We use these to generate parameters that integrate knowledge embedded in the genome-scale metabolic network model, into the most comprehensive kinetic model of the central carbon metabolism of E. coli realized to date. As an application, we performed a dynamical systems analysis of the resulting enriched model. This revealed bistability of the central carbon metabolism and thus its potential to express two distinct metabolic states. Furthermore, since our model-informing technique ensures both stable states are constrained by the same thermodynamically feasible steady state growth rate, the ensuing bistability represents a temporal coexistence of the two states, and by extension, reveals the emergence of a phenotypically heterogeneous population.An understanding of the dynamics of the metabolic profile of a bacterial cell is sought from a dynamical systems analysis of kinetic models. This modelling formalism relies on a deterministic mathematical description of enzyme kinetics and their metabolite regulation. However, it is severely impeded by the lack of available kinetic information, limiting the size of the system that can be modelled. Furthermore, the subsystem of the metabolic network whose dynamics can be modelled is faced with three problems: how to parameterize the model with mostly incomplete steady state data, how to close what is now an inherently open system, and how to account for the impact on growth. In this study we address these challenges of kinetic modelling by capitalizing on multi- This is constantly fuelling the interests of biologists to view and understand the functioning of living cells as an integrated system of molecular interaction networks ..E. coli ycolysis  our modeycolysis , our kinin-vitro conditions most closely matching the conditions of our interest. These conditions were those in which the steady state data we use to parameterize the model were measured in. This approach was taken in an attempt to maximize the consistency between the conditions from which all data is derived. As a result, our model represents kinetics under a particular physical condition, namely an aerobic environment, with temperature of 37°C and pH 7.0   9] and ed pH 7.0 ,16.X], based on cell specific growth rate μ,  of GSMN models are also used to understand cell steady states for a given growth rate, but only in terms of reaction fluxes. Even then, analysis of the model poses an ill-posed problem with infinitely many solutions of the flux distributions . MoreoveWe now demonstrate the power of our kinetic model by applying it to understand changes to the metabolic state of central metabolism of the single cell, during steady state growth conditions. We are particularly interested to gaining an insight into the phenomenon of the emergence of phenotypically heterogeneous bacterial populations. We therefore ask the question of whether central metabolism is able to converge onto more than one metabolic state under the constraints of a fixed steady state growth condition. A change to the metabolic state of the single cell will give rise to a change of its phenotypic profile.During batch culture growth, bacteria preferentially consume glucose, before switching to the alternative consumption of acetate . During In light of this recent insight, we hypothesize that the bacterial population was phenotypically heterogeneous during its steady state growth on glucose , prior to the substrate switch. As a precondition to the emergence of the two phenotypes observed in –19, we p0: Central metabolism, the driver of the rest of metabolism in glucose media, is able to converge onto two metabolic steady states. Each steady state would be defined by a distinct metabolite concentration profile. Furthermore, to prove cells in each state can coexist, both states should be achievable even under the constraints of the same media and steady state growth conditions. Due to the fast dynamics of the metabolism as compared to the gene regulatory response, these metabolic states would be achieved and only exist on a time scale which is short with respect to the time scales that characterize the full dynamics of the cell. The subsequent interplay between metabolism, protein interactions and gene regulation would move the metabolic state of the cell towards what would become an observable phenotype. Nevertheless, since the larger and longer time scale shift of the cell phenotype would follow from the shift in metabolic state, it is sufficient to observe a change in the metabolic state to claim a change in the cell phenotype.H0. To test for the existence of two subpopulations we needed to look for two metabolic states that metabolism can converge onto, with every cell having the potential to converge onto either state. To ensure that subpopulations emerging from each metabolic state can co-exist in the same media and growth conditions, we require three conditions to be imposed: fixed growth rate, which is already fixed as a constant, μ = 0.2 h-1; constant glucose availability, which is already defined in glcDex]/dt = 0; and a fixed cellular biomass, d[X]/dt = 0. This final condition is critical to enable a direct comparison between the concentration profiles of each metabolic state. Fixing biomass amount to a constant value ensures that we are comparing cells of the same size. Moreover, since cell biomass is proportional to its volume, the set of metabolite concentrations defining each metabolic state are therefore compared over the same cell volume. This enables the direct comparison between metabolic states. As detailed in Materials and Methods, we then searched over the metabolic phase space for stable steady states of the kinetic model, firstly solving for d[mi]/dt = 0, and then determining its stability from eigenvalue analysis. To ensure that our search for steady states of the system was not always around the same local minima, and to enable a search for solutions over a large span of the metabolic phase space, simulations were initiated over 2000 times. Each time a different vector of initial metabolite concentrations was generated by randomly selecting values for each metabolite concentration from a uniform distribution with interval . In this way, we found that simulations converged onto the same two distinct steady states.We then performed a dynamical systems analysis of the model in order to test for hypothesis HOur analysis did in fact discover exactly and only two stable steady states of central metabolism. One of these metabolic states was defined by the metabolic profile of the Keio steady state data. This was expected as these data were used to parameterize the kinetic model. The stability of this ‘Keio steady state’ was confirmed from eigenvalue analysis, where none of the eigenvalues were found to have positive real parts, as shown in E. coli does indeed possess the ability to express coexisting metabolic steady states, distinct in their metabolic profiles but identical in growth phenotype. This validates our hypothesis and demonstrates that two subpopulations can indeed emerge and exist prior to any substrate shift. Since our kinetic model represents growth at steady state, this means that the resulting emergence of a heterogeneous population occurs during exponential growth phase, in feed-batch growth conditions. We emphasize that this does not imply heterogeneity in populations grown in continuous culture conditions, like those in the chemostat. This is because any change in growth phenotype, observed on the longer time scale of the full cell dynamics, will be diluted out of the chemostat if the growth rate of the phenotype is less than the dilution rate. In such conditions homogeneity of growth phenotype will persist. This is also why we were able to parameterize our kinetic model with the Keio steady state data, which was based on measures taken from E. coli grown in the chemostat, cultures assumed phenotypically homogeneous.The central carbon metabolism of The striking discovery of exactly two distinct metabolic stable states of central metabolism is in fact the result of the bistable nature of central metabolism. As illustrated in The metabolic state defined by the Keio steady state metabolite concentrations represents an observed phenotype, as the kinetic model was fully parameterized using this multi-omics data. It is important to realize that the alternative metabolic state predicted by the model is, however, not representative of the final state of an observable phenotype. This is because of the assumed time scale difference in the dynamics of metabolism and gene regulation, implicit in the model. We assume that the time scale of the dynamical changes observed in metabolism is much faster than changes at the level of gene regulation. This is why gene regulatory changes are assumed to be at quasi-steady state and enzyme concentrations remain at fixed values. Changes in the profile of the metabolic state of central metabolism will however not remain unchanged when continuing to observe dynamics over a longer time scale. This is because the interplay of the high connectivity between metabolism, protein, and gene regulatory networks of the cell will come into play. This means that the change in metabolic state predicted by our kinetic model is the initial short time scale response of the cell preluding to the full response on much longer time scales. Though on this short time scale both metabolic states have the same growth rate, the role of metabolite flux sensors and their regulation of transcription factors cause a larger scale adjustment that feeds back onto metabolism. This drives a change to the cellular phenotype and its associated growth rate on the longer time scale fully determining the growth of the cell, as demonstrated in the modelling work of . NeverthThe key enlightening observation made in ,18 was th-1. To test our hypothesis, we ask whether the alternative metabolic state predicted by our kinetic model would enable the cell to converge on long time scales onto a phenotype associated to growth on acetate.Experimental observations from the studies of ,21 proviAn understanding of the long time scale response of the cell leading to convergence onto the alternative metabolic state lies in studying metabolite flux sensors. We suggest that metabolite flux sensors drive the continued cellular shift from the alternative state towards a phenotype coexisting with, but distinct to, the Keio phenotype. A number of studies have established the regulatory role of certain metabolites of the central carbon metabolism, whose binding to transcription factors (TF) creates the flux sensors ,33–35. IE. coli acetate assimilation, as estimated from the carbon-13 metabolic flux study in ..E. coli orted in  and [8] orted in , whereasOur construction approach, based on the integration of both steady state multi-omics data and knowledge of reaction fluxes embedded in a parameterized GSMN model, overcame some key inherent problems of kinetic modelling.Parameterizing the GSMN model with steady state multi-omics data empowered the model to replicate the metabolic flux distribution elucidated from the more involved carbon-13 metabolic flux analysis studies. This ensured that this experimentally informed steady state flux distribution is both thermodynamically consistent with the rest of the cell metabolism, on the genome scale, and is directly associated with our fixed growth rate of interest.h-1. Our model construction approach therefore overcame three key inherent problems of kinetic modelling.This knowledge was then used to parameterize the kinetic model, closing the inherently open sub-system of metabolism described by the kinetic model. It further ensured that the steady state flux distribution it describes is also thermodynamically consistent with the rest of the cell metabolism. This also means that we achieve a direct account of the growth rate of 0.2 Recent observations reported in –19 shed The change in the metabolic profile from the Keio metabolic state to the predicted alternative state occurs on a time scale much shorter than the typical time needed for the cell to shift towards the observable phenotype. On longer time scales, the interplay between gene regulation and metabolism in the cell starts taking place, and is thought to be mediated primarily by metabolite flux sensors. This results in the continued shift of the phenotypic state of the cell on the longer time scale of the full cell dynamics. Based on results from the analysis of our kinetic model, three key effects are relevant here: the decreased concentration of metabolite pyr, the somewhat increased repression of glucose consumption by increased G6P concentration, and the slow accumulation of acetate. The combination of these effects seems to give evidence to the hypothesis that the alternative metabolic state continues to evolve towards a cellular phenotype that switches from the consumption of glucose to that of acetate. Since both the Keio phenotype and the hypothesized alternative phenotype emerge in the same media and growth conditions, they are able to coexist.The discovery of bistability and its role in the expression of two stable and distinct metabolic steady states under the same conditions raises interesting evolutionary questions: Why has evolution selected for bistability of central metabolism? What advantage could two steady states of the system add to the survival of bacteria?We conjecture that the alternative steady state indicates a sort of ‘anticipation’ of the need for the cell to transit between the catabolism of glucose and the assimilation of acetate. Intuitively, one may expect that since bacteria have evolved in an environment where the availability of carbon sources are constantly fluctuating, evolution would select for those who are able to make the switch between carbon sources more quickly. Given that the phenotype defined by the Keio steady state faces severe growth attenuation after substrate switching, one may question the role of the Keio steady state. Experimental observation, such as those reported in , show thi.e. low growth rates. It would increase the likelihood that cells switch phenotypes. In fact, the time required for the system to escape a stable steady state is known to be reduced at lower growth rates, as suggested in  + nadp[c] → akg[c] + nadph[c] (+ co2[c])An example is that of the irreversible reaction isocitrate dehydrogenase (ICDH): The studies of  report ticit/Km_icit is present in the equation denominator. This assumption means that the factor accounting for the increased affinity of the nadp-enzyme complex for icit, α, can be assumed to be absorbed into the kinetic value of Km_icit. The kinetic value of Km_icit = 0.029mM, as reported in  and for the vmaxIcdh the interval was . This was done to ensure that the optimization was not stuck within a single local minima. Nevertheless, each time we found the same unique solution: Km_nadp = 0.005mM and vmaxIcdh = 54.829 μmol/mgProtein/min. The resulting curve fit is shown in R is multiplied to the As it is found that the affinity of the enzyme for icit is very weak it is thus assumed that no icit-enzyme complex can be formed, hence no term such as orted in . The unrL and n. These values were estimated by constructing a similar optimization problem as was done above: minimizing the squared vertical distance between curve of the L = 0.3709 and n = 1.0048. The curves of the reaction equation with optimized parameters, including those representing the inhibitory effects of pep, are plotted in This gives us two additional kinetic parameters Other reactions for which a similar approach was adopted were: PTAr, PPC, ME1, and the lumped reaction G6PDH and PGL ; isocitrate lyase (ICL); malate synthase (MALS); and fumarate reductase reactions, one which depends on cometabolite menaquinol-8 (FRD2) and the other on 2-demethylmenaquinol-8 (FRD3). The expression of genes governing the Acs protein is understood to be mainly observed during cellular growth during utilization of acetate -1, a pre-1), considered as a state of carbon-source stress, a population of bacteria would contain two subpopulations, one consuming acetate and the other producing acetate and consuming glucose. Though the study of  + 4h[p] + pi[c] ↔ atp[c] + 3h[c] + h2o[c]Due to the lack of data, the specification of the exact flux of the non-growth associated atp maintenance reaction ATPM  was left as a free variable. Growth associated maintenance is also assumed to be significantly different given the large difference in growth conditions that we impose and those that were used to parameterize the original genome-scale model. Therefore, the stoichiometries of atp in the biomass production reaction, representing growth-associated maintenance were also left as free variables. In the literature, the mechanism of proton translocation of electron transport is not well established and so the exact number of protons carried are unknown . The P:Onditions . Therefonditions . The P:Op] and cytoplasm [c] are not precisely known and so can be set as free variables to optimize. It is critical to realize that for this reaction to remain atomically balanced the difference in the stoichiometry of h[p] and h[c] must remain 1, with one more proton in the periplasm.The stoichiometry of the protons in the periplasm  from the Keio multi-omics database, after setting the Michaelis constant values {Km}.Kinetic parameters of the equations representing the enzyme dynamics are generally of two types: the Michaelis constants vmax values:Two problems arose in the calculation of the Unknown steady state flux values.Missing metabolite concentrations.We determined the steady state flux values of each reaction in the kinetic model from the parameterized genome-scale metabolic network (GSMN) model, especially given that the flux distribution of central metabolism was qualitatively the same as that estimated experimentally . A feasible flux distribution from flux balance analysis of the GSMN model alone can be taken. However we would be left with having to choose a random flux distribution from an infinite number of choices. The flux values we require for our kinetic model are those of the reactions of central metabolism, and the net flux of the connecting reactions.To determine the fluxes of the central metabolism reactions we looked at the carbon-13 fluxomics (C13-MFA) dataset in the Keio multi-omics dataset . We dete-1 (our growth rate of interest).The growth rate flux bounds of the genome-scale model were fixed to a value of 0.2 hThe objective of the linear programming problem was changed to minimize the glucose uptake rate, instead of maximizing the growth rate.From flux variability analysis of this redefined problem we chose and set the minimum acetate secretion and oxygen uptake rates. This was done to ensure that we find the minimal pathway and flux distribution towards our required growth rate.The quadratic programming problem was then defined as the minimization of the squared Euclidean distance between the flux solution space of the redefined genome-scale model and the average of the 13C-MFA flux estimates from the Keio multi-omics dataset.In using programming problem solver Gurobi, via its MATLAB executable function GurobiMEX, the general form of the quadratic programming problem was defined in the following form:Q of the coefficients of the quadratic terms, subject to constraints:for the matrix The flux values of the central metabolism reactions found from this QP problem was unique, in the sense that it was the only flux distribution that minimizes the distance between the C13-MFA fluxes and GSMN model. We then used these values as our steady state flux values for reactions in the kinetic model.The net flux of connecting reactions contributing to the pool of each metabolite of the kinetic model is another key parameter of the kinetic model. These were determined from a flux balance analysis of the parameterized GSMN model, with the problem defined as follows:-1.Set the growth rate to 0.2 hFix the fluxes of the reactions of central metabolism (those in the kinetic model) to the values as determined above (from a minimization between C13-MFA fluxes and the GSMN model).Set the objective of the programming problem to minimize the total sum of all fluxes.Solve the problem to determine the flux values of the whole GSMN model.ci values.Calculate the net flux of the connecting reactions for each kinetic model metabolite, giving us our respective −4 of any reaction. This indicated that the fluxes of the connecting reactions exhibit such a small range of variability that it did not make a difference as to which exact flux value was taken–they are the same to within the error of 10−4.Step 3 and 4 in general do not result in a unique flux distribution of the whole metabolic network, since the degrees of freedom of the ill-posed programming problem far exceed the constraints we set. Note that we are not concerned about the uniqueness of the flux distribution of the whole metabolic network. Our focus is on the flux values of only the 271 connecting reactions. The question remains as to whether the net flux values are unique or not. After constraining fluxes as in steps 1 and 2, we performed a flux variability analysis of the fluxes of the connecting reactions and found a maximum flux range of the order of 10vmax requires the knowledge of all steady state fluxes and metabolite concentrations. However, many steady state intracellular metabolite concentration values could not be measured or were not reported in the Keio multi-omics dataset, which brings into focus the second problem. Recalling the explicit form of vmax, as given in kcat) or even the enzyme specific activity. The values of these kinetic parameters of the enzyme were found either in the literature or were taken from enzyme databases BRENDA or EcoCyc, where available. It is important to note that the value of the enzyme specific turnover rate (kcat) was preferred to that of the specific activity since it is a directly measured property of the enzyme, similar to the Michaelis constant. This means that it would not be subject to a re-normalization, which would have been dependent upon the amount of substrate or enzyme used to obtain that value, like it is done for specific activity. Such a re-normalization can introduce errors further to those of experimental or measurement error. However, where the specific turnover rate was unreported we had to resort to using the value of the specific activity.As seen from vmax must remain as mmol/gDCW/h, the same units as the reaction flux values. The units of the enzyme turnover rate, specific activity and enzyme concentration are as follows:In using the value of either the enzyme turnover rate or the specific activity, the units of the value of Turnover Rate Specific Activity Enzyme Concentration vmax from either of the first two above, its value should be calculated with a scaling factor.Clearly, in order to obtain the correct units of vmax could not be calculated using vmax:Thus, where the value of The parameterised kinetic model is expected to exhibit a steady state profile of metabolite concentrations that are the same as the steady state concentration values from the Keio dataset used to parameterise the model. As a simple check, setting the Keio steady state metabolite concentrations in the ODEs of the kinetic model did indeed find that all ODEs equated to zero, i.e. steady state dynamics. This confirmed that the vector of metabolite concentrations is a steady state of the cell metabolism.Since this metabolic steady state was observed from experiments then it is expected that this state is stable, i.e. small perturbations away from that state will decay in time, and the system will converge back onto the same steady state. Therefore we need to ensure the stability of the state described by the Keio steady state metabolite concentrations, hereafter referred to as the Keio steady state.An initial evaluation of the eigenvalues of the Jacobian matrix of the kinetic model found 2 eigenvalues with positive real parts, shown in Given all parameter and steady state reaction flux values it was still not possible to algebraically solve for the missing steady state intracellular metabolite concentrations, since more than one equation containing the same missing metabolite concentration gave different values.Some reaction equations are only dependent on a single or few of the unknown concentration values, uncoupling them from other equations consisting of other unknown concentration values. This allowed the larger problem to be split into smaller ones: problem 1, finding [2pg] from reaction equations of PGM and ENO; problem 2, finding [6pgc] from reaction equations of PGI and GND; problem 3, finding [cit] and [icit] from reaction equations of ACONTb and ICDH; and problem 4, finding [g3p], [13dpg], [nadh], [xu5p_D], [e4p], [glx], [pi], [actp], and [oaa] from the coupled reaction equations of FBA, TPI, GAPDH, TKT1, TKT2, TALA, PGK, G6PDH, SUCOAS, PTAr, ACKr, PDH, CS, AKGDH, and MDH.vmax was deduced from turnover rates and specific activities from literature, as opposed to being determined from experimental data. Therefore, since we do not know what the 'true' values of such parameters should be with respect to our condition specification we allow this parameter to vary in order to find a feasible value of the missing concentration. Where freedom in the variation of these parameters alone was insufficient to determine the missing concentration value, variation in the dissociation constants was also allowed.As described above, the value of vmax, a1, and the multiplicative factor of Km, a2, were all set as free variables of the problem. The objective was defined as follows:wi. For problems 1–3 the value of w3 = 0, as it was sufficient to adjust only the vmax values, and w2 = 1, so as to leave us with only one weight to find. For these problems the weight was set so as to take the minimum required value to order for at least obj1 to converge to zero, since it is critical for this term to go to zero to avoid discrepancy between the right and left hand sides of the respective reaction equations at steady state.To solve for the set of missing concentrations and parameters of the system of equations, of each of the four problems specified above, we defined an optimization problem. The missing concentration values w1, w2 and w3 for problem 4. However the best option in this case was to leave w1 = 1 and w2 = w3 = 0 so as to allow the optimization to satisfy the most critical constraint. In this case, it should be noted that the values of a1 and a2 were not allowed to vary freely, but were constrained within the closed interval , which was found to the minimal interval to allow obj1 to converge to zero.A similar approach was adopted to determine the weights The system steady state is defined to be the value of all variables (vector of metabolite concentrations) that yield a zero rate of change of those variables:To find the vector of the steady state metabolite concentrations the MatLab function fsolve was used to numerically solve this coupled system of non-linear algebraic equations. The function required an initial guess from which the solver converges onto a local solution, allowing the opportunity to find alternative steady states of the system.−1 as opposed to zero (within a tolerance of 10−6). As an alternative, the rough position of steady states were first found using the fsolve function. This profile of metabolite concentrations was then used as the initial conditions to the ODE solver ode15s, which solved the system trajectories till steady state was reached.Due to the nature of the dynamics of the system, with an apparent spread of time-scales, the solution obtained from fsolve converged poorly, since substituting the solution back into the system of differential equations of the kinetic model gave right hand side values of the order of 10m0, the numerical Jacobian matrix J was constructed and evaluated at the given steady state of interest m0:mi and the function of each differential equation fi. The required partial derivatives were constructed from finite difference calculations based on the definition of the partial derivative, where the partial derivative of the ith function fi with respect to the jth variable mj is given by:−10.Determining the stability nature of each of the steady states found was essential in order to classify whether the respective steady state represented the metabolic profile of a bacterial phenotype, i.e. a stable steady state. To classify the nature of the stability of a given steady state, In, the n x n identity matrix. The MatLab function ‘eig’ was used to calculate all eigenvalues of the given Jacobian. If the real parts of every eigenvalue of the Jacobian were less than  zero, then the steady state was classified as stable, else it was classified as unstable. If there was a case where all eigenvalues had zero real parts but non-zero complex parts, then the steady state was classified as periodic.The eigenvalues of the Jacobian for the given steady state of interest were then determined, λ, by solving:The kinetic model was parameterized using the Keio multi-omics dataset, hence a known steady state of the system is the steady state metabolite concentrations as taken from the Keio steady state. On evaluating the stability of this steady state it was found to be unstable as the real part of two of the eigenvalues of the system Jacobian were found to have positive real parts, as shown in Ai for the ith parameter of interest. Again, since we have no prior knowledge of the extent by which these parameter values should be adjusted, we construct the objective of the optimization problem to minimize the change to these parameter values. Thus, our overall objective of the optimization is as follows:A, subject to the constraint that each adjustment term Ai should take a value within the closed interval . Re(λ) means taking the real part of the complex eigenvalue λ. This will ensure that values are not taken too far from 1, which equates to no change. It is important to realize that the objective is not a continuous function because of the first term of the objective function: max Re(λ), hence it is important to choose an appropriate initiating guess.We setup an optimization problem to minimally adjust a select few kinetic parameters which result in the maximum value of the real part of all eigenvalues of the Keio steady state not to exceed zero into the positive domain. The select few parameters were the dissociation constants of the rate equations that were taken directly from literature along with their respective parameters, where none of these are those parameters already adjusted. They were multiplied by a scaling factor constant S1 Fig(PDF)Click here for additional data file.S2 Fig(PDF)Click here for additional data file.S1 File(PDF)Click here for additional data file.S2 File(ZIP)Click here for additional data file.S3 File(PDF)Click here for additional data file.S1 Table(PDF)Click here for additional data file.S2 Table(PDF)Click here for additional data file.S3 Table(PDF)Click here for additional data file.S4 Table(PDF)Click here for additional data file.


The study of cancer metabolism has been largely dedicated to exploring the hypothesis that oncogenic transformation rewires cellular metabolism to sustain elevated rates of growth and division. Intense examination of tumors and cancer cell lines has confirmed that many cancer-associated metabolic phenotypes allow robust growth and survival; however, little attention has been given to explicitly identifying the biochemical requirements for cell proliferation in a rigorous manner in the context of cancer metabolism.+, acetyl-CoA, and amino acids. Extension of this approach to serine/glycine and glutamine metabolic pathways suggested lower limits on serine and glycine catabolism to supply one-carbon unit synthesis and significant availability of glutamine-derived carbon for biosynthesis resulting from nitrogen demands alone, respectively. We integrated our biomass composition results into a flux balance analysis model, placing upper bounds on mitochondrial NADH oxidation to simulate metformin treatment; these simulations reproduced several empirically observed metabolic phenotypes, including increased reductive isocitrate dehydrogenase flux.Using a well-studied hybridoma line as a model, we comprehensively and quantitatively enumerate the metabolic requirements for generating new biomass in mammalian cells; this indicated a large biosynthetic requirement for ATP, NADPH, NAD+, while also providing justification for various extracellular nutrient uptake behaviors observed in tumors. Collectively, these results demonstrate how stoichiometric considerations alone can successfully predict empirically observed phenotypes and provide insight into biochemical dynamics that underlie responses to metabolic perturbations.Our analysis clarifies the differential needs for central carbon metabolism precursors, glutamine-derived nitrogen, and cofactors such as ATP, NADPH, and NADThe online version of this article (doi:10.1186/s40170-016-0156-6) contains supplementary material, which is available to authorized users. Many parallels exist between the metabolic profiles of cancer cells and normal proliferating cells, including the use of aerobic glycolysis, selective expression of metabolic enzymes with distinct regulatory features, and elevation of amino acid consumption and biosynthesis –6. GrowiA central aim of the field of cancer metabolism is to identify metabolic pathways selectively activated in tumor cells, which likely include crucial biosynthetic pathways, to reveal therapeutic targets , 15. To In this investigation, we use fundamental stoichiometric and mass-balance principles to gain insight into the metabolic behavior of cancer cells using only minimal information about their proliferative needs. Previous investigations have similarly used minimal stoichiometric models to explore the effects of using a variety of objective functions on metabolic phenotype, the sensitivity of growth rate and other fluxes to perturbations, and the consistency between these in silico predictions and empirical measurements in a mammalian cell line , 22. Our3, PO4, and SH, respectively, and the “additional” category represents the contributions of additional inorganic substrates  and hydride groups from reduced cofactors. The total mass contribution of each precursor to every macromolecular component was determined  was included. The demands for complete biosynthesis of all nonessential components  are listed under the “Synthesis” header. Additionally, these demands were modified to consider the scenario in which nonessential amino acids (NEAAs) and fatty acids (FAs) are consumed from the surrounding medium, with the results listed under the “Uptake” header.  and less than 1 % for other associated components  in the “Synthesis” regime  serine or glycine demand to give the fractional fate of each amino acid when it serves as the sole source for 1C units  unit demands per gram DCW were determined by combining the demands for all biomass components for which they serve as substrates Table . 1C unitts Table . GlutathDCW) scaled by their corresponding numbers of carbon and nitrogen atoms, respectively  a minimum uptake profile, where glutamine was assumed to be consumed only for reactions in which other nitrogen-containing compounds cannot serve as substrates ; and (3) a predicted uptake profile, where glutamine consumption is determined from a simulated stoichiometric network of cells cultured in Dulbecco’s modified Eagle medium (DMEM)  Table . For eacM) Table .Flux balance analysis (FBA) , 34 was mentclass2pt{minimThis network was incorporated into the following linear programming (LP) problem:wheresubject to:N = 152 is the total number of reactions, ℳintr is the set of all intracellular metabolites, ℳextr is the set of all extracellular metabolites, where S represents the stoichiometric matrix, bm is zero if metabolite m is intracellular and bm is equal to the specific consumption (or production) flux of metabolite m if metabolite m is extracellular. The final constraints state that irreversible reactions can only take nonnegative values, while reversible reactions can be assigned any real value. Reactions were primarily designated to be irreversible if they were recognized as such by literature and database sources [Z is a specified linear combination of metabolic fluxes, which serves as the objective function for the LP problem.The first constraint is a mass balance;  sources , 25, 26;cn such that Z is equal to the total net carbon consumption rate:For our metformin treatment simulation (see below), we have chosen to maximize the yield of biomass on carbon. To achieve this, we fixed the specific growth rate as a basis and chose the coefficients where −1  [DCW−1 h−1 [−1 h−1, representative of the highly glycolytic A549 lung carcinoma cell line [Biomass composition values were taken from the literature  as descrof 24 h) . Since gCW−1 h−1 . A DCW oCW−1 h−1 . BecauseCW−1 h−1 , 37, a lell line ) was intell line , 37, minell line .Z*, which maximizes biomass yields at the specified growth rate) was determined using the “linprog” LP solver function in MATLAB . However, for a given problem formulation, there are generally multiple flux distributions that have this minimal carbon uptake rate. To avoid the possibility of multiple solutions, we implemented a second optimization program that, in addition to all previously specified constraints, specifies the carbon uptake rate to be equal to the minimal rate Z* (determined from the first problem) and minimizes the two-norm of the flux vector v. The complete problem is therefore a bilevel optimization [The minimal carbon uptake rate   It is notable that, in contrast to the use of NADPH for reducing power, NAD+ is primarily required for biosynthesis in its oxidized form.In addition to their mass contributions to DCW, we computed the molar requirements of each of the major precursors, 1C units, ODCW−1 h−1 expended for cell maintenance estimated for the hybridoma model [However, this profile assumes complete biosynthesis of all nonessential compounds starting from glucose, whereas in practice, many cells will derive significant contributions to TCA cycle-associated compounds from glutamine and obtain nonessential amino acids and fatty acids directly from surrounding media , 41–43. ma model  exceeds ma model .)A number of recent reports have implicated serine, glycine, and one-carbon metabolism as being important for tumors. The gene for phosphoglycerate dehydrogenase (PHGDH), which encodes the enzyme that catalyzes the first committed step in serine biosynthesis from 3PG, has been found to be amplified in breast cancer and melanoma , 12; glyNucleotide synthesis is essential for cancer cells, as well as any proliferating cells, to divide. Unlike amino acids , which can be derived from serum or culture medium to bypass de novo production , 47, 48,2), and ammonium (NH4+)  Fig. . SHMT haThe demand for 1C units for nucleotide  production places constraints on the fluxes through the serine-glycine pathway. We investigated these constraints by analyzing the biomass requirements of serine, glycine, and tetrahydrofolate compounds. The number of millimoles of each substrate required per gram DCW are given in Table metabolic flux rather than metabolite levels themselves is important. Although the link between PHGDH and SHMT is less well understood, regulation of biosynthetic pathways at the committed step is a common motif in metabolism, so it is plausible that knockdown of PHGDH may affect the activities of other enzymes in the pathway, including SHMT. Thus, it may be that even when exogenous serine is added to the medium to bypass the PHGDH reaction, the flux through the serine-glycine pathway, and therefore production of one-carbon units, is still impaired, this could explain why exogenous serine cannot rescue the PHGDH knockdown.These results give insight into some recent findings about the importance of serine and glycine in the metabolism of cancer cells. Previous results have shown an impairment in proliferation in breast cancer cells with amplified PHGDH copy number when the gene is knocked down, but this knockdown does not result in a change in intracellular serine levels and cannot be rescued by exogenous serine . As in tAlthough glutamine is nominally a nonessential amino acid (it can be synthesized through the ATP-dependent condensation of glutamate and free ammonia), it has been extensively reported that glutamine serves as a major biosynthetic substrate for cancer cells , 32, 52.2, the calculation nonetheless provides a suitable approximation .Each molecule of glutamine consumed contains two nitrogen atoms that can contribute to biomass generation: an “amide” nitrogen that is lost when glutamine is converted to glutamate and a “transamination” nitrogen that is lost when glutamine-derived glutamate is converted to αKG. Although these two amine groups are used by distinct biosynthesis reactions, the amide nitrogen, for which there is a considerably smaller biomass demand, can be converted to a transamination nitrogen if it is first liberated by glutaminase to become free ammonia and then added to a molecule of αKG by glutamate dehydrogenase to become the amine group in glutamate Fig. .  , oxoglutarate dehydrogenase (OGDH), and mitochondrial malate dehydrogenase (MDHm), all of which catalyze NAD+-consuming mitochondrial reactions , this is compensated by an approximately twofold increase in total cytosolic redox activity , and lactate dehydrogenase (LDH), respectively, resulting in an increased fraction of glucose being converted to lactate. In addition, as indicated by lower cytosolic malate dehydrogenase activity upon simulated metformin treatment, malate-aspartate shuttle activity decreased in coordination with lower oxidative TCA cycle flux; this is because NADH generated in glycolysis is oxidized in the cytosol rather than being shuttled into the mitochondria for OXPHOS. In total, these results reflect the tight regulation between redox-associated steps across major metabolic pathways—complex I activity within the ETC, NADH oxidation in the TCA cycle, and GAPDH during and LDH following glycolysis—which, solely by satisfying stoichiometric mass-balance constraints on redox cofactors, enables robust maintenance of cellular growth and homeostasis.As previously suggested , 71–73, + regeneration by assessing the sensitivity of NAD+-consuming mitochondrial reactions  to the presence of the two non-ETC reactions predicted to oxidize NADH in the mitochondria, nicotinamide nucleotide transhydrogenase (NNT), and NAD+-dependent glutamate dehydrogenase (GDHNAD). Previous reports have suggested that NNT can promote reductive IDH flux by converting mitochondrial NADH to NADPH [+, but GDHNAD, operating in the reverse direction, became the sole reaction aside from ETC NADH oxidation that regenerated mitochondrial NAD+, fully compensating for the loss of NNT , and glutaminase flux became zero for all cases . Under most in vitro cell culture conditions, glucose concentrations are highly relative to physiological levels , and when tumor cells are sufficiently close to blood vessels, they are afforded access to roughly constant glucose levels. In effect, glucose is “free” for these cells, and there is no cost to consuming it when it is available. Although ATP and amino acids are required to generate the enzymes and transporters needed for high rates of fermentation, this burden is presumably considered in the “Protein” biosynthesis demands (Additional file +, and precursor demands in synthesizing new biomass and how these burdens could be selectively reduced by increasing fatty acid and amino acid uptake. Next, we applied the generated profiles to explore the limits of metabolic behavior in two case studies relevant to cancer cells—the production of 1C units from serine and glycine catabolism, and the contribution of glutamine to total cellular nitrogen and carbon—which demonstrate how quantifying biomass demands can yield insight even in the contexts of metabolic branchpoints. These queries demonstrated that flux through serine and glycine biosynthesis pathways is required for sustaining 1C production for nucleotide synthesis and that glutamine may contribute substantially to biomass carbon as a consequence of its natural role as the predominant nitrogen source. Finally, we incorporated these biomass requirements into a constraint-based FBA simulation that modeled the metabolic effects of metformin, a widely used antidiabetic medication currently under consideration as a potential cancer therapeutic. The resulting flux distributions successfully recapitulated the major metabolic changes observed in cells following metformin treatment and also enabled greater understanding of the interactions within the reaction network that contributed to these changes.In this investigation, we used a series of stoichiometric analyses to elucidate the metabolic requirements of mammalian cell proliferation. First, using a hybridoma line as a model for cancer cell composition, we generated comprehensive profiles of the major precursor and cofactor requirements for biomass synthesis on both mass and stoichiometric bases. These assessments revealed the importance of meeting ATP, NADPH, NAD1C, one-carbon unit; 3PG, 3-phosphoglycerate; αKG, α-ketoglutarate; AcCoA, acetyl-coenzyme A; CS, citrate synthase; DCW, dry cell weight; DHAP, dihydroxyacetone phosphate; DMEM, Dulbecco’s modified Eagle medium; ETC, electron transport chain; FA, fatty acid; FBA, flux balance analysis; FH, fumarate hydratase; G6P, glucose 6-phosphate; GAPDH, glyceraldehyde 3-phosphate dehydrogenase; GCS, glycine cleavage system; GDH, glutamate dehydrogenase; IDH, isocitrate dehydrogenase; LDH, lactate dehydrogenase; LP, linear programming; MDH, malate dehydrogenase; NEAA, nonessential amino acid; NNT, nicotinamide nucleotide transhydrogenase; Oaa, oxaloacetate; OGDH, oxoglutarate dehydrogenase; PHGDH, phosphoglycerate dehydrogenase; PDH, pyruvate dehydrogenase; PPP, pentose phosphate pathway; R5P, ribose 5-phosphate; ROS, reactive oxygen species; SDH, succinate dehydrogenase; SHMT, serine hydroxymethyltransferase; SUCL, succinate-CoA ligase; THF, tetrahydrofolate


However, that need not be true, other times such as the lifetime of an infinitesimal perturbation can be much longer. In the present work, we demonstrate that this paradoxical property can arise even in quite simple systems such as a linear chain of reactions obeying mass action (MA) kinetics. By mathematical analysis of simple reaction networks, we pin-point the reason why the standard relaxation time does not provide relevant information on the potentially long transient times of typical infinitesimal perturbations. Overall, we consider four characteristic times and study their behaviour in both simple linear chains and in more complex reaction networks taken from the publicly available database ‘Biomodels’. In all these systems, whether involving MA rates, Michaelis–Menten reversible kinetics, or phenomenological laws for reaction rates, we find that the characteristic times corresponding to lifetimes of tracers and of concentration perturbations can be significantly longer than τ.When relaxation towards an equilibrium or steady state is exponential at large times, one usually considers that the associated relaxation time  There are many ways to define a characteristic time in a dynamical system. The simplest is via the asymptotic relaxation towards the steady state . We are then left with the parameter In the disordered (i.e. heterogeneous) case we now consider, the rates ‘τc, τt, Tc, Tt) compared with the homogeneous case. However, for stronger disorder, the characteristic times typically do increase significantly with CV. To identify the typical behaviour, we have determined these characteristic times for 10 000 realizations of the disorder and calculated the median values. For τt and τc, we illustrate our results in figure 5a in the case of MA, where those two quantities are equal. The relaxation time increases relatively mildly  at low CV but increases more markedly when CV becomes larger than 30%. Furthermore, instead of having a limit at large N as happens in the absence of disorder, it seems that the presence of disorder makes the relaxation time diverge slowly as N → ∞, perhaps logarithmically.For weak disorder, one expects little change in the values of the characteristic times  is the same as without disorder, namely a − b. At large disorder, this argument fails because the quenched and annealed averages are very different. A simple way to see this is to consider an extreme case where fluctuations are large. Clearly, a very large value of ‘a’ at one site will not compensate a very small value at another site. As expected, at large CV, effects of disorder become very significant. The reason should be clear: Tt and Tc are sensitive to unfavourable reactions  throughout the whole set of reactions. Finally, just as for relaxation times, it seems that the presence of disorder increases the median values of lifetimes by a factor that diverges slowly  as N → ∞.Consider now the effects of disorder on the 4.2.Although quite a few biosynthetic pathways include successive steps forming a linear chain of enzymatic reactions, the one-dimensional systems considered so far remain toy models because in all known organisms, large-scale biochemical metabolic networks have numerous branches and loops. It is thus necessary to consider how characteristic timescales might be affected by such structures. Rather than produce artificial networks including those features, it is more relevant to study directly the various kinetic models of metabolism that have been proposed in the literature. The repository ‘Biomodels’ ,13 proviJt)( and Jc) and (2.9), but see also the electronic supplementary material for additional details.For each of those four kinetic models, we first downloaded its SBML specification  from theThe initial perturbation was taken to be localized on any metabolite of the network. The global lifetime is chosen as the maximum these perturbation lifetimes.Saccharomyces cerevisiae (baker's yeast). It has 17 reactions, mostly of the reversible MMH type, and there are 14 internal metabolites. Glucose is an external metabolite which enters the metabolism and then gets transformed. A total of three compounds can be excreted, all irreversibly. The characteristic times of this model are modest, from a few seconds to a few minutes. Further inspection shows that the ordering of these four values follows the same pattern as in our one-dimensional toy model, namelyτt < τc and Tt < Tc whenever there are Michaelis–Menten reactions subject to saturation effects. Indeed, the saturation of flux in a reaction can prevent a concentration fluctuation from being evacuated but it will not prevent labelled atoms from going through (i.e. from participating to the flux). Secondly, in our toy model, the τs are relatively insensitive to processes inside the network: they depend mainly on reactions close to the excreted metabolites. By contrast, the Ts depend on drift throughout the whole network. Thus, if the network is large one can expect the Ts to be larger than the τs.In Escherichia coli [−1 l−1 compared to 1.5 mmol s−1 l−1). The innequalities equation (4.1) are not respected since τt > τc and Tt > Tc. Model 3 contains the glycolysis and the pentose phosphate pathway, but for a human cancer cell. It has 29 reactions and 34 internal metabolites. The inequalities of equation (4.1) are satisfied except that τc > Tt. This ‘discrepancy’ may be due to the fact that the diameter of the network is modest while saturation effects are important.The other models partly follow this same pattern cf. . Model 2hia coli . It has E. coli [Model 4 contains the reactions for the biosynthesis of purines in E. coli . It has 5.N nodes, the characteristic times of the whole system grow as N2. Our work in this paper focuses on the consequences of drift. For simplicity, we do this in the context of reaction networks operating close to their steady state. If a concentration fluctuation is introduced relative to the steady state, its damping will generally be associated with both a spreading out (diffusion) and also an overall drift. The timescale for evacuating such a perturbation is what we call its lifetime T (cf. equations (2.8) and (2.9)), though in other contexts it can be referred to as the mean residence or transit time. In the absence of drift, corresponding to a simple diffusive regime, the lifetime T scales as the square of the diameter of the network, a scaling that also arises for the standard measure of the time to return to equilibrium, i.e. the relaxation time τ. In most systems, τ corresponds in fact the longest characteristic time and there are no further subtleties. However, for almost any reaction network of interest, one has both diffusion and drift. More generally, out of equilibrium systems will have fluxes, and such fluxes may drive conserved particles out of the network. In the presence of such drift, a perturbation's lifetime T can scale as the diameter of the network, divided by a characteristic drift velocity which is related to the presence of flux and provides the drift intensity. Interestingly, in this out-of-equilibrium situation, the relaxation time τ is no longer informative about the timescale of the (slow) process which evacuates perturbations. In particular, in our toy model consisting of a homogeneous linear chain of reactions, τ does not grow with the system size while T grows linearly. This can be understood quite intuitively from τ) sets in. The perturbation's lifetime can thus be much longer than the relaxation time. We showed analytically how that happened in our one-dimensional homogeneous systems. Indeed, in the presence of drift, the linearized dynamics can be decomposed into eigenvectors, but the leading eigenvector determining τ is concentrated near the metabolites that can be excreted. As a result, τ is quite insensitive to the size of the network while T inevitably increases with network size since the evacuation of a perturbation requires it to cross some fraction of the diameter of the network. When studying the extension to a non-homogeneous system of reactions, it was necessary to take a numerical approach. In our toy one-dimensional network, we introduced heterogeneities into the individual reaction rates. For mild heterogeneities, we find that the effects are small, but as one increases the CV of the reaction rates, the effects of disorder become significantly stronger, increasing in particular the median values of τ and of T. Interestingly, these heterogeneities drive τ to grow with system size as illustrated in N is slow, perhaps only logarithmic with N. Similarly, in the presence of disorder, it seems that T grows a bit faster than N, perhaps logarithmically faster.In dissipative systems, relaxation is often driven by the local dynamics, and as a result characteristic times of the system (and in particular relaxation times) are comparable to that of the individual processes. However, in systems where atoms or other particles are conserved, the diffusion and drift of the conserved quantities can significantly increase system characteristic times. Pure diffusion provides a simple example of this effect: on a linear lattice of The overall phenomena found are most easily understood when the reactions obey MA, but they arise also for MMH reaction laws. For this last case, the presence of a saturation of the flux with concentration of metabolites exacerbates the difference between characteristic times associated with concentrations versus tracers as is illustrated in Tc > Tt but nevertheless raises a flag as to possible artefacts coming from the peculiar and unorthodox form of the kinetic laws introduced in [Given any model network with specified dynamics, it is possible to estimate its relaxation times and lifetimes (cf. equations (2.8) and (2.9)) in the context of concentration perturbations or of tracers. The four associated characteristic times will typically follow the inequalities given in equation (4.1) as they do in the one-dimensional models. If a case leads to anomalous results, either because the inequalities are violated or because some of the characteristic times are unreasonable (too short or too long), the reason for the anomaly should be found or the reliability of the model should be questioned. We encountered precisely this situation for the model  from theduced in . The fac


Shewanella is a genus of facultatively anaerobic, Gram-negative bacteria that have highly adaptable metabolism which allows them to thrive in diverse environments. This quality makes them an attractive bacterial target for research in bioremediation and microbial fuel cell applications. Constraint-based modeling is a useful tool for helping researchers gain insights into the metabolic capabilities of these bacteria. However, Shewanella oneidensis MR-1 is the only strain with a genome-scale metabolic model constructed out of 21 sequenced Shewanella strains.Shewanella oneidensis MR-1 and constructed metabolic models for three other strains, namely Shewanella sp. MR-4, Shewanella sp. W3-18-1, and Shewanella denitrificans OS217 which span the genus based on the number of genes lost in comparison to MR-1. We also constructed a Shewanella core model that contains the genes shared by all 21 sequenced strains and a few non-conserved genes associated with essential reactions. Model comparisons between the five constructed models were done at two levels – for wildtype strains under different growth conditions and for knockout mutants under the same growth condition. In the first level, growth/no-growth phenotypes were predicted by the models on various carbon sources and electron acceptors. Cluster analysis of these results revealed that the MR-1 model is most similar to the W3-18-1 model, followed by the MR-4 and OS217 models when considering predicted growth phenotypes. However, a cluster analysis done based on metabolic gene content revealed that the MR-4 and W3-18-1 models are the most similar, with the MR-1 and OS217 models being more distinct from these latter two strains. As a second level of comparison, we identified differences in reaction and gene content which give rise to different functional predictions of single and double gene knockout mutants using Comparison of Networks by Gene Alignment (CONGA). Here, we showed how CONGA can be used to find biomass, metabolic, and genetic differences between models.In this work, we updated the model for in silico studies of Shewanella metabolism. The developed models provide a platform for a systematic investigation of Shewanella metabolism to aid researchers using Shewanella in various biotechnology applications.We developed four strain-specific models and a general core model that can be used to do various  Shewanella is a genus of facultatively anaerobic, Gram-negative aquatic bacteria found in diverse environments around the globe [Shewanella are of particular interest today because of their possible use in bioremediation in which the organisms convert a wide variety of metals from a soluble to an insoluble form and thus prevent the spread of contamination [Shewanella putrefaciens has been shown to reduce soluble uranium-VI to insoluble uranium-IV [Shewanella strains can also degrade halogenated organics, including polychlorinated biphenyls and possibly explosive nitramines [Shewanella strains have also been metabolically engineered for chemical production [he globe . This eche globe ,2. In adhe globe ,3,4. Shemination . For exaanium-IV . Shewanetramines . Shewaneoduction .Shewanella. These genomic datasets provide insight into both the cumulative (or pan) and conserved (or core) capabilities of this species. Previous studies have used these sequenced genomes to study metabolic subsystems [Shewanella strains. Another recent study looked at the carbon, nitrogen, phosphorous and sulfur utilization capabilities of five different Shewanella strains and reconciled these with genomic data [Currently, there are over 20 sequenced strains of bsystems  and regubsystems  in Shewamic data .Shewanella, from both traditional microbiology and high-throughput “-omics” (summarized in [Shewanella strains [Shewanella genus as a whole [Metabolic modeling provides a way to integrate the wide variety of data available on the rized in ) experimrized in ,12. With strains , models Shewanella oneidensis MR-1 published in 2010 (referred to as iSO783) has been used as a platform to integrate and validate experimental data with computational predictions [Shewanella strains. In this study, we have expanded the previous model for MR-1 based on updated genome annotations and compared model growth predictions to fitness measurements for transposon-tagged mutants [iMR1_799) together with genome comparisons (based on genome annotations) and experimental data to develop the genome-scale metabolic models for three other Shewanella strains, Shewanella sp. MR-4 (hereafter iMR4_812), Shewanella sp. W3-18-1 (hereafter iW3181_789), and Shewanella denitrificans OS217 (hereafter iOS217_672). In addition, we developed a Shewanella core (hereafter Core) model using genome annotations of 21 sequenced Shewanella strains that would represent the conserved metabolic functionalities of all Shewanella strains. Furthermore, we used the developed models to predict and compare the metabolic capabilities of Shewanella strains in utilizing various carbon and electron acceptor sources. We also used a previously developed computational algorithm, Comparison of Networks by Gene Alignment (CONGA) [Shewanella strain.The genome-scale metabolic model of dictions . This mo mutants . We subs (CONGA)  to identShewanella oneidensis MR-1 was obtained from Grigoriy Pinchuk , Shewanella sp. MR-4 and Shewanella sp. W3-18-1 were obtained from Daad Saffarini (University of Wisconsin-Milwaukee). Shewanella denitrificans OS217 was obtained from the American Type Culture Collection . Strains were cultivated at 30°C in Luria Broth (LB) , half-strength Difco Marine Broth (S. denitrificans OS217) or modified M1 medium [1 medium . For groFor growth rate experiments, strains were precultured overnight in 2 mL LB or Marine Broth at 30°C with continuous shaking. Cells were then transferred into 2 mL of modified M1 supplemented with the carbon source of interest at 20 mM concentration and 20 mM D, L-lactate  or 20 mM maltose (OS217) using a 1:100 dilution from the overnight LB or Marine Broth culture and grown for 24 hours  or 48 hours (OS217) at 30°C. The cells were then harvested by centrifugation at 5000 rpm and resuspended in modified M1 medium containing no carbon source to an OD600 of 1–1.5. 5 μL of the cell suspension was then added to 95 μL of modified M1 medium supplemented with the carbon source of interest on a 96-well plate.Growth/no-growth phenotype tests were performed using the same procedure, with the second preculture containing only lactate or maltose at 40 mM concentration. After harvesting, the cells were washed with 1 mL of modified M1 medium to remove any residual carbon source, centrifuged again, and resuspended. Growth curve experiments were conducted in a Tecan Infinite M200 plate reader . Cultures were grown at 30°C in 96 well plates with OD600 readings taken every 15 minutes. Growth rates (1/h) were calculated from the linear fit of ln(OD) versus time, where the slope corresponds to the growth rate. Biomass yields (OD/mmol) were calculated by subtracting the starting OD from the stationary phase OD and dividing by the starting concentration of the carbon substrate. Results are provided in Additional file Shewanella strains was constructed using INPARANOID as previously described [Shewanella strains made it possible to readily identify orthologous groups that had missing members or that contained extra or erroneously grouped members . Missing group members were identified by tBLASTN analysis (genes missing in gene models) or BLASTP analysis . Insertion elements were mapped in each of the genomes as described for S. oneidensis MR-1 [A table with the draft ortholog predictions among the 21 sequenced escribed . This tasis MR-1  to assissis MR-1 . The ortShewanella models iMR4_812, iW3181_789, and iOS217_672 developed in this study were constructed manually using the iMR1_799 as a template, and the gene-protein-reaction (GPR) associations in each new model were constructed based on the ortholog table. Reactions in the iMR1_799 metabolic model were copied to the metabolic models of these strains if the associated MR-1 genes had orthologs in the other strains or if no genes were associated to the reaction in iMR1_799. Genes that did not have orthologs in these strains and their associated reactions were removed from the base iMR1_799 model to obtain draft models that were specific to iMR4_812, iW3181_789, and iOS217_672. Flux balance analysis (FBA) [iW3181_789, iOS217_672, and Core was modified because unlike iMR1_799, they are not capable of producing UDP-N-acetyl-D-galactosamine. The LPS reaction for iMR4_812 was updated based on the structure determined experimentally by Vinogradov et al. [The v et al. .Shewanella strains. Non-GPR reactions were added to the model only if they were predicted to be essential for aerobic growth on pyruvate, resulting in a smaller number of reactions without GPR associations  converts L-glutamate 5-phosphate (glu5p) to L-glutamate 5-semialdehyde (glu5sa). Every Shewanella strain studied has a ProA enzyme that catalyzes the G5SD reaction; however, there are two different orthologs that encode the ProA enzyme, and some strains have only one of the two. Since the Core model represents the collective group and G5SD is an essential reaction (meaning it has to stay in the Core model), the two genes associated with ProA were encoded as isozymes in the Core model. The other three reactions are acetylornithine deacetylase (ACODA), inorganic diphosphatase (PPA), and a sulfate transport reaction (SO4t2).The Core model was constructed based on the genes that were conserved across all 21 sequenced Shewanella models can be found in Additional file The complete list of reactions, metabolites, and genes for all five Escherichia coli  [The mutant fitness data set from Deutschbauer et al.  containsmutants) . In addiiMR1_799 model. The 64 simulation conditions can be mapped to 101 of the 195 fitness experiments . Additional file Only experiments from the “carbon source”, “nitrogen source”, “carbon and nitrogen source”, and the “anaerobic” groups where considered. Experiments from the remaining groups were not considered because they cannot be simulated using the models. Next, experiments that are labeled as stationary phase, saturated, or with added CAS amino acids were excluded from our analysis. In total, we were able to make 35,712 predictions for 558 of the 3,355 knockout mutants (other mutants involved genes that were not in the model) under 64 unique simulation conditions for the Shewanella models  on different carbon sources and electron acceptors  or absent (0) in a particular model or whether the model was predicted to grow (1) or not (0) under a given growth condition.A hierarchical clustering approach was used to gain an understanding of how the four CONGA, or Comparison of Networks by Gene Alignment , is a coiSO783) [iMR1_799) contains additional reactions involved in alternate carbon metabolism (5), cell envelope biosynthesis (1), energy metabolism (3), glycolysis/gluconeogenesis (1), methionine metabolism (1), nucleotide salvage pathways (5), valine, leucine, and isoleucine metabolism (8), and additional transport reactions (19). To evaluate the performance of the original and updated MR-1 models, we compared model predictions to a recent study reporting wildtype and mutant phenotypes [iMR1_799 predicted could support growth (see Methods for details). The iSO783 model could only predict growth for the wildtype strain in 40 of these 64 conditions, indicating that 24 conditions are incorrectly predicted by the original model. When evaluating the growth phenotypes for the subset of mutants (546) and conditions (40) that both models could make predictions for, we found the iSO783 model had an overall accuracy of 85.11% and the iMR1_799 model had an overall accuracy of 85.34%. This was done assuming that mutants with a fitness score less than −3.5 did not grow (see Methods for details). We next evaluated the sensitivity of the iMR1_799 model’s accuracy to the fitness cutoff used to indicate growth or no growth phenotypes   our updaenotypes . Of the iMR1_799 was used as a starting point to generate models for three additional strains. Several alternative carbon metabolism pathways were added to the Shewanella models based on literature data [Shewanella strains  were shown to be able to use arabinose as a carbon source under aerobic conditions . Only 21 essential reactions without GPR associations were kept in the Core model to better represent a minimal model of the Shewanella genus, of which 17 of these 21 reactions do not have GPR associations in any of the models. The remaining four non-GPR core reactions point towards gaps in our knowledge for some of the 21 Shewanella strains. The 673 reactions and 552 genes in the Core model turned out to represent an average of 73% and 72% of the reactions and genes of the 4 Shewanella models developed here, respectively .The Core model was built to provide a representation of the Shewanella genus. In addition, by comparing knockout predictions across the five models, we are able to identify deeper genetic and metabolic differences for each strain. We explore these two levels of comparison in the following sections.By comparing the wildtype version of each of these five models, we are able to identify how each model and thus strain is physiologically different from the entire Shewanella strains, iMR1_799, iMR4_812, iW3181_789, iOS217_672, and the Core model were used to predict growth capabilities of each strain on different carbon sources and electron acceptors. A total of 70 carbon sources and 16 electron acceptors were used in the FBA simulations , 31/36 for iMR4_812 (86%), and 25/36 for iW3181_789 (69%) when compared against experimental data [The reconstructed metabolic models of different tal data ,11, inclShewanella strains that were predicted to grow on the corresponding carbon source and electron acceptor . This result suggests that while iMR4_812 and iW3181_789 have highly similar metabolic gene content, the genes deleted from iMR1_799 and those added to iMR4_812 and iW3181_789 resulted in iMR1_799 and iW3181_789 being more metabolically similar from a network perspective.To evaluate how each model relates to the others based on the presented results so far, heat maps and dendrograms were created for the four models based on metabolic gene content or phenotype predictions (see Methods). First, a heat map and dendrogram was generated based on the presence or absence of metabolic genes in the metabolic models Figure A. From tCONGA is a constraint-based method that can be used to identify functional differences between two models by comparing reconstructed networks aligned at the gene level. We used CONGA to identify orthologous genes to delete such that only one of the two organisms being compared is capable of growth. In this work, we identified three reasons that explain the functional differences found by CONGA: metabolic , genetic , and biomass differences  conditions. The total number of lethal genes is lower in this condition because only three models were analyzed. The iOS217_672 and Core models were excluded from the last condition because they are not capable of growth under that condition.Based on this analysis, we can clearly see that under the aerobic condition, the Core model is the least robust since the Core model has the least number of genes and reactions. Thus, the Core model has fewer isozymes  and alternative pathways to compensate for deleted genes. iMR1_799 and not in iMR4_812 and iW3181_789 because the latter two models have alternative enzymes that do not require CymA for nitrate reductase activity.Furthermore, we mapped the reactions associated with the genes in the gene deletion sets to their respective metabolic subsystems to see if a specific subsystem was responsible for most of the differences identified by CONGA for the single deletion case. Of all subsystems, the Energy Metabolism subsystem stood out with the most number of reactions associated with orthologs deleted by CONGA (14 reactions) and they all appear only under L-alanine plus nitrate conditions. Further investigation shows that all 14 reactions involve the gene associated with the membrane-anchored tetraheme cytochrome c, CymA. Deletion of CymA is lethal in Shewanella strains, MR-1, MR-4, W3-18-1, and OS217 in terms of growth phenotypes using integrated approaches of genome comparisons, experiments, and computational models. Based on conservation of metabolic gene content, we expected that iMR4_812 and iW3181_789 to be the most similar, with iMR1_799 and iOS217_672 being the most different. However, our results revealed that based on predicted growth phenotypes MR-1 is most similar to W3-18-1, followed by MR-4 and OS217 in terms of metabolic capabilities in using various carbon and electron acceptor sources. This suggested that genetic similarity does not always coincide with metabolic phenotype similarity. Some conflicts between our models’ predictions and experimental data suggest there may be regulatory effects affecting cellular phenotypes that are not accounted by our models. Regulons for 82 transcription factors have been predicted based on comparative genomic analysis of 16 Shewanella strains and they also appear to highly vary across the different strains [In this study, we have shown an extensive comparison of four different The Core model reflects the conserved metabolic capabilities of all sequenced strains. Based on analysis of the Core model, it appears that all strains appear to be capable of using pyruvate, amino acids (10 of 20), and fatty acids as sole carbon sources. Interestingly, only oxygen was predicted to be used as an electron acceptor by the Core model, indicating that while many strains can use other electron acceptors, the respiratory pathways and enzymes involved are not necessarily conserved.Shewanella strain of interest. Each genome-scale metabolic model developed in this work will serve as a platform to integrate experimental data with computational approaches for each Shewanella strain, which would be helpful to researchers who study Shewanella for scientific discovery, bioremediation, or metabolic engineering applications. In addition, the Shewanella core model will serve as a base model to develop genome-scale models for other Shewanella strains by simply adding metabolic functionalities that are unique to those individual strains.We also used computational approaches to further investigate the metabolic and genetic differences among these strains under several common growth conditions. Our computational analyses provided more insights into the metabolic capabilities of each The authors declare that they have no competing interests.WO, TV, and JL constructed the five genome-scale metabolic network models. KL ran the experiments. MS and MR analyzed the genomes and provided the ortholog table. WO and TV did the model simulations. WO, TV, KL, and JR analyzed and interpreted the modeling and experimental data. JR conceived of the study. WO, TV, KL, and JR wrote the manuscript. WO generated all five SBML model files. All authors read and approved the final manuscript.Supplementary material including supplementary text and figures. This file contains additional discussion on the growth experiments for MR-1 and W3-18-1, biomass composition, evaluation of mutant fitness data, and CONGA.Click here for fileSupplementary tables. This file contains additional tabular data.Click here for fileXML files for the five Shewanella models in SBML format. This file contains the XML files for the five models constructed in this work.Click here for file


Chlorophyll is one of the most important pigments present in green plants and rice is one of the major food crops consumed worldwide. We curated the existing genome scale metabolic model (GSM) of rice leaf by incorporating new compartment, reactions and transporters. We used this modified GSM to elucidate how the chlorophyll is synthesized in a leaf through a series of bio-chemical reactions spanned over different organelles using inorganic macronutrients and light energy. We predicted the essential reactions and the associated genes of chlorophyll synthesis and validated against the existing experimental evidences. Further, ammonia is known to be the preferred source of nitrogen in rice paddy fields. The ammonia entering into the plant is assimilated in the root and leaf. The focus of the present work is centered on rice leaf metabolism. We studied the relative importance of ammonia transporters through the chloroplast and the cytosol and their interlink with other intracellular transporters. Ammonia assimilation in the leaves takes place by the enzyme glutamine synthetase (GS) which is present in the cytosol (GS1) and chloroplast (GS2). Our results provided possible explanation why GS2 mutants show normal growth under minimum photorespiration and appear chlorotic when exposed to air. Chlorophyll, one of the tetrapyrroles synthesized in green plants, is the major light harvesting pigmentThe biochemical consequences of chlorophyll synthesis should be linked with the central carbon metabolism and other metabolic processes spanned over different cellular compartments, in terms of photosynthesis. Therefore, the involvement of cellular metabolism in chlorophyll biosynthesis requires exploration. However, this knowledge is quite limited as the focus of previous research works were mainly centered on the chlorophyll biosynthesis pathway starting from glutamate (Glu) within the chloroplast. Several groups have studied the enzymes involved in the chlorophyll biosynthesis pathway and their regulations248chlorophyll cycleIt is to mention that we considered only the chlorophyll a synthesis pathway for the present study. Chlorophyll b, which also occurs in plants, is synthesized from chlorophyll a through a series of reactions commonly referred to as Haemophilus influenzaE.coli141516Arabidopsis thaliana18Hordeum vulgare) helps to understand the metabolic behavior of source and sink organs during its generative phaseGenome scale metabolic models (GSMs) represent a list of all the reactions and the associated metabolites which are typically between hundreds to thousands. Availability of complete genomes of different species and annotation of genes (gene-protein-reaction) encourage several researchers to construct GSMs. The first ever reported GSM to be published was of 4 genome scale model (C4GEM)There is also a constant effort to further curate the previously reported GSMs and to analyze them to address new scientific questions. For example, the Arabidopsis model (AraGEM)Flux balance analysis (FBA) has been extensively used281018Oryza sativa japonicaWe curated the existing GSM of Using FBA we identified one of the possible pathways for chlorophyll synthesis .This pathway has 108 reactions among which 22 are cytosolic, 57 are chloroplastic, 10 are mitochondrial and 19 are intra cellular transporters  or NADPH dependent GOGAT (EC 1.4.1.13). Our result showed the involvement of the NADPH dependent GOGAT . This GOThe result also showed involvement of Ser-Gly conversion in the cytosol, which is obligatory for one carbon metabolismThe in-silico reaction deletion strategy was used to identify the essential set of reactions for chlorophyll biosynthesis. We first identified the essential reactions when RuBP carboxylase and oxygenase activity were represented as two independent reactions. A total of 85 reactions were identified as essential, distributed in all compartments. Among them 46 are chloroplastic, 5 are mitochondrial and 17 are cytosolic reactions. A total of 17 intracellular transporters were identified as essential. We also identified that a total of 148 genes are associated with these essential reactions. A list of all essential reactions and associated genes is given in Here, we report experimental evidences supporting a relationship between the decreased expression (or no expression) of a large number of essential genes with reduced chlorophyll content in plant leaves . Some of2, O2 and light (light transporter has been added for modeling purpose) into the cell to be essential for the cellular metabolism. In addition, we found chloroplastic transporters for SAM, AdoHcy, Mal-Glu and Mal-2OG also essential along with some reactions of Calvin cycle .Among the predicted essential genes, the participation of 20 chloroplastic enzymes in chlorophyll synthesis has been reported by several groups34835We found a total of 12 mitochondrial reactions (7 intra-cellular transporters and 5 reactions within mitochondria) to be essential. These mitochondrial reactions are catalyzed by 4 different enzymes - aconitate hydratase (AH), glycinedecarboxylase (GDC), 5,10 methylenetetrahydrofolate:glycinehydroxymethyltransferase/serine hydroxymethyltransferase (SHMT) and isocitrate dehydrogenase (ICDH). These results are in accordance with a few experimental studies those have reported that if the plants are deficient in these enzymes, they would have less or no chlorophyll (i.e. chlorosis), depending on the amount of enzyme available for carrying the reaction; hence, they would appear chlorotic3738In the cytosol, as described in the previous section, we found the methyl cycle to be active. Additionally, we found the enzymes associated with methyl cycle to be essentially linked with chlorophyll synthesis. This is because methyl cycle is required for the synthesis of SAM in the cytosol, which is transported into the chloroplast for the methylation step for chlorophyll synthesis (EC 2.1.1.11). Thus we can infer a direct link between methyl cycle and chlorophyll synthesis. This result is in accordance with the study that had reported the effect of THF synthesis inhibition on chlorophyll production in pea plantReduced expression of chloroplastic geranyl reducatse (CHL P) was studied by expressing antisense CHL P RNA and it was reported that chlorophyll content in the transformants decreased42432 and NH3 in intermediate steps of C2 cycle, the simulation always preferred to include only Rubisco carboxylase activity. Here, we fixed the carboxylation to oxygenation flux ratio (Vc/Vo) of Rubisco at 3:1.Rubisco has both carboxylase and oxygenase activity and its ratio (Vc/Vo) at normal condition is threeThe results showed involvement of 128 reactions in one of the possible pathways for chlorophyll synthesis. 99 reactions were found to be essential which spanned over the chloroplast, cytosol, mitochondria and peroxisome. The photon flux needed was 1092 light flux unit, which was much higher than what we got with only carboxylase activity, i.e. 666.5 light flux unit. The increase in the photon flux was expected due to the involvement of photorespiration. The cytosolic ammonia transporter instead of the chloroplastic ammonia transporter was active along with the chloroplastic Glu-Gln shuttle.min) and maximum (FVA max) flux values of the reactions. Rather, both the FVAmin and FVA max values of all the reactions were equal to the flux values that were obtained from FBA analysis   that calculated the allowable range of flux values that a reaction can carry while achieving the optimal objective value. In our analysis, the minimization of the total flux values of the reactions was set as the primary objective and the flux through the chlorophyll transporter was set to one unit. We observed no variability in the minimum   online. min = FVAmax = FBAval, while for others such as mit_AconDHatase, mit_AconHydr etc. FVAmin = FBAval < FVAmax. Both the cases indicate that these reactions are essential for chlorophyll biosynthesis. The same set of essential reactions was predicted in reaction deletion study (discussed earlier).(i) For some of the reactions such as chl_FPPSYNRXN, chl_PROTOPORGENOXIRXN etc. FVAmin < FBAval < FVAmax. A set of reactions (irreversible) had FVAmin = 0, while the set of reversible reactions had FVAmin < 0, indicating the later can carry flux in both the directions. Both the sets of reactions indicate that these are not essential reactions for chlorophyll synthesis. The reactions carrying variable flux values form alternate metabolic routes and thus indicate the presence of metabolic redundancy in the system(ii) For the remaining reactions we observed that FVAmin and FVAmax equal to 0 and 4 flux unit, respectively. As the flux value of the chlorophyll transporter was set to 1.0 unit in our analysis, the external ammonia that should be transported through the transporters to the cell should be 4.0 flux unit. This ammonia can be transported through either the chloroplastic or the cytosolic ammonia transporter or both. We also observed variations in the fluxes of some of the intracellular transporters.Interestingly, we observed that the external ammonia transporter had FVA4+) and nitrate ion (NO3−). Rice is cultivated in flooded paddy fields. The fact that it prefers ammonium as the nitrogen source is well establishedNitrogen is one of the essential macronutrients and plays a major role in plant growth and crop productivity. Plants take up nitrogen from the soil in two inorganic forms, ammonium ion  (ii) into the chloroplast (ex_ammonia_tx). First, we aimed at obtaining a solution space without fixing the flux through both the ammonia transporters.We considered two transporters for external ammonia – (i) into the cytosol  . This inFurther, in order to study the effect of relative variation in the use of ammonia transporters (and hence of GS activity), we simulated the cellular metabolism by varying the flux through the chloroplastic ammonia transporter from 0 to 4 under two different conditions: case 1: without Rubisco oxygenase activity and case 2: with Rubisco oxygenase activity. The range of flux (0 to 4) through ammonia transporter reflects the constraint used in our simulation, i.e. we simulated the metabolism to synthesize one unit of chlorophyll, which consists of four nitrogen atoms.For case 1, the flux through GOGAT (EC 1.4.1.14) was found to be fixed at 8.5 throughout the simulation. The methyl cycle in the cytosol was found to be linked with the mitochondrial GDC and SHMT via the mitochondrial Gly and Ser transporters. The results showed that the mitochondrial GDC and SHMT had a flux of 0.5 unit, and consequently, the ammonia was released in the mitochondria (via GDC). This ammonia of 0.5 unit flux transports into the chloroplast.Next, two different physiological conditions were imposed on the model to obtain the solution space—(1) activity of cytosolic ammonia transporter was fixed at 4.0, while chloroplastic ammonia transporter was blocked and (2) vice-versa—and the corresponding results were analyzed. The two conditions showed the maximum effect on the activities of the chloroplastic Glu-Gln transporter, GS1 and GS2. The flux through chloroplastic Glu-Gln shuttle was maximum while the flux through cytosolic ammonia transporter was fixed at 4.0 unit and the former gradually decreased with the reduction of the later . The fluFor case 2, i.e. in the presence of Rubisco oxygenase activity, as expected to complete the C2 cycle, the fluxes through the chloroplastic transporter for Mal-Glu and Mal-2OG and the mitochondrial ammonia transporter, SHMT and GDC were much higher compared to what we obtained in case 1 .While we varied the fluxes through cytosolic and chloroplastic ammonia transporters in Case 2, we observed the similar trend (as of Case 1) .For the GOGAT catalyzed reaction (EC 1.4.1.14) 2OG is required as a substrate. Therefore, the import of 2OG into the chloroplast had to be equal to the flux of GOGAT reaction. Thus, in case 1, the flux through the chloroplastic Mal-2OG was always 8.5 unit and in case 2 (involving photorespiration) it was 23.2 unit.Thus, on the basis of the results we can infer that under the relative activity of the ammonia transporters, there exists a clear and an important interlink between the various intracellular transporters , in order to complete the chlorophyll biosynthesis pathway. In specific, while the chloroplastic Mal-Glu and Mal-2OG transporters are always active and essential for chlorophyll biosynthesis, the activity of chloroplastic Glu-Gln depends on the relative activities of GS1 and GS2.2 condition (i.e. minimum photorespiration) but appeared chlorotic when exposed to airIt is known that GS2 is needed for photorespiratory metabolism of nitrogen in chloroplast2 conditionTo synthesize one flux unit of chlorophyll, 4.0 unit of ammonia is always generated in the chloroplast  and slow rate of diffusion, the chloroplastic ammonia could not get sufficient time to diffuse into the cytosol and thus, there would be an accumulation of chloroplastic ammonia. This ammonia accumulation can be as high as 50 times (when exposed to air for 30 min) of what is observed under non-photorespiratory conditionFurther, when we simulated the metabolism with Rubisco carboxylase/oxygenase activity fixed at 3:1  the ammonia released from the mitochondria to the chloroplast increased  under only Rubisco carboxylase activity was approximately 1/4The essential reactions and their associated genes required for chlorophyll biosynthesis span over the three plant compartments  when Rubisco oxygenase activity (i.e. photorespiration) is not considered. Peroxisome comes into play when photorespiration is active.FVA indicates variations in the fluxes through the non essential reactions and existence of alternate path for chlorophyll synthesis. It also confirms the essentiality of the reactions that we predicted by deletion study.Ammonia assimilation, activity of GS1 and GS2 and other intra cellular transporters are linked with the chlorophyll biosynthesis pathway. Variation in the ammonia transporters affects the activity GS/GOGAT pathway and the Glu-Gln antiporter.Analysis of the activity of GS in nitrogen assimilation provides a possible explanation on why GS2 mutants show normal growth under minimum photorespiration and appear chlorotic when exposed to air.In this work we updated the available rice GSM by adding some reactions, intracellular transporters and peroxisome compartments and removing non plant reactions. We used FBA to simulate the metabolism for further analysis and the results allow us to conclude the following:Oryza sativa japonica2 as the sole carbon source. The inputs used in the model are – water, CO2, nitrogen as NH3 and NO3, phosphate, sulphate and photons. Transport reactions were added in the model by which these inorganic nutrients and photon can be transported to the plant cell. The model was used to find the realistic physiological behaviour of leaf metabolism at different light intensities. However, this study did not report anything about chlorophyll synthesis pathway. We should mention that although the previous model included some of the reactions of chlorophyll synthesis pathway but, the reactions were not compartment specific. So, for the present study the model was extended and updated by (i) adding the missing reactions for chlorophyll synthesis pathway along with the existing reactions within the chloroplast module, (ii) adding the peroxisome compartment/module with photorespiration associated reactions and (iii) deleting some non-plant reactions that were identified based on the existing knowledge.We used the GSM of In specific, in the chloroplast module we added- nine reactions for chlorophyll synthesis in the chloroplast  and glycine decarboxylase (GDC). The SHMT is localized both in the mitochondrion and the cytosol of plant cellWhile incorporating the peroxisome compartment we added only 5 photorespiratory reactionsFurther, we also added a few transporters associated with specific compartments. In the chloroplast module, we added two transporters namely T1 & T2 for SAM and AdoHcy respectively59Further, while analysing the previous modelAfter the model was curated it was then checked for stoichiometry inconsistencies. Energy and redox conservations were also checked using the method described for the previous modelFBA aims at deriving a feasible set of steady state fluxes and optimizing the objective function subjected to constraints specified. At steady state, the rate of production of each internal metabolite in the network is equal to its rate of consumption. This state can be represented mathematically as:where v is a vector of fluxes through the metabolic network and S is the stoichiometry matrixhttp://www.gnu.org/software/glpk/). In our analysis, the linear programming is defined asFBA was employed both in model validation (e.g. energy and redox conservation) and analysis. We used the ScrumPy metabolic modeling packageHere, Z is the objective function, v is the flux vector, c is the transpose of a vector of objective coefficients, S is the stoichiometry matrix, and LB and UB are the vectors of fluxes lower bounds and upper bounds, respectively.In most of the analysis  the fluxes of all nutrients and photon are not fixed. However, we have fixed the flux through the chlorophyll transporter at 1.0 unit throughout. The curated model was subjected to linear programming (LP) in order to verify whether the system represented by the model was capable of generating the biomass precursors (including chlorophyll).To find the essential reactions for chlorophyll biosynthesis, the flux of each reaction in our predicted pathway for chlorophyll synthesis was set to zero (one at a time). Then the model was simulated taking inorganic nutrients as inputs to test whether there was a possible path for chlorophyll synthesis.From the modeling point of view, a reaction is said to be essential if the simulation of the model does not find any possible solution space to produce the desired biomass when the flux passing through that reaction is set to zero. The genes associated with this reaction are considered as essential genes. It refers to a cellular situation where the enzymatic activities of these genes are inhibited in such a way that the reaction does not occur and the cell is not able to produce the desired biomass. On the other hand, non essential reactions are those for which the simulation finds alternative reactions to produce the desired biomass. Thus, while the essentiality refers to the non-existence of an alternative solution space, non-essentiality suggests about the robustness of the metabolic space and shows that there exists an alternative solution.To find the allowable range of each of the reactions of the predicted chlorophyll biosynthesis pathway, we did Flux Variability analysisThe optimal objective value of the primary objective function  was computed for one flux unit of chlorophyll synthesis. Then, the primary objective function was set to this computed optimal value as an additional constraint to the linear programming problem. Then for each reaction in the solution space, the reaction flux was maximized and minimized to get the allowable range of flux values.How to cite this article: Chatterjee, A. and Kundu, S. Revisiting the chlorophyll biosynthesis pathway using genome scale metabolic model of Oryza sativa japonica. Sci. Rep. 5, 14975; doi: 10.1038/srep14975 (2015).