Escherichia coli metabolism. In the case of one flux constraint, all feasible optimal flux routes can be derived from elementary flux modes alone. We found up to 120 million of such optimal elementary flux modes. We introduce a new computational method to compute the corner points of the optimal solution space fast and efficiently. Optimal flux routes no longer depend exclusively on elementary flux modes when we impose additional constraints; new optimal metabolic routes arise out of combinations of elementary flux modes. The solution space of feasible metabolic routes shrinks enormously when additional objectives---e.g. those related to pathway expression costs or pathway length---are introduced. In many cases, only a single metabolic route remains that is both feasible and optimal. This paper contributes to reaching a complete topological understanding of the metabolic capacity of organisms in terms of metabolic flux routes, one that is most natural to biochemists and biotechnologists studying and engineering metabolism.High-throughput data generation and genome-scale stoichiometric models have greatly facilitated the comprehensive study of metabolic networks. The computation of all feasible metabolic routes with these models, given stoichiometric, thermodynamic, and steady-state constraints, provides important insights into the metabolic capacities of a cell. How the feasible metabolic routes emerge from the interplay between flux constraints, optimality objectives, and the entire metabolic network of a cell is, however, only partially understood. We show how optimal metabolic routes, resulting from flux balance analysis computations, arise out of elementary flux modes, constraints, and optimization objectives. We illustrate our findings with a genome-scale stoichiometric model of  Escherichia coli metabolism.Organisms depend on huge networks of molecular reactions for environmental sensing, information integration, gene expression, and metabolism. The discovery of general principles of network behavior is a major ambition of systems biology and of great interest to biotechnology and medicine. We present a computational tool that calculates all optimal states of metabolism in terms of pathways, which is arguably the most intuitive and preferred approach to characterize whole-cell metabolism. We show how the space of all feasible flux distributions can be compactly described in terms of a unique set of minimal and feasible pathways, given realistic stoichiometric, thermodynamic, and optimization-objective constraints. This description clarifies the interplay between flux constraints and optimization objectives. We explain why some fluxes are variable and cross-correlate within the solution space while others do not and how multi-objective optimization shrinks the solution space. We illustrate our findings with a toy metabolic model to explain the main insights and apply it to a genome-scale stoichiometric model of  Research in biotechnology and medicine benefits from understanding the metabolic capacity of organisms, including their sensitivities to genetic and environmental changes. Genome-scale stoichiometric models of metabolism , 2 and tThe most common constraint-based modeling method is Flux Balance Analysis (FBA) , 12, whiAnalyzing the solution space and optimizing secondary objectives requires adequate mathematical and computations methods. Several approaches were proposed to give insight into the geometry of the optimal solution space , 25–28, Characterization of the optimal solution space provides valuable insight into how our limited knowledge of constraints affects the prediction of a metabolic state of an organism. The recently developed method, CoPE-FBA (Comprehensive Polyhedron Enumeration FBA) , enumeraEscherichia coli metabolism. Enumerating all non-decomposable flux routes in the optimum requires a more efficient computational method, which we also present in the Methods section of this work. This results in CoPE-FBA 2.0, our tool of choice for analyzing the optimal solution space in terms of network topology.We aim to obtain a better understanding of the interplay between constraints, objectives, and optimality for genome-scale stoichiometric models. We uniquely characterize the optimal solution space by adjusting CoPE-FBA to split each reversible reaction into two irreversible reactions; this yields all non-decomposable flux routes in the optimum. We start by illustrating the differences between the CoPE-FBA outcomes of metabolic models with and without reversible-reaction splitting. Next, we explain the relationship between these vertices and elementary flux modes (EFMs) with an optimal substrate-product yield. Finally, we show that secondary objectives typically collapse the optimal solution space to a unique solution (a vertex) or to a small set of vertices, using the iAF1260 genome-scale model of We developed the toy network shown in Zobj. To constrain the solution space we used one inequality constraint, J1 ≤ 2. Throughout this work, we call this type of  constraint a restricting non-zero flux constraint. The resulting FBA is formulated as the linear program:NJ = 0 is the steady-state constraint with N as stoichiometric matrix and J as flux vector (or flux pathway). Simple metabolic models can be optimized by hand, but linear programming is required for the solution of any realistic genome-scale model. FBA optimization confirmed that, for this set of capacity constraints, maximization of our objective function gives J18 = 1.For our FBA model, we selected maximization of the flux through reaction R18 as our objective function, J18 = 1, i.e. our FBA model is underdetermined. We can describe the optimal solution space with the Minkowski sum , see Rays are irreversible  cycles or input-output pathways. Our toy model does not contain a ray. If at least one of the reactions R2, R3 or R4 would have been irreversible, {R2–R4} would have been a ray .Vertices are the corner points of the FBA polyhedron—the solution space of optimal flux distributions—nd therefore they cannot be represented as a convex combination of other optimal flux pathways (they are non-decomposable). Convex combinations of neighboring vertices form the facets—“edges”—of this polyhedron. Our toy model contains four vertices termed V1–V4 . We can Vertices originate from combinations of alternative flux distributions in CoPE-FBA subnetworks, quickly leading to a combinatorial explosion . In the The representation of the network in its current form—where reversible reactions are not split into two irreversible reactions—complicates the characterization of the optimal solution space; not all non-decomposable optimal pathways are vertices and the set of vertices is not unique. This set of vertices corresponds to the minimal generating set of the optimal solution space, a well-known concept in EFM analysis . For ourIf there is only one upper bound (as in the toy model), all non-decomposable optimal pathways are instances of the optimal-yield EFMs. EFM analysis showed that our toy model has thirteen EFMs of which twelve are operational modes that produce Y with an optimal yield see also .. The reMetabolic models usually contain many sub-optimal modes—modes with a lower yield—or non-operational modes—modes that cannot produce any objective flux. Our toy network was designed to not contain suboptimal operational modes. The non-operational mode is the lineality shown in The EFM analysis further showed that we can describe the optimal solution space with different sets of vertices. For instance, CoPE-FBA gave that {R2} was part of each vertex and {R3, R4} was only part of a lineality. We can reverse this situation by making {R2} part of the lineality and {R3, R4} part of each vertex, hence this decomposition is not unique.To solve the issues with uniqueness and completeness, we exploited an existing technique in the field of EFM analysis: Splitting reversible reactions into separate forward and backward reactions , 32. In For our toy model, each optimal-yield EFM now has a corresponding vertex ., i.e. tsingle non-zero restricting flux constraint  effectively removes a reaction from the system. The set of optimal-yield EFMs still corresponds to the set of vertices . As an example, removing R15 from our toy network would result in the same set of four optimal-yield EFMs and vertices.J15 ≤ 0.5. With this constraint, J18 = 1 cannot be achieved with EFMs that include reaction R15  in our toy model with: Demanding a flux through a reaction that decreases the substrate-product yield (e.g. ATP maintenance reaction) yields different vertices. An optimal-yield EFM through the demand reaction is then added to each vertex. The number of vertices increases if multiple optimal-yield EFMs coexist through the flux demanding reaction (which will then form another CoPE-FBA subnetwork).PL; see PL from the optimal solution space for one (J1 ≤ 2) and two  restricting flux constraints, which gave a minimal PL of 11 and 12, respectively. Next, we determined the PL for each optimal-yield EFM and vertex of the “non-split” and “split” model  in the optimal state. Therefore, for the optimization of secondary objectives in the Analyzing the effect of linealities and rays is counterintuitive because both linealities and rays represent cycles that catalyze no net conversion. This makes them independent from the chosen growth medium and objective function. However, without splitting, linealities and/or rays can influence secondary objectives when they share reactions with one or more vertices. In this case we can construct non-decomposable optimal flux pathways that are not vertices by taking, for instance, a linear combination of a vertex with a connected lineality. An example is the lineality described by {R2–R4} . Adding PL when more active reactions become inactive than vice versa. A reaction becomes inactive when it goes in different directions with the same flux in alternative flux distributions. When J1 ≤ 2 is the only constraint, a convex combination of alternative flux distributions in {R12–R15} . Theoretically, multiple shortest vertices can co-exist. The fact that only a vertex or several vertices optimize the secondary objective is a specific result for pathway length minimization see also .. For inThe vertices discovered with CoPE-FBA are all possible non-decomposable pathways in the optimal state. For the analyses of optimal flux pathways, we can, therefore, focus solely on vertices. These vertices can be compactly described by a set of subnetworks that describe all the variability in non-decomposable optimal flux pathways.A unique characterization of the optimal solution space.Secondary optimization yields an optimal solution space consisting of one or multiple vertices.Rays no longer signify thermodynamically-infeasible irreversible cycles.Reversible-reaction splitting has many advantages for the characterization of the optimal solution space. We first summarize those advantages before we set out to analyze a genome-scale stoichiometric model. Splitting of the reversible reactions leads to:Typically, splitting yields many more vertices and rays . We identified three different mechanisms that contribute to the increase in vertices: (i) splitting can yield additional CoPE-FBA subnetworks that originate from rays or linealities with a input-output relationship different from zero. An example is the lineality given by {R02–R04}  that is Enumeration of many more vertices requires more computational power, hence we developed a much more efficient method, CoPE-FBA 2.0, for enumeration of the optimal solution space of both toy and genome-scale models, which is described in detail in the Methods section. The enumeration requires now minutes to hours rather than days to weeks to complete.Escherichia coli (E. coli) metabolism [6). Since we also used an ATP maintenance demand constraint of 8.39 mmolgDW−1h−1, our vertices are not instances of EFMs. Without this constraint, all vertices in both the aerobic and anaerobic growth condition are instances of their corresponding EFMs (not shown). We found only a few CoPE-FBA subnetworks which together completely reveal the variability in the vertices. Most reactions are inactive after optimizing the objective function . When multiple proteins were associated to a particular reaction via an OR rule, the minimum, maximum or average was taken  or two subnetworks (aerobic case) explain the main differences in eactions . As a co E. coli , 36. In E. coli iAF1260 model with splitting, secondary optimization reduced the solution space to only one or a few vertices  , offers 6 vertices enumerated for E. coli under aerobic growth conditions originate from eight subnetworks with respectively 6, 3, 5184, 3, 2, 54, 2, 2 vertices. This means that while we determined in total only 5256 vertices (the sum), we actually enumerated 120.932.352 vertices (the multiplication) within 15 minutes on an ordinary computer.Enumerating all non-decomposable flux pathways in the optimum is a very demanding task compared to enumerating only a  subset of these flux pathways; especially for CoPE-FBA as presented by Kelk et al . Therefoonly a single restricting flux constraint. Both restricting and demanding flux constraints modify the  solution space. Typically, the optimization problem remains underdetermined and an optimal solution space will continue to exist. We can get a unique solution by adding additional constraints that concern all flux values in the model (e.g. protein cost constraints). Then, the optimal state is an instance of an optimal-yield EFM if there is only a single restricting flux constraint. Alternatively, the optimal state corresponds to a convex combination of optimal-yield EFMs. For this reason, we can also use CoPE-FBA 2.0 to quickly enumerate all optimal-yield EFMs, which can be useful because enumerating the complete set of EFMs of a genome-scale model is a laborious undertaking [The further development of CoPE-FBA facilitated in achieving a better understanding of how optimal flux pathways resulting from FBA arise out of EFMs, use of constraints, and optimality conditions. We recall that the vertices correspond to optimal-yield EFMs if there is ertaking , 38.PL, will often lead to optimal solution spaces. While these objectives have been used frequently to find more realistic FBA outcomes [PL and PC, optimal solution spaces continue to exist , we would not expect E. coli to exploit the unique optimal solution since the difference between this optimal solution and many suboptimal solutions is almost negligible. We do, however, expect E. coli to exploit the “cheap” reactions that cause the bi- or multimodal distribution of vertex cost. Interestingly, in aerobic conditions, our analysis predicted that all cheap pathways exploit ubiquinone-8 which is also the major electron acceptor in E. coli under these conditions [E. coli would be to minimize PL, many different flux vectors give rise to an optimal or near-optimal solution. The multitude of optimal solutions hinders the construction of a hypothesis about PL from individual reactions. In future research we see as possible application of our method, finding the minimal flux distance between alternative optimal flux vectors in different conditions, to answer questions about how species can adapt to changing conditions.In this research, we further demonstrated the use of CoPE-FBA 2.0 for the nditions , 36. If In conclusion, we present a better understanding of the principles of the optimal solution space and an efficient method to enumerate all non-decomposable flux pathways in this state. This paves the way to answer biological questions about the flexibility of organisms while growing at optimal states in a fast and straightforward manner. This work, therefore, contributes to reaching a topological understanding of metabolic functionality in the optimum in terms of metabolic flux pathways. In the future, the development of graphical maps  can furtm metabolites and r reactions, the m × r stoichiometric coefficients are often represented in the stoichiometric matrix N. The stoichiometric coefficient nij is positive if metabolite i is net produced in reaction j, negative if metabolite i is net consumed in reaction j, and otherwise zero. The representation of a metabolic network in a stoichiometric model is particularly useful for constraint-based modeling techniques like Flux Balance Analysis (FBA). By using a linear programming approach, FBA can optimize (maximize or minimize) an objective function subject to the steady-state constraint, thermodynamic constraints, and capacity constraints:c is a vector of coefficients that represent the contribution of each flux in vector J to the objective function Zobj. Next, NJ = 0 is the steady-state constraint. Finally, Jmin and Jmax specify the minimal and maximal flux values for each reaction. In addition to providing a unique optimal outcome of the objective function, FBA provides a corresponding optimal flux distribution Jopt. Most FBA models are underdetermined systems, and therefore, many corresponding Jopt exist. For more details about FBA, we refer to Orth et al. [For a metabolic network of h et al. .Jopt in terms of vertices, rays, and linealities [φk, φk, and ψk represent the vertices, rays, and linealities, respectively. Additionally, s, t, and u represent the upper boundaries of the sum functions indicating the number of vertices, rays, and linealities, respectively. Furthermore, αk, βk, and γk represent the weighting coefficient that satisfy the following constraints: αk ≥ 0, βk ≥ 0, and γk can take any value. In words, vertices can be summed by a convex combination, rays can be summed as a conical combination, and linealities can be summed as a linear combination.The Minkowski sum given in ealities , 29.JopThis Minkowski sum alters  once we sibility , 40.A is a vector of reactions that form the subnetwork [NA and JA are the stoichiometric matrix and the flux vector of the subnetwork, and d is the fixed input-output relationship of the subnetwork. We can also calculate subnetworks (modules) in a flux space with futile cycles. These subnetworks are called F-modules and can be determined via FluxModules [d ≠ 0F-modules essential for optimality, i.e. d = 0F-modules not essential for optimality, i.e. F-modules not essential for optimality are rays or linealities not connected to optimal flux pathways. An F-module essential for optimality can be a CoPE-FBA subnetwork, a ray or lineality connected to optimal flux pathways, or a combination of those.The set of vertices yields a flux space without futile cycles. CoPE-FBA subnetworks are defined within this flux space and have a fixed input-output relationship, which we can write mathematically as:bnetwork . SubsequxModules . We can Determine F-modules and extract the fixed network. We used a Python implementation of FluxModules to quickly determine the F-modules.d for each F-moduleDetermine . To circumvent numerical issues we used rational FBA  to deteReconstruct F-module models. For each F-module we reconstructed a model that consisted only of the reactions and metabolites of the F-module. We added input and output reactions to fix d of each F-module essential for optimality in the optimal solution space. Dummy species were added both the input and output reaction to guarantee use of both reactions.Perform CoPE-FBA as described in Kelk et al. 2012  for each. Enumeration on each F-module essential for optimality yielded all vertices. F-modules not essential for optimality were enumerated to determine the total number of rays.Reconstruct network vertices. We merged fixed parts and the enumerated vertices for all subnetworks.Kelk et al. 2012  developehttp://memesa-tools.sf.net.Enumerating the optimal solution space via CoPE-FBA 2.0 took minutes to hours rather than days to weeks for the original pipeline developed by Kelk et al. 2012 . The CoPE.coli subnetworks, the input-output relationship was the only constraint. Consequently, each enumerated subnetwork vertex should correspond to an optimal-yield EFM of the subnetwork. We successfully used the rank test [v is an instance of an  EFM. First, we determined the zero indices of v. Second, from the stoichiometric matrix N of the subnetwork we eliminated all columns with a zero index in v to create a submatrix Nnz. Third, we used single value decomposition to determine the rank of Nnz. Last, we used the rank–nullity theorem to determine its nullity  and pathway sum of absolute fluxes (PJ), also pathway cost (PC)—a proxy for the minimization of the ATP utilization in protein synthesis—to reduce the size of the solution space.PL is identical to the number of flux carrying reactions, while the PC is identical to the sum of absolute flux values multiplied with cj, the protein cost for each individual reaction. This cost is the scaled length of the proteins that were associated to this reaction, which we used as a proxy for all costs. In other words, cj < 1 when the associated protein length is smaller than average and vice versa. We set cj = 1 when no information about associated proteins was available. Because multiple proteins can be associated to a particular reaction via AND and OR rules, different definitions of cj were used: maximum, average, minimum, and equal. An AND rule corresponds to taking the sum of protein lengths, while an OR rule corresponds to taking the maximum, average, or minimum. Using equal cost is identical to minimizing the sum of absolute fluxes, a widely-used secondary objective. Taking the maximum, average, minimum, or equal definition of cj did not effect the interpretation of our results.As a secondary objective, we used, in addition to pathway length (2 uptake was 18.5 mmolgDW−1h−1) of iAF1260 was obtained from the BiGG database [mmolgDW−1h−1 and we modified the bounds on the O2 uptake reaction to create specific aerobic (no constraint on O2 uptake) and anaerobic (exchange of O2 set to zero) conditions. In all cases, the model required an ATP maintenance flux of 8.39 mmolgDW−1h−1. The model was edited and prepared for enumeration using PySCeS CBMPy [PL, PJ, and PC) was also done with PySCeS CBMPy. We used a mixed-integer linear program to minimize PL and a linear program to minimize PJ and PC.The aerobic restricted version Click here for additional data file.S1 Fig(PDF)Click here for additional data file.S2 Fig(PDF)Click here for additional data file.S3 Fig(PDF)Click here for additional data file.S4 Fig(PDF)Click here for additional data file.S5 Fig(PDF)Click here for additional data file.S6 Fig(PDF)Click here for additional data file.S7 Fig(PDF)Click here for additional data file.S8 Fig(PDF)Click here for additional data file.S1 Text(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.


Pseudomonas putida is a promising host for the bioproduction of chemicals, but its industrial applications are significantly limited by its obligate aerobic character. The aim of this paper is to empower the anoxic metabolism of wild-type Pseudomonas putida to enable bioproduction anaerobically, with the redox power from a bioelectrochemical system (BES).Pseudomonas putida F1 was able to survive and produce almost exclusively 2–Keto-gluconate from glucose under anoxic conditions due to redox balancing with electron mediators in a BES. 2-Keto-gluconate, a precursor for industrial anti-oxidant production, was produced at an overall carbon yield of over 90 % based on glucose. Seven different mediator compounds were tested, and only those with redox potential above 0.207 V (vs standard hydrogen electrode) showed interaction with the cells. The productivity increased with the increasing redox potential of the mediator, indicating this was a key factor affecting the anoxic production process. P. putida cells survived under anaerobic conditions, and limited biofilm formation could be observed on the anode’s surface. Analysis of the intracellular pools of ATP, ADP and AMP showed that cells had an increased adenylate energy charge suggesting that cells were able to generate energy using the anode as terminal electron acceptor. The analysis of NAD(H) and NADP(H) showed that in the presence of specific extracellular electron acceptors, the NADP(H) pool was more oxidised, while the NAD(H) pool was unchanged. This implies a growth limitation under anaerobic conditions due to a shortage of NADPH and provides a way to limit biomass formation, while allowing cell maintenance and catalysis at high purity and yield.The obligate aerobe For the first time, this study proved the principle that a BES-driven bioconversion of glucose can be achieved for a wild-type obligate aerobe. This non-growth bioconversion was in high yields, high purity and also could deliver the necessary metabolic energy for cell maintenance. By combining this approach with metabolic engineering strategies, this could prove to be a powerful new way to produce bio-chemicals and fuels from renewables in both high yield and high purity.The online version of this article (doi:10.1186/s13068-016-0452-y) contains supplementary material, which is available to authorized users. Contrary to renewable fuels, which have steadily increased their share in the energy sector , bulk anEscherichia coli or baker’s yeast, particular advantages in solvent tolerance  = 0.476 × OD600.The strain used in this study was wild-type as 30 °C . Cell de600 = 0.5 (in log phase) cells were harvested by centrifugation , washed, resuspended in fresh DM9 medium, and then transferred into the main cultivations vessels. Anaerobic tests were done in 150 mL anaerobic culture bottles or BES reactors. Anaerobic conditions throughout the experiments were assured by sparging the culture medium with nitrogen. The anaerobic bottles were inoculated in an anaerobic chamber.Pre-cultures were prepared by picking and transferring of a single colony from a LB plate into baffled shake flasks for aerobic overnight cultivation (~16 h) in an orbital shaking incubator  at 200 rpm and 30 °C. When cell density reached OD2) was used as the anode electrode after pre-treatment with a modified cetyltrimethylammoniumbromide (CTAB) soaking method (ClO4)2, K3[Fe(CN)6] were added (1 mM) as redox mediators to the culture medium. These mediators cover a wide range of electrochemical midpoint potentials and were tested for electrochemical activity in the presence of the microbial cells. Measurements of current production over time (chronoamperometry) were used to monitor the electrocatalytic activity of the microbes. Strictly anaerobic conditions were maintained by flushing sterile nitrogen gas through the reactor headspace at a flow rate of around 30 mL/min. Dissolved oxygen concentration was confirmed to be below detection limit (<15 ppb) using an optical oxygen sensor  in preliminary tests. A condenser cooled with 4 °C H2O was used to reduce water evaporation through the headspace due to the flushing.The double-chamber BESs consisted of a double-jacketed sterilisable glass vessel with a net liquid volume of 350 mL serving as the anodic compartment. The cathodic compartment consisted of a 15 mL glass cannula inserted directly into the anode chamber. A circular cation exchange membrane  was mounted at the bottom of the cannula to guarantee ionic connection between anodic and cathodic electrolytes. Additional file g method . In brie2SO4 at a flow rate of 0.4 mL/min. Glucose was detected using a refractive index detector, while the carboxylates were detected with absorbance at 210 nm. Prior to injection, culture broth was collected by centrifugation at 16,000 g, 4 °C for 10 min, and the supernatant was used for HPLC analysis undiluted.The concentrations of glucose, gluconic acid, 2KGA and acetic acid were analysed using an Agilent 1200 high performance liquid chromatography (HPLC) system and an Agilent Hiplex H column  with guard column . In brief, the column temperature was set to 40 °C, and analytes were eluted isocratically with 14 mM HSamples were taken from the electrochemical reactors between 73 and 100 h when the current reached its peak value. In the controls, samples were taken at the similar time point as above when mediators were fully reduced.g, 4 °C for 2 min. Cell extractions for NAD(P) +/NAD(P)H were performed with a modified fast filtration—freeze/drying process  and multiplied by the number of carbon atoms in the respective compound.The carbon balance was determined using the following equation: 2 could not be quantified because of CO2 evolution being miniscule compared to the rate of N2 flushing of the reactor headspace. However, the formation of acetate from pyruvate by P. putida will coincide with CO2 formation, either due to the activity of the membrane-bound decarboxylating pyruvate dehydrogenase/oxidase (EC 1.2.5.1) or to the activities of other metabolic reactions such as the formation of acetyl-CoA, which can be converted to acetate either through catabolic pathways or through biosynthesis processes. The ratio of CO2 to acetate in all these circumstances will be 1:1. Therefore the CO2 yield was assumed to be equal to the acetate yield, major shortcomings of the carbon balance would then point to high activity of pathways producing CO2, such as the TCA cycle or PPP. All product yield coefficients were converted to specific rates using the average planktonic biomass concentration in the systems. In fact, the contribution to the yields from cells forming biofilm was considered negligible.The production of COP. putida F1 is an obligate aerobe, and no anoxic growth in glucose-based mineral medium without oxygen is observed 6]3−) to ferrocyanide 6]4−) within 55–90 h, as suggested by a change in colour of the solution from yellow to green ([Fe(CN)6]3−) to colourless ([Fe(CN)6]4−). The ability to continuously utilise [Fe(CN)6]3− as an electron acceptor was further tested in the BESs, where electrochemical oxidation of the [Fe(CN)6]4− at the anode allowed constant regeneration of the [Fe(CN)6]3− for microbial metabolism. In the absence of a mediator, P. putida F1 did not transfer electrons to the anode, since no catalytic current was detected when no mediator was added 6]4− quantified by a developed optical method  confirmed electrons were released from P. putida F1 to the anode. This electron flux is indicative of the anoxic catabolism of glucose since this was the only electron donor in the system at sufficiently high concentration to induce a transfer of charge of over 850 °C in 218 h. The anode chamber contained 2.55 mmol glucose, and around 10 mmol electrons were released over the course of the experiment. Providing an external electron sink to the cell in the form of an anode and a mediator molecule enabled the wild-type P. putida F1 to stay metabolically active for over 300 h under anaerobic conditions. The concentration of planktonic cells decreased over time similar to the controls lacking the anode P. putida F1 in the form of electrodes and redox mediators results in production of organic acids, additional experiments were performed with the aims (1) to determine the complete product spectrum and (2) to describe the fermentation kinetics in relation to the redox potential of the mediator, through testing of compounds covering a broad range of redox potentials between approximately −0.4 and +0.4 V.After confirming that providing an extracellular electron sink to Em) of the mediators used in this study. Characteristic CV traces at the scan rate of 50 mV s−1 are reported in Fig. Em values are listed in Table 3, centred at around −0.365 and −0.349 V, respectively, whereas Fe(EDTA), thionine chloride, [Co(bpy)3](ClO4)2 and K3[Fe(CN)6] displayed more positive Em, centred at around 0.078, 0.208, 0.310, and 0.416 V, respectively. These values are in good agreement to those reported previously for the same compounds  thusE. coli and Shewanella oneidensis to shuttle electrons extracellularly by coupling with the respiratory chain using NADH as the electron donor. However, when we added these mediators to the cultures of P. putida F1, no significant current production was observed ]. On the contrary, mediators with redox potentials above 0.207 V, that is thionine chloride, [Co(bpy)3](ClO4)2 and K3[Fe(CN)6], demonstrated the ability to accept electrons from P. putida F1 cells 2 and K3[Fe(CN)6] was analysed in detail. For easier comparison with the produced electrons, concentrations were converted to absolute moles using the respective reactor volumes at each time point. Glucose was converted into three detectable products: 2KGA, gluconic acid and acetic acid with the former being the dominant product 2 where not only a higher amount of gluconic acid was observed in transition, but also a net production remained at the end of the experiment. In the case of the K3[Fe(CN)6]-mediated electron transport, all gluconic acid was consumed in the second half of the fermentation, and acetate production was also higher in this process . For both mediators, it was found that around 90 % of the glucose was converted to 2KGA, while twice as much acetic acid accumulated with K3[Fe(CN)6] compared to [Co(bpy)3](ClO4)2 (Table 3[Fe(CN)6]. While it is not possible to quantify the exact amounts of cells growing on the electrodes, the carbon balance indicated that growth would be minimal, which is also in agreement with our visual observations. Using the average planktonic biomass concentration over the course of the processes it was possible to calculate specific rates (Table 3[Fe(CN)6] was much faster and was characterised by a glucose consumption rate that was 36 % higher compared to [Co(bpy)3](ClO4)2 and the same holds true for the rate of electron production. This rate was positively correlated to the redox potential of the mediators used; the more positive the potential, the faster the production 3](ClO4)2 could trigger electron transfer to the anode more rapidly than K3[Fe(CN)6] in spite of having a lower redox potential than the latter  2 gave a higher value than when K3[Fe(CN)6] was used (Table 3[Fe(CN)6] more electrons are lost. Despite these losses, however, it emerges that a BES can be used to produce oxidised products under oxygen-free conditions at high yield, high purity and with minimal production of biomass, and (as it is the case here) without genetic modifications.The carbon balances closed in both studies Table  under thP. aeruginosa  6] in an anaerobic chamber. The intracellular ATP concentration in the BES was much higher than in the anaerobic conditions without an anode provided as electron acceptor . When ccfu/gCDW , 64 and escribed . These f+/NADH and NADP+/NADPH were shifted towards the oxidised species under all conditions  6], because the small pool size of NADPH can experience a redox shift due to the mediator accepting electrons without a measurable difference in extracellular substrate concentrations.Using existing knowledge of the underlying pathway stoichiometry and the measured rates from the previous sections, it is possible to conduct a flux balance analysis using a simplified model  Fig. . The estion Fig. b. This cP. putida KT2440 has been reported to be between 0.92 mmolATP/(gCDW h) (ClO4)2 and K3[Fe(CN)6], respectively, or 1.5–6.5 % and 4–17 % of NGAM, depending which literature value is assumed. Even if the lower value for NGAM is still an overestimation, it seems that an additional energy production must be present, to explain the ongoing metabolic activity of the cells. Since carbon balances were closed and no other products detectable, this indicates that the cells must be able to generate energy through a process coupled to the electron transport process. Under the common assumption that three protons move through the ATP synthase to generate one ATP (ClO4)2 and K3[Fe(CN)6], respectively, could have been generated. This would bring the total energy available within the range of NGAM, making this scenario much more likely than energy production through acetic acid formation alone. While this is only an estimation, it supports the idea that anodic oxidation of carbohydrates in a BES could also lead to ATP generation in the cells, which in our opinion is a prerequisite for maintaining active bio-catalysts over long periods of time and crucial for the viability of BES applications for bio-production.Using the flux analysis to estimate the rate of ATP synthesis through ATP synthase that could be derived through the available proton gradient shows that 1.2 and 1.3 mmolP. putida F1 was able to perform anoxic metabolism, without the need for metabolic engineering and without the formation of biomass as a substrate draining by-product. The redox power from electrode and redox chemicals drove the carbon flux from glucose to 2-Keto-gluconate with a high yield of over 90 %. A survey of different redox chemicals showed that a redox potential of above 0.207 V was crucial and that reaction rates increased with increasing redox potential. Energy was generated in metabolism, but the cells remained largely unable to fully oxidise the substrates to CO2 despite the intracellular redox co-factors being mainly oxidised. However, the study provides a proof of principle that a BES-driven bioconversion of glucose can achieve high yields, high purity and also deliver necessary energy for cell maintenance, and enables a strict aerobe to catalyse production under oxygen-free conditions for over a week. This opens the route to bi-phasic bio-processes, where the catalyst is grown under aerobic conditions and then used for anaerobic catalysis over long periods of time, without observable growth and hence drain of substrate. Combining this with metabolic engineering strategies could prove to be a powerful new way to produce bio-chemicals from renewable materials.By providing an electrode and redox chemicals as extracellular electron sinks, wild-type


Sinorhizobium meliloti that is integrated with carbon utilization data for 1,500 genes with 192 carbon substrates. Growth of S. meliloti is modelled in three ecological niches  with a focus on the role of each of its three replicons. We observe clear metabolic differences during growth in the tested ecological niches and an overall reprogramming following niche switching. In silico examination of the inferred fitness of gene deletion mutants suggests that secondary replicons evolved to fulfil a specialized function, particularly host-associated niche adaptation. Thus, genes on secondary replicons might potentially be manipulated to promote or suppress host interactions for biotechnological purposes.The genome of about 10% of bacterial species is divided among two or more large chromosome-sized replicons. The contribution of each replicon to the microbial life cycle  remains unclear. Here we report a genome-scale metabolic model of the legume symbiont  The genome of some bacteria consists of two or more chromosomes or replicons. Here, diCenzo et al. integrate genome-scale metabolic modelling and growth data from a collection of mutants of the plant symbiont Sinorhizobium meliloti to estimate the fitness contribution of each replicon in three environments. Sinorhizobium and Rhizobium), plant pathogens , and animal and human pathogens . As the bacterial genome is non-randomly organized634891011The last years have witnessed a growing attention towards the ecological and evolutionary implication of the multiple replicon bacterial genome1231Sinorhizobium meliloti is a N2-fixing endosymbiont of legume species that has recently become a model organism for the study of bacterial multipartite genome function and evolution. All sequenced S. meliloti genomes contain at least three large replicons , with some strains hosting additional small accessory plasmids313S. meliloti experiences a complex life cycle and successfully colonizes three distinct niches. Two of these niches are bulk soil and rhizosphere soil , which are quite different environments, with the rhizosphere generally considered to be a nutritionally richer environment due to plant root exudatesS. meliloti is the legume root nodule. S. meliloti can induce root nodule formation in certain legumes and within nodules the bacteria differentiate into N2-fixing bacteroids. Manipulation and optimization of this agriculturally and ecologically important symbiosis is an ultimate goal of the rhizobial research community1617S. meliloti genome, flux balance analysis (FBA), and growth phenotype data for 11 large-scale S. meliloti deletion mutants to examine the metabolic changes accompanying the shifts between bulk soil, rhizosphere and nodule environments. We use an in silico approach to predict the phenotypes resulting from the deletion of 1,575 S. meliloti metabolic genes, estimate the fitness contribution of each replicon within each environment, and thus provide insight into the evolution of multipartite genomes.Here we combine a genome-scale metabolic network reconstruction of the in silico representation of the metabolism of S. meliloti was developed, and the final model that was termed iGD1575 contained 1,575 genes, 1,825 reactions and 1,579 metabolites. iGD1575 accounts for 25.4% of the protein-coding genes in the S. meliloti genome, and the other main features of the model are listed in 12S. meliloti small metabolic model192021As described in the S. meliloti transports glucose into the cell at a rate of 2.41 mmol h−1 per g cellular dry weight. When glucose is provided to the iGD1575 model as the sole carbon source at the experimentally determined rate, a specific growth rate of 0.325 h−1 is predicted, which is consistent with our experimentally derived growth rate of 0.313 h−1 (s.d. 0.002) for S. meliloti grown with glucose. Similarly, it has been shownS. meliloti transports succinate into the cell at a rate of 6.252 mmol h−1 per g protein. Providing succinate as the sole source of carbon to iGD1575 at the experimentally determined value led to a predicted specific growth rate of 0.279 h−1, similar to the experimentally derived growth rate of 0.254 h−1 (s.d. 0.025) for S. meliloti grown with succinate. Measuring the amount of phosphate remaining in the spent growth media following growth of S. meliloti indicated that 63.7 (s.d. 6.7) and 39.8 μM (s.d. 1.5) of phosphate was used per mM of glucose and succinate, respectively. These experimental values are relatively consistent with the phosphate usage values predicted by iGD1575 of 72.7 and 48.5 μM per mM of glucose and succinate, respectively.Previous workS. meliloti; however, flux measurements for 22 central carbon metabolic reactions when S. meliloti is grown with glucose as the sole source of carbon have been reported by Fuhrer et al.S. meliloti was only 0.17 h−1 in the study by Fuhrer et al., indicating that S. meliloti was grown in sub-optimal conditions that presumably effected the flux distribution. Nevertheless, if the flux through these 22 central carbon metabolic reactions in iGD1575 was set to that as experimentally determined by Fuhrer et al., the predicted specific growth rate was reduced to 0.159 h−1, in line with the 0.17 h−1 reported by Fuhrer et al. The good relationship between flux distribution and specific growth rate, and the strong ability of iGD1575 to predict growth rate and phosphate usage when grown with glucose or succinate, suggest that the flux distributions predicted by iGD1575 should represent quantitatively accurate estimations.Little experimental flux data has been reported for S. meliloti to grow with various carbon and nitrogen sources has been well studied by means of the Phenotype MicroArray (Biolog) technology42526S. meliloti to produce, or not produce, biomass  experimentally observed phenotypes for compounds that support growth of iGD1575 were replicated in silico. Some of the discrepancies between the experimental and in silico data represent gaps in our knowledge of catabolic pathways in S. meliloti, while other phenotypes may occur for non-metabolic reasons and therefore not give a phenotype in silico. For example, the S. meliloti deletion mutant ΔB154 is more sensitive to cobalt chelation than the wild typeL-histidine or D-glucosamine may simply reflect cobalt chelation33Carbon utilization phenotypes for a subset of large-scale pSymB deletion mutantsobserved . In siliS. meliloti genome annotationsmb20488. A second example is D-galactosamine, which, as elaborated on in In addition to model refinement, integrating the mutant phenotype data with iGD1575, the DuctApe softwareS. meliloti during transition between bulk soil, the rhizosphere and the nodule were modelled using in silico representations of the nutritional composition of each environment. These took into account the relative ratios of each component in the different environments and the development of these environments are described in the 2-fixing symbiosis as defined previouslyThe metabolic shifts experienced by 10 of the absolute flux through a given reaction that was active in both environments =0.09; P value<0.01 using a Spearman's Rank Order Correlation test, R2=0.95; The metabolic network appears globally similar in both the bulk soil and rhizosphere environments , althougP value <0.01 using a Pearson's χ2-test) were seen in the COG annotations of the genes associated with reactions whose flux or fitness contribution was dependent on the soil environment. This indicated that the reactions important in the rhizosphere were biologically similar to, but functionally distinct from, the reactions important in bulk soil. However, coenzyme transport and metabolism (COG H), and cell wall, membrane and envelope biogenesis (COG M) were more important in the rhizosphere than in the bulk soil. This possibly reflects different coenzyme requirements for the metabolic pathways active in the two environments and the increased succinoglycan content of S. meliloti in the rhizosphere that is necessary to facilitate root biofilm formation. Lipid transport and metabolism (COG I) was over-represented in the bulk soil, perhaps due to the over-abundance of ketogenic amino acids in bulk soil. At the pathway level, only a few changes could not be explained by differences in the nutritional composition and biomass objective functions =1.48). Approximately half of the common flux carrying reactions displayed at least 50% more flux in one of the environments and a further 12% switched directions. In addition, little correlation was observed between the fitness effects of individual reaction deletions in the two environments , and coenzyme transport and metabolism (COG H). On the other hand, the lack of growth of the differentiated bacteroids not surprisingly rendered biomass component biosynthesis  less important. A few additional interesting observations were noted by looking at pathway level changes . The Krein silico single and double gene deletion analyses to determine the contribution of the three S. meliloti replicons to the overall fitness of S. meliloti in each of the tested environments  contributing to fitness in bulk soil that originated on pSymB. Similarly, transcriptomics work with the pea symbiont, Rhizobium leguminosarum, indicated that one of its plasmids (pRL8) is over-represented in genes upregulated specifically in the pea rhizosphereSimilar to the chromosome and consistent with the global R. leguminosarum in the rhizosphere52Even though these data clearly illustrated that the metabolic capabilities encoded by pSymB are either specific or more important for growth in the rhizosphere than bulk soil, we believe that the observed bias is an under-representation of the actual situation. The succinoglycan biosynthetic genes are classified as essential in both the bulk soil and the rhizosphere due to their inclusion in the biomass objective functions; however, they are not truly essential but likely have greater importance in the rhizosphere through facilitating biofilm formation on the legume root. Furthermore, a more complete formulation of the bulk soil and rhizosphere environment may exaggerate the bias. For example, protocatechuate was not included due to a lack of information on its abundance. However, recent work showed that protocatechuate metabolism improved fitness of S. meliloti nodule isolatesIn contrast with the other replicons, the pSymA megaplasmid contributed no fitness-promoting genes . No phen6The biases observed for the importance of each replicon in the different environments were confirmed via random permutations, testing up to 1,000 different nutritional compositions as described in detail in S. melilotiFinally, a comparison of genes differentially contributing to growth in each environment with a recent regulon analysis in 2-fixing endosymbiont S. meliloti, and modelled the metabolic changes associated with niche transition. The switch from bulk soil to the rhizosphere was accompanied by a metabolic fine-tuning, primarily through changes in carbon metabolism and amino-acid biosynthesis. In contrast, moving from the rhizosphere to the nodule involved a comprehensive metabolic reprogramming. This involved essentially shutting off production of all biomass compounds and instead synthesizing co-factors necessary for a successful symbiosis, maximizing ATP production and fixing atmospheric nitrogen.We have completed a comprehensive, manually and experimentally curated genome-scale metabolic reconstruction of a model multipartite genome of the Nin silico fitness contributions of genes included in iGD1575 revealed that the chromosome is not metabolically specialized for a particular niche, but instead encodes the core metabolic machinery that enables growth of S. meliloti as a free-living microbe. In contrast, the evidence indicated that pSymB is metabolically specialized for the rhizosphere, helping S. meliloti to adapt to this environment and utilize the newly available substrates. The analysis failed to detect any environment where pSymA contributed to improved fitness, but it was seen that pSymA functions were solely relevant to the symbiotic process. Concerning multipartite genome evolution, these observations are consistent with an evolutionary scenario where (1) the gain of pSymB first significantly improved the ability of S. meliloti to colonize the rhizosphere as suggested previously42-fixing symbiosis.The analysis of the S. meliloti may be generalizable to other bacteria with a multipartite genome that interact with a eukaryotic host. We hypothesize that secondary replicons might facilitate the start of a host interaction; this is the case for the large Escherichia coli virulence plasmidsWe speculate that our observations here with S. meliloti aimed at its biotechnological exploitation in the context of agricultural procedures.The modelling framework we have developed for this work can be adapted to study other types of biological association  and the metabolic reprogramming that is needed to operate the switch towards a novel ecological niche. Moreover, by demonstrating here that chromids and megaplasmids carry genes that primarily improve fitness in a specific niche, such as host interaction, this work illustrates secondary replicons as a rich reservoir of genes that have potential in synthetic biology applications. Finally, we anticipate that the iGD1575 model herein reconstructed will represent a valuable platform for future manipulations of www.kbase.us) and then manually and experimentally validated and expanded based on published data as described in the S. meliloti model was termed iGD1575 in accordance with the nomenclature standardhttp://sbml.org/Facilities/Validator/), and is available as www.gurobi.com). A detailed description of the modelling procedure is reported in the in silico large-scale S. meliloti gene deletion mutants in iGD1575, identification of essential model genes was performed as described in A draft metabolic model was constructed using the KBase Narrative Interface  to each gene in the model. Between-replicon biases were determined after standardizing by the number of genes from each replicon in iGD1575. To perform the COG analyses of the genes associated with variable reactions during the transition between niches, the COG annotation for each gene associated with the variable reaction classes was extracted from the WebMGA output of the previous COG analysis. Biases were determined after standardizing by the number of genes in each class of variable genes. Statistical significance was determined using Pearson's χ2-tests. The complete list of COG annotations is available as The WebMGA webserverS. meliloti RmP2754 (ΔB180) and a second wild-type control were inoculated from liquid M9-glucose cultures as RmP2754 grew poorly when inoculated directly from an agar plate. Data analysis was performed with DuctApeS. melilotiPhenotype MicroArray experiments using Biolog plates PM1 and PM2A were performed largely as described previously2531S. meliloti was grown overnight in LBmc complex medium600 of ∼0.05 in MM9 minimal medium600 readings were measured every 15 min. Growth rates were calculated between OD600 readings (not corrected for pathlength) of 0.1–0.5 with a previously developed Perl scriptS. meliloti, the phosphate concentrations in the spent media following the completion of the growth curves were determined via the molybdenate blue—ascorbic acid colorimetric method880 of each sample was measured and compared with a standard curve. The amount of phosphate remaining in spent media was compared with the phosphate present in the bacteria-free cultures to determine the amount of phosphate used by the bacteria. As the carbon source is growth limiting in these media, the used phosphate to carbon source ratio was calculated by dividing the amount of phosphate removed from the medium by the initial concentration of the carbon source .To measure the amount of phosphate used by The authors declare that the data supporting the findings of this study are available within the article and its How to cite this article: diCenzo, G. C. et al. Metabolic modelling reveals the specialization of secondary replicons for niche adaptation in Sinorhizobium meliloti. Nat. Commun. 7:12219 doi: 10.1038/ncomms12219 (2016).Supplementary Figures 1-8, Supplementary Tables 1-8, Supplementary Notes 1-6, Supplementary Methods and Supplementary ReferencesContains the analyzed data of all Phenotype MicroArrayTM data  used or generated in this study.Contains all the raw Phenotype MicroArrayTM data that was generated in this study in the form of .csv files.Contains tables that list all the reactions showing different characteristics during growth in bulk soil versus the rhizosphere.Contains tables that list all the reactions showing different characteristics during growth in the rhizosphere versus the nodule.Contains previously published pangenome information and regulon data for all genes that are included in iGD1575.The sbml file of iGD1575.Contains the COG annotations for all genes included within iGD1575, as generated by WebMGA.


Despite their current challenges, we envisage that SMN models have future potential for the design and development of novel growth media, biochemical pathways and synthetic microbial associations.We review approaches to characterize metabolic interactions within microbial communities using Stoichiometric Metabolic Network (SMN) models for applications in environmental and industrial biotechnology. SMN models are computational tools used to evaluate the metabolic engineering potential of various organisms. They have successfully been applied to design and optimize the microbial production of antibiotics, alcohols and amino acids by single strains. To date however, such models have been rarely applied to analyze and control the metabolism of more complex microbial communities. This is largely attributed to the diversity of microbial community functions, metabolisms, and interactions. Here, we firstly review different types of microbial interaction and describe their relevance for natural and engineered environmental processes. Next, we provide a general description of the essential methods of the SMN modeling workflow including the steps of network reconstruction, simulation through Flux Balance Analysis (FBA), experimental data gathering, and model calibration. Then we broadly describe and compare four approaches to model microbial interactions using metabolic networks, i.e., (i) lumped networks, (ii) compartment per guild networks, (iii) bi-level optimization simulations, and (iv) dynamic-SMN methods. These approaches can be used to integrate and analyze diverse microbial physiology, ecology and molecular community data. All of them (except the lumped approach) are suitable for incorporating species abundance data but so far they have been used only to model simple communities of two to eight different species. Interactions based on substrate exchange and competition can be directly modeled using the above approaches. However, interactions based on metabolic feedbacks, such as product inhibition and synthropy require extensions to current models, incorporating gene regulation and compounding accumulation mechanisms. SMN models of microbial interactions can be used to analyze complex “omics” data and to infer and optimize metabolic processes. Thereby, SMN models are suitable to capitalize on advances in high-throughput molecular and metabolic data generation. SMN models are starting to be applied to describe microbial interactions during wastewater treatment,  Community members or metabolic features identified with model predictions can, in theory, be manipulated to control the exchange of metabolic compounds of relevance for environmental protection or industrial applications. Here, we provide an overview of how microbial interactions can be modeled using stoichiometric metabolic networks as well as the main challenges to achieve this. We also describe how such models are starting to be applied to analyze and control natural and engineered environmental systems. Our target audiences are microbiologists, ecologists, and environmental/process engineers who are not currently familiar with metabolic network modeling.Microbial communities, and the biochemical and ecological interactions occurring in and among them, are ubiquitous in nature. They are vital for human as well as for environmental health, and are manipulated in systems ranging from wastewater treatment plants and agricultural crops to human digestive tracts. Advances in computational tools such as Stoichiometric Metabolic Network (SMN) models and their simulation algorithms  are enabling the Newer technologies for environmental assessment, waste treatment, and valuable chemical generation are required to achieve equilibrium between socio-economic development and the environment. Growing concerns about the lack of sustainability of past economic growth patterns, and increased awareness of a potential future water and climate crisis, have made clear that the environment and the economy can no longer be considered in isolation from one another. For instance, the global population is expected to increase by 13%, from 7.3 billion in 2015 to 8.3 billion by 2030, OECD, . This wiMembers of microbial communities interact with one another by trading metabolites or by exchanging dedicated molecular signals to detect and respond to each other's presence , negative (–) or neutral   of process behavior. So that it is possible to estimate the impact that changing independent variables  will have on the service or product of interest Makinia, . Mathemaet al., 2010): (i) generate mechanistic hypotheses from experimental observations; (ii) improve process efficiency by providing a quantitative basis for process design, control and optimization; (iii) estimate the activity of a specific microbial guild; and (iv) investigate the involvement of a specific metabolic pathway in observed processes. However, metabolic models capture only the molecular/biochemical aspect the whole environmental system. For example, a model of a full-scale wastewater treatment system implementing a biological treatment operation  has a hierarchy of sub models as shown in Figure Metabolic models are developed and applied when is necessary to account for detailed microbial physiology . Several culture dependent and independent techniques can be applied to analyze community physiology , ecology (species presence/absence and abundance) and molecular properties . Data generated through these analyses can be encoded and integrated into a metabolic model of the original microbial community. The model is calibrated and validated by iteratively comparing model generated data against experimental data, which is a critical step to establish model reliability. Once that model accuracy is satisfactory, it can be applied to infer metabolic mechanisms, optimize processes, analyze high-throughput “omic” data or design novel catalytic pathways or microbial associations  models—also known in the literature as genome-scale or genome-informed metabolic (GEM or GIM) models—are mathematical representations of cell biochemistry used to quantify metabolic reaction rates and therefore describe cell phenotypes  to be transformed into products ; subsequent reactions form metabolic pathways, which constitute cell metabolism; each reaction is represented as a stoichiometric equation (A and B); the equations are then compiled in an extensive list of reactions involved in the modeled pathways. The network topology concept refers to the web structure formed by metabolites interconnected through biochemical reactions, the biochemical pathway formed through these connections and how metabolites are distributed in different intracellular compartments , of size m per n. Every row of this matrix represents a unique compound i (for a system with m number of compounds); and every column represents a reaction j (for a system with n number of reactions) ; (ii) topological ; (iii) genotypical  (iv) environmental  and upper (βj) bounds of substrate consumption rates; and (v) thermodynamic . As shown in Figure The conversion of an organism or microbial guild SMN reconstruction into a model requires transformation of the reaction list into a mathematical matrix format. Thus, the equations' stoichiometric coefficients are arranged in the stoichiometric matrix  Figure . So thatOnce the metabolic network is captured in a matrix format, different mathematical analyses can be performed. These computational methods have been reviewed in recent publications such as Durot et al. , Kim et v)  in the metabolic network, rather than time-dependent metabolite concentrations  implies that the fluxes of metabolic compound formation j and βj represent the lower and upper bounds for reaction rate vj. A lower bound (α) and an upper bound (β) are in fact set to every reaction. Bounds for exchange reactions represent the flow of nutrients into and out of the biochemical system; while bounds for transport reactions (occurring across cell and subcellular compartment membranes) and metabolic reactions (occurring within the confines of the cell membrane) represent physicochemical constraints on reaction rates due to thermodynamics or catalytic enzyme availability  is modeled by defining specific values of reaction rates using the following form:S) are underdetermined systems, meaning that there are more reactions than there are compounds (n > m), there is no unique flux distribution (v) solution. An optimization algorithm [linear programing (LP) for FBA] is therefore used to find the optimal v that minimizes or maximizes a particular objective function (Z) defined by the user , although other objective functions, such as minimization of resource utilization and maximization of ATP production can be used depending on the simulation condition  is equivalent to the growth rate  of the organism as gDW and mmol units can be eliminated    with stoichiometric coefficients (s) synthetized by N number community members (k)  Figure . A metab) Figure . ReactioThe approach is based on the assumption that all the organisms in the community have reactions in common and exploit the environment in a similar way Table . It treak in the biomass (fk), In a compartment per guild network, each organism or guild is modeled as a distinct compartment of the network and exchangeable metabolites are transferred through an extra compartment representing the extracellular environment  or the ones formed by microalgae and plant growth promoting bacteria , which capture the biochemical transformations  and species biomass  is used for each substrate of interest related to each modeled species. For instance, two Monod equations are included in a model that capture the consumption of one substrate by two species; (ii) the obtained Sk to solve the optimization problem ; (iii) the predicted production rates for compounds of interest and biomass  kinetic and (ii) differential equations, both capturing the process dynamics; and (iii) stoichiometric reaction equations of each modeled species/guild  to define in situ bioremediation strategies for uranium spills in soil. By representing an aquifer as a numeric grid, the hybrid model simulates time and space dependent hydrological, geochemical, and metabolic processes in the spill area. Another innovative tool based on SMN models is the Computation of Microbial Ecosystems in Time and Space (COMETS) , as it does not assume constant yield coefficients  or should not (due to lack of detailed data). These advantages are balanced against its tendency to overestimate the metabolic potential. This is unsurprising, as real communities are not super-organisms. Individuals are membrane-separated and must contend with the logistics associated with matter and energy transport. Consequently, the lumped technique is best for initial work on “poorly” characterized systems  valid metabolic networks are difficult to develop as details of many metabolic reactions and pathways are unknown, this is especially true for secondary metabolic pathways , quantitative polymerase chain reaction data (qPCR), reverse transcription qPCR (RT-qPCR) and flow cytometry  and constraints (αj ≤ vj ≤ βj). SMN modeling uses optimization principles to estimate reaction rates of a given metabolic network. As mentioned before, generally maximization of biomass production per unit of substrate is the most suitable objective function for single-species metabolic networks  an accurate definition of stoichiometric equations based strictly on proven biochemical data by which the chemical compounds and capabilities of mass transformations of the system are defined; (b) correct definition of objective function(s) and the solving method of the optimization problem; and (c) obtaining high fitness  between experimental data and model predictions—the model must mimic at least the consumption and production rates of compounds observed in cultures. Most estimated rates of metabolic reactions cannot be measured experimentally and therefore cannot be validated directly. Nonetheless, data from microarray transcript profiles, transcriptomics, proteomics, metabolomics, and fluxomics [13C-based metabolic flux analysis (13C-MFA)] methods can be used to reduce uncertainty and increase the accuracy of the model‘s predictions (Figure Finally, it is important to recognize the different dynamics scales of biological system. At least four scales can be pointed: evolutionary, environmental, population and cell regulatory. For instance it is suggested that while community's organism lineages fluctuate extensively through time and conditions, the functional content of microbial communities displays stability and correlations with environmental parameters (Klitgord and Segrè, SMN modeling and systems biology can contribute to a comprehensive understanding of microorganisms, their interaction with other species in a community and their interplay with their environment. Understanding how interaction among cells enables the spread of information and leads to dynamic population behaviors is a fundamental problem in biology Xavier, . MeaningThe successful application of SMN modeling to characterize microbial interactions in natural and engineered environmental systems requires recognizing and modeling several abiotic factors influencing process performance Figure . The cheSystems biology tools such as SMN modeling have created the opportunity to develop the next generation of models of environmental process involving biological transformations. Nowadays, cheaper molecular biology and genomics, proteomics, and metabolomic techniques allow us to identify and quantify specific microbial species, full genome sequences, gene expression activity and metabolic compounds Lovley, . In addiOP: Main literature revision and initial manuscript preparation. GL: Revision of sections focusing in microbial ecology and interactions and editorial improvement. NS: Revision of sections focusing in mathematical modeling and main paper editor.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Escherichia coli cultures. FBA flux diversion opens the possibility for more accurate genome-scale predictions of drug synergies, which can be used to suggest treatments for infections and other diseases.Flux balance analysis (FBA) is an increasingly useful approach for modeling the behavior of metabolic systems. However, standard FBA modeling of genetic knockouts cannot predict drug combination synergies observed between serial metabolic targets, even though such synergies give rise to some of the most widely used antibiotic treatments. Here we extend FBA modeling to simulate responses to chemical inhibitors at varying concentrations, by diverting enzymatic flux to a waste reaction. This flux diversion yields very similar qualitative predictions to prior methods for single target activity. However, we find very different predictions for combinations, where flux diversion, which mimics the kinetics of competitive metabolic inhibitors, can explain serial target synergies between metabolic enzyme inhibitors that we confirmed in  Microbial infections are a major burden on societies, and the emergence of drug-resistant bacteria poses an increasing threat to human welfare. Drug combinations can overcome resistance by creating new therapeutic avenues inaccessible to single target drugs –3 or eliSystems biology may provide a solution to this challenge –9, by moA successful approach towards genome-scale modeling is Flux Balance Analysis (FBA) –16, whicHere we have extended FBA modeling to simulate drug effects over multiple doses. We explore new methods for simulating drug treatments with FBA, considering both direct target flux restriction  and a moThe Escherichia Coli iAF1260 model created by Bernhard Palsson’s group at UCSD serves as our bacterial model in this work , which cAll drug effect simulations were performed with an R-script using the R package Sybil (Systems Biology Library for R)  and the ftreat/fwt, where fwt and ftreat are the simulated biomass flux rates for untreated and drug treated bacteria. In both of our model implementations the MOMA quadratic programming algorithm for simulating perturbed biological networks was implemented to find the change in biomass flux. The IC50 value for a reaction describes the amount by which reaction flux must be reduced to inhibit growth by 50%. For FBA-res, flux is directly restricted by a scalar drug concentration, and so the IC50 is the scalar that achieves a 50% growth inhibiting flux restriction. For FBA-div, flux is diverted to a waste reaction, and so the IC50 is the value that achieves 50% growth inhibiting flux diversion. First, a central perturbation of αcent (where αcent = 1+[Inhibitor]/Ki and for simplicity Ki = 1) was found for each target enzyme using a bisection search to yield half the inhibition level of a full FBA gene deletion , covering a ~100x dynamic range  or limiting the amount of mass converted from substrate to product by diverting metabolic mass to a waste reaction (FBA-div). Inhibition values Inhib = 1 - tions in . Simulatic range . For eacic range . GradienWe used simple metrics of single agent and combined inhibitor responses , based oXY (blue point) are compared to the corresponding single agent response values IX,IY (green points), and max(ΔI) = max{IXY - max}, shows the Gaddum “best single agent” expectation /KD). By contrast, in FBA-div, scaling down the reaction affinity corresponds to KM* = KM/α, this time leaving VM* = VM constant, similar to competitive inhibitors. These scaling behaviors are consistent with combination effects seen in kinetic pathway simulations [Differences between the FBA-res and FBA-div methodologies may be understood in terms of standard Michaelis-Menten (MM) modeling for drug-inhibited enzymes. In MM kinetics, the reaction flux ulations , where cFrom a biology perspective, FBA-div can explain serial target synergies through the build-up of metabolite concentrations. The waste stream in FBA-div can be thought of as representing passive regulation that limits substrate concentrations by degradation or export from the system. Simulating with FBA-res assumes that when a drug inhibits a reaction, accumulated mass will slow down the upstream reaction thermodynamically, or induce a gene expression cascade that causes upstream reactions to slow down to the inhibited level. By contrast, FBA-div assumes that upstream reactions cannot sense or adjust to an inhibited downstream reaction on the time scale of the drug inhibition, and substrate is wasted, creating less biomass over time. Also, diverting excess flux to waste mimics processes similar to the phenomenon of metabolic resistance ,38 whichThe FBA-div approach can be extended to metabolic models of pathogens, such as tuberculosis , plasmodExperimental work on drug combinations can be resource intensive, especially for pathogens which require a BSL 3 environment, or when large combinatorial spaces are comprehensively sampled. Thus, computational tools that can explore large-scale models to prioritize such resource-intensive work could significantly accelerate drug discovery research. Because it can accurately predict a great variety of drug synergies, FBA-div has the potential to make a major impact on these therapeutic challenges.S1 Table(XLSX)Click here for additional data file.S2 Table(XLSX)Click here for additional data file.S3 Table(XLSX)Click here for additional data file.S4 Table(XLSX)Click here for additional data file.S1 FigCalculation steps used for the three methodologies compared in this work see .(PDF)Click here for additional data file.S2 FigEach symbol represents the simulated FBA-ko response to inhibiting a single or pair of targets see , with en(PDF)Click here for additional data file.S3 FigEach symbol represents the simulated FBA-res response to inhibiting a single or pair of targets see , with en(PDF)Click here for additional data file.S4 FigEach symbol represents the simulated FBA-div response to inhibiting a single or pair of targets see , with en(PDF)Click here for additional data file.S5 FigExperimentally measured drug-drug dose response matrices, ordered by total activity. The effects range from potentiation-like synergies , through non-interacting pairs , to antagonisms . There were also inactive single agents such as Dfrox and Tcarb for which interactions could not be accurately determined. Synergy scores were calculated and compared to the simulated dose-response matrices.(PDF)Click here for additional data file.S1 Dataset(ZIP)Click here for additional data file.


Saccharomyces cerevisiae expressing the same xylose assimilation pathway produce under anaerobic conditions xylitol rather than ethanol from xylose at low specific xylose conversion rates. Despite intense research efforts over the last two decades, differences in these phenotypes cannot be explained by current metabolic and kinetic models. To improve our understanding how metabolic flux of xylose carbon to ethanol is controlled, we developed a novel kinetic model based on enzyme mechanisms and applied quantitative metabolite profiling together with enzyme activity analysis to study xylose-to-ethanol metabolisms of Candida tenuis CBS4435  and the recombinant S. cerevisiae strain BP000 , both expressing the same xylose reductase (XR), comprehensively.Unlike xylose-converting natural yeasts, recombinant strains of Results from strain-to-strain metabolic control analysis indicated that activity levels of XR and the maximal flux capacity of the upper glycolysis  contributed predominantly to phenotype differentiation while reactions from the oxidative pentose phosphate pathway played minor roles. Intracellular metabolite profiles supported results obtained from kinetic modeling and indicated a positive correlation between pool sizes of UG metabolites and carbon flux through the UG. For CBS4435, fast carbon flux through the UG could be associated with an allosteric control of 6-phosphofructokinase (PFK) activity by fructose 6-phosphate. The ability of CBS4435 to keep UG metabolites at high levels could be explained by low glycerol 3-phosphate phosphatase  and high XR activities.By applying a systems biology approach in which we combined results obtained from metabolic control analysis based on kinetic modeling with data obtained from quantitative metabolite profiling and enzyme activity analyses, we could provide new insights into metabolic and kinetic interactions contributing to the control of carbon flux from xylose to ethanol. Supported by evidences presented two new targets, PFK and GPP, could be identified that aside from XR play pivotal roles in phenotype differentiation. Design of efficient and fast microbial ethanol producers in the future can certainly benefit from results presented in this study.The online version of this article (doi:10.1186/s13068-015-0340-x) contains supplementary material, which is available to authorized users. Saccharomyces cerevisiae that are capable of converting xylose, the second most abundant sugar aside from glucose in lignocellulosic materials, efficiently to ethanol. Engineering efforts pursued in the past focused on two routes, namely the bacteria-type and the yeast-type XA pathway  and acetate were formed instead  faster carbon flux at the F6P node towards C3-carbon phosphates is, therefore, a consequence of a kinetic pull exerted by reactions of the UG rather than by blocking carbon flux through reactions of the oPP pathway. The 13-fold higher Vmax of UG predicted by the kinetic model for CBS4435 cannot be explained by the twofold higher levels of FBA observed for CBS4435. Only little flux control by FBA can be assumed as the reaction operates close to equilibrium  was used as eluent B. The injection volume per sample was 10 µL. Mass spectrometric detection was carried out with an Exactive™ Orbitrap system . Heated electrospray ionization (HESI) was used for negative ionization and masses between 70 and 1100 m/z were detected with a resolution of 50,000 (at m/z 200) in full scan mode. Identical compounds  containing ISTD were used as standards to cover a concentration range of 0.4–100 µM. MS data were analyzed with TraceFinder™-software Version 3.1. . Eleven intracellular metabolites  and three metabolite pools  were quantified for each strain and respective concentrations were calculated as averages from a total of eight samples obtained from two individual fermentations (four replicates per fermentation).For the analysis of intracellular metabolites, xylose fermentations for BP000 and CBS4435 were carried out in a bioreactor (working volume 1000 mL) as described above and by applying 0.25 g/L KHribed by  was usedwas used . For metEnzyme activities were analyzed at 25 °C  and at 30 °C (BP000) from cell-free extracts by means of the initial rate method. Cell-free extracts were prepared at 4 °C from cells metabolizing xylose at the pseudo-steady state using a French Press . Cells were washed once with ice-cold physiological sodium chloride solution and re-suspended in 50 mM potassium phosphate buffer (PBB) pH 7.0 prior to cell disruption. The amount of soluble protein was analyzed using the Bio-Rad Protein Assay  referenced against bovine serum albumin. Time-dependent utilization of NADPH (XR) or NADH  as well as formation of NADH  or NADPH  was recorded at 340 nm using a DU800 spectrophotometer  equipped with a Peltier temperature controller. A molar extinction coefficient of 6.22/cm/mM was used for NAD(P)H. Release of phosphate from Glyc3P over time was analyzed for Glyc3P phosphatase (GPP) activity. Phosphate concentrations were determined from cleared samples treated at 99 °C for 5 min as described by . ComposiR4), the PP pathway (R5), the upper part of glycolysis (UG)  and for the lower part of glycolysis (LG) up to ethanol formation (R10). We did not consider ATP in the model as under the fermentation conditions used the reaction catalyzed by XK should be well saturated by ATP . As botrmation R0. We did–4 mM ]. Ki,NADPH were measured for Sc(Ct)G6PDH and Sc(Ct)GND. The set of kinetic parameters describing a reversible ordered Bi Bi mechanism reported for GmXDH was applied to both XDHs. Similarly, a reported Km,xylulose for ScXK and the set of kinetic parameters reported for ScPGI were used. For lumped reactions R5, R9 and R10, a Michaelis constant of 0.1 mM was assumed.Selection of known and determination of so far unknown model-relevant kinetic data are described in detail in the Additional file http://www.copasi.org [dc) by assuming that on a mass basis the protein content in dry yeast cells accounts for 40 % [R5, R9 and R10 were used in a range of 0.1–10, 1–100 and 1–100 mmol/h/gdc, respectively. Initial concentrations of coenzymes were constrained to ranges reported for BP000 [Time courses of xylose utilization and xylitol production obtained for CBS4435 (this study) and BP000 (this study and from ) were uspasi.org ) was usefor 40 % . Intraceor BP000 . A complqxylose. Two different objective functions (CO2 and ATP formation) were individually applied for linear optimization by linprog .A metabolic reaction network was designed consisting of 32 reactions involving xylose assimilation, PP pathway, oxidative PP pathway (oPP) and glycolysis as well as glycerol, acetate and ethanol production. For XR, one reaction was used for each coenzyme. Upper and lower bounds of experimentally obtained molar production rates of ethanol, xylitol, glycerol and acetate were applied. To capture network flexibility and experimental variations, simulations were carried out at upper and lower bounds and at the average value of