We have recently demonstrated that the rate-limiting enzymes in human glucose metabolism organize into cytoplasmic clusters to form a multienzyme complex, the glucosome, in at least three different sizes. Quantitative high-content imaging data support a hypothesis that the glucosome clusters regulate the direction of glucose flux between energy metabolism and building block biosynthesis in a cluster size-dependent manner. However, direct measurement of their functional contributions to cellular metabolism at subcellular levels has remained challenging. In this work, we develop a mathematical model using a system of ordinary differential equations, in which the association of the rate-limiting enzymes into multienzyme complexes is included as an essential element. We then demonstrate that our mathematical model provides a quantitative principle to simulate glucose flux at both subcellular and population levels in human cancer cells. Lastly, we use the model to simulate 2-deoxyglucose-mediated alteration of glucose flux in a population level based on subcellular high-content imaging data. Collectively, we introduce a new mathematical model for human glucose metabolism, which promotes our understanding of functional roles of differently sized multienzyme complexes in both single-cell and population levels. In normal healthy cells, glucose is converted into pyruvate. Pyruvate then shuttles to mitochondria for oxidative phosphorylation in the presence of oxygen. If the oxygen is limited, however, pyruvate becomes lactate. In addition to its association with energy metabolism, glucose also plays an important role in building block biosynthesis, including the pentose phosphate pathway and serine biosynthesis. This is particularly important in cancer cells because glucose metabolism is dysregulated in proliferating cancer cells in which glucose diverts into building block biosynthesis even in the presence of oxygen. Hence, understanding the mechanism of glucose flux regulation between energy metabolism and building block biosynthesis is important to address altered metabolic phenotypes in human cancer as well as other chronic diseases, including but not limited to diabetes and obesity2.Glucose metabolism consists of glycolysis and gluconeogenesis. Glycolysis converts glucose into pyruvate, whereas gluconeogenesis reverses the sequential reactions to produce glucose3. Recently, it has been shown that human liver-type phosphofructokinase 1 (PFKL) forms cytoplasmic clusters in human cancer cells and further colocalizes with other cytoplasmic rate-limiting enzymes of the pathway, including human liver-type fructose-1,6-bisphosphatase (FBPase), pyruvate kinase M2 (PKM2), and phosphoenolpyruvate carboxykinase 1 (PEPCK1), thus indicating the formation of a multienzyme complex, namely the glucosome4. The size of glucosome clusters becomes larger in human breast carcinoma cells (Hs578T), relative to non-cancerous human breast tissue cells (Hs578Bst), demonstrating the spatial alteration of glucose metabolism in cancer cells4. Similarly, tumor-promoting hypoxic conditions also increased the size of glucosome clusters in human hepatocellular carcinoma cells (HepG2)5. Importantly, our quantitative high-content imaging data4 supported a hypothesis that the glucosome clusters regulate the direction of glucose flux between energy metabolism and building block biosynthesis in a cluster size-dependent manner. Unfortunately, however, it has been challenging to prove the hypothesis experimentally by measuring metabolic activities of various sized glucosome clusters at subcellular levels.Meanwhile, multienzyme metabolic complexes catalyzing glycolysis have been identified in various organisms, including protists, plants, yeast, mammalian neurons and erythrocytes, and human cancer cells11. Along with incorporating in vitro kinetic parameters of the enzymes in glycolysis, some ODE-mediated models describe the importance of bistable behavior in glycolysis with strong emphasis on the known allosteric regulation of the rate-limiting enzymes12. Particularly, recent mathematical models for human liver or cancer cells cover a complicated network beyond glycolysis by including the pentose phosphate pathway, serine biosynthesis, glutamine metabolism, and/or mitochondrial metabolism14. However, mathematical models for glucose metabolism have barely explained yet how a multienzyme complex influences glucose flux in cancer cells in a cluster size-dependent manner.In parallel, several mathematical models for glycolysis have been developed using ordinary differential equations (ODEs) for various model organisms: e.g., bacteria, yeast, virus and human (erythrocytes and liver cells)4, we have formulated a model to accommodate all the members of the glucosome. Our model indeed reveals the impact of their spatial complexation in silico on temporal changes of glycolytic metabolites at a subcellular level in single cells. We further show that our model is capable of predicting metabolic outcomes of a population of cells based on the relative distribution of glucosome clusters in the population. In conclusion, our mathematical model includes not only enzyme kinetics and their allosteric regulation but also spatial compartmentalization of the rate-limiting enzymes of the pathway, thus allowing us to understand the metabolic contributions of glucose flux at both single-cell and population levels.In this work, we have constructed a mathematical model to understand how the formation of a multienzyme complex in glucose metabolism affects glucose flux in cancer cells. Since the glucosome is composed of at least four cytoplasmic rate-limiting enzymes of glucose metabolismSi), 9 enzyme-associated species (Ei) with various forms by which enzyme activities of the rate limiting steps are regulated, 3 metabolic products (Pi), and 28 reactions , products (Pi), PKM2 tetramers (E3*) and glycosylated PFKL (E1gly) are at the basal levels and set them as 0.01. We also assumed that no multienzyme complex (ES/M/L) is formed at the beginning of simulation. An enzyme concentration of each glucosome member is assumed to be conserved, setting as 100. Assuming that all reaction rate constants for the enzymes are in the same order of magnitude, the reaction rate constants of metabolic enzymes are set to 10 as shown in Table k2, k−2, k4, and k−4 so that glycolysis becomes dominant relative to the metabolic shunt to the pentose phosphate pathway and/or serine biosynthesis in the absence of enzyme clusters . Lastly, we assumed that all the metabolic products are produced (kp/s/f) and degraded (δp/s/f) in the same rates, thus setting them to 5 and 0.5, respectively. Note that we provided both forward and backward reaction rate constants in Table We also provide reaction rate constants and initial values for the intermediate concentrations used in our model Tables  and 2. Wci (for medium-sized enzyme clusters) and ei (for large-sized enzyme clusters) in Table 4, we decelerated glycolysis  and accelerated gluconeogenesis . Similarly, based on our hypothesis that the large-sized enzyme clusters will shunt glucose flux to serine biosynthesis4, we changed parameters to direct glucose flux toward serine production . An enzyme activity in the small-sized clusters is assumed similar to the activity of a freestanding enzyme because the small-sized clusters formed by PFKL do not represent a multienzyme complex4. Using the initial values and the reaction rate constants shown in Tables Next, different levels of the enzyme activity depending on the size of glucosome clusters are expressed in terms of the parameters colysis c, c−d ≪ 1i) are affected by small changes in each parameter that we have incorporated in our model. In the sensitivity analysis, we have used the method of partial rank correlation coefficient (PRCC)16 to evaluate the level of the linear association between the input values of the parameters and the output concentrations of the metabolic products. To perform the sensitivity analysis, we modified the publically available MATLAB codes which are developed by Kirschner and coworker16. The default parameter values were set as the values used in our model, and we defined an interval for each parameter from half of the default value to twice of the default value. Then, we used Latin hypercube sampling16 to choose each parameter value in the corresponding interval by assuming that each parameter is uniformly distributed in the interval. Afterward, the sampled parameter values were used to calculate the concentrations of the metabolic products at the end time of the simulation. We repeated the sampling process described above 20,000 times and calculated the Spearman correlation coefficients, which correspond to PRCCs.Importantly, we have also performed sensitivity analysis of the parameters to investigate how the concentrations of three metabolic products (P4. We have employed PFKL-mEGFP as a marker of the glucosome. 2-Deoxyglucose was purchased from Sigma.The plasmid expressing human PFKL with a monomeric form of enhanced green fluorescent protein (mEGFP) was prepared previously (PFKL-mEGFP)Human breast carcinoma cells, Hs578T (HTB-126), were obtained from the American Type Culture Collection (ATCC). Hs578T cells were maintained in the Roswell Park Memorial Institute 1640 medium  supplemented with 10% dialyzed fetal bovine serum  and 50 µg/mL gentamycin sulfate.2, and 95% humidity), followed by ~18–24 h incubation in the CO2 incubator at 37 °C.To prepare cells for transfection and subsequent imaging, Hs578T cells were gently removed from the culture flask by replacing the culture medium with Trypsin-EDTA solution . Fresh, antibiotic-free growth media was subsequently used to harvest and resuspend the cells, followed by plating on glass-bottomed 35 mm Petri dishes (MatTek). When the confluency became ~70–90% on the following day, the cells were transfected with Lipofectamine 2000 (Invitrogen) using the Opti-MEM-I reduced serum media . The Opti-MEM-I medium was then exchanged with the fresh antibiotic-free growth medium after a 5 h incubation  for three 10 min incubations, followed by a ~1–2 h incubation at ambient temperature. All samples were then imaged at ambient temperature (~25 °C) with a 60× 1.45 NA objective (Nikon CFI Plan Apo TIRF) using a Photometrics CoolSnap EZ monochrome CCD camera on a Nikon Eclipse Ti inverted C2 confocal microscope. Epifluorescence imaging was carried out using the following filter set from Chroma Technology; mEGFP detection by a set of Z488/10-HC cleanup, HC TIRF Dichroic and 525/50-HC emission filter.On the day of imaging (~18–24 h post-transfection), cells were washed with imaging solution (20 mM HEPES (pH 7.4), 135 mM NaCl, 5 mM KCl, 1 mM MgClt-tests.For cell-based high-content imaging assays, 2-deoxyglucose (25 mM) was added to Hs578T cells after washing three times with the imaging solution. Images showing PFKL-mEGFP clusters were acquired before and after cells were incubated with 2-deoxyglucose at various time points (up to 6 hours). Control experiments were also carried out with 167 μL of vehicle . To ensure reproducibility, our experiments were repeated at least five times over the course of a few months. Statistical analysis was performed using two-sample two-tail ImageJ processing software  as we have done before4. Briefly, fluorescent wide-field images were processed through ImageJ using a custom script and macro that automates the counting of fluorescent clusters using its built-in module, so-called robust automatic threshold selection (RATS). In this analysis, the images were scaled according to the pixel size of the microscope  before the default parameters for RATS  were used in this analysis. Once fluorescent clusters were selected from an image, the particle analysis module was applied to attain both the number and area of fluorescent clusters within an image. This process was repeated for all subsequent cell images. The operator then evaluated the original cell images against the particle mask to eliminate data in which more than one cluster was counted as a single particle.Cluster size analysis was accomplished using the Pi) represent three metabolic fates of glycolytic metabolites. Importantly, we focus on four cytoplasmic enzymes which spatially organize into multienzyme clusters 4: PFKL, FBPase, PKM2, and PEPCK1. Note that the other ten enzymes are not cytoplasmic or rate-determining in glucose metabolism.Glucose metabolism consists of glycolysis and gluconeogenesis where three irreversible reactions are involved in glycolysis, four irreversible reactions in gluconeogenesis, and seven reversible reactions in both pathways. In our model, we simplify the 14-step pathway by condensing a few reversible steps into one conversion  is not firmly established yet to be included in our model. Fourth, FBPase catalyzes the conversion of fructose-1,6-bisphosphate to fructose-6-phosphate. Since FBPase catalyzes the backward reaction of PFK, the activities of PFK and FBPase are reciprocally regulated by various allosteric metabolites. Similarly, an antagonistic role of FBPase for glycolytic flux was validated to play a role in kidney cancer progression23. However, other than the well-established allosteric regulation, cancer-specific alteration of FBPase is not established yet to be included in our model.In addition, we incorporated cancer-relevant mechanisms of the four enzymes forming the glucosome. First, pyruvate kinase catalyzes conversion from phosphoenolpyruvate to pyruvate. The M2 isoform of pyruvate kinase (PKM2) is predominantly expressed in cancer cells while suppressing the expression of pyruvate kinase M1 isoform (PKM1)4. Small-sized clusters formed by PFKL are single-enzyme assemblies whereas medium- and large-sized clusters represent spatial organizations of multienzyme complexes. When cancer cells display small-sized clusters, the given cells barely include the other sizes of clusters. However, cancer cells showing medium- and large-sized clusters contain smaller sized clusters. Our cluster size analysis has also revealed that HeLa cells with medium-sized clusters show ~86.1 clusters per cell whereas HeLa cells showing large-sized clusters exhibit ~5.6 large-sized clusters and ~25.1 medium-sized clusters per cell4. Accordingly, we assume that 11 medium-sized clusters might form one large cluster in the cytoplasm of cancer cells in our model.Unlike many previous mathematical models for glycolysis, we take into account the recent discovery of the glucosome being formed in various sizes in cancer cells. Briefly, various sizes of PFKL clusters in cancer cells are categorized into three subclasses; small, medium and large-sized clusterP1 represent a metabolic product of the pentose phosphate shunt (green line), P2 is a metabolic product of serine biosynthesis (red line), and P3 indicates a metabolic product of the downstream of glycolysis (blue line). In addition, the activity of non-clustering PFKL or clustered PFKL into small sizes are anticipated to be similar in our model. For the simulation of the cases with no cluster or only small-sized PFKL clusters, we set all the parameters related to the formation of medium or large-sized enzyme complexes as zero . Please, note that the parameters for small-sized PFKL clusters  were also set to zero when we simulated  the case showing no cluster. Consequently, our simulation for no cluster or only small-sized PFKL clusters showed the high level of P3 relative to those of P1 and P2 . According to the publically available MATLAB codes developed by Kirschner and coworker16, we modified to calculate PRCCs in our model . Each selected parameter was perturbed in one direction while all other parameter values were fixed as default values as shown in Table k2 was decreased from 40 to 10 . Similarly, each selected parameter was perturbed in one direction while fixing the other parameter values. The changes in the metabolic product concentrations were shown under the four cases as well. When c−2 was decreased from 10 to 1  at an ensemble level in the four published cases4. To predict the levels of metabolic products at an ensemble level, we multiplied the levels of P1, P2, and P3 of the four cases shown in Fig. P3 appears to be slightly greater than those of P1 and P2. However, relative to Fig. P1 while decreasing the level of P3 at an ensemble level. On the other hand, Fig. P2 increases but the level of P1 decreases relative to the other cases. It appears clear that the simulation is capable of showing that glucose flux shunt from glycolysis to either the pentose phosphate pathway or the serine biosynthesis at ensemble levels, whose trend is indeed consistent with the already known functions of the glucose flux regulators in populations29. Collectively, our mathematical model with high-content imaging analysis is adequate to predict metabolic consequences of glucose flux regulators in a population of cancer cells.We have further evaluated our model by quantifying the changes of glucose flux in the presence of methylene blue, fructose-1,6-bisphosphate or epidermal growth factor (EGF), which are known to regulate the direction of glucose flux at ensemble levels30. However, due to the lack of 2-hydroxyl group, 2-deoxyglucose cannot further metabolize into fructose-6-phosphate in downstream glycolysis, thereby resulting in the inhibition of glycolysis. Accordingly, 2-deoxyglucose appeared to impair cell growth and thus implemented for anti-tumor therapeutics. However, its pharmacological effects on cancer treatment33 remain inconclusive, consequently raising a number of questions particularly including potential metabolic alterations by 2-deoxyglucose in cancer cells.Our model is now applied to assess metabolic consequences of 2-deoxyglucose in Hs578T cells. 2-Deoxyglucose is a competitive inhibitor of phosphoglucose isomerase catalyzing step 2 in glycolysisIn this work, we have employed our mathematical model to predict whether 2-deoxyglucose can potentially alter the direction of glucose flux in cancer cells beyond glycolysis inhibition. First, we performed cell-based high-content imaging assays to validate the metabolic effect of 2-deoxyglucose at single cell levels Fig. . Brieflyt = 10  thus represent downstream pathways of glycolysis, allowing us to investigate how glucose flux changes its direction at metabolic nodes between energy metabolism and anabolic pathways in cancer cells. Based on our experimental data4, we developed a model to predict that medium-sized clusters of glucosomes shunt glucose flux into the pentose phosphate pathway whereas large-sized clusters of glucosome divert glucose flux into serine biosynthesis at subcellular levels. Importantly, our model supports that the changes of relative ratios of cancer cells displaying small-, medium- and large-sized clusters in a population appear to be significant enough to influence overall net metabolic outcomes of cancer cells at ensemble levels. Moreover, our mathematical model is further evaluated to predict the effect of 2-deoxyglucose on the fate of glucose, thus providing new quantitative insights of how 2-deoxyglucose alters glucose flux in cancer cells. Collectively, we conclude that our mathematical model supports the hypothesis that glucosomes divert glucose flux into the pentose phosphate pathway and serine biosynthesis in a cluster size-dependent manner.We constructed a simple mathematical model to understand the cluster size-dependent functional contributions of metabolic enzymes and their multienzyme complexes to cancer cell metabolism. Briefly, glycolysis is interconnected with energy metabolism and anabolic biosynthetic pathways, including the pentose phosphate pathway and serine biosynthesis. Three metabolic products (in vitro enzyme kinetics. Our model explains altered glycolysis in cancer cells that redirects glucose flux into the pentose phosphate pathway and serine biosynthesis in a cluster size-dependent manner. Importantly, we can now predict the direction of glucose flux in the presence of small-molecule drug candidates as long as quantitative high-content imaging data is obtained in single-cell levels. Additionally, we can quantify relative partition ratios of glucose flux between glycolysis, the pentose phosphate pathway and serine biosynthesis in various conditions. Collectively, our mathematical model fully integrates various cancer-associated mechanisms discovered in recent years, thus advancing our understanding of cancer cell metabolism in single cells.It is important to emphasize here that our mathematical model accounting for size-dependent metabolic functions of glucosome clusters is significantly different from other models that mostly rely on Supplementary Information


Whole Genome Shotgun (WGS) metagenomics is increasingly used to study the structure and functions of complex microbial ecosystems, both from the taxonomic and functional point of view. Gene inventories of otherwise uncultured microbial communities make the direct functional profiling of microbial communities possible. The concept of community aggregated trait has been adapted from environmental and plant functional ecology to the framework of microbial ecology. Community aggregated traits are quantified from WGS data by computing the abundance of relevant marker genes. They can be used to study key processes at the ecosystem level and correlate environmental factors and ecosystem functions. In this paper we propose a novel model based approach to infer combinations of aggregated traits characterizing specific ecosystemic metabolic processes. We formulate a model of these Combined Aggregated Functional Traits (CAFTs) accounting for a hierarchical structure of genes, which are associated on microbial genomes, further linked at the ecosystem level by complex co-occurrences or interactions. The model is completed with constraints specifically designed to exploit available genomic information, in order to favor biologically relevant CAFTs. The CAFTs structure, as well as their intensity in the ecosystem, is obtained by solving a constrained Non-negative Matrix Factorization (NMF) problem. We developed a multicriteria selection procedure for the number of CAFTs. We illustrated our method on the modelling of ecosystemic functional traits of fiber degradation by the human gut microbiota. We used 1408 samples of gene abundances from several high-throughput sequencing projects and found that four CAFTs only were needed to represent the fiber degradation potential. This data reduction highlighted biologically consistent functional patterns while providing a high quality preservation of the original data. Our method is generic and can be applied to other metabolic processes in the gut or in other ecosystems. Microbial communities are highly complex ecosystems, harboring a high taxonomic diversity, rapidly varying in time. Focusing on the functional traits of microorganisms instead of species offers an interesting and complementary insight since quite often, owing to environmental selection pressure, traits are less variable in time and shared by many species. By providing gene inventories of otherwise uncultured microbial communities, Whole Genome Shotgun (WGS) metagenomics made the functional profiling of microbial communities possible, since community aggregated traits can be quantified by the abundance of relevant marker genes. Considering a global metabolic process in an ecosystem, we propose a method that exploits gene abundance data to determine combinations of functional traits characterizing this process. When applied to fiber degradation in the human gut microbiota, the method shows that only four complex functional traits are needed to characterize this process. The approach is generic and could be applied to other processes or ecosystems. It allows summarizing complex datasets by a limited number of biologically interpretable functional patterns. Whole Genome Shotgun (WGS) metagenomics is increasingly used to study the structure and functions of complex microbial ecosystems. Thanks to a huge research effort, these high-throughput approaches are constantly improving and have already provided valuable information.Recent achievements –3 for anAs a complement to these taxonomy oriented approaches, WGS metagenomics allows the direct functional profiling of microbial communities through gene inventories of otherwise uncultured microbial communities. The functional annotation of these genes, as well as the evaluation of their abundances requires the mapping of metagenomic reads on one or several functional databases which may include annotated, de novo assembled gene catalogs. It is a challenging task for which bioinformatic tools are still being developed , andChoosing relevant descriptors for ecosystem functions raises several issues. Using arbitrarily predefined pathways helps simplifying the systems description by creating combined descriptors, however it may not reflect all the information in the data. On the other hand, unsupervised statistical analyses such as e.g. principal component analysis (PCA) are quite often used to extract low-dimensional description of these high-dimensional datasets. However, they do not exploit all the richness of available information about biological processes at the individual or collective level, and may lead to irrelevant or hardly interpretable results. To overcome these issues, we propose a novel model based approach, mixing satistical data analysis and system biology. We focus on specific ecosystemic metabolic processes, described by a possibly high number of genes or functional markers abundances. Our aim is to infer a limited number of combined functional traits characterizing these processes, as well as their intensity in the ecosystem.Our approach relies on Non-negative Matrix Factorization (NMF), a popular machine learning technique in data and image analysis. NMF, together with PCA belongs to a wide family of data analysis methods designed to solve blind source separation problems. These questions are widely encountered and cover all situations where a mixture of several signals originating from different unknown sources is observed (here gene abundances in samples) and one wishes to separate them and identify the sources  and the mixture coefficients.NMF was previously used for genomic data mining in the context of microarray data analysis , 13. MorIn  the ideaThe originality of our work lies in the design of a constrained NMF approach where the constraints aim at selecting biologically relevant combined functional traits (the sources) to describe processes at the ecosystem level. The constraints are derived from available prior knowledge in a Bayesian perspective. Moreover, we propose a careful multicriteria selection procedure to select the relevant number of combined functional traits.As a proof of concept, we applied our approach to the modelling of ecosystemic functional traits of fiber degradation by the human gut microbiota based on 1408 samples of gene abundances.functional marker. A functional marker is a group of genes, or modular elements in genes, able to control the production of enzymes involved in a reaction. Typical functional markers are Kegg Orthologies (KO). The abundance of a functional marker is defined as the sum of the abundances of all the metagenes identified as belonging to the group.Quantitative metagenomics allows the study of metabolic processes at the ecosystem level, by producing metagenes abundances with functional annotation. Taking advantage of this information, we consider a metabolic process occurring in an ecosystem. We assume that this process is described by a list of biochemical reactions, each associated to what we call a Our first modelling hypothesis is the existence of patterns underlying functional markers abundances in the ecosystem. Indeed, within a microbial ecosystem, genes can be looked at in a hierarchical fashion. They are first associated on microbial genomes, which are further grouped at the ecosystem level into subcommunities of microorganisms. These subcommunities involve hundreds of different bacterial species linked by complex co-occurrences or interactions. Moreover they are influenced by environmental factors (e.g. nutrients or temperature). The set of functional marker abundances within each of these subcommunities form a characteristic pattern in the ecosystem.X is produced by bacterial species of type 1 and used by bacterial species of type 3 as well as an association between bacterial species of type 1 and 2 for other ecological reasons which cannot be elucidated with the observation of this particular metabolic process only. Therefore functional marker abundances in samples should reflect this structure.This hypothesis is illustrated in the simplistic example of metabolic process in Our second modelling hypothesis is motivated by the fact that even if in many microbial communities microbial species composition varies over time and samples, metabolic processes at the community level are ubiquitous and much more stable in time. Consequently, we assume that the patterns mentioned above are shared by all samples of the ecosystem, in variable proportions because they were selected by specific environmental constraints. For instance, for the gut ecosystem these include anaerobic conditions, temperature or digestion residue composition coming from the host diet. As illustrated on i = 1, …, n and marker j = 1, …, r, the observed frequency aij of marker j in sample i is the sum of the contributions of all CAFTs. This leads tohl =  is the characterization in terms of r markers frequencies of the lth CAFT and wi =  is the vector of the intensities or weights of the k CAFTs in sample i.Following our hypotheses, functional marker abundances in each sample are modelled as mixtures of underlying CAFTs. For each sample hl is defined up to a multiplication by a positive constant, provided that its weights in the samples are scaled accordingly. The ℓ1-scaled version hl/(∑jhlj) can be interpreted as the vector of relative frequencies of functional markers within the subcommunity characterized by trait l.Note that each n × r) data matrix by A, the (k × r) matrix whose lines are the hl by H and the (n × k) matrix whose lines are the wi by W. H will be called the trait matrix and W the weight matrix.In the rest of the paper, we denote the  satisfied by all x in the ecosystem induces a constraint on the CAFTs (the hlj).A first important consequence of our modeling framework is that genomic information can be translated into constraints on CAFTs structure. Indeed, by construction, the CAFT j and j′ are such that for each microorganism in the ecosystem, if j′ is not present in its genome, then neither is j. This implies that for each microorganism x, there is a non-negative constant Rx, j, j′ satisfyingRx, j, j′ = 0 when nxj = nxj′ = 0. Then as a consequence of lδ = supx ∈ EcosystemRx, j, j′.As an example, let us assume that two markers r(r − 1) ordered pairs, for each genome x. This is why we propose to combine genomic information with metabolic information, when possible, in order to select a limited but relevant set of constraints on the CAFTs.In the absence of any other information, exploiting genomic information only could lead to a large number of constraints. For instance, constraining the ratio of abundances in pairs of markers as above requires assessing the existence of constants such that In order to do this, we formulate two additional assumptions. First, we assume that a subset of reactions in the metabolic process under consideration are well known, so that a list of metabolites that are consumed or produced by each reaction can be extracted.Second, we assume that metabolites are partitioned in two classes. The first one corresponds to metabolites that are known to be exported out of the cell, from experimental evidence or published data. The second one gathers metabolites that are actually known to stay within microbial cells, as well as metabolites for which this is strongly suspected. For convenience, these two classes will be called the extracellular and intracellular metabolites, although this may be misleading in some cases.M1 of the class of intracellular metabolites can be derived from genomic information on the microorganisms present in the ecosystem, as well as a positive constant δm1, for each m in M1, such that in each CAFT hl the marker frequencies associated to the production or consumption of m should satisfyM2 of intracellular metabolites such that for each m in M2, each CAFT hl should satisfyFollowing similar steps as in eqs –5, a subδm1,, δm2,].However, the set of metabolites and reactions under consideration is defined in the context of a specific metabolic process, given the available knowledge. Thus it may be that in this process, some intracellular metabolites accumulate in the cells. It may also be that the selected reactions ignore metabolic routes, because they are unknown or correspond to other metabolic processes, that could produce or use the metabolites, and finally it may also happen that we were wrong in assuming that some poorly studied metabolites are intracellular. Consequently, depending on metabolites, either none, one or both constraints M1, M2 and the positive constants δm1, and δm2, is detailed in the Materials and Methods section, as well as their practical approximation from known bacterial genomes.The theoretical construction of the two sets δm1,, m ∈ M1} ∪ {δm2,, m ∈ M2} and FΔ is a coefficient matrix depending on Δ.The set of constraints Note that, although they include metabolic information and take the familiar form of linear inequality constraints W and H which satisfy Eqs ℓ2-columnwise normalization of A, denoted H is then recovered by multiplying each column of ℓ2-norm of the corresponding column in A.The determination of matrices The NMF algorithms which aim at minimizing this distance require the use of regularizing terms in order to lift identifiability problems and filter noisy data during the minimization process. We consider a regularizing term that promotes sparsity over the columns of AFTs see .FΔ such that the k whose entries are equal to 1.Finally, we impose the additional It is well known that problems like k and the tuning parameter α. Parameter selection procedures proposed in most applications of NMF to biological data are based upon stability of the weight matrix W over several initializations of the iterative algorithm used to solve the problem ,  and . These parameters influence the number or nodes (metabolites) included in the sets δm1, and δm2, associated to each constraint. The first option was to compute them as the value obtained on the set of 190 genomes, with a multiplicative factor of 1 and no rounding. The second option was the one presented in the paper: the values obtained from the genomes are multiplied by 1.5 and rounded to the nearest upper multiple of 5. The third rule was the same as the second one with a multiplicative factor of 2. So the resulting constraints rank from the more stringent to the less stringent. The sensitivity was assessed by measuring the concordance index between the inferred CAFT matrices and the CAFT matrix obtained with an unconstrained NMF. We observed that the results were mainly influenced by the thresholds, and that the sensitivity to the computation rule tended to be weaker. For the pair  the deviation from the unconstrained case was very weak (less than 1% on average), for the pair  the deviation was small (less than 5% on average) and it was higher for the pair  (12% on average). Therefore the choice  seems to be sensible on this example.We performed additional inferences with A and W were ℓ1-normalized; the normalized matrices correspond to the repartition of the functional markers (resp. the CAFTs) abundancies among the samples. The distance matrix dA (resp. dW) of A (resp. W) defined as the 1408 × 1408 matrix whose element  is the euclidean distance between rows i and j of A (resp. W) was computed. For each biological sample i, the Pearson correlation between the distance of i to the other samples in A and in W was evaluated:Ci)i = 1, …, 1408 was displayed.The columns of matrices S1 TextThis file details the mathematical motivation for using a unique regularization parameter.(PDF)Click here for additional data file.S2 TextThis file provides details about optimization steps (PDF)Click here for additional data file.S3 Textα based on the three criteria.This file details the selection of the regularization parameter (PDF)Click here for additional data file.S1 tsv FileThis file contains the abundance matrix of the 86 functional markers of fiber degradation in 1408 samples.(TSV)Click here for additional data file.S2 tsv File(TSV)Click here for additional data file.S3 tsv FileFΔ, storing the coefficients of the 38 constraints on the 86 entries of the CAFTs.This file contains the constraint matrix (TSV)Click here for additional data file.S1 TableThis file details the hypotheses underlying the selection of functional markers and metabolites representing simple sugar anaerobic fermentation in the human gut (sheet Reactions and KOs) and provides the list of the GH and PL selected in the model (sheet GH and PL).(XLSX)Click here for additional data file.


Natural biochemical systems are ubiquitously organized both in space and time. Engineering the spatial organization of biochemistry has emerged as a key theme of synthetic biology, with numerous technologies promising improved biosynthetic pathway performance. One strategy, however, may produce disparate results for different biosynthetic pathways. We use a spatially resolved kinetic model to explore this fundamental design choice in systems and synthetic biology. We predict that two example biosynthetic pathways have distinct optimal organization strategies that vary based on pathway-dependent and cell-extrinsic factors. Moreover, we demonstrate that the optimal design varies as a function of kinetic and biophysical properties, as well as culture conditions. Our results suggest that organizing biosynthesis has the potential to substantially improve performance, but that choosing the appropriate strategy is key. The flexible design-space analysis we propose can be adapted to diverse biosynthetic pathways, and lays a foundation to rationally choose organization strategies for biosynthesis. These enzymes allowed the controlled assembly of novel genes, plasmids, and other nucleic acids, and precipitated the rapid spread of molecular cloning technology. Since then, synthetic biology has sought to exploit, adapt, and extend biological systems to benefit society by creating pharmaceuticals, fuels, gene therapies, drug delivery platforms, probiotics, and more. Metabolic engineering, the use of microbes to produce small and large molecules of commercial and scientific interest, has been a particular focus. To this end, synthetic biologists have developed methods to control transcription and translation, knock out native genes to route metabolic flux down desired channels, integrate multiple chemical and physical inputs to make decisions inside microbial cells, and make wholesale changes to the genomes of organisms in high throughput.Synthetic biology traces its origins to the discovery of type II restriction endonucleases3. Historically, acetone-butanol-ethanol (ABE) fermentations using Clostridium acetobutylicum have met with large-scale success, as has the production of penicillin from Penicillium species, but producing biomolecules not native to the host has presented a much greater challenge. Notable examples include artemisinic acid4, as well as farnesene, 1,3-propanediol, and 1,4-butanediol3, but, by and large, the heterologous production of chemicals at industrially viable titers has remained elusive. This is most often due to one (or more) of five ubiquitous roadblocks to biosynthesis: cellular toxicity due to accumulation of intermediates of the biosynthetic pathway; the loss of flux to undesired byproducts; difficulties sustaining sufficient substrate influx; leakage and loss of intermediates into the culture medium; and trapping of product in the host cell due to inadequate efflux  microcompartments, for instance, are protein-bound organelles of approximately 150 nm in diameter. The enclosing protein shell consists of trimeric, pentameric, and hexameric protein tiles with central pores that permit the passage of small molecules in and out of the organelles, but which prohibit the passage of enzymes and other proteins. Building on foundational microbiological understanding of these systems34, we and others have demonstrated control of the formation35, protein content39, catalytic activity40, and transport properties41 of these organelles. Due to their relative simplicity and ease of manipulation, these various protein-based compartments make excellent model systems for exploring the role of spatial organization on metabolism. It is thought that they function both by protecting the cellular contents from toxic intermediates42 and by increasing the local concentration of the kinetically relevant intermediate inside the organelle43.A new paradigm in synthetic biology technologies focuses on this challenge: spatiotemporal organizational of biochemical processes. Organisms in all domains of life exert fine control over when and where biochemical reactions occur, be they responsible for metabolism, information transfer, or cell replication. This kind of organization remains conspicuously absent from most engineered systems. Here, we will analyze one class of these strategies: the spatial organization of metabolism within cells Fig. 24. There2 is concentrated to enhance carboxylation in photosynthetic bacteria–and adapt them for engineering purposes46. The modularity of carboxysomes and other CO2 concentrating mechanism components facilitates reconstitution in other organisms48. An active area of research is reconstitution in plants51, as part of a broad strategy to increase plant yields55. Engineering microbial metabolism with CO2 as the primary carbon source would allow the production of sustainably produced biofuels and other high value products57 and carboxysomes could enhance such strategies. More generally, carboxysomes have been suggested as a modular method for partitioning non-native pathways from native metabolism22. However, we have strong indication that performance of CO2 concentrating mechanisms will depend on how encapsulation interplays with transporters or other exogenous conditions setting the supply of CO259, and further systems analysis is required to realize the benefits of carboxysome-based encapsulation60.Likewise, much work has been done to characterize carboxysomes—compartments in which CO65, possibly due to an increase in the local concentration of the intermediate species66, as well as potentially due to local effects on enzyme performance67. These studies organized diverse biosyntheses, including of mevalonate, resveratrol, 1,2-propanediol, and molecular hydrogen, suggesting that many different enzymatic pathways could be enhanced by scaffolding.Bacterial microcompartment organelles are not the only organization solution available to the metabolic engineer; scaffolds based on protein, lipid, DNA, and RNA have all shown promise in improving heterologous pathway performance. Each of these strategies have been shown to be effective for the enhancement of heterologous biosynthesis in various contexts68. Some modeling efforts have described the potential for kinetic enhancement by scaffolds70. There has also been analytic and computational analysis of optimal compartment size and distribution of enzymes between multiple compartments71. Here, we will explicitly compare organelle-like to scaffold-based organization to better understand the potential trade-offs between the two approaches. Our goal is not to rebuild the reaction-diffusion simulation framework or perform numerical investigations of a particular system, but to provide parametric insight into the design criteria across cellular organization strategies.Having developed tools to control the localization of heterologous biosynthetic pathways to these organizing structures, crucial questions remain: what pathways are suitable for organization? And what benefits might be accrued by organizing pathways in one way versus another? A variety of numerical simulation frameworks exist capable of simulating the spatial-temporal concentrations of metabolites in cellsWe will argue that organization in microcompartment organelles can confer benefits commensurate to substantial enzyme kinetic improvements, and that the choice of organization strategy is impacted both by intrinsic pathway properties and extrinsic culture conditions. All of these factors are important to consider in choosing the appropriate organization strategy for a pathway of interest, and here we demonstrate how the intrinsic and extrinsic factors define the design space of the trade-offs between strategies.Salmonella and other enteric bacteria, and organization using a scaffold   Fig. . To begi43 developed to analyze the native function of the microcompartment organelles. A key result of this analysis is that microcompartments significantly enhance pathway flux for a range of external substrate concentrations. We predict that the natively encapsulated system enjoys a four-order of magnitude enhancement in flux upon encapsulation, as compared to free diffusion of the enzymes in the cytosol43. Appropriately chosen heterologous pathways might also accrue such flux enhancements, as well as potentially reduce the loss of pathway intermediates to the extracellular space.To address the kinetic consequences of encapsulation in Pdu microcompartments, we make use of a modelTo model a scaffolded system, we simply assume that the enzymes in question are localized to a volume equivalent to that occupied by the Pdu microcompartments, but without a diffusion barrier. The velocity of transport between the scaffold volume and the cytosol is set to that of free diffusion. The model formulation we use here is agnostic to the underlying scaffolding platform  or its microscopic organization, as we assume a well-mixed scaffold volume.We analyze the consequences of organization using these two strategies for two model biochemical processes: native Pdu microcompartment metabolism and the heterologous mevalonate biosynthetic pathway. The compounds and enzyme kinetic parameters for each pathway are in Fig. kcat or KM kinetic parameters). We are interested in whether metabolic engineering of spatial organization is worth the additional effort. Here, we use the native Pdu microcompartment pathway as an example. If, for instance, engineering efforts increased the kcat of each of the two key enzymatic steps 100-fold, or decrease the KM of each key step 100-fold, the improvement in flux would be as shown in Fig. We first compare the effects of organization to traditional metabolic and enzyme engineering strategies   Fig. .kcat of each enzymatic step, but the improved flux comes at the cost of greatly increased loss of intermediate species to the extracellular space   Fig. . This trKm for the second reaction in a sequence will benefit from encapsulation, while those with relatively low Km may do just as well with co-localization through scaffolding. Nonetheless, these calculations offer a relatively restricted view of the system, addressing performance for particular pathways under particular culture conditions. We are interested in the performance and robustness of each strategy when applied to different pathways or varying external conditions. The next section addresses these issues by mapping out the range of parameters, or design-space, for which encapsulation or scaffolding would be preferred.These kinds of calculations can be made for any enzymatic pathway for which the kinetic parameters are known (or can be approximated). Already, they provide a design rule for the bioengineer: pathways with relatively high The benefits of encapsulation versus scaffolding can depend on intrinsic factors, such as pathway kinetics (discussed in the prior section) or the cell membrane permeability to the metabolites, as well as extrinsic factors, such as the external concentration of substrate. We examine tradeoffs between flux enhancement and intermediate loss for both intrinsic and extrinsic factors. We initially analyze the effects of varying external substrate concentration independently.For the Pdu system the organelle provides higher flux for all substrate concentrations. However, at lower external substrate concentrations, organizing mevalonate synthesis on scaffolds results in higher flux than localizing it in organelles Fig. . The orgkcatE0 value used to construct the one-dimensional responses with respect to Sext in Fig. kcatE0 value of the second enzyme in the mevalonate synthesis pathway , we predict that organelle-type organization is favored at high Sext but scaffolding is favored at low Sext values  and one cell-extrinsic property  simultaneously Fig. . These dues Fig. . A batchP/Q Fig. . This kikcatE0 for the second enzyme differ by approximately two orders of magnitude between the two systems. These permeability estimates are based on the size and charge of the intermediate (see Methods). We therefore calculate the optimal organizational strategy as a function of these two parameters, and indicate the location of each enzyme system in this design space  of each enzyme  across a wide range of enzyme kinetic parameters. Considering, for instance, the two-enzyme pathway of native Pdu metabolism, we can calculate the optimal strategy as we vary the activity  to probe discrepancies in the performance of different organization strategies. The MATLAB code used to generate the graphics in this manuscript is freely available on GitHub (https://github.com/cjakobson/pduMCPmodel), and we encourage members of the metabolic engineering and synthetic biology communities to explore the organizational performance landscapes for their own systems of interest. We also welcome suggestions of other useful kinetic or organizational regimes to include in future versions of the analysis.Above, we outline the potential for the spatial organization of heterologous pathways to greatly enhance their performance. This approach compares well with traditional enzyme engineering approaches. Furthermore, we describe a general systems parameter analysis to guide the choice of appropriate organizational strategies for metabolic engineering. Several key parameters must be accounted for: (I) enzyme kinetics; (II) substrate and intermediate chemical properties; and (III) external culture conditions. Some of these properties, such as the external substrate concentration and the transport properties of the cell membrane, can influence the supply of substrate to the pathway, while others, such as the presence or absence of competing reactions and the transport properties of the organelle boundary, can influence the loss of metabolic flux to off-target species. We analyze the performance of different organization strategies, and present example organizational recommendations. Moreover, this modeling approach suggests key experiments  cells, to detect and transport metabolites, and to exert dynamic control on short time scales are of critical importance, as well. We posit that parametric studies to map the design spaces of each of these approaches will be key in optimizing biosyntheses.For questions and further information regarding software and models used herein, please contact NMM .et al., PLoS Computational Biology, 2017, in which we explored the native function of the Pdu MCP system in S. enterica. The analytical and numerical approach is described in detail in that manuscript, but the important assumptions can be summarized as follows:We assume a spherically symmetrical organelle or scaffold at the center of a spherically symmetrical cell.We consider the system at steady-state.Sext) and intermediate are constant.We assume that the external concentrations of the substrate . In the case with no organization, we instead use a numerical solution, as the analytical solution does not hold in this regime. The numerical solution at steady state is generated by a finite difference routine implemented in MATLAB; again see43 for more details on the governing equations and boundary conditions used in the numerical routine.In the case of organelle- or scaffold-based organization, a closed-form analytical solution to the governing equations can be found, provided we assume that the metabolite concentration inside the organelle or scaffold region is constant. This solution is used to generate the various figures comparing organization strategies; seea priori estimates of the cell membrane permeabilities according to the methods of Robinson80. The microcompartment shell permeability was set to optimize native pathway flux as described for our prior model43.Enzyme kinetic parameters were available from existing literature, as were estimates of cell size, organelle size, enzyme copy number, and the diffusivity of molecules in the cytoplasm. References for these values are detailed in the tables below. We made The following table summarizes the important model parameters for the Pdu MCP system:In the case of mevalonate synthesis, the parameters are altered as follows:42 or the volumetric titer of mevalonate in a scaffolded system63. To compare with our model, which generates predictions on a molecules-per-cell basis, we must convert these experimental observations to a comparable measurement.For the systems we examine here, previous literature has described either cellular growth on 1,2-PD as the sole carbon source42). Assuming that a bacterial cell has a mass of approximately 0.3 pg and that half of the flux through the microcompartment pathway (by mass) can be used for cell growth, the Sampson growth observation predicts a steady-state flux of approximately 3 × 10−13 μmol/cell-s.For the native Pdu microcompartments, Sampson and Bobik observe a doubling time of approximately 5–10 hours during exponential phase growth on 1,2-PD as the sole carbon source . Assuming constant production over this time and a cell density of 2 OD ~ 2 × 109 cells/mL, this titer corresponds to a steady-state flux of approximately 3 × 10−14 μmol/cell-s.In the case of mevalonate biosynthesis by a scaffolded system, Dueber and colleagues report a titer of approximately 10 mM mevalonate after 2 days of culture, after which time the concentration changes little  was used for all computation and to generate graphical representations of the results.https://github.com/cjakobson/pduMCPmodel) under a GNU General Public License.The model used herein is freely available on GitHub (Supplementary Information


Constraint-based flux analysis was then used to simulate several qualitative and quantitative phenotypes of L. mesenteroides, thereby evaluating the model validity. With established predictive capabilities, we subsequently employed iLME620 to elucidate unique metabolic characteristics of L. mesenteroides, such as the limited ability to utilize amino acids as energy source, and to substantiate the role of malolactic fermentation (MLF) in the reduction of pH-homeostatic burden on F0F1-ATPase. We also reported new hypothesis on the MLF mechanism that could be explained via a substrate channelling-like phenomenon mainly influenced by intracellular redox state rather than the intermediary reactions. Model simulations further revealed possible proton-symporter dependent activity of the energy efficient glucose-phosphotransferase system in obligate heterofermentative LAB. Moreover, integrated transcriptomic analysis allowed us to hypothesize transcriptional regulatory bias affecting the intracellular redox state. The insights gained here about the low ATP-yielding metabolism of L. mesenteroides, dominantly controlled by the cellular redox state, could potentially aid strain design for probiotic and cell factory applications.Obligate heterofermentative lactic acid bacteria (LAB) are well-known for their beneficial health effects in humans. To delineate the incompletely characterized metabolism that currently limits their exploitation, at systems-level, we developed a genome-scale metabolic model of the representative obligate heterofermenting LAB This pathway is fundamentally different from the canonical Embden-Meyerhof-Parnas (EMP) pathway wherein one mole of glucose-6-phosphate is broken down into two moles of glyerone-3-phosphate at the end of the preparatory phase. In PKP, on the other hand, one mole of glucose-6-phophate is converted into one mole of each acetyl-phosphate and glyerone-3-phosphate via phophoketolase, thus leading to mixed fermentation products such as acetate, lactate and ethanol. These properties along with their natural ability to degrade xylan from lignocellulose using endogenous β-xylosidases2 make obligate heterofermentative LAB (e.g. Leuconostoc mesenteroides and Lactobacillus fermentum) one of the dominant species in vegetable fermentations such as Korean kimchi and sauerkraut4. The heterofermentative by-products inhibit the growth of harmful microbes and simultaneously impart taste and flavour to the final food products. In addition, the obligate heterofermentative LAB exhibit several beneficial characteristics to mammalian hosts including antimicrobial activities7, immunomodulatory effects9 and antioxidant activities10. They are also known to improve the microfloral balance in gastrointestinal tract; for example, Lb. fermentum is shown to strengthen it possibly through the increased activity of α-glycosidases and esterases11. In a different study, it is reported that a L. mesenteroides strain produces the prebiotic isomaltooligosaccharides that in turn enhance the growth of Bifidobacterium and Lactobacillus species in poultry chicken12.Obligate heterofermentative lactic acid bacteria (LAB) lacking the glycolytic enzyme, fructose 1,6 bisphosphate aldolase, dissimilate carbon solely through a unique route of glycolysis known as the phosphoketolase pathway (PKP)13, (ii) alternate electron acceptors, e.g., fructose that yields mannitol upon reduction14, and (iii) phosphotransferase system (PTS) mediated transport15. Nonetheless, the underlying molecular mechanisms and their contributions to ATP yield, pH, and redox states still remain elusive. Elucidating such metabolic routes related to the unique cellular phenotype of LAB is, therefore, integral to their successful probiotic application16. For example, metabolic determinants restoring cofactor balance can be identified to modulate the relative abundance of other probiotic bacteria in the gut for imparting beneficial health effects18. To this end, a systems biology approach based on in silico metabolic modeling and omics data integration could greatly aid to decipher the lesser investigated metabolic landscapes of these LAB.However, despite their probiotic abilities and generally regarded as safe (GRAS) status, therapeutic applications of obligate heterofermentative LAB remain largely unexplored. The fastidious growth requirements and low ATP yield associated with the utilization of PKP are considered as the key bottlenecks for their practical applications. Interestingly, the heterofermentative LAB have naturally evolved to meet the cellular energy requirements under specific conditions by using alternate routes comprising (i) malolactic fermentation (MLF)19. The availability of software applications to conveniently implement FBA and related in silico methods20 has enabled the development of genome-scale models (GEMs) for more than 100 species across all three domains of life, thereby facilitating analysis of their intracellular metabolism21. However, with respect to LAB, only a handful of GEMs are available, including Lactococcus lactis24, Lactobacillus plantarum25, Streptococcus thermophilus26 and Lactobacillus casei28 although more than 100 LAB genomes have been sequenced29. Note that these species with available GEMs belong to either homolactic or facultatively heterolactic fermenting groups. To enable the systems analysis of the other important group, i.e., obligate heterofermentative, herein, we present new genome-scale metabolic reconstruction of Leuconostoc mesenteroides ssp. mesenteroides ATCC 829330. The reconstructed model was subsequently validated both qualitatively and quantitatively using the fermentative substrate phenotyping and batch culture data, respectively. The model was also used together with transcriptome data for generating new hypotheses related to energy and redox metabolisms, and their effects on cellular phenotype.Constraint-based flux analysis, also known as flux balance analysis (FBA), is one of the well-established approaches for investigating cellular metabolism at systems-level under various environmental/genetic perturbationsL. mesenteroides was newly reconstructed following established procedures31 (see Methods). Initially, the draft metabolic network was built based on information obtained from the genome annotation32 and biochemical databases such as MetaCyc33, KEGG34 and TransportDB35. Subsequently, the metabolite dead-ends were identified using GapFind algorithm36; new metabolic reactions supported by experimental and literature evidences were added to fill the network gaps. Reaction directionality was assessed using the available thermodynamic data calculated at physiologically relevant pH and intracellular metabolite concentrations as described earlier39 (see Methods). We then used this draft model to explore the minimal nutrient requirements of L. mesenteroides by mimicking the single nutrient-omission experiments conducted using a chemically defined medium (CDM)40. The comparison of in silico predictions with the experiments revealed some discrepancies which were then resolved through further manual curation of the network model. For example, the amino acid auxotrophy experiments confirmed asparagine as one of the non-essential amino acids. However, initial simulation of the draft model gave rise to no growth in the absence of asparagine, as the common asparagine biosynthetic enzymes, i.e., EC 6.3.5.4 and EC 6.3.1.1, were absent. From the genome-annotation evidence, we found the presence of an unique enzyme, aspartyl-tRNA-asparagine amidotransferase (EC 6.3.5.6) in L. mesenteroides, which indicated the possible existence of a non-canonical route for the biosynthesis of asparagine using aspartyl-tRNA and glutamine as substrates41. Similarly, vitamin-auxotrophy data was also used to further enhance the model quality. Folate, an indispensable precursor in the biosynthesis of DNA, was found to be only stimulatory according to the experiments. On contrary, the in silico simulations require its external supply for the cell growth, indicating possible missing annotations in the folate biosynthetic pathway. Therefore, a few non-gene associated reactions were added into the reconstruction in order to complete their biosynthetic pathways. BLASTp homology searches were then performed for the corresponding enzymes which were newly added, thereby substantiating their inclusion. Overall, the curated model was able to predict the auxotrophy of 7 out of 8 vitamins and 19 out of 20 amino acids accurately . We measured the major elemental compositions of L. mesenteroides biomass and compared them with the molar elemental constituents of the biomass equation which is derived from the assembly of the measured macromolecular compositions . The complete list of reactions, metabolites and associated genes accounted in iLME620, and the calculations involved in the biomass equation assembly are provided in Supplemental data http://sbml.org/) in Supplemental data The resultant genome-scale metabolic network of iLME620 with the GEMs of other LAB, Lb. plantarum25 and Lc. lactis24, using the EC numbers in order to gain insights into their unique metabolic features , the low ATP-yielding PKP (one mole of ATP per mole of glucose) is the only route of carbohydrate catabolism in L. mesenteroides 45. Here, we demonstrated a similar thermodynamic advantage of PKP over the EMP pathway by computing ΔrG′° of each reaction in either pathways as well as the net ΔrG′° for the pathways at physiologically relevant anaerobic condition (see Methods). The results showed that PKP has a larger fraction of reactions with negative ΔrG′° values  and a lower net ΔrG′° (−186.8 kJ/mol in PKP vs −178.0 kJ/mol in EMP pathway), highlighting thermodynamic advantage of PKP over EMP pathway.A detailed comparison of glycolytic pathways shows that while both 47. The model predictions showed good agreement for 25 of the total 29 substrates tested. Here, the model was structured in a way that the glycoside substrates among the tested carbon sources are hydrolyzed by their respective extracellular glycosidases before the metabolizable portion of the molecule becomes available for its uptake. The nature of transport of these substrates, the enzymes involved and corresponding gene annotations, if any, are provided in Supplemental data In order to validate the qualitative model predictions, we simulated fermentable substrate phenotyping for various carbon sources and compared the results with experimental literature48 was used to evaluate model predictions, quantitatively. Exponential growth phase data points were used for the in silico predictions based on constraint-based flux analysis (see Methods). In order to mimic the complex medium condition, the uptake rates of all amino acids, vitamins and nucleotides were left unconstrained during the simulations. The values of growth associated maintenance (GAM) and non-growth associated maintenance (NGAM) were constrained at 13.613 mmol gDCW−1 and 1.104 mmol gDCW−1 hr−1, respectively. These energetic parameters were estimated as described earlier25 . Hence, we should carefully estimate the energetic costs and potential errors in quantifying cellular lipid content, as these may vary across different growth environments.We also performed sensitivity analysis to evaluate the robustness of the model predictions, which can be affected by several fixed parameters such as the maintenance energy costs and stoichiometric coefficients of the individual metabolites in the biomass equation (see Methods). The effect of change in energy costs and macromolecular compositions on cellular growth was investigated, thereby identifying protein and GAM as critical components whose variations may affect the model prediction Fig. . We furtiLME620, was used to elucidate metabolic states leading to the unique heterolactic fermentative behavior. For example, constraint-based flux simulations showed that lactic acid production during the anaerobic growth conditions is highly modulated by the tight coupling between NAD/NADH production and regeneration routes , as quantified by flux-sum analysis52, indicates the plausible switch of pyruvate catabolism from alcohol dehydrogenase to pyruvate oxidase. Interestingly, a similar trend involving the induction of pyruvate oxidase activity has been experimentally observed in L. mesenteroides when the culture condition is changed from anaerobic to aerobic mode53. Taken together, these results imply that the dependence of enzyme activities corresponding to the observed metabolic shifts upon oxygen supply can be solely explained on the basis of prevailing intracellular capabilities to restore redox balances.The current model, tes Fig. . Under ad49 Fig. . This ind49 Fig. , as quaL. mesenteroides. In this regard, MLF is an important alternate pathway used by L. mesenteroides for overcoming energy limitations under low-nutrient or unfavorable growth conditions . During the MLF phase of wine production, malic acid is converted into lactic acid, thus reducing the excess acidity and enhancing organoleptic properties of wine. However, it is still challenging to control the rate of MLF during wine fermentation, which further prompts for better understanding of the underlying mechanism. A previous study has proposed the conversion of malate to lactate by malolactic enzyme in a single decarboxylation mediated reaction54. Although lactate is the only final product of the active enzyme complex, the requirement of NAD as an essential cofactor in the reaction indicates the possible participation of oxaloacetate and pyruvate as intermediates13. Hence, the MLF may be represented as the combination of three reactions catalyzed by malate dehydrogenase (EC 1.1.1.37), oxaloacetate decarboxylase (EC 4.1.1.3) and lactate dehydrogenase (EC 1.1.1.28) . While the exact combination of MLF is still debatable55, it is not clear whether the involvement of the central metabolic intermediates, pyruvate and oxaloacetate, in the three-step MLF would affect the flux towards malate. Therefore, we analyzed the cellular phenotype under both scenarios, i.e., one-step and three-step MLF  Fig. . While MLF Fig. . CounterMLF Fig. . This an56. The flux distributions determined with and without the malate supply revealed that while malate does not contribute to the anabolic carbon pool, a single proton excluded via lactate efflux transporter generates additional ATP for higher growth rate . We observe that the ATP yield due to malate consumption increases by 0.25 moles per mole of malate, which is resulted from a reduced flux through F0F1-ATPase. This value is close to the energy gain due to malate uptake seen in Oenococcus oeni, 0.28 moles of ATP per mole of malate56, asserting MLF as one of the alternative energy conserving processes in heterofermentative LAB.Furthermore, we evaluated the role of MLF in the cell growth by characterizing metabolic flux states obtained from the model simulationate Fig. . We obsL. mesenteroides and other heterofermentative bacteria may not utilize PTS for glucose uptake since the single molecule of phosphoenolpyruvate (PEP) produced per molecule of glucose catabolized via PKP would be used up for its own transport57. As a consequence, no PEP would be leftover for the biosynthesis of aromatic amino acids and N-acetylmuramic acid that are required for cell wall synthesis. However, the presence of putative genes encoding glucose-PTS components in L. mesenteroides  as annotated in TransportDB database35 allowed us to analyze the possible cellular phenotype of L. mesenteroides growing on glucose with and without a glucose-PTS transporter. Accordingly, we tested three possible scenarios of glucose transport as illustrated in Fig. Energetics of sugar uptake systems play an important role in the cell growth of most bacteria as they can consume significant proportion of the total ATP generated. For example, sugar-phosphotransferase systems . Therefore, we compared the experimentally determined biomass yields for L. mesenteroides anaerobically grown on glucose as sole carbon source48 with the simulated yields for the two scenarios, with and without glucose-PTS usage. Figure O. oeni58, very much imply that all obligate heterofermentative LAB are capable of utilizing PTS for transporting glucose.Model simulations showed that the usage of glucose-PTS results in significantly increased biomass yield from glucose i.e., the ratio of growth rate to glucose uptake rate Fig. . TherefL. mesenteroides compared to the monosaccharides, glucose and fructose49 although the molecular basis for this observed difference is still unclear. Therefore, we initially performed constraint-based flux analysis to evaluate effects of two carbon sources (sucrose and glucose) on metabolic utilization. As expected, the resultant flux distributions did not reveal any significant differences apart from the initial carbon assimilatory pathways, which motivated us to explore metabolic regulation by profiling the gene expression of L. mesenteroides grown in sucrose or glucose as sole carbon source (see Methods). Subsequently, we carried out metabolic subsystem-wise enrichment analysis using iLME620. Interestingly, the presence of sucrose in the culture medium induced the upregulation of genes encoding sucrose phosphotransferase system (91-fold) and sucrose-6-phosphate hydrolase (72-fold). However, no such induction of genes involved in the substrate assimilation was found for the glucose uptake. In addition to the sugar uptake, several metabolic pathways related to biomass precursor production, including fatty acid biosynthesis, biotin biosynthesis, undecaprenyl diphosphate biosynthesis, and the overall uptake transporters were upregulated  behind such capabilities remain elusive.Sucrose is known to support higher growth rate in  system 9-fold andin silico fluxes derived from a constraint-based sampling procedure and the corresponding changes to gene expression levels (see Methods). Table . This result is interesting as mannitol is the preferred by-product of L. mesenteroides to relieve redox imbalances during fermentative growth conditions, such as the early stages of sauerkraut production3.We then examined the correlation between gene expression and metabolic fluxes, and identified the transcriptionally, post-transcriptionally, or metabolically regulated reactions under sucrose to glucose growth transition by resorting to a method that takes into account the direction of change of the ble Fig. . This rL. mesenteroides ssp. mesenteroides, for better understanding of crucial metabolic modules potentially influencing its industrial and probiotic applications. The in silico growth simulations performed using the model revealed negligible capability of L. mesenteroides to utilize amino acids as energy source unlike other LAB groups59. Such observation is presumably due to the absence of two important processes, the ATP-forming deiminations and proton-motive force generating amino acid decarboxylations, which contribute to energy generation using amino acids in other LAB. They are also known to be involved in intracellular pH buffering59. The absence of such enzymes in L. mesenteroides may therefore explain the relatively low tolerance of the organism to acidic condition. In addition, the negligible amino acid utilization for energy generation explains their existence in many natural ecological niches such as green vegetables or silage43. Besides, it is suggested that, in an association with the gut microbiota, protein-rich diets may lead to the dominance of other LAB over L. mesenteroides.In this study, we presented the first genome-scale metabolic model of obligate heterofermentative LAB, L. mesenteroides. For example, with the exceptions of glutamine and valine, the amino acid auxotrophy predictions were consistent with single-amino acid omission experiments40. The glutamine discrepancy could be attributed to the presence of glutamine synthetase (GLNS) (gene locus id: LEUM_0717) in the model, which can synthesize glutamine using glutamate. However, literature evidences suggest possible in vivo repression of GLNS by GlnR, a transcriptional regulator of nitrogen metabolism whose repressor activity has been observed in low-GC containing Firmicutes, including Lactococcus lactis60 and Streptococcus pneumonia61 under nitrogen excess condition. Hence, with a refined constraint on GLNS repression, we could replicate the glutamine auxotrophy successfully. The in silico predictions identified valine as non-essential in contrast to the single-amino acid experiments which showed it to be essential. Such discrepancy could possibly arise due to the limitations of constraint-based modeling approach which does not capture the transcriptional and translational regulation; although L. mesenteroides has ORFs encoding for all the genes in valine biosynthetic pathway as accounted in iLME620, some of them could be impaired at translational or transcriptional levels, and thus rendering the pathway inactive.The knowledge derived from model reconstruction and curation processes enabled us to speculate some unknown metabolic functionalities in . We ascribe this observation to a substrate channeling-like effect induced by the cellular redox environment, wherein surprisingly the two central metabolic intermediates, i.e. oxaloacetate and pyruvate, form lactate rather than being diverted towards the synthesis of biomass precursors. Existence of such channeling mechanism is further supported by the thermodynamic analysis of MLF: the first step converting malate to oxaloacetate has a large positive ΔrG′° (>30 kJ/mol at pH ≤ 7)62, indicating the channelling of malate towards lactate formation as the best possible scenario to overcome such thermodynamic limitation. Overall, this exemplifies the dominance of redox state as a factor controlling cellular processes in L. mesenteroides. Secondly, we highlighted the possibility of PTS-based glucose uptake in L. mesenteroides. Figure , discussed earlier, we also observe significant expression of the genes encoding components of glucose-PTS along with the putative glucose-permease, glcU in cells grown on glucose , pyruvate kinase (PYK), nucleoside-diphosphate kinase (NDK) and F0F1-ATPase . Interestingly, PYK and NDK fall under the CcpA regulon for L. mesenteroides and other Firmicutes63. Note that the transcriptional regulator, CcpA, has been known to repress glucose-PTS and NDK while activating PYK65. The flux changes of NDK and PYK during the cell growth with and without PTS usage, as depicted in Fig. in vivo glucose-PTS activity, L. mesenteroides could theoretically operate this transporter in a coordinated manner to achieve higher net ATP and growth yield.The obligate heterofermentative LAB possess distinct metabolic pathways to generate/conserve energy. Here, we elucidated two relevant metabolic behaviors to alleviate energy limitations by proposing new hypotheses. Firstly, we suggest that the fate of L-malate consumed via the MLF is independent of the intermediate steps Fig. . We ascure Fig. , discusase Fig. . IntereL. mesenteroides.The integrative analysis of transcriptome data allowed us to delineate the metabolic behaviour and regulation relevant to the higher growth rate observed in sucrose as compared to glucose: (i) upregulation of the genes in sucrose assimilation, (ii) net upregulation of genes for biomass precursor biosynthesis, and (iii) downregulation of PGI, ACALD and RPE which are negative flux control points of mannitol production Fig. , therebyL. mesenteroides, and provided a reliable in silico chassis that comprehensively represents obligate heterofermentative metabolism. Discovery of less studied regulatory mechanisms such as the substrate channeling during MLF described here could aid in robust and efficient design of heterologous pathways66. Evidently, the intracellular redox state has been observed as the major phenotype governing factor in L. mesenteroides. Therefore, the future endeavours to evaluate metabolic capabilities of this LAB should take into account the importance of achieving redox state desirable for specific industrial and therapeutic applications.In conclusion, our work explained several features unique to L. mesenteroides ssp. mesenteroides ATCC 8923 were performed in an anaerobic culture system. Briefly, cells were grown using a chemically defined medium (CDM) developed earlier40, under carbon limited conditions at a dilution rate (D) of 0.1 h−1, with no oxygen in the bioreactor inlet air. The total inlet gas (N2) flow was controlled by mass flow meters  at 1.5 vvm. The pH, stirring speed and temperature were maintained at 6.8 (using 0.5 N NaOH), 700 rpm and 30 °C, respectively. Biomass harvested from the chemostat culture was subsequently used to analyze the macromolecular composition (see next section).Chemostat cultivations of L. mesenteroides is an important prerequisite for analysing the intracellular metabolism at exponential phase of batch culture or at steady state in chemostat, where the primary aim of cell is to grow. Therefore, in order to formulate such biomass equation, we experimentally measured the total protein, carbohydrates, RNA and DNA content, and the detailed amino acid composition of L. mesenteroides from lyophilized cells harvested from steady state chemostat culture. In each case, at least three independent samples, from two independent cultivations, were analyzed.Drafting a concise biomass assembly equation representing the overall cellular composition of Elemental analysis was performed using 1 mg of a lyophilized biomass. After adding 1 mg of V2O5, the samples were subjected to 1000 °C in an oven. The volatile compounds thus released from the sample were measured using an Elemental Analyzer .67. Total protein content was determined by means of the BCA method68. Protein concentration was calculated using bovine serum albumin (BSA) as standard. The total lipid content was determined after methanol–chloroform extraction as described elsewhere69. Genomic DNA (gDNA) and total RNA was extracted from L. mesenteroides grown in the CDM at 30 °C under anaerobic conditions until the cell number reached 108–109/ml. The chromosomal DNA was extracted from the cells using a gDNA prep kit  and RNA extracted using a RNA prep kit . Quantification and purity were measured by nanodrop .Total carbohydrates were determined by the phenol method as described earlierL. mesenteroides cells was determined using the amino acid analyzer  using a cation exchange chromatography column and post-derivatization with ninhydrin as described previously70. Nucleotide composition of DNA was calculated using the GC content of L. mesenteroides genome (37.8%)32. Total glycerolipid, phospholipid and peptidoglycan content, and fatty acid composition were accounted based on bibliographic information  in the equation. Dry cell weight was obtained by weighing the lyophilized cells. Additional details regarding the formulation of biomass equation are provided in the Supplemental data Amino acid composition of the proteins extracted from L. mesenteroides was reconstructed based on the genome annotation32 and information compiled from various databases and literature, following the well-established protocol31. Initially, a draft metabolic network was reconstructed by reconciling the L. mesenteroides specific metabolic and transport reactions collected from KEGG34, MetaCyc33 and TransportDB35 databases. Duplicate and generic reactions were subsequently eliminated from the draft reconstruction using EC numbers and NCBI locus tags as common identifiers. The reconstruction content was then manually curated for reaction directionality, elemental and charge balancing of individual reactions. We employed the thermodynamic data generated by earlier studies39 to assign reaction directionality in the current model using the approach proposed earlier38. Note that those reactions with conflicting information on directionality were assigned to be reversible. The directionality of the reactions, for which no information was available, were determined based on heuristic information available in published literature and/or from biochemical databases such as Brenda71 and MetaCyc33. Metabolic dead-ends were then identified using the GapFind algorithm36 and were subsequently filled in by the addition of new reactions from other organisms based on literature evidences. Here, in order to substantiate the existence of such reactions in L. menesteroides, protein sequence homology of the corresponding enzymes were performed prior for their inclusion. Additionally, certain non-gene associated reactions were included in the reconstruction based on either direct or indirect biochemical evidences from the literature. Finally, the gene-protein-reaction (GPR) associations were manually added to each reaction based on the enzyme subunit and isoenzyme information obtained from the biochemical databases.The genome scale metabolic model of L. mesenteroides while growing on a nutrient rich medium. The biomass equation was maximized while simultaneously constraining the uptake rates of various amino acids and vitamins, and secretion rates of fermentation by-products based on a previously published study40. The optimization problem can be mathematically represented as follows:Sij is the stoichiometric coefficient of metabolite i participating in the reaction j; vj represents flux through the reaction j; vjmin and vjmax respectively represent the lower and upper bounds on the flux through the reaction j; and Z is the biomass objective, where cj denotes the relative contribution of each metabolic reaction to the biomass formation. Flux variability analysis and flux-sum analysis were performed extending the formulation shown above as described earlier72. Briefly, the turnover rate of metabolite i (ϕi) obtained using flux-sum analysis is given byConstraint-based flux analysis was employed to analyze the metabolic phenotype of 72 with Gurobi5 (http://www.gurobi.com) as optimization solver.Amino acid auxotrophic simulations were performed by setting each amino acid uptake rate to zero, individually, while maximizing the growth cellular objective. In this study, amino acid auxotrophy is defined by the condition of > 90% growth reduction due to exclusion of corresponding amino acid from the media. All constraint-based flux analysis simulations including gene-essentiality analysis were performed using COBRA toolboxhttp://equilibrator.weizmann.ac.il). This tool employs a database containing thermodynamic information along with an extended version of the group contribution method to perform the Gibbs free energy calculations73.In order to perform pathway-wise thermodynamic analysis and to calculate the transformed Gibbs free energy changes of the corresponding metabolic reactions under physiologically relevant pH (7.2), ionic strength (0.1 M) and intracellular metabolite concentrations (1μM-10mM), we used the web-based tool, eQuilibrator (The sensitivity of cell growth to variation in maintenance energy costs (GAM and NGAM) and the macromolecular composition was evaluated using two different measures. Firstly, each parameter was individually adjusted within a ± 50% error range, and the corresponding effect on the growth objective was determined. Secondly, sensitivity coefficients were calculated as the ratio of change in the growth objective to a unit change in the stoichiometric coefficient of each macromolecular component in the biomass equation.L. mesenteroides was profiled while growing on sucrose (S) and glucose (G) as sole carbon source in MRS broth. cDNA samples were prepared from the total RNA extracted using a RNA prep kit  from exponentially grown cells of S and G groups in two biological replicates. The oligonucleotide probes  for 1871 genes, designed based on the genome sequence of L. mesenteroides (Genbank accession no. CP000414), were synthesized and printed onto the CombiMatrix 4 × 2 K custom array platform . The probe design, spotting and analysis were conducted by Macrogen. Local-pooled-error (LPE) test and fold change were applied using R 2.4.1 software to determine and evaluate the significance of each gene’s differential expression in S and G groups.The gene expression of iLME620 using the gene-protein-reaction associations (GPRs). Gene-expression fold-change values were converted into reaction fold-change. Lowest fold change value between two or more genes with “AND” relationship was considered to account for the proportional fold-changes between the subunits of an enzyme complex required to effectuate the overall reaction fold-change. For reactions associated with genes having “OR” relationship, the fold-change values were added to account for the additive nature of intracellular enzyme concentrations. Significance of differential expression of various subsystems in S and G uptake conditions was determined using two-sided Wilcoxon signed rank test.The gene-expression data with coefficient of variance (CV) < 0.3 (less than 30% variance between replicate data points) from the quantile normalized microarray datasets of the S and G groups were employed to identify the differentially expressed pathways between sucrose and glucose uptake conditions. To do so, the gene expression values were mapped to the corresponding locus tags in 74. First, the flux solution space of L. mesenteroides growing on S or G was sampled using the OptGpSampler75 implemented in COBRA toolbox. The significance of change between the expression and flux of each reaction was then Z-scored using the formula below:ZiE and ZiF are the Z-scores for expression and flux of reaction i, respectively. E1i and E2i are the expression intensity values and F1i and F2i are the flux values of reaction i in condition 1 (S) and condition 2 (G), respectively. Note that 5000 sample points using 500 steps between each point was required for good convergence, as suggested earlier74. OptGpSampler75 implemented within COBRA toolbox was used to obtain sample points for both S and G conditions. Subsequently, the Z-scores were used to calculate the probabilities of correlation between the flux and gene expression of reaction. Briefly, a reaction is said to be transcriptionally regulated if the product of the probability of expression change of a reaction and the probability of the flux of the reaction changing in the same direction is significant. A reaction is considered metabolically regulated if the probability of no change in its expression level but change in flux is significant. And, the reaction is post-transcriptionally regulated if the probability of change in its expression level not leading to a change in its flux is significant.A Z-score-based approach was used to identify the transcriptionally, post-transcriptionally and metabolically regulated reactionsSupplemental FiguresDataset 1Dataset 2