Escherichia coli that represents 90% of its metabolome. We show that the quantitative metabolomes allowed by the abiotic constraints are consistent with metabolomic and isotope-labeling data. We find that: (i) abiotic constraints drive the evolution of high-affinity phosphate transporters; (ii) Charge-, hydrogen- and magnesium-related constraints underlie transcriptional regulatory responses to osmotic stress; and (iii) hydrogen-ion and charge imbalance underlie transcriptional regulatory responses to acid stress. Thus, quantifying the constraints that the inorganic world imposes on living systems provides insights into their key characteristics, helps understand the outcomes of evolutionary adaptation, and should be considered as a fundamental part of theoretical biology and for understanding the constraints on evolution.Living systems formed and evolved under constraints that govern their interactions with the inorganic world. These interactions are definable using basic physico-chemical principles. Here, we formulate a comprehensive set of ten governing abiotic constraints that define possible quantitative metabolomes. We apply these constraints to a metabolic network of  E. coli.Evolution selects for the fittest but must operate within the realm of the physically possible. Here, the authors present a theoretical framework that allows them to explore how ten abiotic constraints can shape the operation, regulation, and adaptation of metabolism in  Through variations in metabolite levels, metabolic networks sense, adapt to, and influence the local environment to maintain functioning metabolic pathways under diverse and unpredictable conditions5. We have not yet achieved a quantitative understanding of how various environmental variables influence metabolite levels.Life developed under a variety of environmental pressures, such as pH, temperature, and osmotic pressure that have driven the evolution of robust mechanisms of cellular adaptation6. Constraint-based modeling of reaction fluxes, through flux-balance analysis (FBA), has been successful in predicting the growth rate and metabolic phenotypes by imposing mass-balance constraints on the flow of metabolites through the network8. Constraint-based formulation of metabolite levels, based instead on thermodynamic constraints, has also been shown to be feasible10. Unlike FBA, many more biophysical considerations must be accounted for when specifying the constraints on the quantitative metabolome. Moreover, while maximizing the growth rate is an intuitive objective to determine optimal pathway usage, cellular objectives that may underlie the quantitative metabolome have not yet been identified.Constraint-based modeling provides a quantitative framework to study the interactions between cellular metabolism and the environmentEscherichia coli against measured concentrations and known thermodynamic bottlenecks of central-carbon pathways. We then use the ABC-based analysis to evaluate how intracellular concentrations are influenced by the environment and shape biological functions. The ABCs are universal and apply from primitive to modern cells across the tree of life. Thus, this work paves the way to biophysically accurate representations of the quantitative metabolome at scales, where one can ask fundamental questions about the evolution and function of cellular processes.In this article, we introduce a comprehensive set of abiotic constraints (ABCs) on the metabolome. We present an ABC-based analysis to determine bounds on metabolite concentrations for a prescribed environment. We validate the results for a metabolic network of We introduce an ABC-based approach to characterize the constraints that govern the interactions of biological functions with the inorganic world. This approach encompasses ten fundamental and evolutionary classes of abiotic constraints on cellular functions see Fig. a.Fig. 1CMathematically, thermodynamic and solubility constraints are represented by inequalities and the rest by equalities. Together, these ten classes of constraints define a nonconvex and possibly disconnected set of feasible concentration states that is challenging to characterize Fig. b.8. A biologically relevant concentration solution space (CSS) is constructed by restricting the concentrations to those obeying all the ABCs. Thus, the CSS contains all quantitative metabolomes that satisfy the ABCs. Accordingly, the ABC-based analysis can be leveraged to determine bounds on metabolite concentrations and Gibbs free energy of reactions.The conceptual basis for the ABC-based analysis is analogous to the widely used flux-balance analysis11 . They both rest on the assumption that intracellular concentrations are regulated to ensure efficient enzyme utilization, regardless of the growth state12. To achieve a prescribed flux state at minimum protein cost, the first maximizes the thermodynamic driving force of all reactions in the network independently of enzyme saturation levels, whereas the second maximizes the saturation level of all enzymes independently of thermodynamic driving forces. Within the framework of the ABC-based analysis, how well these objectives could represent the functional state of the cell is determined by identifying the location of metabolomic data inside the CSS.An objective function may be used to ascertain a particular concentration state from the CSS. We study two cellular objectives pertaining to the concentration state of the cell, namely the thermodynamic and enzyme-saturation efficiency. These objectives play the same role in the ABC-based analysis as the growth-rate objective does in FBAE. coli, comprising 78 reactions, 72 cytoplasmic, and 11 periplasmic metabolites  cycle, anaplerotic reactions, electron transport chain (ETC), biosynthetic sugar metabolism, and cofactor interconversions are included in this network. Importantly, this reduced network contains over 90% of the observed metabolome by mole and includes all reactions with experimentally measured fluxes14. Therefore, it possesses the most essential characteristics of the global metabolome for the ABC-based analysis.Characterization of the CSS for genome-scale metabolic models is computationally challenging. Therefore, we applied the ABC-based analysis to a reduced metabolic network of 10. Then, we show that the ABCs necessitate the evolution of multiple specialized phosphate transporters. Finally, we provide two case studies, illustrating how the ABCs shape transcriptional responses to stress conditions.We present our results in three parts. First, we show that the ABC-based analysis leads to results that are consistent with concentration and flux data. We also elaborate on the implications of our analysis for other constraint-based approaches, such as thermodynamics-based metabolic flux analysis (TMFA)E. coli15. The FBA model (see “Flux distribution” section) was solved to identify fluxes that best matched their experimentally measured values14 for each carbon source. The resulting flux directions were then used to specify the thermodynamic constraints.We sought to determine whether the ABCs were consistent with available experimental metabolomic data. We considered growth on four carbon sources, including glucose, acetate, pyruvate, and succinate. The flux states of the network were determined using the latest genome-scale metabolic network reconstruction of Ccm  and relatively small root-mean-square deviation (RMSD = 2.3–5.1 mM) between the computed and experimental concentrations across all carbon sources . The hub metabolites simultaneously participate in several reactions, and their possible concentrations are constrained to a narrow range, so that they satisfy all the thermodynamic constraints these reactions are subject to. The lower bound for exported metabolites with a low periplasmic concentration is restrictive  because the cell must retain a minimum cytoplasmic concentration to sustain a thermodynamic driving force across the cell membrane. For a similar reason, the upper bound for imported metabolites with a low periplasmic concentration is also restrictive .We ascertained feasible concentration ranges for all intracellular metabolites in the reduced network when glucose is the sole carbon source Fig. b. The AB14. As a result, their concentrations may be driven towards the CSS boundaries to accommodate a desired flux state. Thus, they cannot be generally well-approximated by the expected values, which are usually interior points of the CSS.To derive order-of-magnitude estimates of cytoplasmic concentrations, we computed expected values for concentrations 13. Nevertheless, it is expected to hold for reactions in central-carbon metabolism, where flux directions alter in response to stress conditions, so that enzymes are efficiently saturated in both directions13.Enzyme-saturation efficiency has been proposed in the literature as a cellular objective to determine optimal intracellular concentrations16. Nonetheless, saturation efficiency could be one of several competing factors determining the functional state of the cell17.We compared the maximum Michaelis constant ods: Eq. ) of metaentclass1pt{minimaentclass1pt{minima17. Through this trade-off, metabolic fluxes are adapted to environmental perturbations18.Thermodynamics play a fundamental role in adaptation. Modern bacteria have an extraordinary ability to grow and survive using minimal environmental resources. To maximize their survival chances, they efficiently allocate available resources to essential biochemical reactions, maintaining a steady flow of materials through all their metabolic pathways. Sustaining this optimal flux state hinges on a trade-off between pathway thermodynamics and proteome allocation. Reactions with a small thermodynamic driving force have higher protein cost and vice versaRT or less, then the violation probability of that reaction is substantially larger than other reactions, providing a qualitative criterion for when a reaction is thermodynamically constraining in a metabolic network.We sought to determine the thermodynamic bottlenecks resulting from the ABCs. We calculated the feasible ranges of transformed Gibbs energy of reactions  or be more restrictive than  those furnished by TMFA Fig. a. The th14. We found several reactions in glycolytic , TCA cycle , and sugar metabolism  pathways with small transformed Gibbs energy of reactions  Flux-direction reversal in glycolysis is often induced by carbon-source and nutrient alterations14. Thus, having near-equilibrium steps enhances the energy efficiency of pathways, enabling the cell to rapidly switch flux directions in response to energy and biomass demands with minimal concentration changes18. (iii) The analysis indicates that there are several thermodynamic bottlenecks in the TCA cycle, hampering its full cyclic operation19. (iv) The results suggest that thermodynamic efficiency (see “Enzyme kinetics” section) is not a fundamental cellular objective that determines the concentration state of metabolic networks.Four major findings from the foregoing results are notable: (i) Near-equilibrium reactions from the ABC-based analysis agree with those previously reported for glycolysisTo quantify the degree to which the additional constraints of the ABC-based analysis can reduce the feasible ranges, we compared the feasible ranges of concentrations and transformed Gibbs energy of reactions furnished by the ABC-based analysis and TMFA when glucose was the only carbon source. We found that the upper bounds on metabolite concentrations and transformed Gibbs energy of reactions from TMFA were on average 728% and 11% larger than those from the ABC-based analysis, and the lower bounds were on average 7% and 87% smaller.21. However, the osmotic-pressure differential and membrane potential likely have changed significantly during the course of evolution from ion-permeable porous membranes in protocells to ion-impermeable lipid-bilayers in modern cells22. This forms a rational basis for chronological postdictions concerning the evolution of alternative pathways.By examining individual ABCs in isolation, one can identify the most dominant constraints under a given condition. Such identification may have important evolutionary implications because each of these constraints could have been dominant at different point in time during evolution. For example, thermodynamic laws are believed to have constrained the evolution of biochemical-reaction networks ever since the formation of primitive cells to ensure the energy requirements and spontaneity of prebiotic chemical reactionsE. coli has two major phosphate-transport systems  and Pst (high-affinity). We sought to determine whether any of the ABCs could have been restrictive enough to hinder the operation of the Pit system in phosphate-limited environment, thereby driving the evolution of the Pst system. These transporters, which differ in their stoichiometry .We, thus, asked: Is it possible to achieve cytoplasmic-phosphate concentrations above 1 mM while satisfying all the ABCs? We computed feasible concentration ranges for the reduced network, in which either the nts Fig. c. While E. coli to demonstrate the transition between the Pit and Pst systems in response to phosphate-starvation stress. Clearly, E. coli can remain functional in a wide range of extracellular concentrations, importing phosphate through the Pit system at high rates when it is available in excess. However, when the Pit system reaches its equilibrium at low extracellular concentrations, E. coli exhibits a stress response by taking up phosphate through the Pst system to retain the phosphate influx, albeit at lower rates. Note that, this is not the case for every membrane protein in E. coli. Cytochrome oxidase in the ETC is an example, where the transition from low-affinity (cytochrome-bo3) to high-affinity (cytochrome-bd) system occurs most likely due to kinetic reasons. Because these reactions are both highly energetic in their forward direction  and reaction charge consumption provided by the ABC-based analysis  and phase II map Fig. b using tsis Fig. b.28, we identified 69 differentially expressed genes (>2-fold change 30 min after osmotic upshift) out of 124 genes associated with the reduced network. Among the primary-response genes that are differentially expressed, those associated with the ETC are all downregulated and those with osmoprotectant transporters are upregulated. Although not explicitly included in the reduced network, potassium importers and sodium exporters are also activated. Moreover, several intracellular reactions are among the secondary regulatory targets. For example, glycolytic reactions (except GAPD) and glutamate decarboxylase (GLUDC) (not explicitly included in the reduced network) are activated, while glutamate synthase (GLUSy) and glutamate dehydrogenase (GLUDy) are suppressed.From the RNA-sequencing data of Seo et al.29. This initial response is followed by a rapid accumulation of glutamate—a potassium counterion—through glutamate importers or its biosynthetic pathways30. Charge and pH neutrality are resumed in phase II upon flux regulations targeting the ETC, glycolysis, potassium and sodium transporters, glutamate transporters, glutamate biosynthesis, and glutamate decarboxylase. Here, the apparent inconsistency between the downregulated glutamate biosynthesis, observed from early stages31, and elevated glutamate concentration is indicative of an active glutamate importer, such as glutamate/γ-aminobutyrate antiporter, in phase I.These observations point to possible connections between reaction charge consumption and transcriptional regulatory responses to osmotic stress. These connections arise from cellular requirements to maintain electroneutrality, pH homeostasis, and a steady energy flow by coordinating glycolytic and ETC reactions. Qualitative connections have been drawn between expression data and ion homeostasis in the literature. For example, an inhibited respiration is regarded as an early response to an alkalinized cytoplasm due to a sudden efflux of hydrogen ions that accompanies potassium intake upon osmotic upshiftγ-aminobutyrate antiporter. We found that glutamate accumulation through these biosynthetic pathways does not affect the net cytoplasmic charge. It also lowers the hydrogen-ion concentration of an already alkalinized cytoplasm in phase I. In contrast, glutamate uptake through the glutamate/γ-aminobutyrate antiporter results in an inflow of negative charge, which can counterbalance the accumulated K+ in the cytoplasm during phase I without affecting the pH, demonstrating the osmoregulatory role of glutamate antiporters (see “Glutamate role in osmoregulation” section for a more detailed discussion).To highlight the significant role that charge-balance and ion-binding constraints could play in transcriptional regulatory processes, we examined the regulation of glutamate in response to osmotic stress as a case study. We computed the intrinsic hydrogen and charge consumption (Methods: Eqs.  and 36)36); see c affects equilibrium constants, Gibbs energy of reactions, and reaction rates according to La Chatelier’s principle25. If a reaction produces hydrogen ions   that are associated with the same reactions (except phosphate transporters) in the reduced network as those involved in osmoregulation. However, there are key differences in regulatory responses between the two conditions: Contrary to osmotic stress, NADH dehydrogenase is upregulated, while phosphate and osmoprotectant transporters are downregulated under acid stress. These gene-expression changes are consistent with the regulatory objective to neutralize the acidified cytoplasm by adjusting hydrogen-ion inflow and outflow rates.To better understand how pH-dependent equilibrium shifts can affect transcriptional responses, we sought to identify connections between reaction hydrogen consumptions and gene expressions in phase-I/II RNA-sequencing datarNH∣ > 1 mol-H/mol-rxn) in the hydrogen map  is much smaller than that of the ETC (ΔrNH = 113.78 mmol-H/gDW/h), even though the fluxes  passing through these pathways are comparable. This feature allows the cell to reverse the flux direction through glycolysis in response to other simultaneous stresses  without significant disruption to pH homeostasis (see “Glycolysis and gluconeogenesis in pH homeostasis” section).First, glycolysis is a major regulatory target. Overall, it is upregulated under acid and osmotic stress. Interestingly, it comprises reactions with high intrinsic hydrogen production (GAPD and PFK) and consumption (PYK). The same is true of charge consumption and production. As a result, the net hydrogen consumption of the entire pathway  whether or not the cell is under stress29, so they can effectively attenuate acidification of the cytoplasm. The upper TCA cycle is downregulated, further promoting this mechanism by directing the flux of precursors from glycolysis and lower TCA towards glutamate biosynthesis.Second, the glutamate-dependent system has been reported as the most effective acid-resistance mechanisms, complementing primary responses+ is the main glutamate counterion when the cytoplasm is alkalinized in phase I with GLUDC counterbalancing hydrogen-ion influx through sodium antiporters and osmoprotectant symporters in phase II. In contrast, under acid stress, hydrogen ion becomes one of the main glutamate counterions when the cytoplasm is acidic in phase I with GLUDC, GLUDy, and GLUSy offsetting hydrogen-ion leakage through the membrane in phase II.As previously stated, these pathways are also involved in osmoregulation. However, unlike in pH regulation, GLUDy and GLUSy are both downregulated in response to osmotic stress. This raises a question as to why GLUDC is upregulated during osmoregulation when pH ≳ 7.5. Here, contrasting transcriptional responses to osmotic and acid stresses in relation to hydrogen-ion balance might offer a plausible answer: Under osmotic stress, KThird, the ETC can contribute the most to hydrogen-ion balance in the cell. However, it is directly or indirectly coupled to many crucial cellular processes, such as the membrane potential, ion transport, energy balance, and redox balance. Therefore, regulation strategies that solely target the ETC would partially disrupt essential cellular functions and reduce the robust adaptability of bacteria to extreme and diverse environmental perturbations.36. Biological functions are subject to myriad constraints. The constraints on the function of abiotic and early biotic cells have been the subject of much discussion from Darwin’s warm-pond hypothesis to the role of geothermal vents at the bottom of the ocean. Central to this discussion is the role of abiotic constraints. Given Francois Jacobs’ quote, these constraints are fundamental and affect the function of ancestral and modern cells. The ABCs, thus, apply to functions across the biosphere.“Those [constraints] that operate at any given level are still valid at all more complex levels” — Francois JacobIn this study, we (i) formulated the ABCs, (ii) developed a computational platform, enabling their application to biological systems, (iii) showed that measured quantitative metabolomes satisfy these constraints, (iv) found that they furnish thermodynamic bottlenecks that mirror isotope-labeling experiments, (v) explained the reasons underlying the evolution of multiple phosphate transporters, and (vi) elucidated the constraints that shape transcriptional regulatory responses to external stresses. These results show the broad applications of the ABC-based analysis to understand biological functions and their origins. In fact, the two are inseparable.37. Despite their expanded predictive scope, these approaches still fall short in one key regard: Metabolite concentrations do not enter the formulation through governing equations or constraints grounded in first principles. To fill this gap, we introduced a constraint-based approach to characterize the concentration state of metabolic networks. This approach predicts feasible concentration and Gibbs-energy ranges resulting from the constraints biological networks are subject to.Constraint-based approaches have significantly advanced in recent years, incorporating more detailed molecular descriptions of biological networks17, namely thermodynamic and enzyme-saturation efficiency. We found that biochemical reactions do not generally satisfy these objectives. Specifically, we identified several reactions from the TCA cycle and glycolysis that operate near their equilibrium during the exponential growth phase. Near-equilibrium reactions lower dissipative energy loss at higher protein cost. They also offer functional advantages, enabling rapid flux-direction reversal in energy-metabolism pathways to robustly achieve new steady states upon a wide variety of environmental perturbations. These observations underscore the complex and multifaceted nature of cellular metabolism, which cannot be fully described by single-objective or oversimplified optimality principles38.We showed that the ABCs are consistent with metabolomic data across carbon sources. To investigate whether intracellular concentrations are associated with optimality principles, we studied two cellular objectives that have been previously considered39. The fundamental constraints we implemented in our analysis are particularly relevant to origins-of-life theories. Specifically, the membrane potential, transmembrane-ion gradients, charge balance, and thermodynamic laws are believed to have constrained the most ancient pathways for the formation of small organic molecules21. Several scenarios have been suggested for the origins of primitive life40. For all these theories to be plausible, one must establish a balance between the availability of an energy source that could have existed on the early earth  and the energy required to operate the most energy demanding step  of the proposed chemistry for carbon metabolism 21. These hypotheses can be rigorously formulated and examined within the quantitative framework we developed here to address some of the fundamental questions concerning the emergence of life from prebiotic chemistry.We studied the role of the ABCs in the evolution of phosphate transport systems. These concepts may be applied in a broader context to prebiotic reaction networks to gain insights into the origins and evolution of early metabolism10. Reaction rates that are sensitive to concentration variations can be effectively controlled through allosteric regulation. Hence, near-equilibrium reactions are expected to rely less on transcriptional regulations than highly exergonic ones.Besides characterizing the quantitative metabolome, abiotic constraints shape regulatory responses to stress conditions. We analyzed osmotic- and acid-stress regulation to establish a relationship between transcriptional responses and reaction hydrogen and charge consumption. We argued that the net hydrogen and charge consumption of the electron transport chain, glutamate biosynthesis, and glutamate transporters can effectively counteract the hydrogen-ion and charge imbalances induced by osmotic and acid stresses, providing an explanation for why they are subject to transcriptional regulation. Other reasons for why certain reactions are regulatory targets have been proposed. For example, reactions with a large thermodynamic driving force are believed to be under stricter transcriptional regulatory control than near-equilibrium ones since their rates are less sensitive to concentration perturbations+ balance, osmotic balance, cell structural integrity, gene clusters and physical proximity, ATP and redox balance), and (iii) regulatory targets . We showed several ways, in which flux adjustments to biochemical reactions can modulate critical intracellular variables  to alleviate stress-induced imbalances, providing a more comprehensive description of stress-specific regulatory responses. The gene-expression activity of glycolytic reactions in response to acid stress is an example, where pfkB and pykA are differentially expressed. Although the corresponding reactions have the largest thermodynamic driving force, they also produce and consume the highest amount of H+ among glycolytic reactions. Therefore, their transcriptional regulation is possibly more related to their role in pH homeostasis than their energetics.An observed stress response is a resultant of overlapping allosteric and transcriptional regulatory processes, the organization and mechanism of which depend on: (i) regulation objective , (ii) regulation constraints . The resulting protonation states can, in turn, bind to several metal ions  in separate steps. These charge states, referred to as species, can coexist in the cell with varying distributions depending on the pH and ionic strength of the solution. Several species can be biologically active under physiological conditions, simultaneously participating in biochemical reactions. In general, all the protonation states and their magnesium-bound counterparts are active in the cell, especially, those with phosphate groups . We account for all the active charge states of a given metabolite, incorporating hydrogen-dissociation and magnesium-binding reactions (up to two Mg2+)N is the number of hydrogen dissociation steps and A represents the minimum charge state of a metabolite in the cell with Kk0,, Kk1,, and Kk2, the respective hydrogen-dissociation and magnesium-binding constants. These reactions tend to run faster than enzymatic reaction, always remaining close to their equilibrium . This allows determining the distribution of species independently from the extension of biochemical reactions. Therefore, we simplify our analysis by lumping all the species together, representing them as a single reactant, with respect to which the abiotic constraints are to be expressedMost metabolites behave as weak acids in the cell, donating hydrogen ion to the intracellular fluid in multiple steps  are implicitly accounted for by incorporating them as additional constraints (the evolutionary constraints) into our model. The foregoing fundamental and evolutionary constraints are mathematically expressed asC the vector of cytoplasmic reactant concentrations 53 affecting the membrane potential Δψ. Similarly, the index sets of periplasmic reactants and transmembrane ions are denoted E. coli . However, it is used to evaluate the saturation level of enzyme and how well it describes the functional state of the cell by comparing metabolomic date with Equations –31) rep rep31) rj is obtained from the standard transformed Gibbs energy of formation S. The intrinsic reaction hydrogen consumption ΔrNjH,, magnesium consumption ΔrNjMg,, and charge consumption ΔrZj are similarly defined. Reactions with ΔrZj > 0 and ΔrZj < 0 consume and produce negative charge in the cytoplasm by convention, respectively. In the main text, we generally refer to ΔrZj as the reaction charge consumption, irrespective of its sign. When necessary, we specifically refer to it as charge consumption or charge production to emphasize the sign of ΔrZj. The same conventions apply to ΔrNjH, and ΔrNjMg,. We use the same notation to denote extrinsic reaction hydrogen, magnesium, and charge consumption. These are defined as the product of their intrinsic counterparts and the respective flux. We clarify whichever is relevant in the context by explicitly stating their units .The standard transformed Gibbs energy rZjτjH, the number of translocated hydrogen ions in reaction j, where τjH, = 0 for intracellular reactions, τjH, > 0 if hydrogen ion is translocated from the periplasm to cytoplasm, and τjH, < 0 if hydrogen ion is translocated from the cytoplasm to periplasm. Exporters are thermodynamically spontaneous in the direction, where reactants are transferred from the cytoplasm to periplasm, and importers are thermodynamically spontaneous in the opposite direction. Note that, rZj does not affect the overall charge balance of the cytoplasmic fluid for intracellular reactions. However, for transport reactions, it measures the net negative charge flowing into or out of the cell.Since biochemical reactions involve transformations between reactants with multiple charge states that exchange ions with the cytoplasmic and periplasmic fluids, they generally do not balance charge, hydrogen, and magnesium ions. Indeed, the reaction charge, hydrogen, and magnesium consumption discussed above are defined to quantify this property. In the following discussion, we make these definitions more precise. Starting with charge consumption, we introduce three components for ΔrZj and ΔrNjH, must be accounted for: While the goal of ΔrZj is to capture how biochemical reactions affect reactant-cytoplasmic fluid charge transfer and the overall charge balance of the cell, ΔrNjH, is defined to measure the contribution of a reaction to pHc. This is based on the assumption that maintaining a near-neutral pHc is a more essential constraint for the operation of biological networks than the overall hydrogen balance of the cell. Accordingly, reaction hydrogen consumption is defined by two componentsSw,j the stoichiometric coefficient of water in reaction j (see “Standard transformed Gibbs energy of reaction” section). As with charge consumption, hydrogen-ion exchanges between reactants and water is assumed to occur on the product side of transport reactions in Eq. , th, th32), mentclass2pt{minimCc a subvector of C corresponding to σ(Ci) and reaction energies Pj. Here, we first identify an interior point q by solving a parametric optimization problem .We define the CSS as a subset of the concentration space, where all the biophysical constraint are satisfied:{Eqs}}.\ \!-\!31)nts Eqs.  and the nts Eqs. lem (Eq. ) that maCs: = ΔΠ/RT. Here, x: = Cc/Ct,c is the vector of cytoplasmic mole fractions, the superscript * denotes scaled parameters or scaled variable, Sc is a submatrix of S containing all the rows corresponding to ℓ the number of linear equalities  in Eq.  wit wit31) wm in Eq.  must be 5555Kis, and Kip, are the Michaelis constants of the substrates and products with κ the enzyme-saturation efficiency, ς thermodynamic efficiency, [E] total enzyme concentration, ns the number of substrates, and np the number of products. Note that the specific form of Eqs.  cannot be realized by every reaction in the network because an unbounded increase in all substrate and product concentrations may conflict with other constraints imposed on the network, such as osmotic balance and molecular crowding. Therefore, a more relaxed efficiency criterion is usually used, where a reaction is considered efficient when it is at least half-saturated in one direction 17. Reversible reactions are required to be half-saturated or more in both directions to be considered efficient. For reactant i, we define the maximum Michaelis constantKi,jm, stands for Kis, and Kip, in Eq. zA is the charge of the minimum charge state of K0,0: = 1 for notational convenience. Next, we introduce the binding polynomialWe discussed in previous sections how to represent the abiotic constraints with respect to effective quantities. These were defined as weighted averages of the respective quantity for species constituting a reactant. The mole fractions of species were the weights in these definitions. Here, we show how to compute these mole fractions from binding constants for a reactant mentclass2pt{minim by Eqs. . Finally25.Before proceeding to calculate the formation energy of reactants, we provide useful expressions to ascertain the formation energy of species from that of the minimum charge state. The formation energies of all the charge states arising from Eqs. –3) can  can 3) c25, the standard transformed Gibbs energy of formation of the species F is the Faraday constant, ψ is the external potential field at the point where Gibbs energy is evaluated, and the superscript ∘∘ denotes the reference state of Gibbs energy at infinite dilution of the respective species. The standard transformed Gibbs energy of formation of reactant NH,A and 45. These methods tune their parameters based on expressions that only account for protonation states. Therefore, using these formation energies in Eq. . Th. Th32). E. coli . We. We32). In this section, we present two methods for characterizing the CSS constructed by the abiotic constraints outlined previously. First, we compute global bounds on cytoplasmic concentrations and reaction energies using global optimization techniques to determined their respective biologically feasible ranges. The lower bounds are obtained by solving by Eqs.  and 48)78\documeY space. Second, we compute expectations and standard deviations of concentrations and reaction energies. Given a random variable X are defined asμ is a probability measure of X, encapsulating all the intracellular dynamics and the related parameter uncertainties . This probability measure, which is expected to be condition specific, is poorly understood in biological systems. Without any information about the probability measure for the organism of interest, the most natural choice for μ is the volume measure. However, as previously stated, Y space, we first describe briefly the mathematical formulation of the CSS in this space.In the concentration space, the feasible concentration ranges can span several orders of magnitude possibly over a disconnected CSS. Therefore, it is more convenient to perform global optimization computations in the n − ℓ)-dimensional manifold in the Y space defined by the linear equalities in Eq.  without reference to the space they were associated with. However, in this section, the components of vectors and covector are denoted by superscripts and subscripts, which are represented by a row and column vectors in matrix form, respectively. The same convention applies in general to covariant and contravariant components of tensors. We also adopt the Einstein summation rule, where repeating a dummy index as a superscript and subscript implies summation over an appropriate range of the index. Assuming that A has a full rank  = ℓ with ℓ < n), we havey on 56. In matrix form, the derivative of φ for A. Let A). Then, φ at the point φ−1. The components of χ can be regarded as the coordinates of φ at the point y. We can now define an induced metric57 for δ is the Kronecker delta tensor, y = ι(q), and * is the derivative of ι, furnishing Let s in Eq.  and \docY space. We generate a one-parameter family of interior points by solvingsj) is the Chebyshev center  of the polyhedron defined by the thermodynamic constraints in the Y space that is restricted to w > 0, the objective function identifies an interior point of this polyhedron that is maximally distanced from all the thermodynamic constraints with respect to the second norm in the Y space, while avoiding arbitrarily large negative values for y. This provides biologically relevant points inside the CSS.Before generating random curves in rive Eq.  for \docy. Here, we outline a computationally tractable technique. First, a vector u = uk∂/∂χk is generated in χk associated with the coordinate chart φ discussed before, where the components uk ∈  are random numbers. The embedding of u in y along the tangent vector 58, Sect. 5.5.3) for Eq.  = y and λ(0) = 0 until one of the thermodynamic constraints is violated. Note that, the constraint y ≤ 0 need not be checked directly because one of the equality constraints in Eq. , a, a\documving Eq.  in the Gmentclass2pt{minimX, defined by Eq.  or K+ from the extracellular environment to modulate its intracellular osmolarity, keeping a fixed osmotic pressure across the cell membrane61. The imbalance caused by these charged solutes can be alleviated by upregulating reactions producing counterions or downregulating those consuming counterions.Under physiological conditions, there is a balance between reactions donating negative charge to , minimally impacting pathways performing other critical cellular functions.To maintain electroneutrality, the cell has many degrees of freedom, as to which reactions to upregulate and which ones to downregulate. Importantly, the robustness of E. coli genome are involved in osmoregulation. Primary transcriptional regulatory targets include potassium transporters 61, osmoprotectant transporters 27, carbon-source transporters 31, sodium transporters 26, glutamate transporter 28, and the ETC 29. Secondary responses affect several intracellular pathways, such as amino-acid biosynthesis, osmoprotectant biosynthesis, central-carbon metabolism, and nucleotide biosynthesis31.Many genes in the rNH ≈ 1 mol-H/mol-rxn and ΔrZ ≈ −1 mol-e/mol-rxn), whereas glutamate antiporters only produce negative charge (ΔrNH ≈ 0 mol-H/mol-rxn and ΔrZ ≈ −1 mol-e/mol-rxn). These features highlight the importance of glutamate antiporters during phase I when the cytoplasmic solution is alkalinized, allowing the cell to rapidly accumulate glutamate and potassium from the extracellular environment, so as to maintain electroneutrality without a significant disruption to pH homeostasis. Therefore, exporting excess glutamate, possibly through mechanosensitive channels 26, when the cell is under no stress could be part of a robust regulatory network in bacteria, enabling them to create an extracellular glutamate pool, which can be used to flexibly handle various stress conditions causing ion imbalances.To elucidate the glutamate-accumulation mechanism by which electroneutrality and pH homeostasis are achieved, we compared the intrinsic hydrogen and charge consumption (see Eqs.  and 36)36)) of trZ (see “Abiotic constraints” section). Recall, ΔrZ reflects the amount of charge exchange between metabolites and the cytoplasmic fluid for intracellular reactions, while it measures the net charge transfer from the periplasm to the cytoplasm for transport reactions. If the overall cytoplasmic electroneutrality is regarded as a more essential osmoregulation objective than balanced intracellular charge exchanges, then it follows from our analysis that glutamate antiporters play a more significant role in glutamate accumulation during osmoregulation than glutamate-biosynthesis pathways—a conclusion supported by differential expression analyses of RNA-sequencing data.Biochemical reactions can affect the cytoplasmic charge in two different ways, both of which are captured by our definition of Δ15. To reliably estimate the metabolic fluxes, we identify the parsimonious solution62 of the resulting FBA model that best matches experimentally measured fluxes14. The parsimonious solution, furnished by minimizing a norm of the flux vector, postulates that the optimal flux state minimizes the total protein cost of the network, assuming that all biochemical reactions have the same protein cost. This objective has been shown to be associated with the flux state of several organisms under various conditions38, and, therefore, is adopted in our study. We formulate the FBA model as a bi-level optimization problem, incorporating the foregoing objectives. To simplify our analysis, we performed several numerical experiments and found that the upper-level objective, measuring the distance between the experimental and predicted fluxes, has the largest sensitivity to the upper bounds on the GLGC and NDPK1 fluxes in our reduced network. Accordingly, we determine the flux state by solvingS is the stoichiometric matrix of iML1515, j, vlb and vub the lower and upper bounds on the flux vector, and θ a vector containing the upper bounds of GLGC and NDPK1. These upper bounds, which are decision variables in the upper level, are linearly expressed in the respective inequality constraints of the lower level. Thus, the lower-level problem of Eq. . Here, we examine this feature in more detail.rNH = −29.08 mmol-H/gDW/h) than glycolysis (ΔrNH = −21.14 mmol-H/gDW/h). This may be attributed to lactate dehydrogenase and lactate exporters, which are active only when pyruvate is the carbon source. These reactions consume hydrogen ion, so they offset the slightly larger hydrogen-ion production of gluconeogenesis.We computed the flux state of the reduced network (see “Flux distribution” section) using glucose or pyruvate as the sole carbon source. When the cell grows on glucose, glycolytic reactions are active. However, when the carbon source is changed to pyruvate, glycolysis is reversed and gluconeogenetic reactions become active. We used the computed flux distributions to estimate the extrinsic hydrogen production of glycolysis and gluconeogenesis and found that the rate of hydrogen production remains almost unchanged when the carbon source is altered  thermodynamic constraints alone and (ii) all the ABCs in Eqs. . As. As14 wh in Eqs. . This isj10, and δj are auxiliary variables introduced into the ABC-based framework to account for these errors.To impose the thermodynamic constraints given by Eq. , we estiInclusion of confidence intervals in the ABC-based analysis relaxes the feasible ranges of metabolite concentrations and transformed Gibbs energy of reactions. Specifically, it increases the upper bounds and decreases the lower bounds. We repeated the computations of the feasible ranges reported in Figs. Further information on research design is available in the Supplementary InformationPeer Review FileDescription of Additional Supplementary FilesSupplementary Data 1Supplementary Data 2Supplementary Data 3Supplementary Data 4Supplementary Data 5Supplementary Code 1Reporting Summary


Dolosigranulum pigrum is a quite recently discovered Gram-positive coccus. It has gained increasing attention due to its negative correlation with Staphylococcus aureus, which is one of the most successful modern pathogens causing severe infections with tremendous morbidity and mortality due to its multiple resistances. As the possible mechanisms behind its inhibition of S. aureus remain unclear, a genome-scale metabolic model (GEM) is of enormous interest and high importance to better study its role in this fight. This article presents the first GEM of D. pigrum, which was curated using automated reconstruction tools and extensive manual curation steps to yield a high-quality GEM. It was evaluated and validated using all currently available experimental data of D. pigrum. With this model, already predicted auxotrophies and biosynthetic pathways could be verified. The model was used to define a minimal medium for further laboratory experiments and to predict various carbon sources’ growth capacities. This model will pave the way to better understand D. pigrum’s role in the fight against S. aureus. Dolosigranulum pigrum is a rare and rather newly identified opportunistic pathogen [Escherichia coli, were already detected in the late 19th century [D. pigrum was first described in 1993 by Aguirre et al. [D. pigrum is a Gram-positive, catalase-negative coccus growing in pairs, tetrads, and clusters [D. pigrum is associated with diseases [pathogen . While o century , D. pigrdiseases ,5,6,7.D. pigrum were determined [D. pigrum is a potential pathogen for humans with exceptional resistance to erythromycin but susceptibility to a wide range of other antimicrobial agents [In 2000, the antimicrobial susceptibility and the sources of 27 clinical isolates of termined . The isol agents .D. pigrum as an opportunistic pathogen to its potential probiotic effect in upper respiratory tract infections in the last years. Together with Corynebacterium pseudodiphteriticum, D. pigrum was identified as the nasopharyngeal species associated with a healthy upper respiratory tract (URT) and resistance to recurrent ear infections [D. pigrum, especially in children [D. pigrum after antibiotic treatment [D. pigrum to antibiotic agents.The focus shifted from fections . Multiplchildren ,17,18,19reatment ,18,20, wreatment . Togethereatment , this miD. pigrum is relevant for the URT and further parts of the respiratory tract. The abundance of D. pigrum is decreased in children with cystic fibrosis (CF) compared to healthy children [D. pigrum seems to produce significantly less biomass than the conventional CF pathogen P. aeruginosa but is crucial for increasing tolerance of the mixed biofilm to most antibiotics [D. pigrum within the microbial communities in patients with CF is currently still not fully understood [children . D. pigribiotics ,23. Howederstood .D. pigrum also plays a pivotal role in the human nasal microbiota [D. pigrum with Streptococcus pneumoniae, it is also negatively associated with Staphylococcus aureus. Approximately one-third of the human population is permanently colonized by S. aureus [D. pigrum as a predictor of the presence or absence of S. aureus [D. pigrum as a potential probiotic due to its inhibiting effects on S. aureus. However, the overall mechanisms behind the inhibition remain unclear. Possible mechanisms include nutrient competition or the excretion of primary or secondary metabolites [As the human nose is part of the upper respiratory tract, crobiota . Additio. aureus . It can . aureus . Its met. aureus . Liu et . aureus . Bruggerabolites .D. pigrum and S. aureus. Currently, 114 GEMs of S. aureus are available [D. pigrum exists. Due to its increasing importance in the community with other microbes, such as S. aureus, S. pneumoniae, or P. aeruginosa, the need for a comprehensive and meaningful GEM is of high interest and high significance.Such hypotheses could be tested using genome-scale metabolic models (GEMs) of the organisms of interest, e.g., vailable , but no D. pigrum and other microbes, its interactions and potential probiotic effect could be elucidated. Such interactions are complex and challenging to understand but vital for successful interventions [With a community model of ventions . Especiaventions ,33. The ventions ,34,35.D. pigrum strain 83VPs-KB5. This high-quality model comprises multiple annotations and extensive manual curation steps. It was evaluated and validated using all publicly available experimental data to this date. With this model, several auxotrophies were confirmed and additional auxotrophies were identified. To facilitate future laboratory experiments, we developed a chemically defined minimal medium with all the nutritional requirements to cultivate D. pigrum. These new findings will pave the way to better understanding D. pigrum’s role in the fight against S. aureus.In this work, we introduce the first genome-scale metabolic model of D. pigrum strain 83VPs-KB5. Based on the latest recommended naming conventions of the community standardization of metabolic models [iDPM21RW. DPM is the species indicator and simultaneously the organism’s prefix in KEGG [D. pigrum comprises 1241 metabolites in 1668 reactions and are encoded by 622 genes. It includes the three compartments cytosol, periplasm, and the extracellular space, which hold 974, 55, and 17 reactions, respectively, excluding transport and exchange reactions. Memote is a metabolic model testing suite that determines for each tested GEM an independent and comparable score within a comprehensive overview. Standardized metabolic model tests and the evaluation of a model’s annotations constitute the score [Memote score of iDPM21RW amounts to 86%. For comparison, the GEM iML1515 of Escherichia coli [Memote score of 91%.The model presented in this article is the first publicly available GEM of c models , this mo in KEGG . The curhe score . The finhia coli , for whihia coli , became The basis for the manual extension was the draft reconstruction automatically curated with CarveMe . It onlyiDPM21RW was evaluated for the production of 15 energy metabolites while no nutrients were available. None of the tested energy metabolites were produced, and thus, the final model does not contain energy-generating cycles. Of the 1499 reactions, 6.23% are blocked reactions, which means that they cannot carry any flux during flux variability analysis (FVA):x. These blocked reactions might be indicators of knowledge gaps.The initial draft reconstruction from CarveMe included only 1499 reactions, 1095 metabolites, and 632 genes. Despite the first impression of a decrease in the number of genes, it needs to be stated that 142 genes were included twice in the initial draft model: once with the prefix G_ and once without this prefix. The duplicated genes were removed, and the 620 genes in the final reconstruction is the number of unique genes. This means that 132 additional genes, 169 reactions, and 146 metabolites were added to the model during the whole manual refinement process. During manual extension based on the KEGG database, 161 reactions, 143 metabolites, and 129 genes were added to the model. An overview of these numbers is given in Memote when looking at the mass and charge balance score: The mass balance score increased from 52.7% to 95.6%, and the charge balance score increased from 43.2% to 93.3%. However, 137 reactions were still mass and/or charge imbalanced, none of which were blocked reactions. With novel insights into metabolites’ protonation statuses, the actual participation of metabolites in these reactions and their accurate stoichiometry, and further manual refinement, this number might be reduced even further.The initial draft model had 858 mass and/or charge imbalanced reactions. After manual refinement of these mass and charge imbalances, more than 82% of the 858 imbalanced reactions were balanced. This increase in balanced reactions is also confirmed by The model comprises annotations to various databases. These annotations were added using ModelPolisher  and exteAdditionally, all genes, metabolites, and reactions were further annotated with a term from the Systems Biology Ontology (SBO) . All metThe model reactions were further annotated using terms from the Evidence and Conclusion Ontology (ECO) ; 38.7% oD. pigrum, five stoichiometric coefficients associated with the macromolecule DNA (deoxyadenosine triphosphate (dATP), deoxythymidine triphosphate (dTTP), deoxycytidine triphosphate (dCTP), deoxyguanosine triphosphate (dGTP), and diphosphate)were updated using the first step of the BOFdat algorithm. In the second step of the BOF dat algorithm, the coefficients of inorganic ions and coenzymes were calculated and updated based on macromolecular weight fractions. Fifteen stoichiometric coefficients associated with coenzymes and inorganic ions were updated, and nine were additionally integrated into the BOF. The coefficients of other macromolecules, such as RNA, proteins, or lipids, could not be updated due to a lack of available experimental data. The same was found for the stoichiometric coefficients of other species-specific metabolic biomass precursors as no required gene essentiality data was available. All metabolites included in the BOF, and their stoichiometric coefficients are listed in the CarveMe creates a general biomass objective function (BOF) during the curation process . This inThe group plugin is available from SBML Level 3 . In totaD. pigrum strains by evaluating their genetic content [After creating and refining a draft reconstruction and its conversion into a mathematical model, the model needs to be verified, evaluated, and validated. In this step, the model-predicted phenotypes are compared with the experimental data . Brugger content . COBRApy content  was usedD. pigrum strains. In our model, growth without methionine supplementation was initially possible, indicating the potential for model adaption and refinement. Nineteen reactions were associated with methionine, which were all carefully checked. We identified and removed four reactions without evidence in KEGG [Brugger et al. identified a methionine auxotrophy in all evaluated  in KEGG , BioCyc  in KEGG , or a si in KEGG . With th in KEGG . An ATP-D. pigrum has a likely auxotrophy for arginine [arginine . We coulFurther auxotrophies for the polyamines putrescine and spermidine were predicted . We coulD. pigrum strain 83VPs-KB5. Thus, the respective reaction was added to the model.The predicted biotin auxotrophy was initially not observed in the model. For that reason, two biosynthesis reactions were removed from the model, both of which did not have gene–protein reaction (GPR) associations. Instead, the biotin energy-coupling factor (ECF) transporter was added. Brugger et al. identified a biotin-protein ligase in two of the eleven investigated strains. We found the gene for the biotin-protein ligase in the genome of + and NADP+ with their respective genes. Only one reaction was adapted, as the described enzyme was reclassified into another Enzyme Commission (EC) number with slightly different reactants. The reaction now additionally requires ATP and water instead of a proton and produces adenosine diphosphate (ADP) and a phosphate.The last predicted auxotrophy pertained to nicotinic acid (niacin) . This auD. pigrum is capable of synthesizing l-glutamine from l-glutamate [l-glutamine. All predicted auxotrophies and biosynthesis are summarized in lutamate . All reqD. pigrum are already reported in the literature [l-alanine, l-aspartate, l-glutamine, glycine, l-serine, l-asparagine, and l-tyrosine could be synthesized de novo in our simulation. For all other amino acids, D. pigrum seems to be dependent on external sources.Several auxotrophies in terature . Thus, wD. pigrum strains using functional genomic predictions [D. pigrum. Our in silico investigations confirmed this finding: only the two reported reactions catalyzed by fumarate-hydratase (FUM) and the TCA-associated dihydrolipoyl dehydrogenase (AKGDH) are present in the model. Those two reactions are illustrated in Besides auxotrophies, Brugger et al. also investigated the carbohydrate metabolism of eleven dictions . They foiDPM21RW does not currently include any V-type ATPase as there is no corresponding reaction in the BiGG Models database [Brugger et al. identified V-type ATPases in all investigated strains, which can hydrolyze but not synthesize ATP . The moddatabase .iDPM21RW does not contain the corresponding reaction BTCOARx, confirming the findings by Brugger et al.The authors investigated anaerobic respiratory reductases and did not identify butyryl-CoA-reductases . iDPM21RiDPM21RW. Additionally, Brugger et al. predicted the presence and absence of various enzymes relevant for homofermentation to lactate. Each enzyme and its corresponding reaction were checked in our model.Further investigations concerned ten reactions from glycolysis, including glucokinase, phosphoglycerate kinase, and pyruvate kinase. All ten reactions were confirmed with D. pigrum and its potential utilization of sialic acids becomes available, the corresponding metabolites and reactions can be included in the model.In the last step, Brugger et al. predicted that putative sialidases utilize sialic acids. Sialic acids comprise a family of monosaccharides with a nine-carbon backbone and significant structural diversity . CurrentD. pigrum was isolated from the sputum, sinuses, the nasopharyngeal tract, blood, and the gastric tract [D. pigrum can grow in these habitats. The growth of iDPM21RW was simulated in chemically defined media, including synthetic nasal medium (SNM) [Vibrio natriegens, with a doubling time of 14.8 min [ic tract . Thus, ium (SNM) , synthetum (SNM) , an adapum (SNM) ,68, and um (SNM) ,70. With14.8 min , resulti14.8 min .D. pigrum is known to grow in the human nose [D. pigrum was tested in this niche. However, without additional metabolites, D. pigrum did not show any growth in a single culture. We first added the already identified amino acids to the medium, for which D. pigrum has auxotrophies: l-isoleucine and l-methionine. Additionally, we identified auxotrophy for meso-2,6-diaminoheptanedioate. This metabolite is required for peptidoglycan metabolism. Despite extensive literature research, including database searches on the KEGG database [man nose . With thman nose , the in database  and BioCdatabase , we coulD. pigrum is also reported to play a role in CF patients, although its role within the microbial community is currently not fully understood [D. pigrum in this synthetic cystic fibrosis medium (SCFM) were evaluated. Similar to the in silico growth of D. pigrum in the SNM, the bacterium did not grow in the SCFM without supplementing additional metabolites. Since we expect the trace elements manganese, zinc, copper, cobalt, and nickel to be contained in the medium even without explicit addition, they are not further examined here. The trace elements were simply added to the medium definition. The other required metabolites were riboflavin, thiamine, nicotinate, 4-aminobenzoate, and, as in the SNM, meso-2,6-diaminoheptanedioate. In their preprint from 2019, Brugger et al. stated that all eleven investigated strains of D. pigrum lacked genes for the biosynthesis of thiamine and the de novo synthesis of niacin/nicotinate/nicotinamide [D. pigrum 83VPs KB was, however, not among the investigated strains. A literature search in several databases, including KEGG [D. pigrum, but no synthesis pathways were available. No significant BLAST hits were detected for the enzyme aminodeoxychorismate lyase, which catalyzes the synthesis of 4-aminobenzoate. After adding the required metabolites to the medium, the growth rate of D. pigrum in SCFM was 0.2824 mmol/(gDW · h).derstood . A chemitinamide . For ribing KEGG  and BioCing KEGG , and BLAing KEGG  and BioCing KEGG , the metD. pigrum was isolated from blood samples and even cultivated in aerobic and anaerobic blood culture bottles [D. pigrum seems to be auxotrophic for those compounds. The in silico simulations predicted a realistic growth rate of 1.908 mmol/(gDW · h) with these metabolites. bottles ,8. A che bottles . This me bottles . For theD. pigrum can grow anaerobically in blood cultures. Despite diverse approaches, we could not yet simulate these conditions in our in silico model. There is still much to discover about D. pigrum, and with additional information and laboratory experiments, the model could be extended to simulate anaerobic growth in blood cultures.As stated above, D. pigrum was simulated in the gastrointestinal tract. A defined medium of the European diet from the Virtual Metabolic Human (VMH) database was used for this purpose [The growth of  purpose ,70. As iD. pigrum’s growth behavior and the investigated auxotrophies indicate specific requirements for its environment and successful colonization. To obtain a detailed picture of all environmental requirements for successful growth, we defined a minimal medium for the growth of D. pigrum with the help of iDPM21RW , riboflavin (vitamin B2), and niacin (vitamin B3) are also required to enable growth. 4-aminobenzoate was already mentioned several times to be crucial for D. pigrum’s growth. For this reason, it was also included in the minimal medium. The same was found for meso-2,6-diaminoheptanedioate, which was also added to the minimal medium definition. Finally, oxygen is also required for the growth simulations, as anaerobic growth is not yet enabled. Within this minimal medium, the simulated growth rate amounts to 0.2784 mmol/(gDW · h).The previous analysis of iDPM21RW . This miiDPM21RW  and 13 tD. pigrum. The previous analysis confirmed several auxotrophies and biosynthetic capacities. To further evaluate the metabolic capabilities, the growth on different carbon sources within the previously defined minimal medium was evaluated. The uptake rate of each tested carbon source was set to 10 mmol/(gDW · h). The available mono-, di-, and trisaccharides were tested as sole carbon sources, as seen in Little is known about D. pigrum’s metabolism was drawn using Escher [A comprehensive map of g Escher . Since aiDPM21RW: the first genome-scale metabolic model of Dolosigranulum pigrum. The basis for the manual extension was the draft reconstruction automatically curated with CarveMe [In this work, we generated  CarveMe .iDPM21RW further. This procedure, however, can be challenging because identifier mapping still holds several difficulties. For this purpose, correct and extensive annotations are indispensable. During curation, we put particular focus on the annotations of reactions, metabolites, and genes. Extensive annotations can hold cross-references to other databases, which facilitates the comparability and interoperability of iDPM21RW with models from other databases.Models curated by ModelSEED and gapseq could be used to extend the already existing model D. pigrum. Reaction or metabolite identifiers are often from different databases, and as already mentioned, mapping is challenging. Strain-specific gene identifiers are, however, sometimes more comfortable to map with the corresponding gene and protein annotation files, and the locus-tag information included. This simplifies model comparisons on gene level.ModelPolisher annotates model instances, such as reactions, metabolites, or compartments but not the genes because they are organism- or even strain-specific. Therefore, the manual addition of gene annotations was required. This was a challenging step because the gene annotations should be strain-specific KEGG identifiers. A direct mapping between the NCBI protein identifiers and the KEGG identifiers was not possible since the NCBI protein identifiers often corresponded to so-called “MULTISPECIES” entries that are not uniquely associated with identifiers.org (accessed on 7 April 2021) [We added cross-references to several other databases and Systems Biology Ontology(SBO) and Evidence and Conclusion Ontology (ECO) terms. ECO terms  provide il 2021) . Each reThe biomass objective function (BOF) was improved using the only available omics data, namely genomics. No transcriptomics, proteomics, or lipidomics data are available, which could be used to further improve the BOF and the model itself by adding detected metabolites, reactions, and genes.D. pigrum. Brugger et al. predicted that no tricarboxylic acid ( TCA) cycle is present [D. pigrum has several auxotrophies, especially for amino acids, resulting from the lacking TCA cycle. D. pigrum is not the only microbe missing parts of the TCA cycle. A large number of bacteria are reported to have incomplete or unusual TCA cycles [D. pigrum. Biochemical experiments are required to either confirm the missing TCA cycle or refine the model by adding newly identified reactions.Multiple auxotrophies are reported in  present . The TCA present . Thus, iA cycles ,77. ThisA cycles . Howeverl-arginine and l-methionine in Escherichia coli [D. pigrum already harbors auxotrophies. Additionally, D. pigrum seems to be auxotrophic for the vitamins thiamine (vitamin B1), riboflavin (vitamin B2), and niacin (vitamin B3). Vitamin B1 has importance for primary carbohydrate and amino acid metabolism [9) [D. pigrum, one could assume that it is also dependent on uptake of the reported B-vitamins. Biochemical experiments are required to confirm all reported auxotrophies.Further auxotrophies concerned polyamines and vitamins. The polyamines spermidine and putrescine are synthesized from hia coli , for whitabolism . Our analism [9)  and, thulism [9) . As thesD. pigrum has difficulties growing on certain media. The synthetic nasal medium (SNM) and synthetic cystic fibrosis medium (SCFM) mimic two niches, where D. pigrum is observed. These habitats, however, are relatively low in nutrient supply. For that reason, metabolites need to be added to the medium definition to enable growth in silico. However, one needs to keep in mind that only single-culture in silico experiments were conducted, combined with in vivo observations. Additional single-culture in vitro growth experiments and coculture in silico experiments might clarify the role of the added metabolites. Sokolovskaya et al. have shown that microbial communities share vitamins. They showed that various mutualisms have evolved between organisms to import and deliver variants of cobamides, including vitamin B12 [Having discussed the multiple auxotrophies, it seems apparent that amin B12 . It needComparing the growth rates between the in silico simulations in the SNM and SCFM to the blood and the gastrointestinal medium, one can observe an increased growth rate for the latter two media. This observation seems reasonable, as the blood and the gastrointestinal medium are rich in nutrients that can be taken up and metabolized compared to the media SNM and SCFM.iDPM21RW, we were able to confirm predicted auxotrophies and growth behaviors. Laboratory and biochemical experiments as well as additional omics data can be used to further refine this first-time genome-scale metabolic model of Dolosigranulum pigrum. This model will pave the way to better understand its metabolism and its interaction and extrusion of the human pathogen Staphylococcus aureus.With our high-quality model, Dolosigranulum pigrum was initially curated using an automated reconstruction tool. Subsequent automated and manual refinement lead to the first genome-scale metabolic model (GEM) of D. pigrum.The first draft reconstruction of Several tools were used for the draft reconstruction and validation, as explained subsequently.D. pigrum strain 83VPs-KB5. This strain was chosen, as its NCBI assembly level is the only complete genome assembly of D. pigrum. Additionally, this strain is the only D. pigrum strain in the KEGG database [D. pigrum in SBML Level 3 Version 1 format [CarveMe is a fast and automated reconstruction tool for curating genome-scale metabolic models of microbial species and communities . It was database . The cod1 format  was curaSubsequently, the ModelPolisher version 2.0.1 was used to annotate the initial draft reconstruction extensively . ModelPoMemote determines for each tested GEM an independent and comparable score within a comprehensive overview. Standardized metabolic model tests and the evaluation of a model’s annotations constitute the score. Well-annotated and consistent models have a high Memote score [D. pigrum model was closely monitored by determining the Memote score in each iteration. Memote was used in its command line version.The metabolic model testing suite, te score . Each imAfter the initial draft was curated and annotated, manual refinement steps followed. All manual steps were conducted using COBRApy  and libSThe chemical formula and charge were missing for 65 of the metabolites. They were retrieved from the BiGG Models database , added tD. pigrum genes were identified. These locus tags are also used in the KEGG database [The ModelPolisher added annotations for all model instances except for the genes. To this point, only the NCBI protein accession numbers from the CDS file were included in the model. A BLAST  search wdatabase . All addD. pigrum strain 83VPs KB5 can be found in the KEGG database [Information about database . The prel-glutamate as well as the proton exchange between cytosol and periplasm. For each metabolite, a dissipation reaction was defined based on Fritzemeier et al. After constraining all uptake reactions to zero, the 15 dissipation reactions were maximized.GEMs can contain so-called energy-generating cycles. These cycles are thermodynamically impossible since models with such cycles can charge energy metabolites without nutrient consumption . FritzemMemote assesses the annotation of model instances with Systems Biology Ontology (SBO) terms [O) terms . SBO terO) terms .Escherichia coli [D. pigrum reconstruction, BOFdat was used [D. pigrum, its genomic DNA sequence was used as input in the first step. Furthermore, parameters for the dry weight composition are required. Since, at the time of writing, no information about the dry weight composition of D. pigrum was available, these parameters were chosen as suggested in the BOFdat documentation. With the DNA sequence and the dry weight composition, the stoichiometric coefficients of the DNA nucleotides deoxyadenosine triphosphate (dATP), deoxythymidine triphosphate (dTTP), deoxyguanosine triphosphate (dGTP), and deoxycytidine triphosphate (dCTP) as well as for diphosphate (ppi) were determined and updated in the BOF. At the time of writing, no transcriptomic, proteomic, or lipidomic data are publicly available. Therefore, the RNA, protein, and lipid macromolecules’ coefficients could not be refined within this work.CarveMe adds a universal biomass equation to the carved model. However, this equation was adapted from the biomass composition of hia coli  to a unihia coli ,89. To fwas used . BOFdat After determining the stoichiometric coefficients of the macromolecules, the stoichiometric coefficients of the inorganic ions and coenzymes followed. For this step, the BOFdat script was adapted to run in the latest Python version. All inorganic ions or coenzymes were either added to the BOF, or their stoichiometric coefficients were updated.Experimental gene essentiality data are required for the inclusion and update of additional species-specific metabolic biomass precursors in step (iii). This step aims to identify condition- and species-specific metabolic end goals. As gene essentiality data are also not publicly available at the time of writing, this step was skipped.The Evidence and Conclusion Ontology (ECO) comprises classes and terms describing different evidence and assertion methods. These terms capture, e.g., the type of evidence that a gene product or a reaction has. ECO terms are helpful for quality control of a model. For every reaction in the model, the GPR association was extracted. All reactions without a GPR were assigned the ECO term ECO:0000001. This term is defined as an inference from background scientific knowledge. For all remaining genes from the GPRs, the UniProt database  was consAll ECO terms were added as annotations with the biological qualifier type BQB_IS_DESCRIBED_BY.CarveMe stores information about annotations and other databases in the SBML notes field. However, this information is better stored in the annotations field. Since CarveMe and ModelPolisher use the BiGG Models database, the same annotation information is stored twice: once in the notes by CarveMe and once in the annotations field by the ModelPolisher. To avoid this redundancy and to decrease the file size, the annotation information was removed from the notes field.With the added annotations, the pathways in which a reaction occurs are included in the model. For every reaction that has an annotated KEGG  ID, the D. pigrum was used and simulated in silico to evaluate and validate iDPM21RW as detailed below.Available knowledge about We mainly used the results from the functional genomic predictions by Brugger et al.  to evaluD. pigrum was considered auxotrophic. If the amino acid could be produced, the amino acid production was set in relation to the sole carbon source (d-glucose). The ATP requirement was calculated by summing up all fluxes of ATP-consuming reactions and by putting them in relation to the amino acid production rate. The CO2 production rate was computed by setting the CO2 transport reaction rate in relation to the amino acid production rate.A sink reaction for every amino acid was added to identify additional auxotrophies. This sink reaction was maximized after closing the respective exchange reaction to limit its availability. The growth rate was fixed to 0.2 mmol/(gDW · h). As a medium, the self-defined minimal medium was used see also . If no aiDPM21RW was further validated by simulating its growth capabilities in four different environments. The first evaluated habitat was the human nose. For this niche, a chemically defined synthetic nasal medium (SNM) is available [D. pigrum is auxotrophic were added as well. As still no growth was possible, we further evaluated and identified missing components until a growth in the defined medium could be simulated.The model vailable ,72. As nThis procedure was repeated for the other three media. The synthetic cystic fibrosis medium (SCFM) mimics the lung of patients with CF and was defined by Palmer et al. . For theD. pigrum holds many requirements for its environment regarding nutrients due to its multiple auxotrophies. We defined a minimal medium specifically for D. pigrum to better cultivate this organism in laboratory settings. For this purpose, we used the SNM medium definition and investigated which metabolites could be removed from the medium while maintaining a realistic growth rate. The uptake rate of each metabolites was set to 10 mmol/(gDW · h). The complete list of minimal medium components is given in D. pigrum on different carbon sources were examined. All available sugar exchange fluxes were extracted from the model and sorted into mono-, di-, and trisaccharides. Each carbon source was tested individually by only enabling the tested carbon source’s exchange reaction and by optimizing the model for growth. Growth was also possible for the available polysaccharides, but these were not further investigated.With the previously defined minimal medium, the in silico growth capabilities of D. pigrum’s metabolism.Escher is a web application for building pathway maps. Reactions, metabolites, and genes can be contextualized within the metabolism of an organism . Besides