metabolites are available at PlantCyc database19.In this work, we propose a method to extract the topological metrics of plant metabolic networks, in order to compare it between different plants, to obtain phylogenetic signal. We considered 17 plants, namely: Chlorophyta, Lycophyta, Bryophyta and Angiosperm that is divided into monocotyledons and dicotyledons. We observed that the local topological measure called hub-score provided quantitative parameters that were capable to group correctly the species studied within their respective clades.Features were extracted using a representative set of local topological measurements from the 17 metabolic networks. These features were then submitted to hierarchical clustering methods which provided means to compare it with phylogenetic data obtained from the plastid DNA primary sequence analysis. The results showed that our method manages to obtain information about kinship relationships, mainly in nodes 19 (version 9.5)  in terms of the average number of reactions (〈R〉) present on each major plant clade. This plot shows that the number of metabolites varies linearly with the number of reactions across the plant clades. This data suggests that the metabolic reactions have been accumulated along the evolution of the species as already verified in earlier works14.We analyzed the size of the metabolic networks and its dispersion throughout the taxonomic classes. Fig. L〉, the incoming and outgoing power-law exponent γin and γout) were calculated for each of the five major clades considered here, i.e. Chlorophyta, Lycophyta, Bryophyta, monocotyledons and dicotyledons. Figure R〉) per plant clade. Observe that only the the in-going power-law exponent is showed in Fig. et al.18. The average path length 〈L〉, varies slightly with the number of reactions, as it was observed in earlier works20. Moreover, as expected, a small slope can be noticed in the curve of the average degree 〈k〉 in function of the average number of reactions (〈R〉) per plant clade, hence the number of nodes (metabolites) increases from chlorophytes to dicots , in-degree (vi)), local clustering coefficient (Ci), authority-score (A(vi)), local efficiency (Fi), betweenness (Bi) and eigencentrality (Ei). We used these former topological metrics since they are related to the connectivity, distance-based and centralities measurements. A feature vector ϕP was composed using the topological measures of m = 1880 metabolites corresponding to the size of the common-metabolites-set .Nine local topological measurements were used independently to assembly feature vectors from the plant metabolic networks studied here, namely the degree  was used to measure the correlation between the distance matrices obtained by the topological measurements and the phylogenetic distance matrix obtained by the plastid gene sequence Rosidae clade; Inside this clade, the species Populus trichocarpa, Manihot esculenta and Glycine max were correctly assigned as Fabidae subclade; and Carica papaya, Brassica rapa pekinensis and Arabidopsis thaliana into the Malvidae subclade. It was also found a correct assignment of species within the Fabidae and Malvidae subclades. The species Populus trichocarpa, and Manihot esculenta were correctly assigned at Malpighiales order; and the species Brassica rapa pekinensis and Arabidopsis thaliana into Brassicales order. These results show the discernment of the method inside the dicots, on the other hand, the same was not observed inside the monocots clade.The dendrogram obtained by the hub-score metrics shown in Fig. Chlorophytes, Bryophytes, Lycophytes, and Angiosperms). These metrics introduce attribution errors only within the group of angiosperms with ramifications including both monocotyledonous and dicotyledonous plants at the same branch.In a similar manner, the other metrics were analyzed as well. The CPCCs obtained by the degree, in-degree, out-degree, local clustering coefficient, authority-score, local efficiency, betweenness and eigencentrality metrics were 0.85, 0.85, 0.88, −0.11, 0.71, −0.19, 0.72 and 0.29, respectively. We show in Fig. common-metabolites-set, however, this dataset excludes those specific metabolites of each plant, which need to be explored as well. Thus, we also analyzed the complete number of metabolites present in all the plants studied here. Therefore, we also considered the full-metabolites-set, which contains m = 4583 metabolites. We repeated all of the experiments shown previously and we have obtained very similar results, i.e. a high discernment among major clades defined by its higher CPCCs, and more particularly, when using the hub-score metric. The distances matrices corresponding to the nine topological metrics using the full-metabolites-set are given in the Supplementary Information We obtained consistent information regarding the discrimination between major clades, as shown in Figs common-metabolites-set and the full-metabolites-set, left and right, respectively. The bootstrap values correspond to 100 random replicas obtained by the hub-score dendrogram with feature vectors containing both dataset, i.e. m = 1880 and m = 4583 characters, using current RAxML 22.In order to validate the method, we compared the dendrograms obtained from the hub-score metric with the phylogenetic reconstruction regarding the 17 plants, i.e. a “guide tree” obtained from the DNA alignment  obtained high confidence values when using the common-metabolites-set as a feature vector.One can observe in Fig. ϕP = {μ1, μ2, …, μm}, i.e. in order to analyze the adequacy of the characters (metabolites) within this vector. Therefore, we built various samples containing, for example, 100, 200, …, 4500 characters in order to build different feature vectors, and then, we applied a bootstrap-re-sampling with 100 bootstrap rounds . The results of this analysis are found in Fig. Moreover, we also analyzed the robustness of the method according to the number of metabolites composing the feature vector et al.14. Although this previous work showed that the metabolic network sizes have an evident correlation with the evolutionary divergence at plant kingdom, the same is not true when considering the size of plant genomes. For instance, the size of the nuclear genome of Arabidopsis thaliana has 125 megabases (Mb) and Physcomitrella patens has 480 Mb with 25,498 and 35,938 genes, respectively24; However, the number of metabolic reactions of these plants is 3424 and 2651, respectively. Consequently, the number of genes per plant is not related to the size of the metabolic network. Preliminary data regarding the metabolic network size raised the question: has the topological structure of a metabolic network been modified in accordance with the evolutionary divergence of plants?We have analyzed the topological properties from 17 plant metabolic networks modeled from the metabolic reactions found at the PlantCyc database aiming to trace evolutionary information from these species. Initially, the number of reactions and the number of nodes (metabolites) in each plant metabolic network were useful to demonstrate the close relationship between their properties and their evolutionary pattern, as already suggested by Chae 18, it confirms that the same highly connected network nodes (hubs) may provide the relation between key metabolites responsible for distinct metabolic functions18. We have shown in this manuscript, that metabolic network posses intrinsic structural patterns that allow being more grouped between similar classes and more disperse from the unrelated ones. We have demonstrated that, conversely, some local topological network measurements  showed variation within the major plant clades.Besides the fact that metabolic networks, in general, have invariable global topological properties such as the scale-free natureChlorophytes (Chlamydomonas), Bryophytes (Physcomitrella), Lycophytes (Selaginella), Dicotyledons, and Monocotyledons are well separated. These results were supported by both the cophenetic correlation and bootstrap analysis, regarding the phylogenetic distance based on the DNA sequence alignment of chloroplast genes2, which correctly establish the taxonomy of 17 studied species. The explanations for such separation are rather complex. However, some more general features of metabolism can help explain them from a broader viewpoint. One possible trend that might help to explain the pattern of the grouping of species found in the present work is the gradual evolution of secondary metabolism during the evolution of plants25. One first step from Chlorophytes to Bryophytes/Lycophytes could be possibly associated with the evolution of the capacity to make lignin by plants from the latter groups. In the Angiosperm groups (represented here by monocots and dicots), secondary metabolism evolved to produce volatile compounds related to plant communication and defense. Thus, the dendrogram that results from hub-score analysis observed in, for instance, the difference in structure, as well as the number of reactions likely reflect the complexity of metabolism.The dendrogram presented in Fig. 26. The secondary metabolism of plants of the two groups are different, but equally complex. Some parts of the metabolism  have even been demonstrated to complement each other27. It also is possible that in the case of Zea, Sorghum, and Brachypodium, the presence of the C4 photosynthesis might have made a difference. Wang et al.28 found that important differences in the topology of the metabolic network of a C3 (Arabidopsis) and the C4 grass maize (Zea), the latter being considered denser, with higher robustness, and better modularity. Such differences might also have influenced the variations found in the present work.The separation of species from Dicots and Monocots is more difficult to explain. The differences might be related to the different genes and corresponding reactions present in both groups of plantscommon-metabolites-set), was able to establish taxonomic correlations by means of topological measures of metabolic networks. This fact indicates that many other modeling strategies can be used to extract more accurate models, thus, allowing better pattern analysis. Besides that, regarding the point of using all the metabolites or just the common ones, we have observed that it is possible to separate monocots and dicots with 100 Bootstrap rounds by using only the common-metabolites-set (m = 1880), notwithstanding, when going throughout the subclades this BS falls. However, on the other hand, when considering the full-metabolites-set (m = 4583), the correct assignment of subclades is improved. This suggests that important evolutionary information is also present in specific metabolites. Moreover, as shown in Fig. common-metabolites-set as much as in the full content of metabolites of each plant.Regarding the technical aspects of the proposed methodology, it is worth to notice that a reduced portion of the metabolic structure, i.e. 1880 metabolites that are common among all the studied plants , which consequently can be considered as a complementary tool for plant phylogenetic analysis. In this manner, different approaches or visions can provide extra information that can be used to corroborate the study of evolution, that apart from being largely studied is not fully understanding yet. Another advantage is that the metabolic network model studied in this work is considered a minimalist approximation of metabolic networks since they were constructed only by considering general aspects of the biochemical reactions. Due to this fact, we believed that many other scenarios of molecular networks can be also analyzed such as enzymes networks, genes, and proteins networks, since they may have rich information within their topological structure. This fact indicates that many other network modeling strategies, for instances, stoichiometric coefficients, and enzymes catalyzers, which could be explored in future investigations, can be used to extract yet more accurate phylogenetic correlations and pattern analysis.29. Besides, PlantCyc contains a trustful reconstruction of the plant biochemical pathways, as it was used in many works36, perhaps future metabolic databases with more complete data would carry out an improvement of the results obtained in this work.On the other hand, one of the limitations of this approach is that it relies on the set of metabolic reactions, which consequently depends on the completeness of the content of the accessible databasesFinally, our findings call for more in-depth comparative analyses of the metabolic pathways of plants of these groups to try pointing out to functional features and to the possibility of including the metabolic networks in plant phylogenetic analysis–and also to other types of organisms–in the future. Not only these initial hypotheses related to metabolic networks evolution can be tested and possibly extended, but this could also open interesting opportunities to implement synthetic biology strategies for plants.Figure 19 (version 9.5). Each plant reaction dataset and its corresponding web references are shown in Table 35  The database was converted to UTF-8 codification in order to avoid invalid characters; (ii) The duplicated biochemical formulas were removed; (iii) The reactions were standardized, for example, NADP(H) was referred as NADPH and (iv) The stoichiometric coefficient that precedes biochemical formulas were removed, since they were not contemplated in this study. With this latter preprocessing, therefore, we have means to model a metabolic network.37, where metabolites (nodes) from substrates are linked to metabolites from products of the reactions , where V is a set of N metabolites (nodes) linked by a set of edges E. Moreover, each metabolic reaction directionality was considered. Thus, each metabolite is individually linked to each other with respect to the reaction arrows . In the case of the bidirectional arrows, two links are considered separately (incoming and outgoing directions). Noticed that as V and E are set, therefore repeated metabolites and/or edges are dismissed.The metabolic network is represented by the adjacency matrix A of N × N, where each element aij is related to each other by a link.The plant metabolic networks were modeled using the set of biochemical reactions from a specific plant. Moreover, we followed the substrate-product network modelm = 1880 metabolites representing those metabolite with high connectivity such as ADP, ammonia, AMP, ATP, CO 2, among others. This dataset is composed by the intersection among all metabolites of plants analyzed here (Supplementary Dataset This dataset contains m = 4583) found in the 17 plants studied  among the 17 plants being studied  is given by D, which assumes zero when it is impossible to reach vj from vi. The average path length L of a network is calculated by finding the shortest path between all pairs of metabolites given byThe local clustering coefficient CP(k) is assumed as the probability of having a node with kin and kout degrees respectively17. Scale-free networks follow a power law distribution, γin or γout are the incoming and outgoing power-law exponent respectively.The in- and out-degree distribution 38, there are two types of nodes: hubs and authorities. Hubs are nodes highly connected, on the other hand authorities are nodes linked by many hubs. HITS algorithm assigns scores to hubs H(vi) and authorities A(vi), and computed them based on the node degree ki considering the participation of each node and their mutually reinforcement. This algorithm assumes the initial condition H(vi) = A(vi) = 1, as established by the equationsAccording to the Kleinberg’s HITS algorithm39. The communication between two nodes j and k, that are not adjacent, depends on the nodes that belong to the paths that connect j and k, i.e. acting as a bridge. Thus, the betweenness Bi of a node i is computed as a function of the number of shortest paths passing through i39:σjk(i) is the number of geodesic paths connecting j and k passing through i and σjk is the number of geodesic paths connecting j and k.We also considered two centrality measures, i.e. the betweenness and the eigenvector. The former metric considers the importance of a node regarding the information load it is responsible in the networki40, it is a metric that scores the influence of a node in a network. Thus, for instance, highest values represent those nodes which are connected to many other nodes which are, similarly, connected to many others. The eigencentrality metric is calculated using the highest eigenvalue λ given by the adjacency matrix A and corresponding eigenvector X40, as follows:Regarding the eigenvector centrality, or simply eigencentrality Eε measures how efficiently information is exchanged over the network41, while the local efficiency Fi accounts for the network’s tolerance when node i is removed, characterizing how well information is exchanged by its neighborhood, and it is defined as:Another metric used for network analysis is the efficiency, which can be applied in both local and global scales. The global efficiency Should be noticed that all of these metrics can be extracted by means of the network properties, being either local or global, thus, degree, in-degree, out-degree, hub-score, authority-score, local clustering coefficient, local efficiency, betweenness and eigencentrality are local topological measurements, on the other hand, power-law exponent, mean degree and average shortest path are global topological measures.MP, a feature vector ϕP =  is composed by the concatenation of the calculated measures of each metabolite, where m is the number of characters (metabolites). In order to obtain an accurate characterization of the metabolic networks, it was necessary a statistical method for feature normalization or dimensionality reduction, therefore, the principal component analysis (PCA) was employed in order to correlate the plant measurements by using a dimensional projection of the original feature space.The metabolic networks were characterized in terms of their topological measurements. We adopted local topological measures extracted from each node. Therefore, for each plant metabolic network i.e., plants from the same cluster are as similar as possible to each other, while plants from different clusters are dissimilar as possible42.In this work, we assumed that a pair of plants are similar when there exist correlated patterns among their metabolic networks that are also similar to their topological measurements, or vice versa. Thus, after determining the projections of the feature vectors, it was calculated a 17 × 17 distance matrix composed of the Euclidean distances between each pair of feature vector , from which a dendrogram can be constructed. In this context, the hierarchical clustering aims to form groups of plants belonging to the same cluster based on their topological characteristics, 21 performed on Matlab 2012a package was employed. In addition, the cophenetic correlation coefficient (CPCC)42 is applied in order to evaluate the consistency between two the distance matrices. For our purposes, the distance matrices corresponding to the topological measurements using the common-metabolites-set  hierarchical clustering method22 was used in order to estimate confidence intervals (BS) in all experiments.The bootstrapping method provided by the RAxML software m within the feature vector, we constructed ensembles of feature vectors, sampling m characters within the 4583 metabolites present in the full-metabolites-set. Each ensemble contains 100 random combinations containing different sizes m = {100, 200, …, 4500} characters. Therefore, 100 bootstrap replicates were considered per each topological measurement.In order to show the adequacy of the number of characters 2. The matrix containing 78 aligned plastid genes from 360 taxa was pruned to generate an alignment with 15 taxa that included the plants used in this study that are present in the PlantCyc database. For the remaining two taxa , the complete plastid genome was downloaded and the 78 relevant genes were aligned with the previous 15 taxa, using the MAFFT algorithm43. This multigene alignment was then subjected to Maximum Likelihood reconstruction using IQTREE44. We reconstructed the phylogenetic relationships for all 17 taxa. We first performed the implemented model tool which yielded the following most appropriate models via AIC: JTTDCMut + F + G4 for 17 taxa. We then performed Maximum Likelihood searches using default parameters, followed by 1000 rapid bootstraps to determine support. Resulting trees (Supplementary Dataset 2 if other taxa than those used in this study were removed.In order to generate a phylogenetic reconstruction as a comparison basis for the method proposed here, we have used a recent phylogenetic reconstruction of all plants as a starting pointSupplementary InformationSupplementary Dataset